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UBC Theses and Dissertations

A study of tonality in selected works of Aaron Copland Creighton, Stephen David 1994

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A STUDY OF TONALITY IN SELECTEDWORKS OFAARON COPLANDbySTEPHEN DAVID CREIGHTONB.Mus.Perf., The University of Western Ontario, 1984M.Mus., The University of British Columbia, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(School of Music)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober, 1994© Stephen David Creighton, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_____________________Department of_________________The University of British ColumbiaVancouver, CanadaDate7L(DE-6 (2/88)UAbstractA Study of Tonality in Selected Works of Aaron CoplandThe analytical literature posits a dichotomy between Copland’s “popular” and“serious” music. Despite different motivic and hannonic structures on the surface,however, these styles are consistent in their underlying use of tonality. Tonics in bothstyles are defined by the same set of tonicizing techniques; and tonics in both styles servethe same function — to define the changing scale-degree function of pcs that are emphasizedin various ways as common to the collections of successive tonics. The most important ofthese changes in scale-degree function are summarized in pitch-class continuity graphs thatshow the relation of the changes to thematic and harmonic form. Detailed analyses, whichcover two “popular” and two “serious” works by Copland, demonstrate the consistencybetween the two styles. Besides demonstrating an underlying stylistic consistency thesegraphs provide useful information about structure in Copland’s music because they confirmstriking features of Copland’s thematic and tonal designs.illTABLE OF CONTENTSAbstract iiTable of Contents iiiList of Figures viList of Tables viiAbbreviations viiiAcknowledgments ixIntroduction 1Chapter One Tonality in Copland’s Works 5Relevance of Tonality to Copland’s Works 5Definition ofTonality 6Chord Roots and Root Successions in Copland’s Music 12Adequacy of Existing Theories of RootDetermination for Copland’s Music 14Idiomatic Rooted Sonorities in Copland’s Music 19Multiple-Rooted Sonorities 21Chord Progressions in Copland’s Music 22Tonicizing Techniques in Copland’s Music 31Isolated Root Motion by Fifth 31Melodic Construction 36Pc-Set Classes in the Bass 41DirectedMotion 44Changes in Texture 49Sustaining a Pc in the Bass 51Repetition of a Root Using Different Verticalities 54Neighbor-Tone Motion 57Summary ofTonicizing Techniques 58The Function of Tonics in Copland’s Music 60Theories ofTonality 60The Appropriateness of Existing Theories ofTonality for Copland’s Music 63A New Theory of Tonal Function 68Copi and’s Motivic and Thematic Designs 70Summary 81Chapter Two Analytical Conventions 82Introduction 82ivSymbols Used in Pc Continuity Graphs 82Sample Analysis of a Larger Passage 88Order of Appearance of Primary Connective Pcsin Pc Continuity Graphs 91Format of the Following Analytical Discussions 91ChapterThree Quiet City 92Form 92Tonality 96Introduction 97PartA 99Part B 103PartC 105PartAl 110Coda 111Pc Continuity 112Stream Generation 112Suspended Streams 118Pc-Scale-Degree Design 119Importance of [0,2,5] 119Palindromic Structure 120Significance ofAmbiguity Between 1C5-RelatedTonic Pcs 123Summary 123Chapter Four Billy the Kid (Orchestral Suite) 126Introduction 126Omission ofMaterial 126Form 127Tonality 132First Movement 132Second Movement (First Half) 134SecondMovement (“Mexican Dance and Finale”) 136ThirdMovement 139Fourth Movement 142FifthMovement 144SixthMovement 148Aspects of Resolution in the Final Tonal Area 148Minor-MajorThird Complexes in the TonicSuccession 152Pc Continuity 153Stream Generation 154Pc-Scale-DegreeDesign 162Aspects of Resolution in the Pc-Scale-DegreeDesign 169The Importance ofMajor and Minor Thirds 172Summary 173Chapter Five Short Symphony, First Movement 176introduction 176Form 176MotivicAnalysis 178Tonality 181PartA 181VPart B 185PartAl 189Motivic Correspondences 195Formal Function of Successions ofThird-RelatedTonics 197Pc Continuity 197Stream Generation 198Suspended Streams 204Pc-Scale-Degree Design 205Motive 1 as the Basis of the Pc-Scale-DegreeDesign 207Focal Pcs 208Palindromic Structure 211Summary 214Chapter Six Piano Sonc#a, First Movement 216Introduction 216Form 216Tonality 220Exposition — First Thematic Area 220Exposition — Second ThematicArea 225Development, Part! 228Development, Part II 234Recapitulation — First ThematicArea 239Recapitulation — SecondThematicArea 241Coda 243Tonal-Thematic Interrelationships 244Pc Continuity 245Stream Generation 246Unusual Techniques of Stream Generation 252Pc-Scale-Degree Design 253Repetitions of Streams 254Transpositional Relationships Between StreamRepetitions 259The First Thematic Area as a Source of Structure 261Summary 263Chapter Seven Conclusion 265Bibliography 275viList of FiguresFigure 2.1 (Analysis of Example. 1.40) Streams Related by a ContinuingMotive 84Figure 2.2 (Analysis of Example 1.39) Streams Related by a RecurrentDyad and Brackets in a Pc Continuity Graph 84Figure 2.3 (Analysis of Example 1.13) Arrows and Chromatic OppositionBoxes in a Pc Continuity Graph 86Figure 2.4 (Analysis of Example 1.44) Overlapping Phrase Marks in a PcContinuity Graph 86Figure 2.5 (Analysis of Example 1.45) Square Brackets in a Pc ContinuityGraph 87Figure 2.6 (Analysis of Example 1.46) Dotted Line in a Pc ContinuityGraph 88Figure 2.7 (Analysis of Example 2.1) Complete Pc Continuity Graph ofa Larger Passage 90Figure 3.1 Summary of Thematic and Tonal Designs in Quiet City 93Figure 3.2 Pc-Scale-Degree Design in Quiet City 113Figure 33 A Second Interpretation of R5-1 116Figure 3.4 Palindromic Structure in the Pc-Scale-Degree Design of Figures3.2 and 3.3 121Figure 4.1 Summary ofThematic and Tonal Designs in Billy the Kid(Orchestral Suite) 128Figure 4.2 Pc-Scale-Degree Design of Billy the Kid (Orchestral Suite) 155Figure 4.3 Summary of the Most Important Focal Pcs in Figure 4.2 170Figure 5.1 Motivic and Tonal Summary of the First Movement of the ShortSymphony 177Figure 5.2 Pc-Scale-Degree Design of the First Movement of the ShortSymphony 199Figure 5.3 Palindromic Structure in the Pc-Scale-Degree Design of Figure5.2 212Figure 6.1 Summary ofThematic and Tonal Designs in the First Movementof the Piano Sonata 218Figure 6.2 Pc-Scale-Degree Design of the First Movement of the PianoSonata 247Figure 6.3 Transpositional Relationships Between Repetitions of Streams inFigure 6.2 260List of TablesTable 3.1 Summary ofTn-Related Passages 93Table 4.1 Summary ofTn-Related Sections 129Table 4.2 Repetition of Groups of Streams in Figure 4.2 163Table 5.1 Summary ofTn-Related Passages 177Table 6.1 Summary ofTn-Related Subsections 260VIIAbbreviationsR Rehearsal number in text1 5 1 Rehearsal number 5 in example() Measure number 5 in exampleadd6 Added sixthFIG Jazz chord combining pcs of triads built on F and GG3(4) Pitch/register(s) statedAG:2 Key: scale-degree function{ } Unordered setOrdered set[J T-TI pitch-class set-typeA . S. Appalachian SpringB.K. Billy the KidP.C. Piano ConcertoP.S. Piano SonataP.V. Piano VariationsQ.C. Quiet CityR. RodeoS.S. Short SymphonySpecial symbols on the pitch-class continuity graphs are explained in Chapter 2.ixAcknowledgmentsI am heavily indebted to Dr. John Roeder for his enthusiasm, patience,understanding and foresight in the writing of this thesis. I also wish to thank Dr. WilliamBenjamin, Dr. Gregory Butler and Dr. Eugene Wilson for their considerable help. Finally,I wish to thank my wife Elizabeth for her continued support and patience.Excerpts from the following works have been reprinted by the kind permission ofBoosey and Hawkes, Inc.“Suite from AppalachianSpring,” © 1972 (B.&H. 19979). All rights reserved.“Suite from Billy the Kid,” © 1941 (B.&H. 16725). All rights reserved.ConcertoforPianoandOrchestra, © 1929. International copyright secured. Allrights reserved including Right of Public Performance for Profit.“Four Dance Episodes from Rodeo,” ©1946 (B.&H. 9037). Copyright for allcountries. All rights reserved.PianoSonata, ©1942, renewed 1969 (B.Ps. 27). Copyright for all countries. Allrights reserved.Piano Variations, ©1932 (C.C.P.7). International Copyright secured. All rightsreserved including right of Public Performance for Profit.Quiet City, ©1941 (B.&H. 18805). Copyright for all countries. All rightsreserved.Short Symphony (No.2), ©1955. All rights reserved.1IntroductionThere is a marked trend in the analytical literature to describe a dichotomy in AaronCopland’s music between “popular” and “serious” works. In making such a division,authors such as Julia Smith and Arthur Berger are acknowledging immediately recognizabledistinctions in the types of themes and in the complexity of the tonal language thatcharacterize the two different styles of music.1 Copland’s “popular” music is said to havefolk-like melodies and a much simpler harmonic language; while Copland’s tseriousmusic is said to have more disjunct melodies and to use complex harmonic structures.Indeed, Copland himself has indirectly acknowledged a dichotomous interpretation of hiswork. He refers to the Short Symphony, the Piano Variations, and the Piano Sonata aslinked by a “serious” style,2 and admits that his “popular” works grew out of his search inthe early 1930’s for a “simpler” style, a style that could communicate more directly to anaudience.3However, Copland’s crucial statement “I wanted to see if I couldn’t say what I hadto say in the simplest possible terms”4does not eliminate the possibility that his “popular”and “serious” works explore similar structural issues. Indeed, it makes such a similaritymore plausible by suggesting an underlying unity of expression. This underlying unity isacknowledged by most authors when they admit that Copland’s works have a characteristicand unmistakable sound.5 Some authors, such as William Schuman, proclaim the artistic1Julia Smith, Aaron op1and: His Work and C’ontrihution to American Music (New York: E. P. Duttonand Company, Inc., 1955), pp.119, 191, 198 and 234; Arthur Berger, “Copland’s Piano Sonata ,“ inPartisan Review 10 (1943): 187-190; and Wilfrid Mellers, Music in a New Found Land: Themes andDevelop.’nenis in the History ofAmerican Music (London: Barrie and Rockliff, 1964), p.97.2Aaron Copland and Vivian Penis, Gopland: 1900 through 1942 (New York: St. Martin’s/Marek, 1984),pp.165, 208 and 330. Minna Daniel, in her comments about Copland on p.115 in the same monograph,recalls that Copland rcierred to the Piano Variations, Statements and the Short Symphony as his “hard-bitten” pieces.3Arthur Bcrger, Aaron copland (Ncw York: Da Capo Press, 1990), p.27.4Aaron Copland, The New Music 1900-1 960 (London: MacDonald, 1968), p.160.For example, Andre Previn states: “A fascinating aspect of Copland’s compositions is that his particularvoice, his handwriting, is discernible even in his most dissonant works.. .Copland belongs to that handful oftwentieth-century composers who have managed to be instantly identifiable.” Neil Butterworth, The MusicofAaron Copland (Gloucester: Toccata Press, 1985), p.6.2value of Copland’s “popular” music on the basis of the sophisticated transformations thatCopland applies to his folk song materials:The Copland sound transforms traditional American folk material into the mostsophisticated art by discerning potentialities in simple music that could only beconceived by an artist of extraordinary perception...To the uninitiated it couldalmost seem as though there were two separate composers at work. Not so, forthe same Copland sound that informs the popular music is, in its unique way,heard in the masterworks he has created in every medium.6In his book about Copland, Arthur Berger also indirectly recognizes an underlyingunity. He comments that the “workmanship and substance” of Copland’s “workaday”music “do not fall appreciably below the level of his more ‘serious’ or more ‘abstract’works,” and he claims that in several cases this level is equal.7 Berger later argues thatCopland “has not abandoned his more serious thinking for folk potpourris” even where“popular” pieces such as Rodeo and Billy the Kid are concerned.8 Mellers suggests astronger link in the following statement:The commonly expressed view that Copland’s “popular” works of the thirtiesare in some way a denial, even a betrayal, of his earlier integrity would thusseem to be illusory. The simpler style of the ballets and film music does notbelie the techniques of Copland’s previous “abstract” pieces, though themusic’s deliberate lack of progression or development may be less disturbingwhen allied to recognizable, folk-like tunes and to physical action or visualdrama. ..The difference between the ballets and the abstract works consists, thatis, rather in the nature of the material than in the treatment of it.Copland himself explicitly downplays a dichotomy in his work. For example, hewrote a letter to Arthur Berger (dated April 10, 1943) suggesting that the latter’s article6Copland and Penis, op. cit., p.354. A small part of Copland’s genius for transformation in this regard canbe seen by looking at the variation formulas in Appendix 1 (pp.254-260) of Copland’s What to Listen Forin Music (New York: McGraw-Hill Book Company, Inc., 1939). These are variations for piano on the folksong “Ach! du lieber Augustin.” The characteristic Copland “sound” is particularly evident in the relatedvariations 1 a and 3a on pp.255 and 259, which are labeled as harmonic and rhythmic variants respectively.What is interesting about these examples is the dc-emphasis of the underlying conventional harmonicprogression that results from sustaining the tonic pc in the bass and the use of parallel five-three chords inthe right hand. In addition there are certain sonorities as, for example, the trichord {G, A, D} in thepenultimate measure of variation la, which commonly appear in CopLand’s music. Copland’s idiomaticrooted sonorities will be discussed below on pp.19-22.7Berger, Aaron Copland, pp.37-38. Bergen does not list specific works by Copland to illustrate thisassertion.8lbid., p.73.9Mellers, op. cit., p.87.3about the Piano Sonata “overdoes the dichotomy” between Copland’s “severe” and“simple” styles, giving the impression that only the former was intended as serious.10Copland’s distress about this kind of general critical reaction to his earlier comment about“simplicity” in his original autobiographical sketch (from 1939) lead him to qualify it whenit was reprinted in Copland: 1900 through 1942:The mention of an “imposed simplicity” was taken to mean that I had renouncedmy more complex and “difficult” music, turned my back on the cultivatedaudience that understands a sophisticated musical language, and henceforthwould write solely for the “masses.”...these remarks of mine emphasized apoint of view which, although apposite at the time of writing — the end of the‘30’s — seem to me to constitute an oversimplification of my aims andintentions, especially when applied to a consideration of my subsequent workand of my work as a whole...11In The New Music 1900-1960 Copland also directly refutes a dichotomousinterpretation of his work when he discusses how the critical reaction to his latest piece(Connotations) “brought to the fore once again a continuing discussion concerning theapparent dichotomy between my ‘serious’ and my ‘popular’ works.” He statesI can only say that those commentators who would like to split me down themiddle into two opposing personalities will get no encouragement from me. Iprefer to think that I write my music from a single vision: when the resultsdiffer it is because I take into account with each new piece the purpose forwhich it is intended and the nature of the musical materials with which I beginto work. Musical ideas engender pieces, and the ideas by their character dictatethe nature of the composition to be written.12A unity of purpose among Copland’s “popular” and “serious” works is revealed bya detailed study of tonality in representative pieces from the 1930’s- 1950’s. Thisdissertation presents such a study. The pieces were chosen to represent the period whenCopland was most influential on the development ofAmerican music. This period was10M Anthology of Letters of Composers (New York: Alfred A. Knopf, 1946), pp.403-404. In the sameletter (p.403) Copland attempts to quantify what his “simpler works” represented artistically: “What I wastrying for in the simpler works was only partly a larger audience; they also gave a chance to try for a homespun musical idiom, similar to what I was trying for in a more hectic fashion in the earlier jazz works. Inother words, it was not only musical functionalism that was in question, but also musical language. I liketo think that in Billy and Our Town...l have touched off for myself and others a kind of musical naturalnessthat we have badly needed — along with ‘great’ works.”1 Copland and Perlis, op. cit., p.317.12Copland, op. cit., p.168.4also when the dichotomy between Copland’s tpopular and “serious” music wasapparently the strongest. Despite seemingly substantial stylistic differences Copland’s“popular” and “serious” musics in this period are very closely related.This study will prove that there is a close relationship between the apparentlydistinct styles. It will show that Copland’s “popular” and “serious” works share a commonset of tonicizing techniques, which are used to establish tonics and to modulate from tonicto tonic. These techniques focus on the connections between the pc collections associatedwith successive tonics by emphasizing pitch-classes that are common. Detailed analyses offour representative works will illustrate these techniques.5Chapter 1Tonality in Copland’s Works1.1 Relevance of Tonality to Copland’s WorksTonality, although it can involve quite sophisticated notions of hierarchy andcounterpoint, minimally entails two basic principles. The first is that a tonal passage ofmusic “has a tonic” in the sense that there is a pitch-class about which we hear the other pcsin the passage to be organized. Secondly, tonality involves the idea that a tonic functions tocreate musical form. For example, distinct sections may be distinguished by differenttonics. Or the change from one tonic to another may signal a musical process such asdevelopment, or variation, or closure.Some notion of tonality is useful in analyzing Copland’s music because its themesand sections — like those in earlier tonal music — have tonics. Moreover, most large-scaleformal divisions in Copland’s music are supported by a change of tonic. Only very rarelyis there a major sectional articulation in a piece by Copland that is not delineated by achange in tonic. Copland’s habit of reinforcing thematic and textural contrasts by shifts intonics even suggests that tonality plays a much more important role in his works than hasbeen commonly acknowledged.Most analyses of Copland’s music, including those presented by Julia Smith,Arthur Berger, Neil Butterworth, and Quincy Hilliard, make only passing references totonal centers and to the function of tonal changes. This trend towards overly briefsummarization is particularly noticeable in Julia Smith’s monograph which, despite itspioneering status in the analysis of Copland’s music, severely limits observations ontonality in favor of descriptions of Copland’s thematic structures. Her discussion of thefirst movement of the Piano Sonata — indeed a very interesting example of Copland’s use oftonality — confines analysis of tonality to comments about the keys of the first and second6themes in the Exposition.’ Neil Butterworth’s comments on tonality in this movement,which are fairly representative of all the analyses in his book, add nothing substantial toSmith’s except that he asserts (without demonstration) that the whole movement can becharacterized by a single tonic, which is the same as the first tonic.2 Berger’s comments ontonality, while very perceptive, invariably treat only short segments of different pieces.Since his comments on tonality are intended simply to show general stylistic traits inCopland’s music they do not account for the tonal structure of entire pieces.3 Hilliard’sanalyses of Copland’s music presents more detailed information on the tonal structures ofpieces. However, he often omits many of the tonal connections on the surface of amovement. In at least one case — the first movement of the Short Symphony — this resultsin an incorrect assertion of a global tonic.4 Hilliard seems so intent upon relating the tonalstructures in Copland’s music to traditional practice — he thinks, for example, that thepresence of tonics must necessarily mean the presence of a global tonic — that he ignoresmany of the special characteristics of those structures.1.2 Definition ofTonalityIt is unlikely, given Copland’s training and milieu, that traditional tonality (whereevents are organized around a global tonic) would be manifest in his music. In fact, justthe opposite is true. Copland’s use of tonality is no more traditional than that of hisAmerican and European contemporaries. We can not assume that “tonality” in Copland’smusic will be organized around a global tonic. Therefore, we will adopt definitions oftonality and tonal function that seem best suited for Copland’s music as it is.1Julia Smith, Aaron Cop!and: His Work and Contribution to American Music (New York: E. P. Duttonand Company, Inc., 1955), p.232.2Neil Butterworth, The Music ofAaron Copland (Gloucester: Toccata Press, 1985), pp.84-85.3Arthur Berger, Aaron Copland (New York: Da Capo Press, 1990), pp.67-9.4Quincy Hilliard, “A Theoretical Analysis of the Symphonies of Aaron Copland” (Ph.D. dissertation,University of Honda, 1984), pp.100-101. See also below, pp. 181-195.7To say Copland’s music is “tonal” means that in a given passage there is a pitchclass which is perceived as the “tonic,” and that this pc belongs to a diatonic collection(i.e., the pc set-type [0,1,3,5,6,8,10] or a selected subset or superset thereof) that is treatedas referential. We understand the pitch classes in the referential collection as diatonic scale-degrees of the tonic. Copland uses six of the seven available orderings of a diatonic scaleas referential. The only ordering that he avoids altogether is <0,1,3,5,6,8,10> — theLocrian collection (e.g., the referential collection {B, C, D, E, F, G, A} when B is atonic). He tends to prefer the orderings that form the major mode and the Dorian,Mixolydian and Aeolian collections. Hexachords are most commonly used as subsets.Three of the most common hexachordal subsets in Copland’s music are {0,2,4,5,7,1 1}(the lower pentachord of a major scale plus the seventh scale-degree), {0,2,3,7,8,10} (theAeolian collection with no fourth scale-degree) and {0,2,4,5,7,9} (the lower hexachord ofa major scale).5 Only infrequently in his “serious” pieces, as, for example, in the firstmovement of the Short Symphony, is a subset of only four or five pcs used as a referentialcollection. In all of these passages, however, the collection itself has minimal impact on ananalysis because the tonic is very strongly established by motivic preconditioning.Because tonal areas in Copland’s music often contain more than seven pcs we mustdiscuss ways in which we distinguish between collectional and non-collectional pcs. It isvery difficult to specify these ways precisely because our perception of collectional andnon-collectional pcs is so dependent upon the musical context in which they appear.However, there are some general rules of thumb that help. We generally hear a pc ascollectional if it is stated many times in a given passage and is not constrained to a melodic5Other hexachordal subsets of the diatonic scale that occur as referential collections in Copland’s musicinclude {O,2,4,7,9, 11 } (the major scale with no fourth scale-degree), and {O,2,3,7,9, 1O} (the Doriancollection with no fourth scale-degree). Occasionally Copland will expand one of these hexachordal subsetsby a pc that duplicates the scale-degree function of one of its members. For example, the first subset listedabove — the set {O,2,4,5,7, 11 } — is sometimes expanded by an additional lowered third scale-degree. That is,in an F tonal area pc Ab would be added to the diatonic collection {E, F, G, A, Bb, C}. This results in aseven-note collection that, while not diatonic in itself, is a subset of another collection, called the “diatonicoctad,” that will be discussed presently.8formula such as a neighbor-tone motion. Conversely, we generally hear a pc as noncollectional if it is only stated once in a given passage and is constrained to a melodicformula such as a neighbor-tone motion. Copland’s music also makes a distinctionbetween collectional and non-collectional tones based on octave representation: generallynon-collectional tones are present in fewer registers than collectional tones. Because wecan not exactly specify rules such analytical decisions will be explicitly justified in futureexamples.The definition of tonic above raises the question of how tonics are established inCopland’s music. The three most basic ways are accenting the tonic pc, accenting the thirdor fifth scale-degrees, and emphasizing the tonic pc as the root of a repeated sonority. Thefirst two techniques are particularly evident in monophonic contexts, for example the firsttheme of the second part ofAppalachian Spring (at R7 to R7+3). Here A becomes thereferential pc of the collection {A, B, C#, D, E, F#, G#} because of the metrical andagogic accents on pc A in a melody that ends with the A-major triad (i.e., <C#5, E4, A3>).Examples 1.1-1.3 below provide examples where tonics are generated in homophonictextures by accenting the first, third and fifth scale-degrees; Example 1.4 quotes ahomophonic passage where all three techniques define the tonic pc.Example 1.1 shows a characteristic passage from the third movement of the ShortSymphony where an Ab tonic is generated by agogic and contour accents on pcs Eb andC/Cb in the rhythmically animated lines and by sustaining pc Ab in the bass.6 All of thepitch classes in the referential collection of this passage {Ab, Bb, Cb, C, Db, Eb, F, Gb}are understood as diatonic scale-degrees in relation to Ab, that is, pe Bb is Ab:2, pc Db isA AAb:4, pc Eb is Ab:5 etc. Since there are only seven diatonic scale-degrees we mustunderstand certain pairs of pcs in this passage as major and minor versions of the samescale-degree; here pc Cb is Ab:b3, and pc C is Ab: 3. The eight-note referential collection in6This passage is only the beginning of a larger Ab tonal area, throughout which pc Ab is sustained.9Example 1.1, which is one of a family of collections described generically as the “diatonicoctad” in the Literature,7is common to both Copland’s “popular” and “serious” works.8Example 1.1 Tonic as the Referential Pc of a Diatonic CoUections.s. , III, J-3ff.A____ I—L—I —---LJ&I Lil:J.I-. — .-I I-I IFL.i-.__ ——q-_ r•I--Referential CollectionI I _1,.Example 1.2 shows the fifth variation from the Piano Variations. In this passageaccents (agogic, metrical and dynamic) on E define that pc as the tonic of the referentialcollection {D#, E, F#, G, A, B). The third and fifth scale-degrees of this collection arealso weakly accented: pe B receives a contour accent because B6 (R6+5 and R6+7) is thehighest pitch of this variation; pc 0 receives a metrical and dynamic accent in R6+4 andR7-2.71n the literature on Stravinsky these collections are referred to as representatives of the “eight-note diatoniccollection” or “diatonic octad.” Paul Johnson, “Cross-Collectional Techniques of Structure in Stravinsky’sCentric Music,” in Stravinsky Retrospeclives (Lincoln: University of Nebraska Press, 1987), pp.55-56; andJoseph Straus, An Introduction to Post-Tonal Theory (Englewood Cliffs: Prentice Hall, 1990), p.96.However, this term is meant to apply to a collection that is generated from the juxtaposition of twoseparate diatonic collections. The presence of two diatonic scales in a single octad allows Stravinsky toassert different tonal centers with the same collection. My use of this term in the present context does notimply that such conditions necessarily pertain to all instances of this collection in Copland’s music.8For example, see the second theme (mm.58f1.) of the first movement of the Piano Sonata where 0 is thereferential pc of the collection {G, A, Bb, B, C, D, ES, F} and R8ff of the orchestral suite of Billy the Kidwhere F is the referential pc of the collection {F, G, Ab, A, Bb, C, [D], E}., r r”’1)I-. _I - —. — - — — —21-L-- L T—T---- — -— ‘IJr£III 4Irr__r-—FflL41 iq) i —.—-r — “-i — ‘si’Tonic Pc10Example 1.3 excerpts a passage from the second movement of the PianoSonatawhere the texture of falling sixths, the metrical accent on the sixth {A4, F5} (m.195), andthe accent on pes A and C (mm.194, 196, 197, 199, and 201) makes us hear F as thereferential pc of the collection {F, G, A, Bb, C, D, Eb}. The tendency of pc B in m.200retrospectively to assert A over F as the tonic of the passage (and to change the referentialcollection) is negated in m.201 when it becomes clear that B functions as a chromatic upperneighbor tone to pc A. Because this melodic function allows us to hear pc B as a noncollectional tone it confirms our more traditional hearing of F as the tonic of this passage.Example 1.2 Tonic as the Most Accented Pc in a Passage11Example 1.3 Tonic Pc Established by Emphasis on the Third and Fifth Scale-degreesP.S.,II,mm. 194ff.() —S. 200•4IdI2jReferential Collection[;I [, •jPdIPITonic PcExample 1.4 shows a passage from the first movement of the Short Symphonywhere the emphatic repetition of the A-rooted sonority {C#2(#), A3, D4, A4, E5} (and theabsence of another emphasized root) makes us perceive A as the tonic of the eight-notereferential collection {A, B, C#, D, E, F#, G, G#}. Pc All in R3-3 is considered to be anon-collectional tone because the only time it occurs it functions as a chromatic upperneighbor tone to pc A.9 The third and fifth scale-degrees are also emphasized as repeatedtones in the lowest and highest voices respectively.9Pc A# does not fit our third general rule of thumb (pp.7-8) about non-collectional tones — it occurs in thesame number of registers (4) as the collectional pc B.Example 1.4 Tonic as the Most Emphasized Root in a Passagess. ,1, []÷4ff.Referential CollectionA12Examples 1.1-1.4 are all characteristic of Copland’s music in general. They shareone important feature — all three passages have roots and emphasize tonic-triadic scale-degrees but lack functional root progressions. On this basis one might draw a generaldistinction between Copland’s music, which is clearly grounded on traditional techniques,and traditional tonal music: Copland’s music does not usually employ all of thecharacteristic techniques of traditional tonal music at the same time.The fairly straightforward passages shown in Examples 1.1-1.4 might be taken tosuggest that Copland’s music relies upon traditional perceptions of diatonic collections, thatis, on the listener importing a sense of tonic which the music then confirms. However,simply hearing the referential collection in itself is not a sufficient condition to establish thetonic of a passage because Copland does not use only the two most familiar (traditional)orderings (i.e., the major and minor scales). He frequently uses the other (modal)orderings, particularly the Mixolydian (as in Examples 1.1 and 1.3) and Dorian modes, asreferential. Thus, we need confirmation from the context — an emphasis on the tonic-triadicscale-degrees — to make a tonal interpretation of a given referential collection.1.3 Chord Roots and Root Successions in Copland’s MusicWhile many passages of Copland’s music lack root progressions, some of hishomophonic textures do have roots, and occasionally a succession of these roots helps todefine the tonic. For such passages we need to define what constitutes a chord, and howwe derive a root for that chord. Chords are tones that either sound together or are groupedtogether by convention (i.e., an Alberti style accompanimental pattern where a bass tone isgrouped together with the chord that follows it). Some verticalities are generated frommelodic phenomena (i.e., the confluence of passing and neighbor tones) and do notrepresent rooted chords. For example, the sonority {Ab3, CM, AM, Db5, Gb5} in m.3of the first movement of the Piano Sonata is generated by the confluence of two passingtones (pcs Gb and Db) and two neighbor tones (pcs Ab and Cb). The reason why we hear13roots for some chords and not for others is due to the context. Obviously, if a given chordis a complete representation of a traditional chord (a triad, seventh or ninth chord) we canuse its literal intervallic structure for root determination. However, treating all ofCopland’s more unusual sonorities as incomplete representations of traditional chordslarger than the triad is not beneficial in analysis except where the resulting roots arereinforced (by a functional progression, or by the phrase structure) within the context.That is, the context must provide us with a compelling reason to hear a given verticality asan incomplete representation of a more familiar chord. As a result, root assignments infuture examples will be discussed if they include any “incomplete” chords.Chord roots help generate a tonic only when they occur in a succession that is tonic-or dominant-directed. The most effective root successions for the generation of a tonic PCare those which mimic the cadential progressions <V, I> and <IV, I> of a more traditionalcontext (for example, the root successions <F, C> and <G, C> in a C tonal area). Quiteoften the latter (tonic) function coincides with a metrical accent. Other chord rootsuccessions, such as <D, G> in a C tonal area, define tonics in Copland’s music at times(i.e., as C:<II, V>) but these are weaker because other independent factors are oftenrequired to corroborate the tonic. In contrast, however, a stepwise root succession such as<G, F, E> does not necessarily define a C tonic because the corresponding progression,<V. IV, III>, is not directed toward the dominant.10 Thus, chord roots, if present, onlydefine tonics when we can hear them function in a tonic- or dominant-directed progression.10Quite often a succession of any triads (within a diatonic collection) helps us to narrow the possibilitiesfor the tonic down to a few candidates. However, such successions, unlike <V. I> and <IV, I>progressions, do not necessarily point to the actual tonic of a passage. Thus, they do not establish a tonicbut confirm it in a more general way.141.3.1 Adequacy of Existing Theories of Root Determination for Copland’s MusicIt would be useful in understanding Copland’s music to have a theory of tonalitythat is adequate and sufficient, a theory that consistently produces meaningful results anddoes not, for example, identify the root succession <V, IV, III> as central to the generationof a particular tonic. But it is very difficult to formulate such a theory for Copland’s musicfor several reasons.Part of the problem lies in deriving plausible roots for his chords. Let us considerthe adequacy for Copland’s music of two theories for determining roots: traditional tonaltheory and Hindemith’s theory of best intervals. The former, proceeding from thedefinition of a rooted triad, allows incomplete representations of seventh, ninth, eleventhand thirteenth chords — chords very common in Copland’s music — to have roots when rootsuccession obeys tonal syntax. Thus, we can hear the second chord in R20+1 of Billy theKid as a dominant-eleventh chord because it occurs in the middle of a tonally syntacticprogression — <I, IV, Vii, I> — in Bb (at R2Off.).Traditional theory cannot identify — or misidentifies — the roots of some melodicallygenerated chords in Copland’s music when tonal syntax is not operative. Example 1.5shows the opening Bb tonal area of the second movement of the Short Symphony.” (Bbis the tonic of this passage because pcs Bb, D and F are emphasized in the highest voice —Bb begins each (three-note) melodic cell, and pcs D and F receive agogic accents in R18-i-5and R19-4 and R18+1 respectively — and the first melodic cell, which begins on Bb andends on F, has an F-rooted sonority as its goal). At least five chords in this passage, thosemarked by the symbol “?“,can not be identified as incomplete representations of otherrooted chords, and therefore can not participate in a succession of roots, because they cannot be construed as part of a dominant- or tonic-directed tonal progression in Bb. It seems1 ‘The Bb tonic is, however, challenged to a degree by references to F as tonic.I4I,I I Ii’-’)4 i:-‘ ‘— c.—. -r— —.1 ,, - -.__P...—bci——I-?-%-L I’..I._. .1 —z- I,, ‘I J4iI In——-I_-.s: - fl[ L.. I__I g1—2I?II,c,—.—9I I 91...-[ __fiL9J.I I---I I)r,-.kC.,t.jF.:::.[E:rk1 .•I II --F-Hindemith attempted to generalize traditional tonal root theory. He ranks intervalsby their harmonic strength and asserts that every chord has a single root.12 Hindemith’stheory of root determination often identifies roots in Copland’s music that are not the bestanalytic interpretations of his chords. Examples 1 .6a-d show four cases where certaincharacteristics of the context (i.e., neighbor-tone motion, placement of the chord within aphrase or section, or the surrounding harmonies) suggests a better analytic interpretation ofthe root of a chord. In Example 1 .6a Hindemith’s theory suggests that pc A# (Bb) is the‘2paul Hindemith, Craft ofMusical Composition Book I (Mainz: B. Schotts SOhne, 1970), pp.81-83; andDavid Neumeyer, The Music ofPaul Hindemith (New Haven: Yale University Press, 1986), pp.56-60.According to Neumeyer (pp.33 and 56-57) Hindemith’s theory of root determination, introduced in The Craftof Musical Composition I, evolved into a more context-sensitive form in his later works — The Craft ofMusical Composition III and IV — by replacing the rule of the best interval under certain circumstances.Because context is so crucial to understanding roots in Copland’s music we will consider Hindemith’s laterversion of root determination in our present discussion.,-2-——‘-_) —15fruitless to persist with such analysis when presumed “altered” chords are not governed by,or subordinate to, an inferable tonal syntax.Example 1.5 Melodically Generated Chords in Copland’s Musics.s.,n, ff.AIi . I___I I IN—A I___L-J’J16root of the chord marked by the symbol “?“. However, this chord is better explained as anon-rooted neighbor chord that is generated from the confluence of three neighbor-tonemotions — <E, F, F>, <A, AL A> and <A, Gil, A>. In Example 1.6b Hindeniith’s theorysuggests that pc A is the root of the chord marked by the symbol “?“. However, pc Bb is abetter choice for the root because of the descending-fifth pitch motion <F2, Bbl> in thebass and because this chord marks the climax of a Bb tonal area. Example 1 .6c shows adifferent kind of problem, the presence of multiple roots. Hindemith’s theory, whichallows for only one root in a sonority, suggests that pc F# is the root of the chord markedby the symbol “?“.‘ However, this chord is registrated to bring out two distinct harmoniccomponents — a Bb-major chord in the highest three voices and an F# major-minor six-fivechord in the lowest four voices — and thus suggests that we hear Bb and F# simultaneouslyas roots. The double-root analysis is more attractive than the Hindemithian analysisbecause it is more consistent with the nature of the harmony in the passage: the threehighest pcs of the chord at R29-1 are the same as those in the preceding Bb-rooted chord(R29-2); and the simultaneous reference to two major triads a major third apart recalls theopening melodic gesture of this section which generates the first chord in Example 1 .6c(R28). Example 1.6d shows a passage whereT10-related seven-four chords (marked byboxes connected with an arrow) do not generateT10-related roots — E and D — asHindemith’s theory suggests.’4The root of the first of these chords sounds like B becauseof the simultaneous emphasis on pc B in the soprano and because the following (A-rooted)sonority at R3÷3 is similarly based on a seven-four chord in root-position.15 However,13Pc Bb is clearly the root which is suggested by the rule of the best interval. However, in this particularchord this rule is superseded by the last of the four corollaries that Neumeyer lists (“the appearance of afamiliar sonority in the lower voices”). Neumeyer, op. cit., p.57.14The second corollary that Neumeyer lists under Craft11! suggests that B might be a possible root for thefirst chord because it is the root of three different intervals (i.e., B2-D4, B2-A3 and D4-B4). Neumeyer, op.cit., p.56. However, an E root is also suggested using this same corollary because E is similarly the rootof three different intervals in the chord (i.e., B2-E4, D4-E4 and E4-B4). Because most of these E-rootedintervals have higher values than the intervals which have a B root and E is also suggested as a root by thebest interval we chose E as the root of this chord.‘5The first corollary that Neumeyer lists for Craft III asserts that pitch “doubling can have an influence onchord-root calculation insofar as it enhances the potency of one note: if this note is the root, the chord may17we hear D as the root of the second of these Tio-related chords for two reasons: the trumpetmelody at R5+ 1 resolves pc G to pc F# like a dissonant seventh above a sustained D four-three chord; and the melodic references to a G-major or -minor triad around this sonority(i.e., R5-2, R5- 1 and R5+2) allow us to integrate a D root into an implied dominant-tonicprogression in G. More traditional considerations of voice-leading and harmony wereinvoked in Example 1 .6d to determine the proper chord roots. Examples 1 .6a-d show thatHindemith’s theory is not responsive enough to contextual influences and is, therefore,inadequate for root determination in Copland’s music.16be stronger — more clearly defined — than its chord class might suggest.’ Neumeyer, op. cit., p.56.However, Neumeyer does not make an explicit connection between this and the following corollary andsuggest that doubling could contribute toward making us hear a root other than the best root.16Charles Shackford also makes this observation in his review of Craft III. Charles Shackford, Review ofUbungsbuch fur den Dreislimmigen Sarz by Paul Hindemith, Journal ofMusic Theory 16 (1972), pp.257-259.Example 1.6 Applying Hindemith’s Theory to Copland’s Musica) S.S. , I b) S$., ifiRoots:(H)A Bb A A Bb C# Bb F# Db(better) A (NC) A Bb Bb C# Bb DbI F#18A practical solution to the problems encountered in attempting to apply these twotheories lies in admitting that many factors affect the way one perceives the root of thechord. Root perception is not simply a matter of what intervals of pc collections are formedby the pitches that sound together. Part of root perception results from our previousexperience as tonal listeners. For example, we tend to perceive particular pitch registrations— such as the voicing 1-3-7 (e.g., the chord {G3, Bb3, F4}), or an interval of a seventh, ora sustained interval of an octave — as rooted because they sound similar to more traditionalrooted chords (i.e., seventh chords or simple triads). However, another part of rootperception in Copland’s music, as demonstrated above, is contextual. The importance ofcontext makes it impossible to derive comprehensive formal rules for root determination inCopland’s music. In the interests of simplicity, then, this thesis will assume a traditionalmethod of root determination is viable because, comparatively speaking, it generatesmeaningful roots more consistently than Hindemith’s theory for Copland’s music. Explicitd) Q.C..jff.19references will be made to ambiguous chord roots when it is relevant to the discussion oftonality.1.3.2 Idiomatic Rooted Sonorities in Copland’s MusicIdiomatic rooted sonorities in Copland’s music include not only familiar chordssuch as major and minor triads’7and complete chords larger than the triad — particularlyseventh, ninth and thirteenth chords18— but also special “added-note” chords (chords basedon a triad) and recurrent types of “incomplete” chords. Examples of “added-note” chordsare shown in Example 1.7a-e. These include the added-sixth chord (Example 1.7a), themajor triad with an added ninth (Example 1 .7b), chords with both the major and minorthird (Example l.7c), the major triad with an added raised fifth (Example 1.7d) and severalother less traditional combinations as, for example, a major six-three chord with a minorninth above the bass (Example 1 .7e).Example 1.7 “Added-note’ Chords in Copland’s Musica) S.S. , Ill b) B.K. c) P.V. d) B.K. e) S.S. , I“Incomplete” chords are far more numerous than “added-note” chords in Copland’smusic. Some authors, like Berger, view Copland’s “ingenious omission of ‘essential’17Diminished and augmented triads occur only rarely in Copland’s music.18The complete thirteenth chord is considerably more rare in Copland’s music than either complete seventhor ninth chords. One example of a complete thirteenth chord is the sonority {C2, G3, EM, A4, F5, BbS,D6, F6} that is sustained in mm.59-60 of the first movement of the Clarinet Concerto..020chord tones” as one of the prime reasons why Copland’s music of this time wassuccessful.’9Berger believes that Copland’s sonorities became “fresher and moreimaginative” as his textures became more and more diatonic.20 Most often these chords areincomplete seventh and ninth chords in root position (see Examples 1 .8a-b; and 1 .&-drespectively). Copland often adds another dissonant tone to incomplete seventh chords as,for example, in the characteristic seven-four chord that occurs in both his “serious” and“popular” pieces (see Example 1 .&). Infrequently Copland will use an incomplete rootposition thirteenth chord (see Example 1.80.21Example 1.8 “Incomplete” Chords in Copland’s Musica) P.S. ,I b) S.S. ,ffl c) S.S. ,1 d)S.S. ,ll e) Q.C. f) S.S. ,ll19Machlis states that “the careful spacing” of Copland’s chords is a “delight to those who examine hisscores” and helps Copland “achieve the clean, transparent sound that is one of the hallmarks of his style.”Joseph Machlis, Introduction to contemporary Music (New York: W.W. Norton, 1979), p.390. Bergerargues that the “matter of chord spacing may possibly turn out to be one of the great contributions of thelast few decades and Copland stands close to Stravinsky among those who are responsible for it.” Berger,op. ciL, pp.70-71.20Berger, op. cit., p.70. Copland suggests a different origin for these “new” harmonies — his exposure tothe twelve-tone technique as early as 1928. He comments: “For me as a composer the twelve-tone methodwas a way of thinking about music from a different perspective.. .It was an aid in freshening the way I wroteat a time when I felt the need of change. ..It forced me into a different, more fragmented kind of melodicwriting that in turn resulted in chords I had rarely used before. Thus my harmonic writing was affected inthe Piano Variations and in the works which followed — the Short Symphony and Statements forOrchestra.” Aaron Copland and Vivian Perlis, Coptand: 1900 through 1942 (New York: St.Martin’s/Marek, 1984), p.182.2tContext plays a large role in hearing a Bb root for this chord. The sonority in Example 1.8f is the goalof a cadence ending a Bb tonal area.Bb..F-øB7 13B4 Bb93 7S211.3.3 Multiple-Rooted SonoritiesOne of our criticisms of Hindemith’s theory in the analysis of Copland’s music wasthat it did not allow multiple roots for the same chord even when these are clearlyemphasized by context. In Copland’s music multiple roots can be heard simultaneously fora chord if one of three conditions obtains: the pitch registration emphasizes polytnadicconstruction; the texture is divided into two separate tonal strands; or the chord combinesstriking intervallic characteristics of chords that appeared earlier and had different roots.Example 1 .9a shows a chord whose pitch registration emphasizes F- and C#-major triadsin the lowest and highest registers respectively and, thus, suggests that we hear both F andC# simultaneously as roots. Example 1 .9b shows a chord that results from a division ofthe texture into two tonal strands. The superposition of a melody that accents pcs G, Bband D above a re-articulated F#-rooted chord suggests that we hear two simultaneous roots—0 and F#. Example 1 .9c shows a chord which combines striking intervalliccharacteristics from two previous chords with different roots. The chord at R15+ 1combines the bass minor ninth and fifth of the 0-rooted chord at R5-2 with the outer voicestructure of the D-rooted sonority at R3-1. This suggests that we hear both D and Gsimultaneously as chord roots. Examples 1 .9a-c are all drawn from an orchestral work, inwhich timbral differences help to stratify the texture.22ir’f/ LIp Lb.—1t p‘ - IT —-+1 +1=-2 +9:p 1pRoots: C#+F# G+F# G+D [0 + Dl1.4 Chord Progressions in Copland’s MusicIn classical tonal music most roots function in a progression. Indeed it makes nosense to attribute a root to a chord unless that root functions syntactically. The problemwith rooted sonorities in Copland’s music is that the roots rarely connect into recognizableprogressions, that is, into progressions directed towards dominants and tonics. Thus theydo not function to create tonics in traditional ways.There are some untraditional ways that chord roots do function to define tonics inCopland’s music outside of progressions. For example, Copland has several methods ofgenerating a tonic pc by emphasizing the root of a chord through changes in texture andlorby other accents (recall Example 1.4). These techniques will be discussed more fully later.Further, the first and last roots in a piece by Copland sound like tonics unless there are verystrong syntactical factors — a root succession or tonal preconditioning — that contradict thathearing. Thus, our predisposition to hear the C root that begins of the first movement ofthe ClarinetConcerto as the tonic is subsequently confirmed when C is generated as a tonicby neighbor-tone motion around the {C, E} dyad using pcs from the C-major collection.Example 1.9 Chords With Multiple Rootsa) Polytriadic Construction b) Tonal Strands c) Combining the Striking IntervallicCharacteristics of Previous ChordsS.S. , Ill S.S. , Ill S.S. , I_________________± ±AI23Similarly, our predisposition to hear the final E-rooted sonority of Billy the Kid, {E, G#,B, C}, as a tonic chord is confirmed because that sonority concludes material that we arepreconditioned to hear in E. However, the final C root of Quiet City does not fit thismould. C does not sound like a tonic here but, instead, like a dominant, because we arepreconditioned to hear the material it concludes as having F, and not C, as its tonic. Thebeginnings and endings of pieces are rather special situations whose effects result from ourgeneral listening experience of tonal music and not specifically from our experience ofCopland’s music. There is one important aspect of Copland’s music, however, that doespredispose us toward certain channels of hearing: whenever there is a passage with just asingle rooted sonority, that root is almost always either the tonic or the dominant. Example1.1 demonstrated a tonal area with a single tonic root. Example 1.10 shows a passagefrom Quiet City where the only explicit chordal root in an Eb tonal area is the dominant.22The first chord has a Bb root because the voice exchange in the outer voices between pcs Fand Bb makes pc G in the first chord sound like a neighbor tone to pc F in the secondchord. The Eb tonic is generated by the metric accent on the first and fifth scale-degrees.Example 1.10 astheOnlyRootinaTonalAreaQ.C. ,j-7ff..-3A Ii. I Ii. IA I IL — —- -..:- I/c’‘)E--1 ,h LI I Ir I‘1J,—Ji iJ’..I..— 3_J—I;--—-P)\,7-4-221 am interpreting the inferable Eb-major triad in the melody as a representation of the tonic pc and not asan implied tonic harmony.24Although there are some passages where it is possible to find conventionalprogressions that generate a tonic (as, for example, at R2ff. in the “Saturday Night Waltz”from Rodeo ) these passages are exceptional and do not truly represent Copland’s typicalharmonic style. In fact, Copland’s music, unlike more traditional music, does notgenerally use chord progressions as the primary means for tonic generation.23 There aremany passages in Copland’s music, some very long in length, where traditionalprogressions are not active. These passages contain either a single rooted sonority or asuccession of chord roots that are not tonic- or dominant-directed.One instance of a long passage where functional progressions are absent is shownin Example 1.11, which presents a sketch of R47÷2 to R49- I of the third movement of theShort Symphony. Example 1.11 shows two complete tonal areas — A (R47+2ff.), Db(R48ff.) — and the beginning of a third — the F tonal area which ends the movement (R49-2ff.). None of these areas contain a functional progression; rather shifts betweensuccessive verticalities are coherent because of stepwise voice leading. At R47+2 inExample 1.11 an A tonic is generated in the melody by accents on the first, third and fifthscale-degrees.24Harmonically, R47+2 to R48-1 can be summarized as the repetition of anA-major six-three chord that is modified by a major ninth above the bass (pc Eb).However, this repetition is obscured because, once established at R47+2, the altered A-major chord is not literally present until R48-2 because the bass and soprano motions areout of synchrony with each other. (Arrows in Example 1.11 show explicit statements ofthe altered A-major chord.) That is, statements of pcs A, C# and E in the soprano do notoccur at the same timepoints as statements of the dyad {Db2, Eb3 } in the bass, which is thegoal of a neighbor-tone motion; rather these pcs sound together with statements of the23Virgil Thomson makes reference to the subsidiary nature of harmony in Copland’s music with theobservation that Copland’s “conception of harmony is not form but texture. Virgil Thomson, “AmericanComposers VII: Aaron Copland,” Modern Music 9/2 (1932), p.68.24Example 1.11 does not show the metrical setting of this passage because of its great length. Assertionsabout accents, therefore, must be verified using the published orchestral score.190 0eii0 00I04111I‘III0E 4 4 4-CD IIri‘7140 0414.II I4 114—414<1114 IWF1 1i-i26neighbor bass dyad {D2, E3}. Despite this lack of synchrony, however, the dyad {D2,E3} retains its melodic function and, therefore, does not suggest a second rooted sonorityfor the passage. The lack of synchrony between bass and soprano obviously weakens therepetition of the A-rooted sonority that is the harmonic basis of this passage. However, italso contributes to our understanding of connection between the initial A tonic of Example1.11 and the preceding Db tonic of R44 to R47- I (not shown in Example 1.11) because itemphasizes certain motives in R47+2ff. that are derived from motives in R44ff.25At R48-lff. step motion connects this modified A-major six-three chord to amodified Db-major six-four chord which begins the second tonal area in Example 1.11.One can infer D and G roots for the intervening sonorities, {C2, D3, F#6} and {Bbl, C3,G6} respectively, which result from this step motion because these chords mimic a V4/2-i6progression in G minor. However, such a progression is non-functional in a traditional Dbcontext, nor is it used by Copland in other works to define a tonic. Rather, Db is definedas a tonic by the accent on pcs Ab, F and Db in the melody and by other techniques thatwill be discussed later. The Db tonal area in R48ff., like the preceding A tonal area, alsocontains only a single harmony — the Db-major six-four chord — because the consistentemphasis on two neighbor-tone motions in the inner voices, <E4, F4> and <04, AM>respectively, makes the potential dominant chords in R48+5 (beat 4) and R48+7 (beat 2)sound like the result of melodic elaboration.The subsequent F tonal area, of which only the first measure is shown in Example1.11, is similarly not prepared by a chord progression. We know that F is the tonic of thepassage beginning at R49-2 because of preconditioning — F was the tonic the last time this25For example, the bass dyad {Db2, Eb3 } at R47+2 is a restatement of the interval formed by the lowesttwo pcs of the Db-rooted chord ({Db2, Eb3, Gb4, Db5, F5, Ab5}) which is repeated from R44 to R46+3 inslightly different registrations. Similarly, the opening melodic motive <A, B, C#> and bass line <D, Db>at R47+2 are derived from two earlier motives at R46-t-2 to R46+4: <G#5, A5, B5, C#6> in the strings andwoodwinds, and <D5, Eb5, D5, C#4, C4, C#4> between the trumpet and horn. The succession <1), C#>is emphasized in the latter by accents on each statement of pcs D and C#.27bass line was heard at R30-2. In R49-2 F succeeds Db as a tonic by the simple expedientof juxtaposing an F-rooted chord, {F1, D2, F2, C3, Ab3(4,5), C4(5,6)}, with the Dbmajor six-four chord. The arrival of the F tonal area is particularly striking because thedramatic change in texture, which articulates the Coda of this movement, is notcomplemented by a functional chord progression as it would be in more traditional tonalmusic.The examples already cited in this chapter demonstrate that functional progressionsare not a necessary condition for tonic generation in Copland’s music. Example 1.11 alsosuggests that successions of chord roots in Copland’s music, when they are present, oftendo not fit into recognizable functional progressions and that frequently they are severelyobscured, or even eliminated, by an overriding emphasis on melodic lines.There are no inferable dominant-tonic progressions between successive tonics inExample 1.11. In the rare passages in Copland’s music where such progressions can beinferred they are usually so subtle and de-emphasized that it is debatable whether weperceive them at all. Examples 1.12 and 1.13 show two other passages from the thirdmovement of the Short Symphony where the inferable dominant-tonic progressionsbetween successive tonics are exceedingly difficult, if not impossible, to hear. Example1.1 2a quotes a passage where Bb is succeeded (at R40) by B as the tonic. We canretrospectively hear the Bb-rooted sonority which ends the Bb tonal area — {F3, D4, Bb4,Gb5} — as initiating a dominant-tonic progression in B. Example 1.12b shows how thischord, interpreted as B:V#71#5 ({E#, Cx, A#, F}), progresses to the altered B six-fourchord in R40+3. This dominant function, however, is very difficult to perceive because pcGb derives from the coloristic use of the whole-tone scale {Bb, C, D, E, F#, G#} abovethe static Bb six-four chord harmony sustained in R39ff. and, therefore, does not soundlike it is an essential chord tone. Example 1. 13a quotes a similar passage where Coplandconnects B and Ab tonics by an inferable dominant-tonic progression. Example. 1.13b28shows that the final chord of B progresses to the Ab-rooted sonority that is melodicallyunfolded in R42-4 to R42 in a manner that mimics the progression Ab:V5b5-I. Theinterpretation in Example 1.13b hinges on understanding the bass F in R41+5 as a lowerneighbor tone to G. Experientially, however, the listener is much more aware of the returnof. Eb5 as the soprano pc of the chord, and the chromatic descending step motion in thetenor (<B3, A3, Ab3>), than of the implied root succession <Eb, Ab>, which is, at anyrate, only perceived retrospectively.2626The emphasis on Eb, as a pc common to the referential collections of the B and Ab tonics, and thecomparative dc-emphasis of the implicit dominant-tonic progression suggests a different interpretation ofthe formal function of tonality in Copland’s music which will be discussed below.Example 1.12 Underlying Dominant-Tonic Progressiona)S.S.,ffl, ff,Roots: BbTonics: (Bb)BB9B:V I33 66229IIExample 1.13 Underlying Dominant-Tonic ProgressionS.S. , Ill, j ff.___________L-r-mIr-A ..—.____I I_____________-_________—- lil• t’pJ.b -y - I - I - I r. -i):3 —- I P P4 LLLIk. IrTonic: (B) Ab- J Jj jj—1.F.—----r 4•ITh9:7 FNrr -T‘1,—wrt TTR ‘I Li I II -e) Ir.• L’.•1 •-.h4 . L— - . --—— --, r’Tonic: (B) AbAb:Vbb3 ICopland’s music adopts the dominant-tonic principle in other ways besidesinferable progressions between successive tonics. There are innumerable subtle referencesto the dominant-tonic relationship in Copland’s motivic textures.27 This may involve astrategically placed repetition of a particular motive as, for example, in the first part of QuietCity where the repetition of the “nervous, mysterious” sixteenth-note motive (in thetrumpet) links non-successive dominant and tonic chord roots (Ri and R3-6 respectively)in an F tonal area. Or it may result from a division of the texture into two separateharmonic streams as, for example, at R9+3 in the first movement of the Short Symphony,where the texture of a Cl tonal area is divided into an oboe melody that states the tonic triad(Cl-major) and a bassoon melody that simultaneously states the dominant triad (G#major). Quite often Copland will make reference to V and I using a motive in the bass.27Rudolph Reti makes a similar comment about Debussy’s music. Reti argues that Debussy “obviouslyuses the pitches of a dominant-tonic progression, rather than their harmonic idea, as a structural device.”Rudolph Reti, Tonality, Atonality, Pantonalily: A Study of Some Trends in Twentieth-Century Music(New York: The Macmillan Company, 1958), p.26.b)A ..I30For example, at R37÷ 1ff. in the third movement of the same work, statements of the cell<C3, A2, F2, Bbl> in the piano, bassoon and double bass are overlapped to create thedyadic succession <{F2, C3}, {BbI., A2}> and, thereby, to suggest the root movement<F, Bb> in a Bb tonal area. In each case cited above Copland mimics the effect of adominant-tonic progression but casts it in a unique (melodic) form which effectively existsoutside of root successions.The presence of so many chord roots in Copland’s homophonic textures, however,leaves the analyst with a fundamental choice: we can either discover new, consistentprogressions of roots that define tonics, or we must find other functions of roots. Areview of Copland’s music reveals that he is quite conservative when he writes functionalroot progressions. In Copland’s music, unlike that of other twentieth century composerssuch as Scriabin,28relatively conventional progressions such as <bli, V. I> are extremelyrare29 and more unusual chromatic progressions such as <bil, I> are notably absent.Instead, Copland constrains his root progressions to more familiar patterns — <IV, I>,<V, I>, <II, V>, <VI, V> and <IV, V>. The one striking exception to this rule is the jazzprogression <b(k)VI1, I>, which occurs in a tonic-defining role in at least three differentpieces: the first movement of the Short Symphony at R1+2 to R2-2 (i.e., D:<i, vii, i>),Billy the Kid at R43+1 (i.e., A:<VII, I>), and R13+l to R13+2 of “Hoe-Down” inRodeo (i.e., A:<VII, i>).The examples cited above suggest that there are other significant processes inCopland’s music besides chord progressions that are used to generate tonics. The mostimportant of these processes will be defined below as tonicizing techniques.28James Baker, “Scriabin’s Implicit Tonality,” Music Theory Spectrum 2 (1980), p.2.290ne instance of this progression occurs in “Corral Nocturne” from Rodeo at R5-2 to R5 where pc C isdefined as a tonic by the progression <V. bvi, bil, V. I>.311.5 Tonicizing Techniques in Copland’s MusicA tonic in Copland’s music is normally generated by the confluence of severaltonic-defining processes simultaneously or within a relatively brief timespan. Tonicgeneration sometimes involves the activation of a chord root as a tonic by an emphasis on achord, for example by changes in texture or by phrase elisions. But Copland uses othertechniques, some of which are idiosyncratic and need to be discussed here. The mostimportant of these techniques are: isolated descending- and ascending-fifth motion of roots;triadic melodic structures; arpeggiation of special pc-set classes in the lowest voice;“directed motion;” textural and thematic articulation of a rooted chord; pedal tones;reiteration of a root; and neighbor-tone motion. Most of these techniques are reinforced byaccenting the tonic pe or a tonic-rooted sonority. Many of them appear in classical tonalmusic, but in combination with tonic-defining root progressions. Because suchprogressions are often lacking in Copland’s music, it is useful in characterizing his style tocatalogue these techniques.The techniques mentioned above often interact either simultaneously or within asmall timespan to support mutually a single tonic. Normally a pc will be introduced as atonic at some timepoint by one technique but will be confimed later by other techniques.Most commonly one of these techniques will be perceived as primary (i.e., the techniquewhich suggests the tonic most strongly) and the others as secondary. As a result, in manyof the examples of individual techniques, other processes defining the same tonic arepresent.1.5.1 Isolated Root Motion by FifthFifth root motions are used at isolated moments in Copland’s music to generate atonic. The term “isolated” here signifies that the fifth motion is not the culmination of along series of roots that function in a progression but simply occur without preparation at32particular moments in a piece.3°Descending-fifth (ascending-fourth) root motion mimics adominant-to-tonic tonal motion. Similarly, ascending-fifth (descending-fourth) motion ofroots mimics a subdominant-to-tonic tonal motion. Neither of the chords whose rootsdefine the fifth motion need be a pure triad. The roots are not necessarily the lowestsounding pcs of the chord. However, this is preferred by Copland perhaps because itallows a greater variety of interval structures above the bass. For example, one often finds“incomplete” chords that are similar to characteristic seventh and ninth chords foundelsewhere in Copland’s music.A simple descending-fifth pitch motion can also create a tonic, even if these pitchesare not roots, if it is supported in the musical context by specific rhythmic, textural andmotivic features. For example, a descending-fifth pitch motion creates a tonic if the firstpitch, sustained by itself at the end of a tonal area, functions as an anacrucis to the secondpitch, which appears as the root of the first chord in the following tonal area. Similarly, adescending-fifth pitch motion creates a tonic if the pcs these pitches represent havejustbeen heard as chord roots and if the second pitch is sustained in the bass. Descending-fifthpitch motions are important for tonic generation in Copland’s music because they oftenresult from the severe attenuation of an underlying descending-fifth root motion.The dominant type of fifth root motion is more prevalent in Copland’s music thanthe subdominant type. Coplancl rarely makes the first chord the tonic when the followingfifth root motion to IV or V constitutes the only root succession in a passage.3’ He alsoavoids the ordered pitch interval of —7 in a <I, IV> progression when the roots are in thebass. Although both descending- and ascending-fifth types of root motion are used inhomophonic textures, only the former is used to generate tonics in emphasized pitchmotions where the tones are not necessarily roots.30lndeect, the isolation of these root movements enhances their ability to generate a tonic.31 One example can be found in mm. 173-195 of the first movement of the Piano Sonala. Here theharmonic underpinning of an A tonal area is the progression <i, iv>. See below, pp.237-238.33Fifth root motion plays a more important role in generating a tonic when the secondchord (the harmonic goal) is accented (i.e., by duration, metrical placement, contour ordynamics). Accents are often supported by a change in texture and a rhythmic caesura (acessation of rhythmic activity created by held tones or rests). Generally in Copland’smusic agogic accents support tonic definition but they are not sufficient to define them.Root motions of a fifth define a tonic more strongly if both chords are major or minor triadsbecause this most closely resembles traditional tonal gestures.Examples 1.14-1.18 below show characteristic passages from Copland’s musicwhere descending- and ascending-fifth root motion generates the tonic. Example 1.14shows how a descending-fifth root motion <F, Bb> is attenuated to become a descending-fifth pitch motion that defines Bb as a tonic. An F-rooted sonority, {Fl(2), Abl(2)}, issubposed under a Bb-rooted sonority, {Bb4, Db5, F5, C6, F6}, in the first two measuresof the excerpt causing Bb and F roots to sound simultaneously. When the F-rooted chordis finally heard by itself it resolves to a Bb that is no longer heard as a root. However, PCBb does become a chord root after only a short delay: Bb, sustained in the bass while themotto of the first theme is restated above it, is the root of the first two sonorities of themotto (the last two sonorities in Example 1.14).In Example 1.15 a descending-fifth motion of roots, appearing in attenuated form,generates a D tonic. In this passage Copland plays with the convention of a dominant as ametrical anacrucis to the tonic: D is established by the pitch motion from A to D in the bass,but rising major sixths in the inner voices obscure the root properties of the preparatory A.D is, however, unmistakable as a tonic despite the effacement of the dominant root. It isalso supported as a tonic by other factors: the highest voices of the first and last chords inthe repeated three-chord gesture are D-major triads; and the <A, B, D> melodic cell in thehighest voice is familiar in jazz music as a D-tonic motivic gesture. The D-rooted chord isaccented by metrical placement and increased duration.Example 1.14 Attenuated Descending-Fifth Root MotionP.S., I, mm.237ff.I F I‘Aif I9FA 4 —F1—Ui LJ .L)-—IbJ-.. — 4.FLh ri. - —4—.-— I-Roots: Bb Bb Bb BbTTonic: Bb34,.—ii I l I & - -‘_Fmotto offirst themej —4tr.-J —J— —Cd.II:. II—-•F[Bb] BbExample 1.15 Attenuated Descending-Fifth Root MotionP.C., I, -1ff.‘Roots: [A] D [A] DD tonic35Example 1.16 shows a passage where a tonic-defining descending-fifth pitchmotion is used by Copland as a bridge between monophonic and homophonic textures.The monophonic passage in Example 1.16 ends with a long G5 in the trumpet; at R7 thistexture is replaced by a homophonic texture whose first chord root is C. This establishes Cas a tonic right from R7, in a way that is similar to a traditional dominant-tonic rootprogression. Later events confirm C as a tonic: the progression Vb5/4/3-1b7 at R7+1 toR7+2; and the C—Aeolian collection. The voicing of the passage emphasizes the fifthbetween G5 in the trumpet and C5 in the first violins: melodically, as the ordered pitchinterval of—7 between successive pitches in the highest voice; and harmonically, as asustained interval.Example 1.16 Descending-Fifth Pitch Motion as a Bridge BetweenMonophonic and Homophonic TexturesQ.C. , [].2ff. JA l.—3.I, I . I II — I 11. — — p —r i.’& i ii -zz-—Roots:Tonic:I1._J I I It)d—,.I *-cendii-.xi-J I 7 I 7-—--g-fifth pitch motionI, I I--- ICCExample 1.17 shows a passage where an ascending-fifth type of root motion notemploying pure triads generates the tonic.32 Here a D-major chord, {D2(3), A3, D4,F#4(6,7)}, is established as a tonic by a plagal motion from a G-rooted ninth chord, {G3,A3, D4, B5(6), D6(7), F#6(7)}. The D-major chord receives a metrical accent. This <IV,32Thc rhythm has been simplified in Example 1.17— the re-articulated chords in the strings are simplynotated as sustained.36I> root succession becomes, through repetition, the harmonic underpinning of thefollowing D tonal area. Other factors again confirm D as a tonic: the emphasis on pcs F#,A and D in the first violin melody <F114, G4, A4, G4, F#4, E4, F#4, D4>, and use of theD-major collection. We are also, however, predisposed to hear D as a tonic at R34 becauseof the unusual appearance near the end of the previous C tonal area (at R33ff.) of the fifth{D4, A4}, and because of the woodwind melody <A4, A5, D5, F5, A5, F#5, A5> (notshown in Example 1.17).IExample 1.17 Ascending-Fifth Root Motion“Buckaroo Holiday,” R., []-2ff.A‘‘—..1Irr-.A —c-r)-’1‘,-II U.. - -P’ff7III-p w;1 ‘--‘ —i’-— IIII_ø Ie)4,-..li C.L-. C.-.‘ffI I-“.-—- S a — IT1 . I IyrRoots: G DTonic: (C) D1.5.2 Melodic ConstructionA top-voice diatonic melody that brings out the pcs of a major or minor triadindirectly through accents, or directly by arpeggiation or repeated fifth motion, activates theIA -_________________ L)I - II — F -p - :j rn—‘ I —+4 F rid.--iALIAu-‘3FrRoots: 0Tonic: (D)D37root of that triad as a tonic. This tonic is said to be “melodically generated.”33 Copland’smelodies tend to emphasize triads as part of a diatonic collection. Often the collection in themelody affirms the root of the emerging triad as a tonic because it corresponds to traditionalusage (i.e., the pitch-class content of the melody is constrained to a transposition of <C, D,E, F, G, A, B> and the root of the triad is the first tone of the collection). Copland tends toconstrain the pitch-class content in his melodies to the major mode and the Dorian,Mixolydian and Aeolian collections. Only occasionally will he make referential a moreunusual modal collection, such as the Lydian collection. (One example of a referentialLydian collection appears in the passage quoted in Example 1.17.)Most often Copland’s melodies will either use all the pcs of the referential collection(for example, the melodies in Appalachian Spring), or all but one of the pcs (like several ofthe melodies in Billy the Kid ). Although accents tend to appear on all members of thetriad often it is the tonic pc itself that receives the most accent. The most emphaticexamples of such accent, such as at R12 to R15 of the Piano Variations, forcefullyarticulate the tonic pc as an accented pc ending short repeated phrases. More complexAexamples of melodic generation tend to place greater emphasis upon 5 than upon the root.Some of these melodies have discernible harmonic rhythms or harmonic groupings thatfollow the traditional syntax of <I, V. I>, bringing Copland’s music very close to33Reti discusses “melodic tonality” in Debussy’s music and discusses a passage from Debussy’s musicwhere the harmony results from parallel chords. He argues that these “chords” are “in essence notharmonies at all, but rather chordal melodies, enriched unisons” and that the tonic of the passage is notdefined by them. Reti, op. cit., pp.23 and 26. Copland alludes to the importance of melody in his owncompositional process in certain statements from What To Listen For in Music. For example, Coplandargues that “the thing that takes the place of a story in music is, as a rule, the melody” and begins his listof compositional ideas with a “one-line melody.” Aaron Copland, What to Listen For in Music (NewYork: McGraw-Hill Book Company, Inc., 1939), pp.6-7, and 23. Copland also alludes to the importanceof melody as inspiration when he talks about how he only had the cowboy tunes themselves when he waswriting Billy the Kid. Copland and Perlis, op. cit., p.279.3’tThe pcs which are omitted most consistently from Copland’s melodies are the seventh and fourth scale-degrees. For example, in the orchestral suite of Billy the Kid Bb:4 is not used in the melody of the“Mexican Dance” (R2Off.), G:4 is not used in the Finale (R2411.) and Ab:7 is not used in the tin-whistlemelody at R6ff. These omissions change the diatonic collection into the pentatonic scale, which is used inmany folk songs. However, Copland also frequently omits 6. This can be seen in the melody inAF at R8ff.of the same work. Occasionally, Copland will omit a more modally significant scale-degree like 3 in hismelody. This occurs at R4ff. of Billy the Kid when F is the tonic. See below, p.113.38traditional music at times. This tendency is more pronounced in some of the “popular”pieces as in, for example, the “Shaker” tune from Appalachian Spring. Copland’stechnique of melodically generating a tonic by accents, however, is clear even when suchtraditional methods are not employed. The presence of tonics in monophonic passages inCopland’s music assures us that melodic generation is sufficient by itself to generate atonic.Examples 1.18-1.20 quote passages from Copland’s music where tonics aremelodically generated in homophonic, heterophonic, and monophonic texturesrespectively. Example 1.18 provides a simple example of a homophonic texture where a Dtonic is melodically generated. Pc D is prominent in the repeated four-measure phrasebecause it begins, ends and is stated frequently in the middle of the melody. The D-majortriad is prominent in R5+1 to R5+2 and in the corresponding passage R6-3 to R6-2. Thereferential collection in the melody is the D-major collection. Pcs C and Eb are noncollectional tones because they are constrained to the brief triplet-sixteenth-note figure andprepare the collectional tones C# and E respectively which follow. This perception isenhanced by the material in R4ff. (not shown in Example 1.18) where pcs C# and E appearin the dominant chord in a <1, V, I> progression in D-major.39(Example 1.18 Melodic Generation of a Tonic in a Homophonic Context“Hoe-Down,” R.,r 3—,(I.. ffi •‘1— I, •1“ 4,— ,. I IITI-,I.ID 1’ U“fl— -, I I3•-•I. —- IJ## 4.)‘-‘... “fl..JL I —-‘---..‘#44I I II I I-I--—.‘#44l#s-I I. Isf—#4 4Example 1.19 provides an example of a melodically-generated tonic within aheterophonic texture. An F tonic is melodically generated in this passage. Pc F, prominentas the beginning and ending pc, appears as every other note in the first two measures ofeach four-measure phrase. Agogic accents in the first, third and fourth measures of everyphrase bring out members of the F-major triad (i.e., A4, C5 and F4 in the antecedentphrase). The repetition of the last measure of the consequent phrase causes successiveagogic accents on F. The pitch-class content of the upper voice in the original, and laterheterophonic, doubling of the melody is the collection {E, F, G, A, Bb, C}, which is asubset of the F-major collection. This example verifies our assertion that melodicgeneration of a tonic is sufficient to create a tonic by itself: there are no other supportingtechniques that confirm F as a tonic.Y1t2 Ek ml I -III I._‘I I.‘#44Tomc:D r3iA —11I I II II]—ri ..J I I I — ..J — ..J ..J‘ I I- —..#44Example 1.19 Melodic Generation of a Tonic in a Heterophonic ContextB.K., []ff.Allil.Li -I:LI IIL_LII-—- -0-0—II I II IL..LII‘ I IL._.IVg I It)Fti I rI L I flp I,-.-.-\, rJ. I.ij P) IA 1.9 V I ri I I I1 —I— I “I II x-IrIr, I 12 —.-. II Ir2 1.1r-—I—‘.. I—Ira..IExample 1.20 provides a more complex example of a melodically generated tonic ina monophonic texture. Unlike earlier examples of melodic generation, there is an initialambiguity in the sense of tonic caused by accents; D only gradually assumes primacy overA as tonic.35 The most consistent accent (of contour, meter and dynamics) is given to thePC A, and not the pc D. D becomes the tonic because of the strong pitch associationbetween A and D (i.e., pc A moves to pc D three times), and because of the emphasisplaced on pc F# (i.e., F# is followed by a rest each time it is stated in Example 1.20). Thepitch-class content of the melody is a subset of the D-Mixolydian collection.35This interpretation is confirmed later in mm. 162-170 when a transposition of this theme up a major third— suggesting F# as a tonic — is supported by the F#-rooted sonority {A2, F#3, C#4, F#4}. See below,p.238.40LFti rr,I_ S 1 I I I I I- —, —— -j -J I I I—. • rJ 1 T FE -r 2 2 9 L I I I i a r 2 2I II I II I I I I II I II-7-—a’Tonic: FAl,- ,—I I41Example 1.20 Melodic Generation of a Tonic in a Monophonic ContextP.S., I, mm.133ff.> >II,11.5.3 Pc-Set Classes in the BassA melodic presentation of special pc-set classes in the lowest sounding voiceestablishes a sense of tonic. By “special pc-set classes” is meant either a simple major orminor triad, or a major or minor triad modified by one additional tone (modified triads).The latter includes sonorities such as seventh chords, minor-major chords, and triads withan added fourth. The root of a simple triad does not have to be accented to sound like atonic, although such accent is relatively frequent. Accent is particularly important whentriads modified by a tone are presented melodically because this helps define the root and,thereby, resolves any ambiguity. Normally the root of the triad being arpeggiated will alsoappear concurrently as the root of a chord. Melodic presentation of triads is more commonthan melodic presentation of modified triads.Example 1.21 shows a passage that is based upon the melodic presentation of atriad in the lowest voice. The D tonic is generated, at least in part, by the bass arpeggiationof the pitches of this triad.36 The initial tone of the arpeggiation, D4, receives accent from360ne might also hear passing references to a Bb tonic in this passage because of the manner in which thedyad {Bb4(5), D6}, created by doubling the melody in parallel thirds, is agogically accented at the end ofmm.68, 70 and 73. The melodic cell cD, C, A, Bb> by itself also alludes to a Bb-major collection.However, there are other important (contextual) reasons for hearing D as the tonic of this passage. Theseare discussed below on pp.225-227.k142contour and meter: D4 is the highest pitch of the arpeggiation and always occurs on thedownbeat. Other factors support D as a tonic, notably the presence of only D-rootedverticalities over most of the passage, the metrical emphasis on D-rooted sonorities with Din the bass, and the modified D-Aeolian collection.Example 1.21 Bass Arpeggiation of a TriadP.S., I, mm.67ff.A I 0# :$ S 4 k,_EE1p I — — nrj— I ii — LL2mI — — nt a r — fir. I ii— p- —I—-Ii--h--—-4_V S It)-IY- I ill‘P1w;J 1I%.— I,. III— I—,—, F “I— Iai’-r%. a,.III ,I Ii-r-I Lie--— ,,I— I I--L‘ I I’ ‘I I’Roots: D Bb E FTonic: D FExample 1.22 shows a passage where a melodic presentation of a modified triad,{G#, B, D#, F#}, generates a G# tonic. G# is emphasized as the final pitch in a two-measure phrase that is repeated in the bass. This example shows that of all the voices thebass most strongly defines the tonic; accents in the upper voice suggest B, but this isweaker than the G# defined by the bass. Descending-fifth root motion also supports G# asa tonic: in mm.43 and 48 the D#-rooted sonority {D#3, C#5(6)} is succeeded by the G#rooted sonority {G3, B4(5)}.43Example 1.23 provides a more complex example of this technique. Here themelodic presentation of a modified triad, {C, Eb, E, G}, generates a C tonic. Themodified triad appears first at R14 and R14t-2 in the grace notes that introduce the highestvoice, but also gradually manifests itself in the lowest voice of the two-part texture. Whatis particularly interesting about Example 1.23 is how the modified triad {C, Eb, E, G} isused to reinterpret pc Eb from the tonic pc in a monophonic texture to the (minor) thirdscale-degree of C in a homophonic texture.37 C is confirmed as a tonic in R14-i-2 to R14+3by a descending-fifth root motion (<C, G>) that is implied by the successive majorsevenths {G, F#} and {C, B}.37The shift in tonics in this passage focuses our attention upon the changing scale-degree function of pc Ebin much the same way as that observed earlier in Example 1.13.Example 1.22 Bass Arpeggiation of a Modified TriadP.S., II, mm.43ff.Roots:Tonic: G#1.5.4 Directed MotionDirected motion defines a tonic in either homophonic or monophonic textures.38 Ina homophonic texture it involves the bass line in a series of chords. The bass line moves ina single direction, and ends on a pitch that is accented by duration or meter and that belongsto the pc that is the root of its chord. The terminal chord in directed motions is often amajor or minor triad, perhaps because this gives the clearest root definition. The bass linemust contain at least two pitches that are not members of the terminal chord. Thisrestriction distinguishes directed motions from tonic arpeggiations in the lowest voice (i.e.,arpeggiations of the triad associated with the tonic pc). Such a distinction is desirablebecause directed motion is usually a motion towards a new tonal area, that is, it establishes38Roy Travis uses the term ‘directed motion” to denote a middleground structure which spans an entirepiece. Roy Travis, “Directed motion in Schoenberg and Webem,” Perspectives ofNew Music 4/1 (1966):85-89. This thesis, however, uses the term to denote a pattern on the surface of the music which articulatesa new tonic and (often) a new thematic section.Example 1.23 Bass Arpeggiation of a Modified TriadA,[-2ff.( 7t)-A — ‘ VI44I I.Li —‘‘ . r ‘IL. . - IL - ‘i:— jp.pg zY•g J fg77 —. I I ITonic: (Eb)AriH-.1pIPLV•--, CI I U- I— I I-s-i:4r ‘V.4LIi A dj Jfr qr - —d TZ_A i :i II•“- 11 II... ‘I— I45a new tonic while arpeggiations occur within a tonal area that has already been established.The intervals between successive pitches in the lowest voice are not restricted to “steps”(i.e., the ordered pitch intervals of 1, 2, 10 or 11). That is, a directed motion can present asuccession of quite different interval sizes. Although Copland uses perfect fifthsoccasionally, the most common intervals in directed-motion lines are seconds, thirds,perfect fourths and sixths. The registral span of the motion and its direction is notrestricted. Copland does seem to prefer ascending motion for this type of gesture, perhapsbecause such ascent often gives a contour accent to the goal pitch.39Directed motions also occur in an attenuated form in two-part textures, and inpartially or entirely monophonic passages. When a directed motion occurs in a two-parttexture it retains all of the characteristics of a directed motion in a fuller homophonic textureexcept that the lowest voice is no longer the bass of a succession of verticalities. When adirected motion occurs in a monophonic passage it takes one of two forms: a single line(possibly doubled at the octave) moves in one direction and ends on an accented pc and thispc either becomes the root and lowest pc of a chord (partially monophonic context)40or isconfirmed as a tonic by another technique (partially or entirely monophonic context).Directed motions in monophonic passages exhibit all other conditions of directed motion ina homophonic texture (i.e., PC content, types of intervals, registral span and directionalpreference).Unlike melodic generation, directed motion is not sufficient in itself to establish atonic. In Copland’s music directed motion indicates a tonic that is subsequently confirmedby other techniques. In order to show this dependency, each example of directed motion39A contour accent occurs when the goal pitch is the highest (or lowest) pitch within a relatively long andthematically significant segment (i.e., the first thematic area of a sonata form, an entire variation of avariation form, or a major section of a ternary form).40lmplicit in the partially monophonic context is a complementary change of texture (i.e., a shift from asingle pitch-class to a multi-pitch-class texture) marking the accented pc as a goal.46below includes enough of the following passage to show the presence of another tonic-defining technique which confirms the same tonic.Example 1.24 shows a directed motion in a homophonic texture that generates a Ctonic: C4, the bass pitch of a C-minor triad, receives a durational accent and terminatesdirected motion from an initial Bbl. The sense of direction towards an accented goal maybe enhanced, as in this case, by the voice leading of the other parts. However, such voiceleading in non-bass parts does not establish the terminal pitches in those voices as tonicsbecause they are not pitch representatives of the root and the lowest pitch of the chord. A Ctonic is confirmed in mm.38ff. by the repetition of a series of parallel minor five-threechords whose roots define a <i, iv, v> progression in C. C is also supported as a tonic bythe C-Aeolian collection.Example 1.24 Directed Motion in a Homophonic TextureP.S., I, mm.35ff.A 1. .LJ. :_____ ____I(I...1 n1-—.—---——— jd2*______1nrr9directed bass motion C tonicRoots:C FG C FGExample 1.25 shows a directed motion in a two-voice texture that generates an Abtonic. The initial three-note motive, melodically generating a Db tonic, is transformed intoa directed-motion line in the lowest voice. Ab5, the root of the twelfth {Ab5, Eb7},receives an accent of duration and terminates motion from an initial AM. Ab is confinnedas a tonic in R3-2ff. because of the melodic presentation of an Ab major-major seventh— I I44L ‘-- I..p,.---EZ -,-Ir’A,.I I I 7.&i I I i7L’.l I-— I‘VAb tonic[p[,,_ L,0’p P K i iiF) - — —-- I •i •£4 4 ‘4Roots: AbRoots: CAb)Example 1.26 shows two related directed motions in a partially monophonic contextwhere the goal pc becomes the lowest tone and root of a major triad. These descendingdirected motions (replicated in one or more octaves) occur in the last five measures ofExample 1.26. The lowest octave of the first directed motion (R7+6) starts on D5 andterminates on El, which is accented by dynamics, contour (as the lowest pitch in thisvariation), and duration. In R8-4 El becomes the lowest tone of a major triad whose rootis E. This directed motion is repeated in the following three measures but with the lowestoctave starting on G4 instead of D5 (the second pitch of the original directed motion). Theterminal pitch El becomes the lowest tone of an E-major triad in R8-l. It is more emphatic;I:directed motion47chord in the highest voice simultaneously with the incomplete melodic presentation of anAb-minor triad — <CM, Ab3> — in the bass. We are also predisposed to hear an Ab tonicin R3-2ff. because of the transpositional relationship (T1) to R2+3 (not shown in Example1.25) when G was a tonic.Example 1.25 Directed Motion in a Two-Voice TextureII’____1J==J48than the preceding directed motion because of the longer duration of the E-major chord.The beginning of the passage in Example 1.26 also contains a repeated two-measure phrasethat mimics an ascending directed motion. It does not qualify as a directed motion,however, because the terminal pitch, E4, is not the lowest tone of the subsequent E-majortriad at R7+ 1 and R7+4. We also tend to hear E as a tonic in this passage because of themotivic structure: the melodic cell that emphasizes pe E at the beginning — <G, Eb, F#, E>— is T3 of the original four-note motive (mm. 1ff.), which was stated in a C# tonal area; andthe preceding variation, which also has E as its tonic, uses this motive at the same pitchlevel.Example 1.26 Directed Motion in a Partially Monophonic TextureP.V. , []ff.49Example 1.27 shows a directed motion in an entirely monophonic context where theterminal pc is confirmed as a tonic by another tonic-defining technique. The ascending linebeginning on Cl terminates on F5, which is accented by dynamics and increased duration.An F tonic is confirmed by the melodic construction of the following theme, statedmonophonically and emphasizing members of the F-major triad, which this directed motionprepares.1.5.5 Changes in TextureIn a homophonic texture the root of a verticality is activated as a tonic if it is statedby the lowest voice, and if the verticality is emphasized as the end of a thematic group byan ensuing, significant change in texture. At the end of an important thematic groupCopland frequently follows a rooted chord with a dramatic reduction in texture (i.e.,changes in register, density, numbers of voices and levels of rhythmic activity) to articulatethat chord as the end point, or goal. The terminal chord also usually receives a metricalaccent. This recalls a technique of traditional tonal music, in which the end point of agroup is usually determined harmonically by a cadence (i.e., <V, I>), and in whichExample 1.27 Directed Motion in a Monophonic TextureA.S. , -i-2ff.directed motion F tonic50subsequent textural changes after the cadence reinforce the sense of beginning a newgroup. In Coplanci’s music, however, end points are often not determined by harmonicprogressions. Occasionally a series of chords mimics the gestural sense of a traditionalcadence to define an end point but avoids syntactic relations in the root succession (ifpresent). Texture is, thus, left as the sole means of defining — retrospectively — an endpoint. Despite the lack of syntactic harmonic support these end points are as significant toform in Copland’s music as they are in traditional tonal music. Chords articulated at endpoints in CopLand’s music often carry over into the next group; they are used to elidebeginnings with endings. This gives such ending chords an emphasis that makes themsound like traditional tonics.This technique is used at R6 in the first movement of the Short Symphony (seeExample 1.28). Following an interruptive passage at R4ff. expressing a Bb tonic (ofwhich the last two measures are shown in Example 1.28) an alternation between twochords — {F#1(2), G3, B3, D4} and {A1(2,3), C#4, E4} respectively — becomesprominent. This alternation initially seems to support the root of the second chord (A) as atonic, because of its greater relative stability and the previous association of the samecollection with an A tonic at R3 to R4-l. Ultimately, however, it expresses a B tonicbecause the texture reduces to a single (octave doubled) line immediately following thestatement of the B-rooted sonority at R6. Traditional harmonic progression does notestablish the B as a tonic, of three chords, because the stepwise root movement of thesethree sonorities does not include a dominant-tonic progression.51Example 1.28 Textural Changes Defme the TonicS.S.,I, +4ff.___ ________ ___-9:9 2çTonic: (Bb) ! r1__g • ‘___97 5 - - C “ 7_____8____ ___ _ ____—Tonic: B1.5.6 Sustaining a Pc in the BassA tonic is generated when a pc sustained in the lowest voice is a member of a majoror minor triad that is arpeggiated, or emphasized by accents, in a higher voice.4 Most41Reti alludes to the way pedals support our understanding of the tonic when, in a discussion of a passagefrom Debussy’s “Reflets dans I’eau,” he concludes that the constantly sustained Ab pedal “adds an increasedfeeling of oneness” to the “tonical impulses” of the melodic lines. Reti addresses Debussy’s lengthy pedalsand concludes that they “help to let the melodies be understood in their own melodic right and not as52commonly the sustained tone in the lowest voice is the root of the triad, as this creates thestrongest sense of tonic and is, therefore, less dependent upon other techniques forconfirmation. However, the third and fifth of the tonic triad can be used in a similar way.Often when a bass pedal is employed there are references to verticalities with the same rootas that of the articulated triad, and the pitch-class content is constrained to a diatonic (sevennote) collection.Copland’s music has numerous examples of this technique. Example 1.29 shows apassage where the sustained pc is the root of the triad arpeggiated in the melody: A3,initially sounding by itself, is sustained in the strings while the clarinet arpeggiates the A-major triad (<A4, C#5, ES>). The arpeggiation ends on a sustained ES, making a perfectfifth with the lower A. This activates an A tonic, which is supported by the A-majorcollection.42Example 1.29 Sustaining a Pc in the BassA.S., mm.lff.iii______1?W4 —— J(t‘J,.— ..,— —‘9:4—0A‘ i:ITonic: AExample 1.30 shows a passage where the fifth scale-degree, Fl, is sustained in thebass while a concurrent melody brings out the tonic Bb-major triad through rhythmic(agogic) accents. Other elements confirm Bb as a tonic: the descending-fifth pitch motion<F6, Bb5> in the highest voice; the ascending tenor line reiterating the sixth <F, D>; themelodically extended harmonic progressions.” According to Reti this helps to distinguish them fromclassical melodies. Reti, op. cit., pp.23 and 27.42A is confirmed as a tonic by a subsequent plagal root motion, <A, D, A>, between successive ninthchords in Ri to R2-i (not shown in Example 1.29). This plagal root motion is repeated over the larger Atonal area (whose beginning is shown in Example 1.29) until P.S.53dynamic and durational accent given to the Bb-major six-four chord; and the BbMixolydian collection.43 But these do not overshadow the stabilizing and tonic-generatingeffect of the sustained fifth scale-degree in the bass.Example 1.30 Sustaining a Pc in the Basss.s. , in, [] ff.-l-J—-,-——-—---——---—-—----+,t----,z, •1I Ir -r-’—,I I —4:. I II‘)LI_ I—----.-,. —,- r= I fppTonic: BbExample 1.31 shows how Copland uses this technique in a characteristic way todefine a tonic and facilitate a smooth modulation. In this passage the functions of Db3 andBb3, which are sustained as the lowest pitches starting at R19, are reinterpreted. Thestrong articulation of a Bb tonic prior to RI 9 dissipates after R 19 when the otherwise clearroot succession in fifths, <D, G, C>., is broken by the statement of the dyad {Db3, Bb3}.Initially this dyad suggests the return of the Bb tonic by implying a Bb root. However, themelody in the highest voice generates a new Gb tonic at RI9ff. by accenting pcs Db, F#and A: Db5 begins each two-measure phrase and is preceded by a rest; an agogicallyaccented F#4 ends each two-measure phrase; A5 receives an accent from contour in R19+3;and the longest notes in the top-voice melody, in R19+1 and R19+3, are members of theF#-minor triad. This example shows that the effects of the sustained tones and theaccentual structure of the top-voice melody are, in this case, mutually dependent. Thesustained tones require confirmation from the melody in order to negate our expectation of43The referential collection is Bb-Mixolydian and not Bb-major because pc Ab and not pc A functions asthe seventh scale-degree in the larger Bb tonal area whose beginning is quoted in Example 1.30.54a Bb root; the top-voice melody needs the confirmation of the sustained tones toaccommodate the increasingly chromatic texture of R19+lff.(kt! . ARoots: Bb DTonic: (Bb)Al1‘V? L I’ I•t)Roots: Gb-Tonic: (Gb)tr2.ljo c (Bb?) GbGb— -‘-V1.5.7 Repetition of a Root Using Different VerticalitiesSeveral different verticalities that express the same root within a relatively brieftimespan activate that root as a tonic. This is one of the least traditional techniques thatCopland uses to establish a tonic. Sometimes no contrasting root will appear within thetimespan in which the tonic is emphasized.Example 1.32 shows an instance of this technique in the first movement of thePiano Sonata. In this passage four verticalities have Bb as a root: the minor third {Bb, Db}(mm.1 and 6); the tetrachord {D, F, Gb, Bb} (mm.1 and 6); the tetrachord {Bb, Db, C, F}(mm.2, 3, 7 and 8) and the trichord {Bb, F, Ab} (m.12). The first, third and fourth ofExample 1.31 Sustaining a Pc in the BassA.S., -3ff.AlA Iy I ‘ I ] I I &EEEEE::1 - II,-’ -‘Z: 2 4,E---4 4 - 4 I P 4Iii jiji .j_ -I If2Jv-p_____ I):55these verticalities receive accent: the first verticality by meter and by its special status as thebeginning sonority of the piece; and the third and fourth verticalities by meter and duration.No sonority in the passage has a root other than Bb. The second and third verticalities inmm.3 and 8 respectively, which are the only other potentially rooted chords that do nothave Bb as a root, result from the confluence of passing and neighbor tones in a gesturethat seems directed toward a restatement of the tetrachord {Bb3, Db4, CS, F5}. Thepresence of four verticals that express the Bb root, combined with the lack of other rootedchords that express different roots, establishes Bb as a tonic that governs the opening ofthis movement. Other factors, particularly the references to Bb-rooted triads in the outervoices in mm.l-2 and 6-7, support this tonic.:$4Bb (none)(none) (none)Example 1.32 Repetition of a RootP.S., I, mm.lff.A Ii.•0 —. —frb[p< :._—-I j, , — r ‘• r— 3 -‘ 1’ L 4 4 4Roots:Tonic:AlBb BbBbBb Bb(none)(none) (none)I J’ L9Vi IBb Bb Bb..2___. -ThtI-_____i—- I——-.----Z-ILL L. 6.-—-J.(none) (none) BbRoots: (none)Tonic: (Bb)56Example 1.33 shows a passage from the third movement of the Short Symphonywhere the reiteration of the Ab-rooted sonority {Abl, G4, C5, Eb5, Ab5} generates an Abtonic. No sonority in this passage has a root other than Ab. Ab is supported as a tonic bythe metrical accent given to the Ab-major triad in the highest voices in the first threemeasures of R18, by the contour accent on the bass Abi (the lowest pitch in this passage),and by the descending-fifth pitch motion <Eb2, Abi> in the bass. At R34-1 thepunctuating chord disappears in order to prepare for a new Eb tonic, which arrives atR34+4.ik£ I.!L.1lQ1Example 1.33 Repetition of a Roots.s. , Ill, [] if.AkL)r2kJA’ ,rr ,),-.I II I .7Ip I — —. rip I ,a rip- I,. I - Ir,I : iv Pd1 8 J I 8 I . 8 Ii I ‘11-- L’ •Roots: [Ab] Ab [Ab] Ab Ab AbTonic: AbA( ‘ 1.I)1•-Yi - -r’...: r r—--J’I I 1 .71 III.—. I II -I I— I I I)-p.AbRoots:Tonic: (Ab)571.5.8 Neighbor-Tone MotionComplete neighbor-tone motion — where two statements of a rooted chord frameanother sonority — activates the root of the framing chord as a tonic if the framing chordreceives accent from duration or meter, or has special status as the beginning sonority of animportant section. Neighbor-tone motions are most effective when the lowest pitch of theframing chord is the root and there is step motion (i.e., ordered pitch intervals of 1, 2, 10or 11) in all voices within the pitch-class collection treated as referential. Example 1.34shows a passage from Billy the Kid where a G tonic is first established by neighbor-tonemotion.44 A G-major six-three chord ({B3, D4, G4}) encloses two separate completeneighbor-tone motions that establish a G tonic. This enclosing chord receives accent fromduration — in each measure it is re-articulated over more eighth-notes than the neighborchord — and meter — it occurs on the downbeat of each measure until R24+5. Theneighbor-tone motions establish G as a tonic before the entrance of a eight-measure melodyat R24+2, which emphatically confirms G through melodic generation.Example 1.34 Neighbor-Tone Motion Defining a TonicBJC.fjff.IIIITonic: GExample 1.35 provides a more complex example, in which the tonicizing effects ofthis technique are severely attenuated by the pitch-class content.45 An E tonic is generated,at least in part, by a complete neighbor-tone motion embodied in the oscillation between an44The passage has been simplified rhythmically: the re-articulated chords in the strings are represented inExample 1.34 by sustained tones.45The separate melodic lines identified in Example 1.35 (i.e., in the woodwinds and strings respectively) areboth stated in triple octaves in the piece. Only the lowest octave of each melody is given in this shortscore.58enclosing root position E-major triad and a root-position Fit major-minor seventh chord.46E is supported as a tonic by other factors, for example, the directed motion toward theinitial E-major chord at R 1, and the agogic accent on E4 in the inner voice motive <B3,F#4, E4> in the third trumpet and cellos. The tonal definition provided by the neighbor-tone motion is obscured by the superimposition of two melodies, the first of which (in thewoodwinds) weakly emphasizes B in R1+1 and Rl+2. This emphasis causes anambiguity between E and B tonics because the stated diatonic collection — {B, Cit. Dit, E,Fit, Git, Ait} — is much more familiar as the B-major collection than as the E-Lydiancollection. Copland’s techniques, however, largely point to an E tonic in this passage.471.5.9 Summary of Tonicizing TechniquesCopland uses eight techniques to establish tonics: isolated descending- andascending-fifth motion of roots; triadic melodic structures; arpeggiation of special pc-setclasses in the lowest voice; “directed motion;” textural and thematic articulation of a rootedchord; pedal tones; reiteration of a root and neighbor-tone motion. The description of thesetechniques constitutes a précis of Copland’s harmonic style in that they define whatCopland does and does not do to establish roots and tonics. These techniques will providecriteria for a meaningful tonal analysis of Copland’s music.46The E tonic of Riff. is weakly anticipated at R1-2 (beat 3)ff. when the three-note fragment <B3(4),F#4(5), D4(5)> is followed by the three-note fragment <B3(4), G#4(5), E4(5> such that the third <G#, E>sounds on the downbeat of RI-i. However, this third is obscured because the voice-leading of RI-2 (beat3)ff. contains two step-ascents that continue to the downbeat of Ri: the second pc of each successive three-note cell, which is metrically accented, generates the ascent <F#, G#, A#, B>; the third pc of eachsuccessive three-note cell generates the ascent <D, E, F#, [G#]>.47This interpretation is confirmed retrospectively. For example, the elements that establish D as a tonicjust before P3 (when the second theme is introduced) are the same as those that earlier defined Eat Riff.:the three-note motive, which is transposed down a tone so it ends on an agogically accented D; and thewhole-tone neighbor chord motion, which is similarly transposed down a tone so we get an alternation ofmajor chords whose root succession is <D, E, D>.59Example 1.35 Neighbor-Tone Motion Defming a TonicP.C. , I, W -2ff.A i 47 s ..!i.) 7 7(MFqA-,.,--——.—.-. I PI ‘‘ii (. ii i-.4.,II—äøzi:LJ.Melody 1 Vs):(1(A[119I in— —..- In_I I I•1-- I-.V:1ur’1.Melody 2 (Strings)-J”—F-r3ff-l .w LJ W(f, II*7—LiI ti F . . —. . nr’ — I I 11 I ...I3r.)1L—-frTonic: E)AI601.6 The Function of Tonics in Copland’s MusicWe have seen in the above examples that tonics are prevalent in Copland’s music.But what purpose do these tonics serve? Their musical function is inextricably tied to someof the most salient characteristics of Copland’s music: a general avoidance of chordprogressions; the lack of a specific harmony consistently used as a prefix to tonicharmonies; the severe de-emphasis of the dominant key; the preponderance of static, non-developmental themes; the use of transitions that rely upon underlying step-progressions,and non-functional root successions, for coherence; specific types of tonal ambiguities; andother important surface features. In order to be meaningful for the analysis of Copland’smusic, a theory of tonality must account for these special characteristics.1.6.1 Theories of TonalityOne possibility for the tonics in Copland’s music is that they are organized into ahierarchy that expresses a global tonic, that is, the hierarchy of tonics as a whole expressesthe global tonic, rather than each tonic expressing it in isolation. Two very differenttheories — prolongational and Hindemithian — allow for a hierarchy of tonics. Let usexamine the suitability of each for Copland’s music.Prolongational theory has been expanded so greatly since Schenker’s death that ineffect we must consider a host of related approaches ranging from “pure” Schenkeriantheory to the subsequent extensions of that theory in the analysis of post-tonal music.Extensions to Schenkerian prolongational theory are numerous in the analytical literature.For example, Cinnamon’s articles reveal that Liszt maintains the essence of a traditionalprolongational structure but transfers all of the structural characteristics normally associatedwith V to other harmonies. In Blume und D14ft this harmony is 111L48 A much more48Howai-d Cinnamon, “Tonal Structure and Voice-Leading in Liszts Blume und Duft,” In Theory Only 6/3(1983): 12-24, and “Tonic Arpeggiation and Successive Equal Third Relations as Elements of TonalEvolution in the Music of Franz Liszt,” Music Theory Spectrum 8 (1986): 1-24.61comprehensive approach to prolongational theory in post-tonal music, one that does notinvolve the transference of dominant-qualities to non-dominant harmonies, is suggested byFelix Salzer. His monograph StructuralHearing presents numerous prolongationalanalyses of works by Stravinsky, Bartok, Hindemith and even Copland.49 Saizer tries toshow how these diverse composers use the dominant-tonic axis and other, contrapuntallydefined, structures as frameworks for directed motions that establish tonality.50 Bakersummarizes Saizer’s analyses as showing that a traditional triadic component is “prolongedby means of an embellishing ‘contrapuntal-structural chord’ which serves as the centralmember of the structural axis of the piece.”51 Other authors, such as Wilson, take Salzer’sapproach one step farther to argue that a simple departure-and-return model, even oneoutside of a dominant-tonic axis, must be considered as legitimately “prolongational.”52Travis and Morgan, among other authors, have gone even further and tried to developtheories to account for prolongations of dissonant sonorities.53 Although these “liberal”approaches have been criticized in the literature54there are, nevertheless, othercontemporary studies in which a modified Schenkerian prolongational theory has beenconvincingly applied to fairly complex twentieth-century “tonal” music.55 For example,Baker’s study of Scriabin’s voice leading reveals some very important aspects of Scriabin’smusic — incomplete spans, spans with elements widely scattered among several registers,49Salzcr sketches excerpts from Appalachian Spring, “Three Excerpts from Our Town,” and the ending ofthe first movement of the Piano Sonata. These works are discussed as Examples 239, 412 and 416respectively. Felix Salzer, Structural Hearing: Tonal coherence in Music (New York: Dover Publications,Inc., 1962), Vol. 1, pp.134, 192, and 194 and Vol. 2, pp.75, 178 and 182-187.50Ibid., Vol. 1, pp.204 and 227.Jamcs Baker, “Schenkerian Analysis and Post-Tonal Music,” in Aspects of Schenkerian Theory (NewHaven: Yale University Press, 1983), p.155.2Paul Wilson, “Concepts of Prolongation and Bartok’s Opus 20,” Music Theory Spectrum 6 (1984), p.88.-3Rov Travis, “Toward a New Concept of Tonality?,” Journal ofMusic Theory 3/2 (1959): 257-284, andRobert P. Morgan, “Dissonant Prolongations: Theoretical and Compositional Precedents,” Journal ofMusic Theory 20 (1976): 49-92.4Baker, “Schenkerian Analysis and Post-Tonal Music,” p. 168; Ernst Oster, “Re: A New Concept ofTonality (?),“ .Jour,,al ofMusic Theory 4 (1960): 85-98; David Neumever, op. cit., pp.49-SO n. 1; andJoseph N. Straus, “The Problem of Prolongation in Post-tonal Music,” Journal ofMusic Theory 31/1(1987): 1-22.55j have not included Neumeyer’s study of Hindemith’s music because, although his analytical methodinvolves hierarchic stages, it is significantly different from a Schenkerian approach by his own admission.Neumeyer, op. cit., pp.49-SO fn.1.62and spans that run out of synchrony with each other and with the majority of parts thatdefine the harmonic progression.56 The lack of synchronization between related spans isparticularly important because it obscures and conceals the relatively conventional harmonicprogressions underlying most of Scriabin’s music. There are also other convincinganalyses, such as Benjamin’s study of Stravinsky, that take a more collectionally-orientedperspective on tonality and prolongation.57An adjunct to the modified prolongational theories cited above is the “double-toniccomplex” that, originating with Robert Bailey, has been explored mostly in articles byChristopher Lewis.58 According to Lewis, pieces that use a double-tonic complex exhibitthe following four characteristics: they exploit common or ambiguous harmonic functions;they prolong two tonics in alternation or succession; they use one tonic to resolve thedominant of the other and they superpose lines or textures implying one tonic upon thoseimplying the other.59 The background structure of a piece employing a double-toniccomplex entails an irreducible conflict between these two tonalities, and not the6Jamcs Baker, The Music ofAlexander Scriabin (New Haven: Yale University Press, 1986). Thismaterial is presented in a summarized form in James Baker, “Scriabin’s Implicit Tonality,” in Music TheorySpectrum 2 (1980), pp.17-IS. Baker’s study is doubly important to the study of tonality in Copland’smusic because Copland by his own admission was “very Scriabin-conscious” in the period around the timehe went to France to study with Boulanger. Edward T. Cone, “Conversation with Aaron Copland,”Perspectives of New Music 6/2 (1968), p.59.7WilIiam E. Benjamin, “Tonality Without Fifths: Remarks on the First Movement of Stravinsky’sConcerto for Piano and lVi,id lnsiruinems,”In 1’heo’ O,,lv 2/11-12 (1977): 53-70 and 3/2 (1977): 9-31.8Thc term “double-tonic complex” was apparently coined by Robert Bailey in HDasLied.L)o,lderErde:Tonal Language and Formal Design,” which was read before the American Musicological Society inOctober, 1978. Bailey makes some references to this concept in Richard Wagner: Prelude andTransfigurationfrom “Tristan and Isolde “ (New York: Norton, 1985), pp.121-146. While Bailey doesdiscuss how the Prelude contains references to both A and C tonics, he does not specify what generalconditions a piece of music must exhibit in order to generate a double-tonic complex, and he does notdiscuss the ramifications for a Schcnkerian analytical approach. To my knowledge Lewis is the only authorwho explicitly talks about “double-tonic complexes” per se in the literature. Christopher Lewis, “Into theFoothills: New Directions in Nineteenth-Century Analysis,” Music Theory Spectrum 11/1 (1989): 15-23and “Mirn)rs and Metaphors: Rellections on Schoenberg and Nineteenth-Century Tonality,” NineteenthCentury Music 11/1 (1987): 2&42. However, Lewis notes that Schoenberg also makes reference, ifconsiderably more obliquely, to the principle behind a double-tonic complex when he discusses “fluctuatingtonality” in two of his own compositions — Orchesierlied, Up.5, no. 5 (“Voll jener Susse”) and Op.6, no. 7(“Lockung”). Arnold Schoenberg, Theory ofHar,non-y (London: Faber and Faber, 1978), pp.384-85. In“Mirrors and Metaphors” Lewis shows that a double-tonic complex is pertinent to the tonal structures ofWagner’s Tristan und Isolde, and Schoenberg’s 0p.6, nos.1 (“Traumleben”) and 7(”Lockung”) and Op.8,no.5 (“Voll jener Susse”).“Mirrors and Metaphors,” p.40.63Schenkerian Ursatz. This conflict also affects the foreground because it allows certaindissonant chords, which result from the simultaneous statement of both tonic chords, to actas a resolution at cadences and, therefore, to be understood as essential structuralelements.60 Since either tonic triad may predominate at the beginning or at the end, adouble-tonic piece may begin in one key and end in another.6’Hindemith’s theory also allows for a hierarchy of tonics.62 The tonal centers thatare generated from Hindemith’s degree-progression (the root succession within a tonalsphere) — create a second, higher-level degree-progression. This succession of higher-leveltones generates in turn a single, overriding tonality (a “tonal center of a higher order”) forthe entire piece.63 This higher tonic may be juxtaposed with other tonics in the seconddegree-progression that either support or compete with it, so a global tonic, like a localtonal center, might also be weakly defined.64 Hindemith’s theory is a little vague about theeffect of cadence in the second degree-progression (of tonics) and the status of the finaltonic in a piece. Although his theory allows other conditions, Hindemith’s examplessuggest that pieces are artistically satisfying if they end with a tonic that is also theoverriding tonic.1.6.2 The Appropriateness of Existing Theories of Tonality for Copland’s MusicSome of the analytical theories cited above are relatively easy to dismiss for theanalysis of Copland’s music. On the one hand, certain of the prolongational theories, suchas the pure Schenkerian approach and the double-tonic complex, can be shown to be60Ibid., p.30.ljyjs “Into the Foothills,” p.17.62Hindemith, Book 1, pp.142-163; Neumeyer, op. cit., pp.49-56 and 61-81. According to NeumeyerHindemith also discusses hierarchy in craft iii, pp.137-145. Neumeyer, op. cit., p.6163Hindemith’s criteria for the selection of this “global” tonic are the same as those which applied to theoriginal degree-progression... “Here, too, the tonal center that reappears most often, or that is particularlystrongly supported by its fourth and its fifth, is the most important.” Hindemith includes a chart thatdescribes the minimum number of chords which are necessary to establish a tonal center. Hindemith, Book1, pp.151 and 136.64Ibid., p.151.64inappropriate models for this repertoire. For example, a pure Schenkerian prolongationalapproach is relatively easy to discount. One reason is that the pcs highlighted by the typicalforeground leaps in Copland’s themes do not form middleground step-patterns. Arepresentative example of this problem is the registrally disjunct motive that opens the firstmovement of the Short Symphony (see Example 1.36). This theme successively highlightspcs D and C. We might hear these pcs organized into the middleground step-pattern <D6,C6, B5> from m.6 to R1-4 (beat 3). However, this requires a host of assumptions. Wemust hear the D-rooted harmony in m.6 to be the dominant of, and therefore directedAAAtoward, the G-major triad in m.8, and to hear the middleground step-pattern as a 5-4-3descent in a G tonal area. This is extremely difficult to hear for three reasons: foregroundchord progressions are absent; the chord in m.7, although dissonant, sounds like an arrival;and a prolongational structure does not match what is projected on the surface. We are farmore aware of the characteristic ambiguity between D and G tonics that is projected on thesurface than a tenuous step-pattern on a prolongational midclleground. Theinappropriateness of this approach is indicated by the nearly complete lack of conventionalSchenkerian analyses of Copland’s music in the literature.6565The only prolongational analysis of an entire piece by Copland in the analytical literature is Allen Forte’ssketch of number 3 of the Four Piano Blues. Forte’s analysis shows that a ii7 chord is prolonged. AllenForte, Contemporary Tone Structures (New York: Bureau of Publications, Teacher’s College, ColumbiaUniversity, 1955), pp.63-7 and 160-166. Hilliard’s tonal analysis of the Short Symphony does notinclude prolongational sketches.65Similarly, the double-tonic complex is an inappropriate model for Copland’s musicbecause of the general lack of progressions expressing a single key, let alone two at thesame time. The few passages containing multiple concurrent tonal strands do not occupyentire sections or movements but merely individual local phrases. Even there, theconditions for a double-tonic complex fail to obtain. For example, let us inquire whetherthe first movement of the Short Symphony, which begins in D and ends in C, satisfies theExample 1.36 Difficulty in Connecting a Middleground Step-Pattern8Ld. - -E•Roots: D ?----GG:V[D: V7/IV IV]?66four conditions Lewis lists for the existence of a double-tonic complex. This movementdoes not present C and D tonics in alternation or succession (condition 2) because C doesnot even appear as a tonic until the beginning of the final part of the tripartite form.Further, C is not heard to “resolve” the dominant of D (condition 3) because A is neverfollowed by C in this movement. Similarly, D does not “resolve” the dominant of Cbecause G is introduced as a tonic so much earlier than D in the form, before we are evenmade aware that C is important to the tonal structure. Finally, in the rare instances in thismovement when there is a bitonal texture, which might satisfy the fourth condition, thetonics involved are not those which begin and end the movement. In fact, the onlycharacteristic of double-tonic pieces which even remotely obtains in Copland’s music is theuse of certain chords that sound like they fuse two different tonal events as, for example,Copland’s numerous quasi-jazz “dominant” chords. Unlike the sonorities cited by Lewis,however, the chords used by Copland usually initiate, and do not conclude, a cadence.Only very rarely is a tonic chord “fused” with the subdominant as, for example, at R6 toR7 and R9 to RiO in “Hoe-Down” of Rodeo. Here, however, the ambiguity between twodifferent roots — D:I and D:1V respectively — does not represent a double-tonic complexbecause G is not a tonic and because the “fused” sonority initiates a plagal cadence to a Dmajor triad that is stated melodically in the following phrase (e.g., at R7 and RiO,respectively).Hindemith’s theory is also an inappropriate basis for the analysis of Copland’smusic but for different reasons. Undeniably we can find chord roots in almost everypassage from Copland’s music, and we can organize a succession of these roots to define atonic either weakly or strongly.66 Similarly we can derive a global tonic from the degree66Hindemith’s theory, as a compositional aid, restricts the ordering of roots in only minimal ways. Hesuggests four factors which are detrimental to an effective degree-progression: the absence over a long periodof the intervals of the fourth and fifth; the melodic interval of the tritone; broken chords of any easilyrecognized species; chromatic progressions (successions of minor seconds) and the obscuring of tones in adegree-progression by elaborate melodic treatment. Hindemith claims that virtually any succession can beused to generate a tonic. The difference between these successions is the strength of the tonic which is67progression that is created by the tonic succession. What we lose in using Hindemith’sprocedure is our awareness of specific relationships between the collections of successivetonics. We also lose the richness of tonal allusion in individual tonal areas that results fromCopland’s motivic structure, which occasionally makes the roots of certain chords seemambiguous or not present at all.67 Copland’s tonal areas are also often clouded by anambiguity between 1C5-related tonic pcs. This type of ambiguity, which is particularlystriking in transitional passages, can persist throughout most of a piece, for example, QuietCity, as we shall see.On the other hand, there are some extensions of prolongational theory that are muchmore difficult to dismiss. For example, it is hard to dismiss the type of approach adoptedby authors such as Salzer, particularly without performing an exhaustive study ofprolongation in Copland’s music, because they do describe some important structuralaspects of Copland’s music. However, it is possible to show that, at least with regard tothe ending of the first movement of the Piano Sonata, Saizer’s prolongational approachmisrepresents the tonic succession on the surface of the music and thus distorts the functionof that succession.68 Salzer loses sight of the surface tonic succession when he seeks todescribe the entire passage as organized around a “dominant polychord” — {F2, Ab2, Bb3,Db4, C5, F5} — which fuses the dominant and tonic chords.69 In thus organizing hissketch around a dominant-tonic axis, Salzer ignores the local tonic of mm.2lOff., which isDb. The prolongation of this polychord is severely weakened when, after beingprojected: Hindemith’s preferred successions (movement by a fourth or a fifth) project a tonic more strongly.Hindemith, Book I, pp.145-148 and 139-142.670ne instance of a chord root becoming ambiguous occurs in m.5 of Quiet City: overlapping versions ofthe pc-set 102,51, which are stated in different voices, make it unclear whether the root of the chord {Bb2,C4, D4, G5, F6} is G or Bb. One instance of successive chord roots disappearing can be found in R48 ofExample 1.11: the potential D and G roots in this measure disappear because of the concurrent emphasis onmelodic step-motion in all voices.68SaIzcr’s sketch of the ending of the first movement of the I’iano Sonata appears as example 416. Salzer,Vol. 1, p.194 and Vol. 2, pp.182-187.69Baker argues that Salzer effectively interprets this passage as a prolongation of a simple triad because ofSaizer’s statement that “the chord built on the bass will always be the stronger one, and it is the bass and itschord which will determine the chord grammatical status of the whole chord cluster.” Baker, “SchenkerianAnalysis,” p.156, and Saizer, Vol. 1, pp.192-3.68emphasized so strongly in the bass in mm.197-209, the dyad {F, Ab} disappears at m.210just when Db is established. Saizer is correct in identifying that pcs F and Ab are importantto the passage. However, there are more compelling ways of hearing their function.Copland emphasizes them as being common to the collections that support the Db and Bbtonics in mm.2 10ff. and 237ff. respectively. Pcs F and Ab are accented in the lowestvoices near the end of the Db tonal area in the concluding gesture of a bass arpeggiation ofthe Db-major triad. These pcs are then clearly heard as the fifth and (lowered) seventhscale-degrees at the beginning of the subsequent Bb tonal area. The surface tonicsuccession <Db, Bb> therefore focuses our attention on the new scale-degree functions thatpcs F and Ab acquire. This is a more immediate connective role for pcs F and Ab in thetonal structure than the somewhat abstract functional prolongational role proposed bySalzer.1.7 A New Theory of Tonal FunctionSince theories of functional tonality do not satisfactorily or reliably relate tonicsuccession to form in Copland’s music, this dissertation will explore how tonics createfunctional distinctions among pitch classes, distinctions that are essential to form. On onehand, tonics can bring out similarities between pc collections by emphasizing the samescale-degree function in analogous places in the form, such as at the beginnings ofsections. Successive tonics, on the other hand, can differentiate pcs that are common tosuccessive collections by giving them different scale-degree functions.The role of shared pcs in Copland’s music is obvious and compelling. Numerousexamples can be found where a significant reduction in texture isolates a pc that is commonto the collections of successive tonics and, thereby, creates a surface connection betweentonal areas that are otherwise unrelated. One example of this characteristic technique can befound at R22 to R23 in “Buckaroo Holiday” from Rodeo (see Example 1.37). At R23 Dsucceeds Db as the tonic. We know that R23 initiates a D tonic because it is a transposition69of the folk-song (“If he’d be a buckaroo by his trade”) used in this section. The shift fromA ADb to D is accomplished by the reinterpretation of pc Gb from Db:4to D:3. What ischaracteristic about this connection is the change in texture, which isolates Pc Gb from theaccented Db:”IV” harmony and then sustains it before introducing a new collection andtonic.70As we shall see, emphasis of common pcs permeates every aspect of form inCopland’s music. This suggests that a much different view of the formal function of tonicsshould be considered in analyzing it. Tonics are a way of making scale-degree distinctions70The introduction of the new collection at R23 is crucial in our perception of a shift to a D tonic at thispoint because otherwise we would hear pc A in terms of Db:iv. The importance of collections to the tonalshift here is reminiscent of a similar process which William Benjamin finds in the first movement ofStravinsky’s Concertofor Piano and Wind Instruments. Benjamin, “Tonality Without Fifths,H 6369Example 1.37 Isolating a Pc When the Tonic Changes“Buckaroo Holiday,”R. ,ff.AIiIP1 — —f’AV t,S IS&! IS IS I.1-S I1.1 r I.,m——‘2[1kItL-..ItJiL .. I I I’I 7r.JJfliI I I’ I -p.-A— .£Db:, Lr Ilk I‘4E I I I I I)-‘3--1->1,>-D—D1.s..DTI I II II- r - r. r, I I —. -si—.f-I •—______—Db: “IV” rLWGbasDb:2—asD:I’D:I70between different members in the referential collection. The function of tonics is to makeapparent the new meanings that emphasized pcs acquire over the course of a piece and toemphasize the commonality between successive collections. This function of tonics isconsistent with the nature of Copland’s themes and transitions and the special types of tonalambiguities that arise.7’1.7.1 Copland’s Motivic and Thematic DesignsCopland’s motivic and thematic designs are set up to project continuously one ormore emphasized pcs, instead of creating linear progressions as in more traditional tonalmusic. Across the transition between two successive tonal areas, certain pcs common tothe two collections are emphasized by agogic accents in an outer voice, or by placementwithin an important motive. Occasionally this agogic emphasis arises from simplysustaining the pcs. In Example 1.38 pc E, sustained at the end of an A tonal area, is stillsounding when the next tonic, Bb, is melodically generated. This makes us focus on theA Achanging scale-degree function of pc E from A:5 to Bb:4. Quite often the pc we hear ascommon is present throughout the first tonal area. For example, in Example 1.39 F#, themost prominent pc in the bass in the E tonal area at R9-3ff., is later sustained in the highestvoice at R9+3 when C# replaces E as the tonic. This makes us focus on the changingA Ascale-degree function of pc F# from E:2 to C#:4. However, unlike Example 1.38, we alsofocus on the changing scale-degree function of a second pc, G#, because that pc issustained together with F#.7 definition of tonality suggests another broader aspect of consistency in Copland’s music — an artisticapproach where methods of composition are incorporated only in Copland’s own terms. For example,Copland adapts tonality to his own purposes — to emphasiie the loreground connections between successivetonics — in much the same way as he apparently adapts a simpler version of the twelve-tone method muchlater in his career. With regard to the latter Copland has said that he was “interested in the simple outlinesof the theory, and in adapting them to my own purposes.” Cone, op. cit., p.68.I OQ C)‘C)C) 0 a-C) 00 Icj>..>72The common pcs can be associated with a motive in the soprano, or the bass, or anentire accompanimental pattern that continues from one tonal area to the next. Acontinuation of a motive in the soprano can be seen in Example 1.40. Here a simple two-note motive — <B5, A5> — ending a D tonal area is continued while the tonic changes toA.72 Maintaining this motive as the tonic changes underlines the changes in scale-degreeA A A Afunction of pcs B and A respectively from 6 and 5 to 2 and 1. Although this motive isinitially obscured (mm.175- 178) because pc A sounds together with pc B above it, themotive returns in its original rhythmic setting at m.179. A continuation of a motive in thebass can be seen in Example 1.41. The last pc — B — of the motivic fragment in the bass<B#l(2), G#2(3), B 1(2)> acquires an unexpected meaning when it is repeated twomeasures later. B is no longer heard as the bass pitch of a tonic C# minor-minor seventhchord but, rather, as the root of E:V. This makes us focus on the changing scale-degreefunction of the pc B from C#: 7 to E:5. The shifting of scale-degree function when anentire accompanimental pattern is maintained from one tonal area to the next can be seen inExample 1.42. The accompanimental pattern established at the end of an F tonal area,<F3(4), E4(5), G4(5)>, is maintained while the tonic shifts to C. This makes us focus onA A A A Athe changing scale-degree functions of pcs G, F and E respectively from 2, 1 and 7 to 5, 4Aand 3.72We are predisposed to hear a D tonic at the beginning of this excerpt because of preconditioning — D wasthe tonic the last time this material was heard (mm. 133ff.). See below, pp.234-237.tTlI>74CtExample 1.42 Continuation of an Accompanimental Motive When the Tonic ChangesB.K.,j÷lff.A I i I I I I I___________I,,r._.. I I • I • I IEEiH-rrT’FFII ‘-.I I-..JI I IL..I I I I ITonic: F []A I t -ft.-..---. L. I L—s--- —---- p .—••:;---J•I I i•’ I Ii•I Ii)hIJI VI 11 U& I I1---,IL.’iI.r‘I I IL._.‘I-..*-S.LA ItI4IUi r rI II8— —.LI ITonic: CpcGasF: —4C:.pcFasF:1 )C:4pcEasF:? )C:----Examples 1.37-1.42 have shown some rhythmic ways that Copland emphasizesone or more pcs as common to the collections of successive tonics. The emphasis on thesepcs make us perceive each as a “primary connector,” by which we mean the most notablepc that connects two tonics. (We will later refer to these changes of scale-degree functionas primary streams of pc continuity.) However, there are other ways in which Coplandestablishes a pc as the primary connector between the collections of successive tonics. Oneof these involves setting up a conflict between the primary connector and another pcpreviously defined as the same scale-degree (chromatic opposition). Another involvesmaking the pc connector a chord-factor of a sonority that does not function locally within aprogression. Both processes occur in Example 1.43 to establish as primary connector thePC F, one tone of the recurrent dyad {F, Ab} that is prominent in both the D and G tonics(i.e., R2-1, R2, and R2+2). Conflict of scale-degree function occurs at R1+5 when pc Ftt75is heard as the minor third scale-degree of D in a melodic motive after pc F# was previouslydefined in Rl+l as the major third scale-degree. Pc F is then emphasized at R2÷2 in thefollowing G tonal area as the root of a minor triad that does not function locally in aprogression. Indeed, the triad makes F the strongest root that is heard in the entire G tonalarea.73 These techniques help us to keep pc F in our ears and emphasize its changingscale-degree function from D:3 to G:Common pcs are also often established as primary connectors in Copland’s musicby an overlap between two successive tonal areas. Overlaps occur when the precisetimepoint of change from one tonic to the next is obscured; they normally result when acadence makes us retrospectively reinterpret ambiguous harmonies. Example 1.44 shows apassage where ambiguous chord functions in R3 1-4 to R3 1 obscure the exact beginning ofthe Ab tonal area that succeeds the initial F.74 Pcs C, Eb, and F are all common to thecollections of the Ab and F tonics. Pc C is particularly striking as a common tone betweenF and Ab because C5 is sustained in the highest voice in both tonal areas in Example 1.44(i.e., at R30+3, [R31-3] and R31+2). However, pcs C, Eb and F are also emphasized byagogic and metrical accents in the outer voices during the period of overlap. Thisaccentuation makes their connective role between the F and Ab tonics in Example 1.44—A A Athe ways pcs C, Eb and F change scale-degree functions respectively from 5, b7 and itoAA A3, 5 and 6— more readily apparent.73The bass F in R2+2 is also emphasized by the rhythm (i.e., it receives a metrical accent and is followedby a rest) and by the tritone leap (to pc B), an interval that seldom occurs between successive notes inCopland’s melodic lines. We also hear pc F as a common pc to the D and G tonics because it isconsistently paired with pc Ab in both tonal areas.74Example I .44 begins in the middle of the F tonal area. The ambiguous chord functions which obscurethe beginning of the Ab tonic are discussed below on p.141.I F!1I1-‘3-ci.40Rru Fl I4I\78On a few rare occasions Copland emphasizes a common pc by placing it in only asingle strand of a bitonal texture that succeeds, or is succeeded by, another tonal area with asingle tonic. Example 1.45 shows a passage where an A tonal area is succeeded by asimple bitonal CIC# texture that is generated by transposing the bass line of an essentiallyC-major texture up a semitone. Because pc B is so heavily accented (by dynamics, metricalplacement and duration) in R44-3 to R44-+- 1 it is relatively easy to hear it as a connective PCbetween the different tonal areas in Example 1.45. However, the change in scale-degreeA Afunction of pc B from A: 2 to C:7 at R44 is made even more striking because B is notpresent in the (low register) C# strand of the bitonal CIC# texture that follows the A tonalarea.Example 1.45 Common Pc Constrained to one strand of a Bitonal TextureBK.,A_> >“f — >. > >“1IA I II I,L.JII IIri , 11 —,).j;-i..I -I I 1 ii IL\J:::) I141I -, -W__ I I_ I TI_! I51 I r141lLI-a-r - p - r1— I pr. --—-— •_-‘7$pcBasA:Tonic: Ap p-14-—1 IC bkonal textureC#— pc B as C:779Under very special circumstances in Copland’s music we can hear pc connectionsbetween tonics that are separated by another tonal area. This invariably involves specialtypes of preconditioning. Example 1.46 shows a passage with three tonal areas —A (R46-3ff.), Eb (R46ff.) and CIC# (R46+4ff.). We can hear a clear pc connection, the recurrentdyad {C, C#}, between A and CIC#. That is, we can hear pcs C and C# change scale-A A A Adegree functions respectively from 3 and 3 at R46-3 to 1 in the C tonal strand and 1 in theC# tonal strand of the bitonal texture at R46+4. This connection is only possible becauseof preconditioning induced by the larger context: Example 1.46 is an excerpt from a rondoform where the “A” material recurs in the C/C# bitonal texture and where subsequentcontrasting sections, at least in the beginning of the form, have A tonics. This leads us toexpect the C/C# bitonal texture at R46, when the contrasting material of the A tonal area hasfinished. The Eb tonal area also sounds like an interpolation because the material it stateswas previously heard (at R42ff.) in C/C#. Obviously, the interpolation of Eb between theA and C/C# tonal areas generates separate pc connectors between A and Eb, and betweenEb and C/Cit respectively. However, the connective pcs between the A and C/Cit tonalareas are not completely overshadowed by the new connective pcs generated by Eb: we caneasily hear pc C as a common tone to the collections of all three tonics in Example 1.46,that is, we hear pc C change scale-degree function from to to 1.til0riI4.I.ni; I:0811.8 SummaryA tonic establishes distinct scale-degree functions for every pc in the referentialcollection. As tonics change, so do the scale-degree functions of each pc. In tonal music,these changes of scale-degree function are not particularly important when we hear thetonics functioning hierarchically to prolong a global key. But in Copland’s music, whichlacks such a prolongational hierarchy of tonics, such changes are crucial to form. Indeed,Copland usually emphasizes changing scale-degree function. These common pcs arecharacteristically emphasized within Copland’s thematic and motivic structures by accentsin prominent voices (i.e., outer voices, or the most rhythmically active lines) or byattaching a specific (melodic) behavior to a common pc. Common pcs are particularlyobvious in passages of Copland’s music where functional progressions are absent. One ofCopland’s favorite textural devices — a reduction in texture to a single pc — is particularlyimportant in establishing common pcs.The resulting changes of pc scale-degree functions created by particular tonalsuccessions reveal interesting continuities and a formal patterning that is not obvious usingconventional analytical methods. Four basic patterns emerge from an analysis of thesechanges: a repeated focus upon a particular pc at important moments in the form; arepetition of a succession of scale-degree functions on different pes; a continued emphasison a particular scale-degree function at the beginning of sections; and a repetition of anordered series of focal pcs particularly at the ends of related sections. Quite often thesepatterns will reinforce aspects of the thematic form.82Chapter 2Analytical Conventions2.1 IntroductionIn the last chapter we saw how common pcs are emphasized in Copland’s thematicand moti vie structures. The present chapter introduces the symbols that are used in thefollowing analyses to represent characteristic features of connection between successivetonics in Copland’s music. It also presents a brief analysis of a larger passage as a simpleintroduction to the analytical techniques that are applied in the analyses of Chapters 3-6.2.2 Symbols Used in Pc Continuity GraphsThe following analyses will take the form of a graph of twelve lines showing howthe twelve pcs are given various scale-degree functions as they connect successive tonalareas within the music in question. This will be called a “pc continuity graph.” Each linelists the changing scale-degree functions of the respective pc connectors as a series of“streams.” Scale-degree functions are only listed for the pc if it is emphasized as aconnector at that point in the music; mere membership in successive diatonic collections isnot sufficient to establish a pc as a connector. That is, an emphasized connective pc isrepresented on a graph by successive scale-degree figures appearing on top of a horizontalline, which indicates the period of time in which the pc can be said to be active in a stream.Special symbols demarcate and identify the nature of these streams. The symbol —I,occurring at the end of the horizontal line, marks the termination of a stream, that is, thepoint at which the corresponding pc stops functioning as a connector in the music. Thesymbols P and S identify pes as primary and secondary pc connectors, respectively,between collections of successive tonics. We ascribe primary or secondary status to a pcconnector based on the emphasis it receives in the context: primary connective pcs almost83always appear in outer voices and are emphasized by agogic accents, or by placementwithin an important motive;1 secondary connective pcs, while emphasized as common pcs,are not as prominent as the primary connective pcs in the passage. Because the analysis isdesigned to identify streams of continuity, every change of tonic is shown to be supportedby at least one primary connector.It is possible to have multiple simultaneous primary streams that connect twosuccessive tonics. These streams may be generated in the context by accents and otherforms of emphasis on pcs that are not consistently associated with one another insuccessive tonal areas. We will call these unrelated simultaneous pc streams. However,the pcs these streams represent may be related to one another in the context because theyparticipate in a recurrent dyad or trichord that is common to both tonal areas (e.g., the {F,Ab} dyad in Example 1.43), or because they are members of a motive that continues fromone tonal area to the next (e.g., the <B, A> motive in Example 1.40). Pc connectorsrelated by a recurrent dyad or trichord will be represented in analyses by connecting therespective pc streams by a vertical line with the symbol. “I” (an abbreviation for interval);2pc connectors related by a continuing motive (abbreviated as “M”) will be represented inanalyses by connecting the respective pc streams by a vertical line with the symbol “Mn”where “n” represents the number of a specific motive that is identified elsewhere. Becausepcs related by a recurrent dyad or a continuing motive are never equally emphasized in thecontext analyses will rank these connective pcs according to their relative prominence, thatis, a graph will show the most prominent connective pc as P1, the next most prominentconnective pc as P2, etc.1AII of the pcs which are noted with regard to Examples 1.37-1.46 would have their changes in scale-degreefunction shown in primary streams in a pc continuity graph.21 have used an abbreviation for interval — “I” — for streams that are generated from recurrent dyads andtrichords because it creates less new terminology (i.e., it allows the use of one symbol in place of two —the separate abbreviations “D” and “T” for dyad and trichord respectively), and because it reinforces thesimilarity of the technique that generates these streams.84Figures 2.1 and 2.2, which analyze the primary connective pcs of Examples 1.39and 1.4.0, demonstrate how pc streams related by a continuing motive or by a recurrentdyad respectively would appear in a pc continuity graph. These related streams are ranked.In Figure 2.1 pc B is identified as the more important of the two connective pcs (andtherefore labeled “P1” in the graph) because B5 is the highest pitch in the first fourmeasures of the A tonic (mm.175-178); the label “Ml” on the vertical lines connecting pesB and A indicates that they belong to a motive that is present at both mm. 171, in the D tonalarea, and 175, in the A tonal area. In Figure 2.2 Pc F# is identified as the more importantof the two connective pcs (and therefore labeled “P1” in the graph) because pc F# isstrongly emphasized in the bass in R9-4 to R9 and because it is the highest pc of the dyadthat is sustained when the tonic changes: the label “1” on the vertical lines connecting pcsGil and F# indicates that they belong to a dyad that sounds at the ending and beginningrespectively of the E and C# tonal areas. Figure 2.2 also demonstrates an additionalsymbol — brackets above and below successive scale-degree figures. This symbol is usedto indicate that the enclosed pc(s) are sustained when the tonic changes.3Figure 2.1 (Analysis ofExample 1.40) StreamsRelated by a Continuing MotiveMm.: 171 175Tonic: D AFigure 2.2 (Analysis of Example 1.39)Streams Related by a Recurrent Dyadand Brackets in a Pc Continuity GraphR: J9 -3 9+3Tonics: E C#I 1F’B G#- P23 5I I IBb G - I II I IF’ F’A F#- 11-2 43By “sustained” we mean a pc that is held over a tonal shift either literally, by use of a tie, or figuratively,by re-articulation or a very short rest (i.e., with a duration of one or two eighth-notes).85Other special symbols will be used in the analyses to represent differing degreesand types of connection between successive tonics. The first two of these — arrows andchromatic opposition boxes — result from characteristics of referential collections inCopland’s music. Arrows toward or away from a scale-degree figure for a given pc showsthe nearby presence of another pc in the music performing the same scale-degree function.Boxes around two simultaneous representations of a scale-degree figure for a specific tonicindicate that the referential collection of that tonic incorporates a chromatic oppositionbetween two of its pcs, that is, that two collectional pcs perform the same scale-degreefunction. Figure 2.3, which is an analysis of the primary connective pcs in Example 1.13,includes an arrow and a chromatic opposition box. In Example 1.13 related primarystreams are generated on pcs Eb and B because the dyad {B3, D#5} is emphasized inchords in the B and Ab tonal areas (i.e., at R41+4 to R41+6 and R42 respectively). (PcEb, labeled as P1, is considerably more prominent than pc B because it is sustained in thehighest voice in both tonal areas.) The arrow in Figure 23 indicates that pc C is heard asthe third scale-degree of Ab before pc Cb; the chromatic opposition box in Figure 2.3indicates that both pcs Cb and C belong to the referential collection of Ab where theyfunction as opposite representatives of the third scale-degree.4‘1The chromatic opposition between pes Cb and C in the referential collection of this Ab tonic wasdiscussed earlier in connection with Example 1.1. See above, pp.8-9.86Figure 2.3 (Analysis of Example 1.13)Arrows and Chromatic OppositionBoxes in a Pc Continuity GraphR: 41J÷4 42Overlapping phrase marks (the symbols7c ) are used to reflect overlaps betweensuccessive tonal areas, when the connective pcs are momentarily heard as having twodifferent scale-degree functions simultaneously. Figure 2.4 graphs the primary connectivepcs (Eb, F, and C) that were discussed with regard to Example 1.44. The overlap marks ineach of the three pc streams at R31-3 shows their ambiguity of function. For example, PCA AF sounds at that point both as F: 1 and Ab:6. Notice also that the pc stream on Eb beginslater than the others because it is not present from R30÷3 to R3 1.-- .?_‘___[Tonic: B AbC-B-Figure 2.4 (Analysis of Example 1.44)Overlapping Phrase Marks in a Pc Continuity GraphR: 1301+31311-3 I 31f +2Tonics: F 1cb AbFEEbC-P-b7—5—5-—-F-- P.5—5—3—3_f87Square brackets that do not contain a scale-degree figure are used to indicate thelack of a scale-degree function. They are used oriiy when the texture is divided into twoseparate strands that have different tonics and when a connective pc belongs to thereferential collection of only one strand.5 Square brackets are used in Figure 2.5, whichgraphs the primary connective pc (B) that was discussed in connection with Example 1.45.A AIn Figure 2.5 pc B is described as C:7!C#:I I or7/[ I in the bitonal texture because itsabsence in the low register suggests that it belongs only to the referential collection of C.Figure 2.5 (Analysis of Example1.45) Square Brackets in a PcContinuity GraphLz 1441-4 1441Tonics: A CC#B--- -P-i7/ I--A dotted line in a pc stream indicates that the stream is temporarily suspended eitherbecause it is (briefly) displaced by another pc that has the same scale-degree function, orbecause a collection that does not contain that pe generates interrupting streams. The lattercondition obtains only when preconditioning makes us hear the passage in a particularmanner, as discussed above in connection with Example 1.46. A dotted line is used inFigure 2.6, which graphs the related primary streams on pcs C and Ct present in Example1.46. The stream on pc Ct is suspended when the Eb tonic enters because pc C# does notbelong to the Eb referential collection.5Because these strands are created by a specific registration of pcs I will consider only those pcs that areliterally present in a given register to be members of the referential collection of the corresponding strand.88Figure 2.6 (Analysis of Example 1.46)Dotted Line in a Pc Continuity Graph23 Sample Analysis of a Larger PassageFigures 2.1-2.6 above show incomplete analyses of the pc-scale-degree design ofshort passages containing a single shift in tonic. Figure 2.7 gives an analysis of a largerpassage, shown in Example 2.1, where the tonic changes three times. That passagecontains a series of successive transpositions of the melody in R44+ 1 to R44-i-4. Becausethe first tonic is melodically generated all of the subsequent tonics in this passage are alsomelodically generated. At R46— 1, G# is expected. However, a change in the bass leads toa melodic generation of Cit as tonic. The final tonics, E and C# respectively, are notated asoverlapped because it only becomes clear retrospectively that R46- 1 initiates a shift in thetonic. The resulting pc-scale-degree design in Figure 2.7 is very simple. At each pointwhere the texture changes, one pc common to both major-scale collections changes scaledegree function. This pc starts each new transposition: pc C in R44÷5, pc E in R45, andpe Git in R46-l.I0 0[ E [ [ [ [ [..4—’LI4it41141 ‘I ‘1;iC I:; ‘ 1 L I; 1;rn I(ç c :,I i1 L’=:izI11114I4- h IlL 114ft4 114f4 bFigure 2.7, like Figures 2.1-2.6, omits references to the thematic design of thepiece because it is a very short excerpt. In the following chapters, graphs of entiremovements or pieces will include a comprehensive summary of the thematic design inseparate lines between lines indicating measure numbers and tonics.Figure 2.7 (Analysis of Example 2.1)Complete Pc Continuity Graph of a Larger PassageR: 44 +5 145 I I 461-1Tonics: Ab C E E C#B -.Bb -.A -Ab P-3._3—5--[--G -. -F# -.F -.B -. P.3—1-4Eb -.D -Db -C -. -i—I—F90912.4 Order of Appearance of Primary Connective Pcs in Pc Continuity GraphsGraphic analyses simplify the foreground of the music to a degree because they donot represent the precise timepoints where a pc is emphasized within a given passage. Forexample, in a passage of music that contains three tonal areas the pc streams that connectthe first two areas will be presented in entirety in a graph before the pc streams that connectthe second and third areas are begun. However, this representation often does notcorrespond to the way the pcs are emphasized in the second tonal area: frequently the pc(s)that connect the second and third tonics are emphasized before the pc(s) that connect thefirst tonic to the second. This approach was chosen because it made the connectivefunction of pc streams (particularly simultaneous primary streams that are related by arecurrent dyad or a continuing motive)6much clearer, and because the exact time ofemphasis of connective pcs is not germane to the types of analytical conclusions we willdraw.2.5 Format of the Following Analytical DiscussionsThe next four chapters present analyses of four pieces: Quiet City; Billy the Kid; thefirst movement of the Short Symphony; and the first movement of the Piano Sonata. Thesepieces are fairly representative of techniques in Copland’s “popuLar” and “serious” styles.Each analysis begins with an overview of the thematic and harmonic form, thenproceeds to a pc continuity graph. Due to copyright restrictions, the scores can not beincluded here. It is assumed that the reader will have the scores at hand.A conclusion chapter following these analyses will draw together observations toshow the essential unity of style between Copland’s “popular” and “serious” music.6A clear example of this can be found in the streams that begin the pc-scale-degree design of the firstmovement of the Short Symphony. For example, the recurrent {F, Ab} dyad that connects the G and Atonics (at R2+ 1ff. and R2+4ff. respectively) is emphasized two measures after the pc (E) which connects theA tonic to the subsequent Bb tonic at R4. See below, p.199.923.1 FormChapter 3Quiet CityThe form and tonal structure of Quiet City are shown in Figure 3.1. A summary ofthe thematic content is included in Figure 3.1 because it is relevant to the form. Themotives composing those themes are shown in Example 3.1. Subsections with the samelabel have material related by To, except as noted in Table 3.1.Example 3.1 Summary of Thematic Content in Quiet CityMotive 1(m.1ff.). Motive 2 (W+lff.)A - Tr A. ‘, ,) = I:4 I I i .i.Motive 5 ( [+1ff.)AlFormal divisions in Quiet City are determined by changes in texture, tempo, andthematic material. However, unlike more traditional music, the changes in these parametersdo not always reinforce each other, so the unity of parts is not always clear. At R5—1, forICl&Ij I I II’•3 - =Motive 3 ([] ff.).._lI I. Ii’1 .J I I I I r tz. I I I I I- ITI”Motive 4 ( -1ff.)A1-11I - II I 11 I I I.II.?fS--iA IL fr1JI ii I II 1I I “II&. I I I .I I ._ -Motive 6 ([]÷1ff.)A-0I i iiFigure3.1SummaryofThematicandTonalDesignsinQuietCityR:11111214121+5131141+2151-1161-4161÷3171181191-6Parts:IntroductionABSections:a‘albbicb2(trans.)Subsections:abalbiccic2c3ddlc5Motives:1212334,33,43,4,[3]:3,4,[3]2 ITonics:FF/DEbCEbMm.:I91+1+6liolliii11211131114111511161+41171-1Parts:CAlCodaSections:db3(trans.)b4a2a3Subsections:efele2c6c7c8c9a2b2a3Motives:6766a3331217777Tonics:DEbFTable3.1SummaryofTn-RelatedPassagesSectionsSubsections‘IT1bc4T1c3elT2e(melody)c7T1c3(melody)94example, a new (chordal) motive is introduced, but there is no change in texture, as a singlemelodic line punctuated by sustained chords continues. The lack of textural contrastsuggests that the passage is a continuation of the second part of the piece.’ Similarly, thepersistence of a bass motive at R 12 suggests that the following material, whichrecapitulates material from part A, continues C.The resultant formal structure in Figure 3.1 is unusual. In six parts, Quiet City iscomprised of an Introduction and Coda that flank a set of variations which, in turn, frametwo contrasting sections, B followed by C. All parts except Al subdivide into twosections. However, the changing relationship between sections differentiates the parts ofthe form: sections within the Introduction, Coda and part A are related by variation, butsections in the other parts of the piece are contrasting. A similar differentiation of the partsof the form results from the relationships between successive subsections: in theIntroduction and Coda these are contrasting, but in all other parts these employ variation.Figure 3.1 shows how the formal functions of variations of section b change duringthe course of the piece. Reprises of this section do not have the same thematic weight asthe original. Rather, they function as transitions at the end of parts B and C. For example,the material in R9-6ff. is a variation of the material (c4) that ends part A in R6±3ff., yet itacts as a transitional passage between parts B and C. Similarly, the material at R12 isthematically related to that of R9-6, but it too fulfills a transitional role as the preparation forthe material in Rl4ff. At R14 section b regains its thematic status when the original melodyof R3, transposed up a semitone, begins part Al. At the same time, part Al restores theclear successive variational process of part A, which was negated in parts B and C whencontrasting thematic elements entered.1After this new triadic motive, the trumpet plays a transposition of an earlier motive (R3+2), so themotivic integrity of part A is maintained.95The use of the same material at R6+3 and R9-6ff. reinforces a textural parallelismthat obtains between the beginnings of every part in the form: each beginning expandstexturally from a single note. So the variations of the section b material, which link partsA, B, C and Al, also share an opening textural gesture (an expansion from a single note)with the otherwise contrasting Introduction and Coda. This helps, along with the recurringEb tonic, to establish an underlying unity between the somewhat disparate parts of thepiece. Other elements, which will be discussed later under “Pc Continuity,” confirm thisunity in different ways.The unusual formal structure revealed in Figure 3.1 probably has its origin in thefact that Quiet City originated as incidental music for an experimental play of the same nameby Irwin Shaw.2 Copland conceived the trumpet part in Quiet City to represent the centralcharacter of that play, a trumpeter named David Mellnikoff. According to Copland thischaracter “imagines the night thoughts” of many different people in a large city and playshis trumpet to “express his emotions and arouse the consciences of the other characters andof the audience.”3 In the same passage Copland said that he wrote the music to reflect the“inner distress” of Melinikoff, citing as an example the “nervous, mysterious” qualitativeindication which characterizes the trumpet’s first entrance in RN-I. The episodic dramaticstructure of the play accounts for a musical form that uses many themes connected by asingle, recurrent, melody which remains in one tonic. Unfortunately, the script of the playis unavailable so we can not specify an exact correspondence between Shaw’s play andCopland’s music. However, we might surmise that the musical form of Quiet City2The original play was performed only twice and at the performers’ own expense. To my knowledge it hasnever been perlormed since its brief, abortive debut in 1941. The play remains unpublished. Moreinformation on its plot can be found in: Neil Butterworth, The Music ofAaron Coplsznd (GloucesterToccata Press, 1985), pp.80-81; Michael Shnayerson, irwin Shaw: A Biography (New York: G.P.Putnam’s Sons, 1989), pp.95-96; and Harold Clurman, The Fervent Years: The Story of the Group Theatreand the Thirties (New York: 1-lill and Wang, 1957), p.23 1. According to Shnayerson the original draft ofthe play is on hic in the Irwin Shaw Collection at Mugar Memorial Library, Boston University.Shnayerson, op. cit., p.432.3Aaron Copland and Vivian Penis, copkmd: 1900 through 1942 (New York: St. Martin’s/Marek, 1984),p.287.96parallels the shifting focus in Shaw’s play between the “night thoughts” of Melinikoff andthe other characters in the play. From this perspective, the characteristic textural device thatunifies the beginnings of all the parts of the piece could be interpreted as another musicalmetaphor (besides the recurrent melody) for the “night thoughts” of Meilnikoff thatsimilarly guide the drama of Shaw’s play.The formal correspondences surmised above are emphatically supported by theorchestration of the first two (non-successive) variations of section b — sections bI and b2 —in that the main melodic line of bi and b2 is stated by the trumpet.4 The orchestration ofthis material changes in R12 when the strings, and not the trumpet, carry the same melody.The accompaniment of this melody by the bass line of the previous theme might indicatethat Mellnikoffs “night thoughts” are influenced by his environment and by the dreams ofothers as might be represented by the contrasting melody in section d.3.2 TonalityTonic pcs in Quiet City are often obscured by the simultaneous tonicization of pcs afourth above or below (i.e., pcs that are 1C5-related). Such conflict is particularly evidentin transitional sections, as, for example, in section bi (R5-lff.). Sometimes this ambiguityis generated in a passage because the expected resolution of a familiar harmony, forexample, a major-minor seventh chord, is negated at the end of a tonal area by anunexpected pc collection. For example, at R9-6 the Eb tonic is challenged by a Bb tonicwhen the crucial seventh of the Bb seven-four chord, pc Ab, is succeeded by pc A. In theareas of conflict between 1C5-related tonic pcs, the analysis in Figure 3.1 chooses the pcthat is emphasized over most of the tonal area to be the tonic of the passage.The problem of tonic identification is compounded by the preponderance of the pcset-type [0,2,5] both melodically and embedded within chords. For instance, the opening4Section b is different from sections bI and b2 because the melody is orchestrated for the English Horn (orOboe).97of the work is permeated with representatives of this set: the Viola line <C4, F4, D4> inmm.1-3; the characteristic verticality {D4, G5, F6} in m.4; the cello line <F3, Bb2, G2> inmm3-7; and the vertical trichords {G2, Bb2, C4} and {C4, D4, F6} in m.5. Theembedding of several different versions of this set sometimes makes it difficult to hearsingle roots, because these different versions usually have different fifths and, therefore,imply different roots. For example, it is unclear whether the root of the chord sustained inmm.3-5 is G or Bb. The transposition of entire chords, themselves composed ofoverlapping forms of [0,2,51, sometimes directs entire passages as, for example, in R2 toR2+5. This transformational process obscures the chord roots in these measures.3.2.1 IntroductionThe opening tonal area is characterized by an ambiguity between C and F. Theinsistent emphasis on pc C, which is reinforced by the cadence to an octave-tripled pc C atRI, initially draws our attention away from the F tonic that eventually emerges as superior.F is suggested as a tonic when the second note of the opening interval <C4, F4> becomesthe bass tone of the sonority {F4(5), C6} in m.2, making pc F the first and strongest chordroot of the entire first section, and by the diatonic collection {F, G, Bb, C, D}, which is asubset of the F-major collection. The transformation of this opening interval into anostinato in the first violin, which is repeated over the entire first phrase, suggests we hearthe cadential C chord root at Ri as F:V. This suggestion is confirmed when the subsequentintroduction of a minor seventh in the trumpet theme (the “nervous, mysterious” theme thatCopland cites) above a sustained C4 suggests F:V7. Our perception of C as F:V is furtherstrengthened in the subsequent trumpet cadenza when a single statement of pc B, theleading tone of C, is immediately followed by Bb, the same pc which inflected the C chordroot toward an F tonic in Rl+ 1ff. C persists as a chord root in the first chord of the nextsection, {C4, D4, Bb4, C5, F5, C6} in R2, because the tripling of pc C disposes thelistener to hear a dominant-ninth chord with a suspended fourth.a98However, despite this emphasis on C as a root from Ri to R2, the climactic F rootof R3-6 is not prepared by a descending-fifth root motion. Instead the pcs from the chordat R2 are rearranged at R2+ 1 such that Bb, and not C, is generated as the root (see Example3.2a). This change in the chord root is made more obvious because the pcs in the pizzicatobass motive of R1-3 (<Bb3, Dl(2), G3, Fl(2)>.) are reordered in R2+lff. to form a Bbmajor triad in the first three notes (<D1(2), Bb3, Fi(2), G3>). All but one of the pitches inR2÷ 1 to R2+2 are then transposed down a major third in the next two measures. This isshown in Example 3.2a by an arrow labeled “T8” connecting the blocks. It is difficult toassign a root to the resulting chord {Gb3, Ab3, Db4, Eb5, Db6}, at least in R2+3, becauseof a conflict between the T8 transposition and the intervallic structure. The transpositionleads us to expect an Eb root for this chord but its intervallic structure simultaneouslysuggests Gb as a root. However, when pc Gb moves as a passing tone to pc Ab in thecello our perception of the root of this chord is fundamentally changed. We gravitatetoward Bb as the root because the first three notes of the pizzicato bass motive <Bbl(2),Ab3, Db2(3), Eb2(3)> form an incomplete Bb minor-minor seventh chord. Thus,although Bb is clouded at R2+3 it is effectively sustained as a root from R2 to R2÷4. Thesubsequent plagal resolution to the F root in R2÷5 is reinforced by the <F6, Db6, F6>motion in the first violin. The net result of the T8 transposition is a contrast between themajor and minor mode representations of the subdominant of F. This modal contrast in theIntroduction foreshadows the harmonic structure in the following part A, which shows asimilar contrast between IV and iv.99Example 3.2a) Root Succession in UJ+1 to L1÷5 b) Step-Descent in [] toThe restatement of the “nervous” sixteenth-note motive above the F root at R2+5does, however, draw our attention to the shift away from the C root of Ri and thus, at leastsymbolically, effects the expected dominant-to-tonic resolution. This resolution isfacilitated in R2ff. by the incorporation of the same motive into an inner voice of thetexture, the English horn. The resulting line, <C4, Bb3, Ab3>, presents the minor-modeversion of the F: 5-4-3 descent that is reprised in R2+5ff. when the trumpet states themajor-mode version above the sustained F (see Example 3.2b).3.2.2 Part AThe ending tone of this descent becomes the first tone of the following melodythrough an elision. This phrase elision creates a similar elision of tonics, as shown inFigure 3.1, because it introduces a new pe collection. The subsequent D tonic of part A,however, does not become clear until at least R4-2. Initially, the pc collection which isintroduced at R3 — {D, E, F#, G, A, B, C#} — seems to be oriented toward a B tonicbecause the accented B4 in the melody is supported by a B-rooted sonority (a seven-fourchord). However, the arrival at R4-2 of the second chord in this section, {A3, B3, D4,Roots: C Bb FF: V 1V iv I<C5, Bb4> source set (Bb, C, D, F, 0) <C5, Bb4>100E4, G4}, reorients the pcs into a D-major collection because it sounds like a dominantseven-four chord in D. The second chord — {A, B, D, E} — registrally inverts the lowesttwo pcs in the first chord. This recalls the similar transformational relationship between thechords in the first two measures of R2. Example 3.3 summarizes the harmonicprogression of R3 to R4+4. It posits a <vi, V. vi, 116> progression in D.Example 3.3 Root Succession from [J to_________+2/1.Roots: B A EB ED: vi V iv j6 j jj 6In R5- I a very strong conflict is initiated between D and G tonics because the chordprogression mimics, at a pitch level five semitones higher, the <vi, V> progression thatobtains between the first two chords of part A. Example 3.4 summarizes the harmonicprogression from R5- 1 to R6. The first three chords of R5- 1 resemble a contrapuntalexpansion of the progression G:<vi, vi6> because of the stepwise bass line and because thetop three notes in the first and third chords—{A3, D4, G4} — are identical. This harmony,like that in R3+1, is similarly directed to a sonority that sounds like the dominant sevenfour chord of G.101Example 3.4 Root Succession in -1 to []L1 +3/ F / I &1V .s. ‘ .s.________‘1_7-[6] 7-[6] 4—[3]Roots:E D D A[G: vi viV VID:I VOther elements, outside of the seven-four chord, appear to confirm a shift in tonic.For example, the introduction of pcs F and Bb weakly suggests that D is no longer thetonic because they are not members of the established D-major referential collection.Further, the melodic fragments in the trumpet and first violin around R5- I are saturatedwith G-major and -minor triads. This strongly suggests a G tonic.G is not given sufficient strength, however, to overshadow D as the tonic of thepassage because of the emphasis on pc D melodically and as a chord root. For example,D5 and D4 are accented in the trumpet and first violin melodies from R5 to R5+7. In R5-i-3pc D is emphasized in the bass because it unexpectedly becomes the first bass tone and onlyroot in the repetition of the chordal gesture from R5- 1. The next statement of this gesture(R6-2) transforms it such that the final D-rooted chord, which is crucial to the perception ofa G tonic, is replaced by the original dominant seven-four chord of R3+3. The shift inroots from D to A is underlined in R6-2 because A, like D in the preceding statement, isalso the first and only root in the gesture. The return of the A root is accompanied by thereturn of the referential D-major collection from R3 thus weakening any reference to a Gtonic. Retrospectively, then, we understand the appearance of pcs F and Bb at R5- 1 not as102indicating a change in tonic but, like R2ff. in the preceding F tonal area, as underlining anopposition between D:IV and D:iv.Because the tonal ambiguity of this passage is difficult to resolve, the followingdiscussion on pc continuity below will include a hypothetical structure which assumes a Gtonic as well as D. This will be presented in order to prove that both interpretationscontribute to an understanding of the pc-scale-degree design.The trumpet melody, which heralded the return of the D-major collection in R6-5, isrestated in R6+3 transposed up a tone as the introduction to the next subsection. However,the tonal implications of this transposition are denied in the next measure when the melodycontinues a semitone lower than expected. This not only introduces an unexpected pccollection and tonic but also results in the D tonic being left (at R6+2) on the dominantchord. This establishes an important precedent for the Coda, which is similarly left open-ended.The next tonal area is also difficult to determine as it seems to be equally poisedbetween Eb and Bb. Eb is strongly suggested melodically in R6+3 because of the T1relationship to R6—4 and because of the embedding of members of the Eb-major triad withinthe descending trumpet line. It is suggested harmonically in R6+5 when a truncatedversion of the chordal gesture of R5-1 ends on a Bb-rooted harmony. However, unlikeearlier versions this truncated version is tonally ambivalent because the Bb-rooted chorddoes not have a minor seventh to strengthen the implication of Eb, and because the rootprogression <Eb, Bb>, by itself, can be heard as representing either an Eb or a Bb tonic.Eb is, however, suggested by the registration of the Bb-rooted sonority in R6+6: the T1relationship of the outer voices of this chord to those of the A-rooted sonority in R6suggests that we hear pc F in R6+6 as Eb: just as we heard pc E in R6 as D: Further,Eb is only briefly contradicted for one measure in R7-3 when pc A, a tone most easilyheard in connection with Bb, is introduced. For these reasons, Figure 3.1 identifies Eb,103and not Bb, as the tonic for the passage. The tonal opposition between Eb and Bb, whichis encapsulated in pc A, is greatly intensified the next time this material is stated at R9-6.On this basis, the passage may be viewed as the first of two references to the muchstronger Eb tonic that will be established at R12.3.2.3 Part BAt R7 a C tonic is melodically generated by the line <G5, C5, Eb5> that resultsfrom the overlap of the last pc of the trumpet line with the first two pes (<C5, Eb5>) of anascending third line in the first violin (i.e., <{C5, Eb5}, {D5, F5}, {Eb5, G5}..>). TheC root of the first chord in R7, emphasized by sustaining G5 above C5, is preceded by asustained G5. This descending-fifth motion in C parallels the earlier ascending-fourth pitchmotion in F (mm.l-2). C is supported by the C-Aeolian collection and by two importantroot progressions: a dominant-tonic root progression into R7+2 when the English Hornstarts its phrase, and a subdominant-tonic root progression into R8 when the eight-measurephrase is repeated (see Example 3.5). Part B also continues the emphasis on 1C5-relatedtonic pcs that was begun in the preceding part. Pc F is emphasized in the bass from theregistral climax of the phrase, in R7+4, to the end of the phrase, where it appears as theonly root other than the tonic C, and F is the root of the harmony on which the C tonal areainconclusively ends in R8+6. Reading an F tonic here would parallel our hearing ofprominently sustained pcs in previous sections. That is, the sustained G at R7-1 would beheard as F: ust as the sustained E at R6 was heard as D: and the sustained F at R6÷5Awas heard as Eb:2.104Example 3.5 Root Succession in []-i to [] N!L_uJ iEE-I I— . • .. . . . _ . .I ‘): •P\ V P • pPp Pp pRoots: C G C— F C— F— F CC: i j b7 4 jv7 6 jbl iv iv i3 5The return of the material of R6+3 at the same pitch level in R9-6 brings back thetonal opposition between Eb and Bb. The Eb-major triad, embedded within the descendingline in the trumpet, confirms Eb. The truncated chordal gesture at R9-4, unlike R6+5, endswith the same chord as in R6 but transposed up a tone. Because this earlier chord has adominant function we are predisposed to hear a similar function in R9-3, especially sinceAb, the seventh of the chord, was not present the last time we heard Bb as a chord root(R6+6). The gesture in R9-4ff., like that in R6-2ff., also presents a single root, the pc Bb.However, pc A has an even more prominent role in contradicting the Eb tonic because itcounteracts Ab as the seventh of Eb:V7. Surprisingly, pc A is further emphasized: it is thelast pc of the section and it persists across the part division at R9 into the next tonal area.The most interesting aspect of R9-6 is how subtly the melody shifts our perceptionaway from the previous C toward the Eb tonic when compared to the earlier statement ofthe same material at R6+3, which shifted abruptly from D to Eb. For example, thedescending melodic line in the trumpet at R9-6 could also be construed as generating a Cminor-minor seventh harmony, which is the most recurrent C-rooted chord in the previoustonal area (R7ff.). This suggests that the descending trumpet line is not only preparing the105new Eb tonal area but also, simultaneously, closing the previous C tonal area by offering a(melodically realized) resolution for the subdominant chord in R8+ Part CAt R9+ 1 the highest voice of a two-part texture melodically generates a D tonic bythe initial repetition of the motive <D4, D5>, which agogically accents D5, and by the leapin R9+5 from D4 to an agogically accented A3. This final A of the phrase is sustained withpc D, allowing D to emerge as the last root of the phrase. Initially, this D tonic issupported collectionally by the pentachord from the D-major collection — {D, E, F#, G,A}.At R9+6 a new motive, shown as motive 7 in Figure 3.1, suggests an A tonicbecause it emphasizes pc A in the bass and pcs A and C in the soprano. The three-noteostinato in the bass in R10-2 (<A, D, E>) seems to confirm A as a tonic because it mimicsthe bass line of a <I, IV, V. I> progression in A and is supported by several verticalitiesthat have A as a root. However, A does not become the tonic because the manner in whichmotive 7 is incorporated in the following section is reminiscent of a “vamp” in popularmusic. The references to A in this passage temporarily cloud the D tonic (established atR9ff.) in much the same manner that references to G (at R5- 1ff.) clouded the D tonic(established at R3ff.).5 In RiOff. motive 7 becomes an ostinato accompaniment toT2ofthe melody from R9+ 1ff. (motive 6). This motivic transposition does not result in a shiftin tonic and, therefore, it changes our perception of the first note of motive 6 from D: ItoD:.6The references to A begin to dissipate at RiO with the entrance of motive 6. AtR1O+5ff. several characteristics of the D tonal area at R3ff. — the peculiar F#-minor triad51t is relatively easy to hear the correspondence between R5- 1ff. and R9+6ff. because pc A is stronglyemphasized in each passage.6The shift of the first note of motive 6 to the second scale-degree recalls the implied change of pc A to G:at R5-2ff.106that inflected its original melody (i.e., R4-1, R4+2 and R4+6) and the tetrachord {E, F#,A, C#} on which the first two sonorities of the chordal gesture at R6-2 are based — areassimilated into the motivic texture.At Ru the sonority {A1, C#5, E5, F#5, A5} initiates a passage that is directed infive different voices to the D-rooted sonority {D1, F#5, A5, B5, D6} of R11+5. Example3.6a shows the voice leading of this passage. Example 3.6b summarizes this motion as asuccession of five-voice chords. For example, the outer voices at Ri 1 move by contrarymotion to pc D: the step ascent <A5, B5, C#6, D6> in the soprano sounds above the stepdescent <Al, Gi, F#1, El, Dl> in the bass. The notes in the soprano are supported byparallel six-four chords within the referential D-major collection. The three-note motive,which the bass tone begins, is modified in each measure such that the second and thirdnotes rise by step until the original pattern, <A, D, 13>, is restated five semitones higher(<D, G, A>) in R12-3. Any sense of harmonic progression in these measures is avoidedby sustaining the first tone of the bass motive and increasing the size of intervals betweenall three notes by registral displacements. The eventual shift of the first note of this bassmotive from pc A to pc D is foreshadowed in the previous D tonal area (R3ff.) by the shiftin root (from D to A) between two sonorities (R5 and R6 respectively) that share A as acommon tone in the bass. Also, the prominence of pc B in this climactic sonority, as theAnon-essential sixth, recalls the earlier emphasis given to B as D: 6 at the beginning of part A(i.e., R3+1, R4, and R4+3). However, the expansion of texture, which results fromcontrary motion between the bass and other, higher voices, recalls the textural shape whichis given to the first half of the phrases that begin in R7 and R8 in the C tonal area of theprevious part. This reference to elements of the D and C tonics at R3ff. and R7ff.respectively, which are themselves followed by Eb tonics, in turn foreshadows the returnof the Eb tonic in R12.107Example 3.6a) Step-Progression in [ to []+5 b) Five-Voice Voice-Leading Model. :!- -+2 +3 +4 +58- 8- 8- .1.1___ ______________.• •qt’ tT5The transformation of the first tone of the three-note bass motive into the tomescale-degree at R12-3 is important three measures later when the transposition of thismotive up a semitone becomes the basis for an Eb tonal area. Unlike R12-3, the three pcsin the transposed bass motive in Rl2ff. become the roots of a repeated <I, IV, V. I>progression generating an Eb tonic.7 Eb is supported by the accents on Eb in the melody,and by the use of pcs from the Eb-Dorian collection.The arrival of Eb as a tonic at R12 is significant because it marks the ending pointof an important step-progression in the bass that links the ending of part A to thebeginnings of parts B and C (see Example 3.7). This step-progression, which linksprominent vertical fifths at the beginnings of sections, begins in R5 when the tonal areas ofpart A were inflected by an ambiguity between 1C5-related tonic pcs. The linear intervallicpattern 5-5-5-5-5 is particularly evident on the surface of the music at R6-3 to R6+6 andR12-1 to R12 because the recurrent <D, Eb> tonic succession imbues successive sopranopcs in Example 3.7 with identical scale-degree functions: pcs E and F function respectively7The chords {Ebl(2), EM, AM, Bb4, Eb5, Abs. Bb5, Eb6}, {Abl(2), Db4, EM, AM, Bb5}, and {Bbl(2),Ab3, Db4, EM, DbS(6)} have Eb, Ab and Bb roots respectively.108I., A A Aas D:2and Eb:2; and pcs A and Bb function respectively as D:5 and Eb:5.8 The step-progression is, however, obscured in the approach to the {D, A} fifth in R9+5: the step-motion from F, which ends the C tonal area (R7ff.), to the D of R9+5 is interrupted by thematerial of subsection c5, which suggests the return of the {Bb, F} fifth in R7-5.Example 3.7 Step-Progression in [] torn1Li-iH0• -.(9: : : :AtR13 we hearT2of the two-measure phrase which began in R12÷2.9 However,an F tonic is not generated at R13 because the final sonority in each measure has beenmodified such that it generates F, instead of C, as the chord root. This removes the central<1, IV, V. 1> progression that earlier defined the Eb tonic. Further, R13 is marked by thestatement ofT1 of the melody from R6-4ff. This suggests a continuation of the Eb tonic (atRl2ff.) that is subsequently confirmed in R13+3ff. by a <II, V7> progression in Ebgenerated by a change in the order of the pcs in the three-note bass motive at R13 (i.e.,from <F, Bb, C> to <F, C, Bb>).’°R 13ff. is formally significant because it combines some of the characteristics of theD (R3ff.) and Eb tonics (R6+3ff. and R9-6ff. respectively). For example, at Rl3ff. the8Pc Bb is the only soprano pc in Example 3.7 that is not sustained in the highest voice in the actualcontext. Bb is, however, the most prominent upper-voice tone at R12 because it is sustained in the highestregister of the trumpet.9The T2 transposition in the trumpet recalls the interval of a major second which characterizes the“nervous, mysterious” theme in the Introduction. The orchestration for trumpet is also important because itreprises R6-t-5 when the trumpet similarly sustained pc F as Eb:2.10’fhe reordering of these pcs is significant because it recalls a similar reordering of pcs in the bass in theIntroduction (the pizzicato bass motive) where Bb was also a root.109shift from F (R13) to Bb (R13+3) as the root of the final chord of the measure is similar tothe shift from D (R5) to A (R6) between the chords in the earlier D tonal area that shared pcA in the bass. Further, the relationship between the ending chords of R13 and R13+3 issimilar to that between the chords at R3+ I and R4-2 in that at least two pcs are registrallyinvariant. That is, Eb4 and F4 are common to the last chords of R13 and R13+3, and D4and E4 are common to the chords of R3+l and R4-2. Rl3ff. also recalls the Eb tonics atR6+3ff. and R9-6ff. because it re-establishes the pc collection (Eb-major) that wasreferential when Eb first became a tonic (R6+3), and it recalls the dominant seventh chordthat was contradicted the last time Eb was a tonic (R9-6).At R13+2ff. the simultaneous use of two different lC5-related transpositions of themelody from R5+2ff., T3 andT8, recalls the central tonal opposition that has characterizedthe Eb tonic since its first appearance at the end of part A. A Bb tonic is suggested by theT8 transposition and by making pc Eb sound as the minor seventh in the F-rooted chord onbeat 3 of the first three measures of R13. The T3 transposition is also important, however,because it implies the F tonic that will arrive when the final part of the piece begins.The material in Rl2ff. sounds transitional because there is an underlying step-progression in Rl2-3 to R14+I (see Example 3.8). The sonorities in Example 3.8a areconnected by a linear intervallic pattern, 8-8-8-8-8, between the soprano and bass which isaccompanied by a second linear intervallic pattern, 5-5-6-6-7-7, between the bass andtenor. The step-progression in RI 2-3ff. overlaps with the ending of the previous stepprogression (shown in Example 3.7) because the first two chords of the former (R12-3 andR 12) are also the final two chords of the latter. These step-progressions are similar incertain ways. For example, the bass lines of both step-progressions contain a movementfrom pc Bb to pc C. Example 3.8b shows, however, that there is an even closercorrespondence between the step-progressions of R5+Sff. and RI 2-3ff.; T8 of the initialtwo chords of the former gives the final two chords of the latter.Example 3.8a) Step-Progression in [] -3ff.+2 +4 -2 [] +3 to -:L +1ø.< 5 5 6 (5) 6 7 7(.• I,. I;’eI Ip. p• •b) Transpositional Relationship-l +1Ep wi110-F1\TLii3.2.5 Part AlAt R14 the material of the first section of part A is transposed up a semitone. Thisgenerates an Eb tonic for the same reasons that the D tonic was generated in R3ff. Thetransposition at R14 of the entire texture of R3 provides an important confirmation of themany T1 relationships which connect the material of the Eb tonic to that of previous tonalareas — that is, the bass motive in R12-3 and R12, the chords in R6 and R13+3 (beat 3),and the melodies in R6-5 and R13-l — and helps to establish Eb as the culmination of anongoing process. For example, when the collection of the D tonic of R6 is suddenlysupplanted by a new collection in R6+3, a melody resembling T1 of the trumpet line at R6-4 is sounded. In subsequent statements of this material (R9-6, R12) it comes to resemblemore closely the original melodic line until R13, where it becomes identical. The gradualmetamorphosis of this melodic line into a shape identical to the original parallels the111increasing tonal direction towards an Eb tonic. The importance of Eb is emphasized at R14when it is sustained as the tonic of the following part.The only modifications to the original material from section b result when Coplandterminates the melody in the tenth measure and makes a quasi-cadenza from the lastmeasure. This results in ending the Eb tonal area with the Bb-major triad, thus making animplicit reference to the conflict between Eb and Bb at R6+3 and R9-6 and a directreference to the similar ending of the D tonal area, when Eb was first introduced as a tonic.This Bb harmony is followed by a statement of the octave <F4, F5>, soundingsuccessively in the trumpet and English Horn respectively. The octave focuses ourAattention on pc F as Eb:2 (recalling a similar emphasis on pc F at R6+5 and R9-4 of thepreceding Eb tonics) just before F becomes the tonic pc at R16 as the opening material ofthe piece is restated. This focus on the second scale-degree is reminiscent of R5-lff. whereA A Apc A was implied to function as G:2, pc E sounded as D:2and pc F sounded as Eb: CodaThe final part presents basically the same materials as the Introduction, only in atruncated form. Thus, an F tonic is generated in Rl6ff. for the same reasons as in mm. 1ff.However, this material has been affected by the ambiguity between 1C5-related tonic pesthat characterized part A. In R16÷ 1ff. the F root never reappears as expected. Instead,Copland retains the C root of the trumpet cadenza as the final root of the piece leaving the Ftonal area open ended. This C root does not have sufficient strength to overpower the Ftonal preconditioning and become a tonic in its own right even when the interval <G4, C4>appears, almost like an afterthought, in R17+3.Imprinting an inconclusive open ending onto the final tonal area of the piececontributes significantly to the unity of the piece (if not to its closure) as it makes the finaltonic reflect the open endings of the D and Eb tonics in part A. In this way the introductory112material is shaped by the central theme which guides the form of the piece, and is related tothe single tonic — Eb — which constitutes the focus of the piece.3.3 Pc ContinuityFigure 3.2 graphs the pc continuity structure of Quiet City. Primary streams ofconnection reflect the most emphasized pcs which are common to the collections ofsuccessive tonics. In some cases, especially where many pcs are common to the pccollections of successive tonics, secondary pcs are shown which, although emphasized,may not be obvious. These secondary streams of connection were chosen either becausethey are related to a nearby primary stream or because they help to clarify processes in thepc continuity structure.3.3.1 Stream GenerationOne of the most important means of generating a primary stream of connectionbetween successive tonics in Quiet City is the sustaining of a pc from one tonal area intoanother. This occurs at R7 and R9+ 1 when parts B and C respectively are articulated. Themost striking of these two passages is the latter, because pc A, which encapsulates thecharacteristic ambiguity between Eb and Bb, is accented at the end of the Eb tonal area.Two sets of paired primary streams in Figure 3.2, in mm. 1ff. and R7ff.respectively, result from emphasizing a common dyad or trichord within different chords ofsuccessive tonal areas. For example, paired primary streams on pcs G and D connect the Fand D tonics at R3 because these two pcs are prominent in the trichord {D4, G5, F6} in theF tonal area, which is stated in mm.3, 7, and R1-2, and in the crucial dominant sonorityS.-’‘2-b7--+5- I-I-‘RL‘3—5—--3--S-3—-I•I--.:..--I:1::::::1 5-J ----S-3Figure3.2Pc-Scale-DegreeDesignofQuietCityR:m.iIiiI21-1I21+5Parts:IntroductionSections:aalSubsections:abalbiTonics:F31141-2151-1I61-4161+371181I91-691+1+6ABCbb1cb2(trans.dcci:c2c3c4ddlc5efF/DEbCEbDB BbA AbG F# F E Eb D CII :r--iii [ : 16[:L_JI37L55.114—f--E:EEZ—II.IIIIEE= EEEEEE=========Figure3.2(cont.)B BbA AbG F#-F E Eb-C#C-.!7”S—3;b34L LLztzLR:9-1+6hotIiii112111311411151161+41171-1Parts:CAlCodaSections:db3(trans.)b4a2a3Subsections:efele2c6c7c8c9a2b2a3Tonics:DEbFS-5P-2—6115{A2, B3, D4, E4, G4} in the following D tonal area, which is stated in R4-2. Both pcs Dand G, however, are emphasized as common to the collections of the F and D tonicsoutside of this particular interval because of accents in the outer voices: pc G receivesagogic accents in the bass in m.5 and R4+2 and in the soprano in R2-1, R4-2 and R5-2; pcD is accented by register as the lowest bass pitch (Dl) in the first two sections (i.e., in Ri-3, R2+2, and R5-i-3) and by agogic accents in the melody from R5 to R6-5. Thecomparatively stronger emphasis on pc G at the beginning of the D tonal area makes thestream on that pc more important as a connector in Figure 3.2. Three primary streams,which are generated by emphasizing a common trichord, connect the C and Eb tonics inpart B. For example, the streams on pcs F, Bb and G are generated by emphasized chordsin the C and Eb tonal areas that share the trichord {F, G, Bb}. In the C tonal area thistrichord forms the outer voices of the sonority {F2, Ab3, Eb5, G5, Bb5} which marks theregistral climax of the repeated phrase (i.e., R7+4, R8+4) and the sonority {F2, Ab3, F4,G4, Bb4} which ends the first phrase (i.e., R8-1). In the following Eb tonal area the outervoices of the first chord, {F1(2), D4, G4, Bb4} in R9-4, place a similar emphasis on thistrichord. The sustaining F5 in the trumpet in R8+5 and R9-4 makes the stream on pc F themost important. The stream on pc Bb is considered to be the next most important in thegroup because Bb is accented as the soprano pc of the sonorities in the C tonal area andemphasized by a voice exchange, which involves pcs Bb and F, in the two chords of theEb tonal area.If, however, one considered a G tonic to be present at R5— 1 then a third group ofprimary lines, which resembles those just discussed, would appear in the pc-scale-degreedesign of the piece (see Figure 3.3). These primary lines are generated by the prominenceof the trichord {D, G, A} in the sonorities {A1(2), G3, C4, D4} and {A1(2), G3, D4, E4}which are sustained in R5 and R6 respectively. These streams are ranked in a similar way116to those of R7: pc A is the most important line because it is so emphatically accented in thebass; and pc D is ranked second because it receives agogic accents in the melody in R5ff.BBbAAbGF#FEEbDc#CFigure 3.3 A Second Interpretation of —1/\/\/\/\/\117Some of the streams in Figure 3.2 are generated by a continuing oscillation betweentwo pcs which are common to the collections of successive tonics, but which occur withindifferent motives. For example, at RiOff. the primary streams on pcs C and C#, whichinitially conflict chromatically as different versions of D:, result from the alternation of C5and C#(Db)5 in two different motives, motives I and 7 respectively, in the D and Eb tonalareas. The alternation between C5 and C115 in the D tonal area (RI 1-3, Ri 1-1 and Rl 1+1)is answered by a similar alternation between Db5 and C5 in the Eb tonal area (Rl2, R12+3,R 12+4 and R 13-1). However, because these alternations are heard within differentmotives the two streams are not paired in Figure 3.2. This technique is also used togenerate the secondary stream on pc Fl which accompanies the primary streams on pcs Cand Cl. For example, the type of emphasis Ofl pc Fit at RI 2-3ff., which is effected by theneighbor tone motion <F#5, E5, F#5> in an otherwise static, sustained chord, is recalled inRI 2+1 when the melody incorporates the neighbor tone motion <F5(6), Gb5(6), F5(6)>..This correspondence, as in the paired primary streams of the same section, is similarlyreinforced by a literal pitch connection involving F#5.Other techniques which generate primary streams in Quiet City include emphasizinga common pc by successive agogic accents in the outer voices, by following it with restseach time it is stated or by eliding phrases, as in the first movement of the ShortSymphony, to make the ending pc of one tonal area function simultaneously as thebeginning pc of the next. The use of successive agogic accents and rests occurs in R16where primary streams on pcs C and F connect the central Eb and F tonics. The stream onpc C results from the successive agogic accents on that pc in the soprano and bass voices ofboth tonal areas (i.e., R14+l and R16+4, and R14+l, R15-2, R15+1, R17-1 and R17-4respectively). The stream on pc F is similarly generated from agogic accents on pc F in thesoprano in R 16-4 and RI 6+3. However, pc F is also emphasized because of the rests thatdemarcate the beginning and ending of the octave F in the trumpet. The use of elision to118focus our attention on the changing function of a particular pc occurs at R3 where pc A,A AAwhich is ostensibly the goal of the 5-4-3 descent, simultaneously introduces a new motivethat has a different pc collection. The arrival of pc A at R3 is emphasized because theearlier descent in the English horn (R2ff.) predicted that the third scale-degree, which hadbeen avoided to that point, would be Ab and not A. This conflict is shown in Figure 3.2Aby the use of an arrow to the initial 3. The importance of pc A to the D tonic issubsequently underlined by the successive agogic accents in the bass (i.e., R4-2, R5,R5+5, and R6).3.3.2 Suspended StreamsSeveral of the streams in Figure 3.2 are briefly suspended when the connective pcis momentarily replaced by another pc that has the same function. For example, theprimary stream on pc D at mm.Iff. is identified as suspended at R2+3 because it ismomentarily replaced by pc Db as the sixth scale-degree. The line remains suspendedthrough R2+5 because pc D, although implied by the return of the original collection, is notA Aexplicitly restated. At R3 we hear pc D change scale-degree function from 6 to 1. Theprimary stream on pc C initiated at R9+6 is suspended at RI 1+2 when C is replaced by C#as the seventh scale-degree. At RI 2 we hear pc C change scale-degree function fromA ATwo secondary streams that are suspended, <4,6> on pc B in Riff. and <5,4>on pc A in R3ff., are included because they anticipate the primary stream on pc A,which articulates part C. At first the secondary stream on pc B, in particular, isdifficult to hear because of the relative insignificance of that pc to the F tonal area.However, this connecting stream is quite important motivically because it recognizes theeventual transformation of the fragment <C5, B4, G4, D5>, which begins the trumpetcadenza, into a melodic ostinato in R5+2ff.1193.3.3 Pc-Scale-Degree DesignThe most important structural division in the form, R14 (part Al), is not delineatedby a change of tonics. The parts that do have tonal shifts, however, are marked by primarystreams that end with 5. The first two of these connecting primary streams are identical.AAFor example, part A is articulated by the primary stream <3/5> on pc A and part B isAt’articulated by the primary stream <3,5> on pc G. The streams which articulate the otherA AAparts similarly end on 5: part C is articulated by the primary stream <4,5> on pc A, andthe Coda is articulated by the primary stream < > on pc C. That is, at R9+1 we hear pcA AA change scale-degree functions from 4 to 5; and at R 16 we hear pc C change scale-A Adegree functions from 6 to 5. Like the characteristic device of textural expansion from aAsingle note, the repeated focus on 5 as the terminal function in a primary connective streamunifies every part in the form that is marked by a change in tonic.The emphasis on the fifth scale-degree in the pc-scale-degree design is supported bysurface features of the music. For example, by far the most prominent pc of the opening Ftonal area (mm. 1ff.) is C, the fifth scale-degree. Similarly, the only part division notdirected by a change in tonics, part Al (Rl4), is marked by the sustaining of the fifth scale-degree of Eb (Bb5) in the trumpet. The interval of a fifth is also very prominent in the step-progressions that underlie R5-lff. and R12-3ff.3.3.4 Importance of 10,2,51The resulting primary articulative streams on the pcs A, G and C manifest the peset-type [0,2,51 that permeates the opening of the piece. This association is suggested inthe pc-scale-degree design over the entire piece by the broader shift in focus from pc G(m. I to R9-6), to pc A (R9-6), which culminates in a focus on pc C in R9+6ff. Otheraspects of the pc-scale-degree design support this characterization. For example, in R7 thepaired primary streams on pcs F, Bb and G similarly form [0,2,51. The primary streams120on pcs D and A, which articulate part C, similarly combine with the stream on pc C(R9+6ff.) to form 10,2,51. [0,2,51 is suggested at Riff. by the streams on the pcs A, Band D and at the end by the successive primary streams on pcs D, C, and F at R9-6ff.The use of overlapping forms of 10,2,51 to create chords that represent larger set-types as in, for example, 10,2,4,7,91 in R2 and 10,2,5,71 in R2+1,’’ suggests another wayin which the pc-scale-degree design might be said to reflect this set. 10,2,5,7 I contains asubset— 10,2,71 — that is intervallically similar to 10,2,51 and is also present in the pc-scale-degree design. 10,2,71 is formed by streams on pcs D, G and A at the beginning of thepiece (the opening primary streams), over the part division at R14 (part C), and at thebeginning of section bI in Figure 3.3.The surface of the music also contains at least one important motivic reference to[0,2,71 — the three-note bass line of motive 7. This bass line is emphasized in part C inAthree important ways: itis transformed such that the first note shifts from D:5 (Rl0-3ff.) toAD: 1 (RI l+5ff.); it is the only motive of section d that continues into section b3; and it istransformed at R13+3 by a change in the order of its pcs.3.3.5 Palindromic StructureOne of the more curious aspects of the pc scale-degree design is the way an initiallypalindromic structure, which is incorporated into the Introduction and parts A and B, isoverlapped at R9+ 1ff. by a structure emphasizing the seventh scale-degree. Thepalindromic structure, which is shown in Figure 3.4, is most clearly expressed when theA AAstream <4.3.5> on pc 0 in R3 to R7 is retrograded on the same pc from R7 to R9+1. ThatA A Ais, in R3ff. we hear pc 0 change scale-degree function from 4 to 3 to 5; this progression isA Areversed in R7ff. when we hear the same pc change scale-degree functions from 5 to 3 toA A A AA4. Accompanying this stream at R3ff. are two other streams, <5,4> on pc A and <1,7>I 1Th Irst tour pcs of the piece — {C, D, F, G} — also form the set 10,2,5,71._..-.1—2—5—P2-4--Figure3.4PalindromicStructureinthePc-Scale-DegreeDesignsofFigures3.2and3.3R:m.1131151-1161-4161*371191-69li-iParts:IntroductionABCSections:abbicb2(trans.)dSubsections:acc2c3c4dc5eS5I-1’I—B-Bb--A-Ab-G-F#--F-E-Eb--c#-.C---P1-2-P2- 6-------- —1-‘I-%,.4-1-—3-—3—.5.L_J,%.-5—,‘—.3—I%—S—3—------P1—-4----2zz::ziz:::I—7-%I.5I-ai---Figure3.3122Ofl PC D, which are also retrograded on the same pcs at R9-6ff. That is, at R4-2ff. we hearA A A Apcs A and D change scale-degree functions respectively from 5 and 1 to 4 and 7; thisprogression is reversed in R9-6ff. when we hear the same pcs change scale-degreeA A Afunctions from 4 and 7 to 5 and 1. Palindromic structure is also created when the initialAAprimary streams <2,4> and <3/5> in mm.lff., which occur on pcs G and A respectively,are retrograded in paired primary streams on pcs F and G at R7. This palindromic structureis enhanced if one admits the streams in Figure 3.3, which are shown in brackets in FigureA A3.4, because the ending function of the streams on pcs G and A at R6-4, which are 4 and 5respectively, are the first functions of the streams on pcs F and G respectively at R7. Theresulting palindromic structure unifies the first three variations of section b (i.e., sectionsbi, b2 and b3).The pc-scale-degree design in R9+ 1ff. contrasts with the preceding palindromicstructure in that it initially focuses on streams that begin on 7 and that have not been statedprior to this point. For example, at R9÷6ff. we hear pc C change scale-degree functionA A A A Afrom 7to 6 to 5, and at RiOff. we hear pc C# change scale-degree function from 7 to b7.However, this focus is actually a continuation of a series of streams beginning on whichis begun at R7ff. when the palindromic structure itself is starting to become obvious. ForAexample, the focus on streams that begin with 7 is initiated in R7ff. when the streamAA AA<b7,5> on pc Bb is followed by the stream <7.1> on pc D. That is, at R7ff. we hear pcA ABb change scale-degree function from b7 to 5, and at R9-6ff. we hear pc D change scale-A A AAdegree function from 7 to 1. The <b7,5> stream on Bb at R7ff. is confirmed as the originof this unusual structure when the stream on pc C in R9+ 1ff., which begins onultimately ends with 12 This overlapping structure effectively serves to unify the secondand third variation of section b (i.e., sections b2 and b3).origin of this series of streams sharing the same initial scaic-dcgrcc function might conceivably betraced back to Rift. because of the striking use of 4 at the beginning of the streams on pcs B and A at RI1233.3.6 Significance of Ambiguity Between 1C5-Related Tonic PcsAmbiguity between 1C5-related tonic pcs is an important expressive idea of thispiece. The emphasis on 1C5 is translated to the pc-scale-degree design in two ways: byexpressing simultaneous primary streams (either paired or unrelated) on 1C5-related pcs,and by stating or 4 at the beginning or ending of various different streams. Pairedprimary streams are presented on 1C5-related pcs at the beginning of the piece (on pcs Dand G) and at R7 on the two most important of three simultaneous primary streams (i.e.,those on pcs F and Bb).’3 Unrelated (simultaneous) primary streams are presented on1C5-related pcs at R9-6ff. (on pcs A and D), and at Rl4ff. (on pcs F and Bb). The pcscale-degree design also reflects 1C5 by the presence of so many streams that incorporate 2as their beginning or ending function. This focus is especially notable in those unusualstreams which use 4. The emphasis on the fourth scale-degree becomes even morepronounced if one includes the hypothetical streams in Figure 3.3. For example, theA AA AA AAstream on pc 0 uses 4 in three different parts, <4, 1>, <1,4> and <4,3> respectively. Theinitial stream <2i> is restated immediately in a stream on pe D.3.4 SummaryThe foremost question we had in examining tonality in Coplands music is howtonics and their successions relate to form. We can summarize the most important featuresof Quiet City to address this question. Despite their unusual and contrasting placementswithin parts in the thematic design, the crucial thematic variations on the b section areunified tonally throughout parts A, B, C and Al by a recurrent Eb tonic. This unity isand R9-6 respectively. That is, at Rift. we hear pc B cl,ang scale-degree function from too, and at R9-6ff. we hear pc A change scale-degree function from 4 to 5.3Pcs F, Bb, D and G arc. themselves, representative of the most crucial ambiguities of’ the piece — thosewhich characterize the Introduction, Coda and part A. For example, pc F represents the ambiguity betweenF and C tonics which characterizes the opening and closing parts of the piece. Similarly, pc Rb representsthe ambiguity between Eb and Bb tonics at the end of part A. Finally, pcs D and G represent theperplexing and, perhaps, unsolvable ambiguity between D and G tonics at R5-1. The significance of thesepcs is alluded to in the molivic structure of the Introduction. For example, the part of the pizzicato bassmotive of Rl-5 to RI-I that Copland reorders in a repetition at R2ff. involves the pcs F, Bb, D and 0.124strikingly emphasized at R14 because the return of the A material is not supported by achange in tonics. As a result, Al becomes the only part in the form that is not marked by atonal shift. We might surmise that the recurrent Eb tonic has programmatic significance asa tonal counterpart to the “night thoughts” of the central character in the play. Parts A, Band C are also, however, unified by an important underlying step-progression (as shown inExample 3.7). This focus on the unification of the variations of section b significantlyreduces the importance of a return to F because this tonic is limited to the parts that framethe variations — the Introduction and Coda.The tonics in Quiet City create a structure of pc streams — the pc-scale-degree design— that adds significantly to our understanding of the piece. The pc-scale-degree designconfirms a unity in the piece independently of the specific thematic and tonal designs in thatAevery part that is marked by a tonal shift has a pnmary stream that ends on 5. Theemphasis on the fifth scale-degree could also be interpreted as another manifestation of thevertical interval of a fifth, which was the first harmony heard in the piece (m.2). Theemphasis on 1C5 in the pc-scale-degree design (through simultaneous primary streams andthe use of andb) recalls the importance of tonal ambiguities between 1C5-related tonicpcs within individual tonal areas in the Introduction, Coda and parts A, B and C.However, the pc-scale-degree design also reflects other features of the surface of themusic. For instance, the succession of primary streams recall the pc set [0,2,5], whichpermeated the motivic structure of the Introduction. The latter in particular contributes toour understanding of unity in Quiet City because it shows how the material of theIntroduction affects the rest of the piece. The pc-scale-degree design, however, also showssome of the conflict which occurs in the thematic design as a result of the placement of thevariations of section b. It shows a palindromic structure overlapping with another structurethat, mimicking the larger emphasis on focuses on streams that begin with. Thepalindromic structure also contributes to our understanding of unity in the piece because it125confirms the continuity between parts A, B and C that is suggested by the underlying stepprogression.126Chapter 4Billy the Kid(Orchestral Suite)4.1 IntroductionIn the previous chapter we saw a pc-scale-degree design that revolved around therepetition of the fifth scale-degree at the beginning of major parts in the thematic design.This parallel was reinforced on the surface of the music by a recurrent textural device thatcharacterized the beginnings of all parts and by a long-term step-progression featuringparallel fifths that unified the central portion of Quiet City. In this chapter we will discusspc continuity in Billy the Kid, which is one of the earliest and most famous of Copland’s“popular” works.1 Despite predominantly conventional local tonic procedures, Billy theKid is worthy of study in the present context because it demonstrates tonal structuralprinciples that are similar to those found in Quiet City. We will see that the pc-scale-degreedesign of Billy the Kid, unlike that of Quiet City, revolves around the repetition ofparticular streams on different pcs and the large-scale repetition of an ordered series of focalpcs. The pc-scale-degree design for Billy the Kid also has a deeper significance than thatof Quiet City because it offers several ways to hear the unique tonal structure of the suite asclosed.4.1.1 Omission of MaterialThe analysis presented below is of the orchestral suite derived from the ballet. Itassumes that, despite Copland’s omission of one-third of his original material, the tonalstructure is planned, not a haphazard result of cuts. This assumption is particularly1Copland testifies to the great popularity of Billy the Kid with his statement “I cannot remember anotherwork of mine that was so unanimously well received.” See Aaron Copland and Vivian Penis, copiand:1900 through 1942 (New York: St. Martin’s/Marek, 1984), p.283.127important because the most crucial point in the analysis below — R27A — is one of the twoplaces in the suite where entire scenes from the ballet have been omitted.24.2 FormThe form of Billy the Kid, shown on the top four lines of Figure 4.1, follows thedescriptive titles which CopLand apparently supplied to mark the movements in the originalscore of the orchestral suite.3 According to Copland the suite matches the main action ofthe ballet in six connected movements: “The Open Prairie,’ “Street in a Frontier Town,”“Card Game at Night,” “Gun Battle,” “Celebration After Billy’s Capture,” and “Billy’sDemise.”4 The problem with this description is that the second movement spans atremendous portion of the suite — from R6 to R29-3. Copland argues that this very largeand thematically diverse movement (“a kaleidoscope of tunes”)5is unified because thecowboy songs and Mexican dance fulfill a programmatic purpose — the portrayal of a streetin a frontier town. However, authors such as Julia Smith and Neil Butterworth suggestthat Copland’s second movement, in fact, contains two separate movements. Smithidentifies R2Off. as the proper third movement and, using a label coined by Lukas Foss forhis solo piano arrangement of Billy the Kid, calls it “Mexican Dance and Finale.”6 The“Mexican Dance” begins at R20 and the “Finale” begins at R24. Because of the obviouslydifferent characters of these passages Figure 4.1 correspondingly shows the secondmovement as divided into two halves at R20.2The other passage affected by the omission of entire scenes is R49 where four scenes — “Billy in Prison,”“BilI’ Lost,’ “Billy Finds Refuge with His Sweetheart” and “Garrett Kills Billy” — are omitted. A muchless significant omission in the suite occurs at R54 when a phrase repetition in the ballet disappears.3All except the first two of these titles are absent from the published score of the suite. See Copland andPerlis, op. cit., p.385 n.13.4lbid., p.284.5lbid.6Julia Smith, Aaron copiand: His Work and contribution to American Music (New York: E. P. Duttonand Corn pany, Inc., 1955), p.1 89. However, in a later catalogue of Copland’s works (see p.304. n. 31 a)Smith lists seven titles for the suite, the first six of which are what she discusses on p. t89. The seventh,“The Open Prairie Again,” implies a much different structure for the suite which will not be discussed.Smith also arrives at a six movement form because her fourth movement includes Copland’s “Card Game atNight” and “Gun Battle” as a single movement.Figure4.1SummaryofThematicandTonalDesignsinBillytheKidR:m.iIil121÷4131141151161171+4+8181-3181+1191+4Movement:I“OpenPrairie”11.1“StreetinaFrontierTown”Sections:aala2a3a4a5a6bbi(ant.)c(ant.)bi(cons.)c(cons.)cib2Rondoforms:A[A/BIA/B]BATonics:CFCAbFAbFCCXFR:Movements:Sections:Rondoforms:b3(ant.)c2[ATonics:liol+41111-4liii_1121_11411151+2_1161_+5_1171_I181_1191-41191:1201(11.1)b3(cons.)c3c4d(trans.)efelc5b4g(trans.)hIB/A]BBtrans.CDCBAtrans.BbDbFDAfl.2AXDDR:1211122112311241I25AII26A1127Al12811291-3I30I1311-31311+2—Movements:(11.2“MexicanDanceandFinale”)ifi.“CardGameAtNight”Sections:hiih2jjij2k(trans.)a71m11Rondoforms:Tonics:(Bb)GBbGBBXAbAbFF)cAbAb00Figure4.1(cont.)R:13311351+2+81361+71371+51381-41391140114111421143114411451-21461-1-41471Movement:IV.“GunBattle”V.“Celebration”Sections:nnin2n3n4n5n6n7n8oolpqo2rp1o3o4Rondoforms:AABCADBAATonics:ACAAEbCC#C#C#Table4.1SummaryofTn-RelatedSectionsR:14911501151115211531Movements:(V.)VI.“Billy’sDemise”Sections:sslaaSa8Rondoforms:EETonics:GCFEc5T9cb4T9b2a7T8a2plT3p[I1][T0]130The suite has a largely continuous, or through-composed, form. Most of themovements, with the exception of the second, do not have a strong internal division. Manyare based on fairly simple forms. For example, the first, fourth and sixth movements relyupon variation of the material stated at or near their beginnings, while the third movement isa simple ternary form. The fifth movement is also loosely based upon a traditional form —the rondo. This form is identified using capital letters in the fourth line of Figure 4.1. Thethird line of Figure 4.1 shows the varied recurrence of material in the entire suite.The second movement is very unusual because its two halves, R6ff. and R2Off.respectively, have two different forms: the first has an unusual rondo form and the secondhas a variation form.7 The unusual quality of the rondo in R6ff. (shown in the fourth lineof Figure 4.1) is caused by the interpenetration of the antecedent and consequent phrases inthe second and fifth segments of the rondo (i.e., those starting at R7 and RiOrespectively).8 However, this rondo is also obscured by references to a ternary formcreated by the striking introduction of new thematic material in R14, and by therecapitulation of the material from R8+ 1ff. in RI 7ff.The fourth movement (“Gun Battle”) is also unusual because it has a uniquejuxtaposition of six short repeated motives, each with its own fixed timbre. These shortmotives, shown in Example 4.1, are developed only in limited ways, by rhythmicextension or truncation. The rhythmic flexibility of this material presents a distinctlydifferent character from that of the rest of the suite. This musically underlines the drama byevoking the posse’s chase after Billy and the gunshots in the ensuing battle.7Smiths analysis of the form allows her to characterizes this rondo form as the basis of an entiremovement. See Smith, op. cit., p.190.8The eight-measure periods which represent A and B in this rondo are interpenetrated when the first four-measure phrase of B is stated before the concluding four-measure phrase of A. This results in a largerpassage that is neither A nor B but a mixture of both. The fourth line of Figure 4.1 shows the second andfifth segments by enclosing brackets around its constituent parts (i.e., 1 1). Smith apparently ignores thisinterpenetration because she claims that the second and fifth segments of the rondo should be B and Arcspectively, that is, the rondo form (excluding the two transitional passages) should be labeledABBAABCDCBA. See Smith, op. cit., p.189.The through-composed form of the suite is modified by one important recapitulationof material, the restatement of the “open prairie” music at the end, which creates a cyclicform.9 The cyclic quality of this recapitulation is heightened here by the near exactrecapitulation of the first and sixth sections of the first movement (sections a and a5). The“a” material also appears at R28, but its brevity makes it sound, in retrospect, as aforeshadowing of the more substantial recapitulation in the sixth movement. Yet theallusion to a larger rondo form, created by this internal restatement of the opening material,links the widely separated rondo forms in the second and fifth movements. Therestatement of the opening material at R28 also helps to associate the setting in the fourthmovement, “at night, under the stars,” with the “open prairie” setting in the firstmovement.t0Several other works by Copland as, for example, the Short Symphony, the Piano Sonata, Quiet city andAppalachian Spring, have a similar cyclic aspect to their form.10Viewing the third movement as a substitution for the first is also relevant to the tonic succession in thesuite because the tonic at the beginning of the third movement acts as a substitute for the expected return ofthe opening tonic of the suite. This is discussed below on p.140.131Example 4.1 Summary of Motivic Content in”Gun Battle”Motive 1 (]) Motive 2 ([]) Motive 3 (+2ff.)9:.J[1H14 Ti iilow strings, piano, trumpets, snare drum high sthngs, woo w dstimpani, harpMotive 4 ([}4ff.) Motive 5 ({] ff.) Motive 6 ([}6ff.)I 1 r1 HIxylophone, high woodwinds, piano strings brass13243 TonalityA summary of the tonic succession in the suite is given in the fifth line of Figure4.1. The processes that generate these tonics are closer to conventional harmonictechniques than the tonic-defining processes in Copland’s “serious” works. As a result,the tonics in the suite tend to be relatively clear and free of the ambiguity whichcharacterizes much of Copland’s music. What little ambiguity there is in the suite resultseither from a special type of varied reprise or successive recombinations of short motives.These will be discussed later. Many of the local tonic successions in the suite are,however, inflected by overlappings that result from preconditioning or harmonies withambiguous functions.One of the most interesting questions about the tonic succession of Billy the Kid iswhy, after alluding to C as a global tonic at R27A and R51, the suite ends with an E tonicin R53. The following discussions on tonic succession and pc continuity will addresssome of the ways this concluding tonic is resolutive within the tonal structure, instead ofdismissing it as a programmatic device.4.3.1 First MovementThe opening C tonic, suggested by the durational accent on the fifth {C4(5), G5} inthe first two measures, is generated by a descending-fifth root motion: the G-rooted chordin R1-2, {G1(2), A3, C4, F4, C5, G5} (the jazz chord FIG), progresses (two measureslater) to a C-rooted fifth, {C2(4), G4}. The fifth {C2(4), G4} is subsequently stated onthe downbeat of the next ten measures. At R2, the removal of this harmonic underpinningmakes us concentrate on the Eb-major triad, thus raising the possibility of an Eb tonic forthe same melody. This implication is very important for future tonal events (i.e., those atR28) and has a direct bearing upon special patterns within the pc continuity structure.However, Eb is not generated as a tonic for three reasons: the C harmonic underpinning is133absent only briefly; the melodic line in R2+4, <Eb5, D5, C5, Eb5>, makes a clearassociation between the pcs Eb and C; and there is no root progression in Eb. At R2÷4 theoriginal harmonic underpinning is restated, thereby removing any root quality we mighthave heard Eb to possess.At R4-3 the transposition of the bass motive <C2(3), G 1(2)> down a tone (to<Bbl(2), F1(2)>) predisposes the listener to hear a similarly transposed tonic, Bb. Thesemeasures do indeed focus on Bb as the root of the chord {Bb3, C4, Db4, EM, Ab4, Bb4,Db5(6), Eb5(6), Ab5(6)} and a Bb tonic is suggested in a small way by the presence of thepcs {Ab, Bb, C, Db, Eb, F} from the Bb-Aeolian collection. Unlike C, however, Bb isnot supported by a descending-fifth root motion because pcs Bb and F are stated below thesame chord. Thus, despite the appearance of Db, a pc which has not been heard in thesuite until this point, Bb does not displace C as the tonic of the passage.The function of pc Db at R4—3 is clarified three measures later when the bass motiveis again transposed, this time down a fourth (to <F2, C2>): Db forecasts the subdominantfunction of an F tonic that arrives at R4. F is generated as a tonic by a descending-fifthroot motion (<F, C, F>) when both pcs in the transposed bass motive become chordroots1 in the first three measures of R4, that is, pc F is the root of the sonority {F2, Ab3,G4, Bb4} and pc C is the root of the following sonority {C2, Bb3, F4, G4, D5}.’2 An Ftonic is also supported in R4 to R5- 1 by the metrical accent given to the F-rooted sonoritiesand by the transposition (T7) of the bass motive.At R5 C returns as a tonic when C-rooted, instead of F-rooted, sonorities aremetrically accented. This return to C is foreshadowed by the chords which are metricallyaccented from R3+4 to R5- 1 (see Example 4.2). The outer voices of these chords are1n the preceding statement of this motive (at R4-4 to R4) only the first pc (Bb) was a chord root.12Thc chord sustained above pc C does not always have a C root. For example, the chords at the end ofR4+3 and R4+4 sound like an extension of the F minor-minor seventh chord stated on the downbeat and,thus, suggest an F root. Pc C eventually returns in the two measures before R5 as the root of the chordson beat 2.134directed towards pc C: the highest voice states the ascending stepwise line <G4, Ab4, Bb4,C5> and the lowest voice states the descending line <C3, Bb2, F2, C2>. The terminal pcC of both lines coincides with the last root (C) stated in the F tonal area (Ri-i). Thefollowing chord (R5) reasserts the original tonic function of the C-root.Example 4.2 Accented Sonorities in J+4ff.4.3.2a Second Movement (First Half)At R6-l the texture is reduced to a single sustained pc, Eb, over which an Ab tonicis melodically generated. Ab is followed at R8+ I by an F tonic that is also melodicallygenerated. The change from Ab to F is obscured because the eight-measure periodsassociated with each tonic are interpenetrated: the opening four-measure phrase of F isstated before the concluding four-measure phrase of Ab. The F tonic, established at R8+ 1,is succeeded by a C tonic at R9 when the transposed theme, melodically generating a Ctonic, is superimposed over an accompanimental pattern previously generating the F tonic.C is supported by the C-major collection and by durational accents at R9+i and R9+7. Fgradually reemerges as a tonic over C in R9+7. This return, implied by the reappearance ofthe pc Bb, is suggested by the alternation of Bb-major and C-major triads in the highregister. These triads sound like the progression F:<IV, V> above a tonic pedal. Thechange of texture at R9+7, which results from the introduction of chords and theelimination of the (lower) harmony voice from the texture, seems to support a change intonic. However, F only gradually emerges through this progression as more significant135than C, which is suggested melodically by the repetition of the ending gesture of the Ctonal area (<E6, G6, C6>). As a result, the passage has been analyzed in Figure 4.1 as atonal overlap. At RiO the theme is transposed to Db above a {Db2, Ab2} pedal andalternating tonic- and dominant-chords in Db ({Ab3, Db4, F4} and {Ab3, C4, Eb4, Gb4}respectively).’3At Rl4ff. a series of chords creates an alternation between Bb- and C-rootedchords.t4 These roots are defined at R15 as part of a <IV, V, I> progression in F.’5However, F is generated as a tonic in R14 to R15 before this harmonic resolution by theoutlining of an F-major triad in the highest voice (i.e., <F, C, F, A, C>), and by the F-major collection. F is confirmed as a tonic in the first two measures of R15 by therepetition of the harmonic progression <I, III, IV, V>, and by the new melody at R15.This melody grows from repetitions of the cell <CS, Bb4, C5, G4, F4> and associates itsmost insistent pc, C, with pc F in the fifth that is repeated at the end of phrases (i.e., <CS,F4> at R15+Sff.).This material is interrupted in R17 by the reappearance of material from section ctransposed to D. At R18, like R9, a superimposition of similarly transposed material fromsection b2 redirects the passage away from D toward an A tonic. The subsequent tonaloverlap between A and D, which we expect to mark the return of D, occurs in a differentmanner in Ri 8+4ff. than in R9+4ff. Pc G returns but the D- and G-rooted harmoniesarticulated on beats I and 3 of R19-4ff. ({D4, F#4, C#5, D5, ES, A5} and {B3, D4, F#4,G4, B4, D5} respectively) are much less coherent than earlier. This is because thet3The presence of a tonic pedal at R 10ff. retrospectively offers another reason to hear pc F in R9÷7ff. as atonic pedal.14The first chord (at R14) has only a Bb root, despite the C4 pedal which links the first two chords of theseries and the fourth {C, F} between the outer voices, because of the emphasis given to the fifth {Bb, F}through doubling. Similarly, the relatively high register of the D-minor triad at the end of R15-1articulates a D root that is so weak that it does not obscure the dominant-tonic relationship expressed withinthe chords which frame it. The dominant-to-tonic resolution is Further supported by register because thelowest tones of the respective chords, C4(R 15-I) and F4(R15), are in the same register.Thc root movement in R14 to R15 closes the <IV, V> progression that was implied at R9+7 when Fwas last a tonic.136harmonization of the melody in sixths is never replaced by another texture as it was inR9+7ff., and because the rhythmic complexities, which are created by the interplay of theimitative lines, work against clear root identification. It is not until the cadence into R19that the plagal relation between the G and D roots is clearly established, making D strongerthan A.4.3.2b Second Movement (“Mexican Dance and Finale”)In R20 a Bb tonic is generated harmonically by the progression <I, IV, Vii, I>.Bb is supported as a tonic by the Bb-major collection and by the emphasis on pcs Bb, Dand F in the outer voices. At R22 a new tonic emerges through a modification of the rearticulated chords that alternated in the Bb tonal area. 0 is set up as a tonic by neighbor-tone motion around the pitches of a 0-major chord, by the 0-major chords that start eachof the two-measure phrases in the same registration (with the root in the bass and the fifthin the soprano) and by the G-Mixolydian coLlection.’6The tonal shift from Bb to G is obscured because the alternation between F4 andG4 remains constant in the top voice of the chords in both tonal areas.’7 At R23- 1 theneighbor sonority previously functioning in support of a 0 tonic, the chord {G2, C3, A3,C4, F4, G4(5)}, is retrospectively redefined as an altered dominant of Bb because itreintroduces the progression expressing Bb.When G returns as a tonic in R24 it is initially expressed by the same neighbor-tonemotions which suggested G in R22. G is confirmed as a tonic two measures later by theaccent on the pcs D and 0 in the melody, but it is obscured initially by references to E,which is prominent as an upbeat in the four-measure phrases. The first four-measurephrase also ends on an E minor six-three chord, but this is not a strong reference because16n contrast, the neighbor chord has three different pcs — C, A, and 0 respectively — that appear in thesoprano. This makes the restatement of the root-fifth registration of the G-major chord more striking.t7Thc temporal placement of these pitches in the Rb tonal area — F4 is stated in odd-numbered measures and04 is stated in even-numbered measures within the phrase — is reversed in the 0 tonal area.137the placement of a G chord with an added sixth at the same point in the repetition of thisphrase makes us retrospectively hear the harmony of R24±5 as similarly expressing a Groot.18References to E are subdued at R25A by the reappearance of pc F, which has notbeen heard since R24+5. It is now in the bass for the first time. This deflects the harmonytoward the subdominant of G. What starts out as a simple gestural reference to C as thesubdominant of G becomes increasingly directed toward C as a tonic in its own right by theaccumulation of references to the characteristics of previous C tonics. For example, thetransformation of the simple texture of R24 into the very striking and commanding textureat R26A, which uses the entire orchestra, recalls the C tonic of R5, the last time a fullorchestral texture was heard in the suite. Further, the outer-voice pattern of the passagefrom R27+4 to R27A, like the passage in R4+ 1 to R5- I, can be heard as alluding towardthe voice leading model that is shown in Example 43. The string (and flute/piccolo)melody in R27+3 to R27A-3 emphasizes the opening step of the soprano in this pattern bychanging the pc accented on the downbeat of each measure in R27+3ff.: in R27+3 toR27+4 the accented pc is G; in R27+5 to R27+8 pcs G and A are alternately accented; andin R27A-3ff. pc A is accented. The final pc of this melody in R27A-1 (beat 4) — pc B — isaccented by contour (the piccolo B7 is the highest pc of the G tonal area) and by dynamics.The sudden contraction in register at R27A suggests that we hear the B on beat 4 of R27A-1 to function differently than previous occurrences of that pc, that is, pc B is no longerheard at R27A-1 as an upper neighbor tone to pc A. If we accept the model in Example 4.3then the implied soprano ascent in R27+4 to R27A (<G, A, B, C>) provides the major‘8H’ever, this repetition simultaneously introduces an alternation of two dyads, {G3, E4} and {E3, D4},around a sustained G3 which further emphasizes the pc E. An H tonic is also alluded to by the conjunctvoice leading in the bass in R25 to R25A in that the seventh {E3, D4} at R25+3 and R25A-1 can be heardto frame the alternating sevenths {D3, C4} and {C3, B3}. The termination of the bass line <E3, D3, C3,D3, E3> on pc B (at R25A- 1) is demarcated by the addition of a third note, a second above the lowest note,within the parallel sevenths in the bass. This predisposes us to hear an H minor-minor seventh chord fromR25 to R25A-1.mode version of the ascent in R4+ 1ff. (<G, Ab, Bb, C>) created between accentedsonorities at the end of the F tonal area in the first movement (recall Example 4.2).138IExample 4.3 Step-Progression in [] +4ff.... [±]11) ______.__; • [-.1+4I27AI- -1 127A1-—,--r1 .— I:.,The voice leading directed toward C, however, is interrupted by the dramaticstatement of pc Eb by itself at R27A. In some ways, this pc actually strengthens the senseof a C tonic. For example, Eb makes the continued perception of G, the explicit tonic fromwhich motion is directed in the passage, increasingly tenuous because Eb is not present inthe established G referential collection. Further, the falling bass line that introduces pc Ebat R27A — <F, E, Eb> — recalls the E-Eb opposition that characterized the C tonic in R5.Moreover, the simple act of succeeding a C-oriented passage with an octave-doubled Ebrecalls the similar association of Eb with a C tonic at R6. Finally, the alternation of pc Ebwith a G-eleventh chord is suggestive of the alternation between tonic and dominant chordsin C minor. This allusion is emphasized when pc Eb, sustained above a rising step-progression in the bass which treats pc G as a goal, inflects the sustained pc G in thedirection of a tonic six-four chord in C minor. Example 4.4 presents a tonal interpretationof the step-progression underlying this passage.r—. p p,—- U14. —139Example 4.4 Tonal Interpretation of Step-Progression in 27A -1ff.•. ;- [7. . —-- -------i:-• [7.___-1 127A I -2 +4 -3(9.- .[7C: [j6 I V [iJ V(57) bVI2 3Ultimately, C fails to be established as a tonic simply because no root-position Charmony is allowed to sound after G is sustained in the bass. In fact, a C tonic is veryexpressively denied by the reprise of the “open range” theme with a new pc collection thatcontradicts C. Because C is never explicitly realized as a tonic, the analysis in Figure 4.1shows G, and not C, as the tonic from R24 to R28- Third MovementHowever, the parallel of R27Aff. to R6 is even deeper than the mere implication ofa C tonic. As at R6, Eb here also leads to an Ab tonic, although its arrival is artfullydelayed until R29-3. The melody in R28ff. suggests Ab because of its T8 relationship toR2ff. (i.e., down a major third). But it is perhaps easier to hear B as a tonic because thecollection in the melody, which has only one pc in common with the G referentialcollection, is so unexpected that it makes us focus even more intently upon the B-majortriad that opens the theme. The first two notes of this triad are, to some extent, anticipatedat R27Aff. in the bass line where the oscillation between pc Eb and the G-eleventh chordresults in the repetition of the third <Eb4, B4>. Moreover, the pedal G helps to negate ourexpectations of an Ab tonic because the resultant harmony, which has a major third,140precludes our hearing a transposition of the minor-minor seventh chord that permeated themelody in R2.The same G pedal is also, paradoxically, detrimental to our perception of B as atonic because the most accented pcs in the bass suggest, at least as far as the downbeat ofR28, that we hear pcs G, B and Eb to form the augmented chord {Eb, 0, B}. The tonalambivalence of this augmented chord, which can potentially function as V#5 in C, E or Abrespectively, contradicts a B tonic and suggests instead the Ab tonic which arrives in R29-3. Ab is satisfying because we can hear it as a substitution, by a deceptive cadence, for theexpected C tonic which was foreshadowed in the G tonal area from R25A on.The Ab tonic, presaged by the reprise of the Eb interruption and by thetransposition of the “open range” theme, arrives at R29-3, where it is melodically generatedover an Ab2 pedal. Retrospectively, this arrival facilitates hearing pcs Eb and 0, which aresustained in R28-2, as rooted not by C but by Eb. Under this hearing, the B-major triad atthe opening of the melody of R28 becomes incorporated into Ab as a jazz extension of adominant chord (i.e., the chord {Eb, G, B, F#}) which resolves to the tonic in R29-3 (seeExample 4.5). The sustaining of pc G in the bass until the oboe states <B4, A#4, G#4>,which is the transposition of the crucial line that negated the implication of an Eb tonic atR2, reinforces this hearing. Although Ab is clear after R28, it is not clear in prospect atR27A. As such, the implication of Ab does not fully negate the initial perception of a Btonic. Thus, the B and Ab tonics are marked as overlapped in R28 of Figure 4.1. Thesupport of Ab, when it finally does arrive, by the Ab-major collection, and not by the Abminor collection that is predicted by the “open range” theme, marks Ab with the samecharacter of modal mixture that infused the C tonal areas in the opening movement.141Example 4.5 Implied V-I Progression in []-2ff.-2 +43Ab: V6 V J#3—3The F-Aeolian implications of the quoted folk-song at R29ff. are realized at R30.Here an F tonic is generated by the plagal progression <I, LV, 16>. F is understood as thetonic because F-rooted harmonies begin and end the repeated three-measure phrase. AtR31-3 the Ab-major opening phrase of this movement is reprised, but it does not dislodgethe F tonic yet. Instead, the F and Ab tonics are overlapped from R3 1-3 to R3 1 + 1, and Abdoes not clearly return until it is melodically generated in R31+2ff. The main cause of thisoverlap is the ambivalent association that the first and last chords in the repeated series<{Ab2(4), C5}, {F3(4), Ab4}, {C3, EM, Ab4}, {Eb3, C4, G4}> have respectively withF and Ab roots and C and Eb roots. At the beginning the first chord has an F root becauseit is preceded by a C-rooted sonority (the fifth {C4, G4, C5}) and followed by an F-rootedsonority (the second chord in the series). The repetition of the series, however, makes thesame chord sound like it has an Ab root because the fifth motion <Eb3, Ab2> in the bassfollows the third chord of the series, which has an Ab root. This relationship subsequentlycauses a reevaluation of the root of the fourth chord of the series from C (as F:v6) to Eb (asAb:Vadd6).The tonic succession in the third movement, <Ab, F, Ab>, is transpositionallyrelated to the tonic successions of the two halves of the second movement: it is TiO-related142to that which opens the “Mexican Dance and Finale” andT0-related to that which opens thesecond movement. Because both of these earlier successions continue with a restatementof the second tonic of the pattern (i.e., G at R24, and F at R7+8) we expect an F tonic toarrive at R33.4.3.4 Fourth MovementHowever, it is not F but A that becomes the tonic of the fourth movement becauseof the percussive reiteration of pc A following the A-rooted minor third {A, C}. Thismakes the only other harmony in R33 to R35+l, the third {F, A}, sound like A: VI. TheA tonic is, however, clouded by references to an F tonic starting as early as R35 because ofthe emergence of the ostinato <Fl, Al, Fl> from the repeated bass A of R33ff. Theconflict between A and F tonics continues in the motives heard later within the movement.For example, motives 3, 4, 5 and 6 (Example 4.1) can refer to either an A or F tj.l9Ultimately, the ambiguity between F and A is resolved in favor of the latter when the bassostinato <Fl, Al, Fl> is displaced at R39 by a repeated A, the derivational origin of thatostinato. Pc A here is even more emphasized than at R33ff. because it constitutes the entiretexture.The motivic material of this movement recalls key elements of the passagepreceding the pivotal reprise of the “open range” theme (R27+3 to R27A). For example,the implied ascent from pc G to pc C (shown in Example 4.3) is recalled at R36 when thestring motive in R36 traces a descent from pc C to pc G using the same pcs. This motivealso alludes to the withholding of pc C at R27A because its first five pcs focus on analternation between B and C. Similarly, the alternation between pcs F and E, which was so‘9Motives 4 and 6 are particularly interesting because they suggest that Copland’s music is imitatingcertain characteristics of Stravinsky’s centric music. For example, both of these motives suggest the chord{F, A, C, E} (a 047e tetrachord) within a passage that treats the diatonic octad {A, B, C, D, B, F, F#, G} asa referential collection. This superficially conforms to characteristics which Johnson notes in music byStravinsky that exhibits a major-third polarity. See Patti Johnson, “Cross-Collectional Techniques ofStructure in Stravinsky’s Centric Music,” in Stravinsky Retrospectives (Lincoln: University of NebraskaPress, 1987), p.56.143emphatic in the bass line from R25A to R27A, is recalled in the prominence of pcs E and Fin several of the motives. For example, E and F are prominent in the beginning of thewoodwind motive in R35+2, and they registrally frame the arpeggiation of the F major-major seventh chord, <F4, A4, C5, E5>, in the xylophone motive in R36-4. The mostimportant correspondence, which is the brass chordal motive of R36+6 shown in Example4.6, simultaneously refers to both voices in the voice-leading model of the passage leadingup to R27A. For example, the conjunct voice leading in the outer voices of these chordsrecalls the earlier ascent <G, A, B>. Similarly, the contrary motion that exchanges pcs Eand F in the outer voices of the first two chords recalls the emphasis on pcs F and E in thebass in R25A to R27A. Finally, if one groups the descent in the strings (<C, B, A>)together with this motive then a descending (stepwise) root progression, matching the bassline of the chords, emerges.Example 4.6 Brass Chordal Motive ([] +6ff.)[String Descent]I —5 —5Roots: F E DThe accumulation of these motivic references to R27A recalls the C tonic that wasimplied, but expressively withheld, when G was a tonic. The brass motive, in particular,seems to suggest C partially because C would logically be the next root if a fourth chordwere added but also because the juxtaposition of this motive with the string melodyalternating pcs B and C makes the final sonority sound like ii7 in C. Besides offering a144sense of connection to, and continuity from, R27A these references are also important inpreparing the return of C as a tonic in the next movement.4.3.5 Fifth MovementAt R40 the texture is divided into strands: an upper strand melodically generating aC tonic,20 and a lower strand generating C# by a repeated ascending-fourth pitch motion.Julia Smith suggests this bitonal setting is meant to approximate an out-of-tune player-piano which is entertaining the town in celebration of Billy the Kid’s capture.2 Thestandard accompanimental pattern — accented bass note followed by a [melodically realizedJchord — seems to support this interpretation because it is divided between the two strands.If one transposes the bass line down a semitone the entire passage becomes unequivocallyC major. The contrasting pitch level of the bass line, however, is particularly importantbecause it casts new perspectives on the pcs which are emphasized in the melody andintroduces unexpected roots. This is shown through the contrast of Examples 4.7a, whichgives a pure C-major context by transposing the bass down a semitone, and 4.7b, whichshows the actual passage. For example, PC B at R40+ 1, which is an embellishing majorseventh in Example 4.7a, is a minor seventh which suggests a possible resolution to pc Ain Example 4.7b. Similarly, pc A at R40+4, which is a non-essential sixth in Example4.7a, acts as the resolution of the dissonant pc B and becomes an essential tone as the rootof an A minor-major six-three chord in Example 4.7b. Finally, pc F at R41, which is theseventh of a dominant seventh harmony above a tonic pedal in Example 4.7a, is the third ofa C#-major harmony which sounds throughout the measure in Example 4.7b.20Because of the strong accent on pc B (R40-t-1) the first three pcs of the upper strand — <G4, A4, B4 —initially seem to support a G tonic. However, this imtial reference to G is not sufficient to overshadow theC tonic that is generated by the melody as a whole. The allusion to G is important because it recalls thelast time G was a tonic — R24ff. — and, thereby, represents the first element in a series of subsequentreferences in the fifth movement to the voice-leading structure shown in Example 4.3.21Smith op. cii., p.190. There are, however, other non-programmatic reasons for the opposition betweenC and C# tonics that are revealed by the tonal structure of the movement as a whole, as we shall see.(IExam le 4.7a) 4 +lff. With Bass Transposed Down a SemitoneA(Iø1•411-dr.. -- —-IIw4r=Roots: C---b) Actual Context of j÷1ff. flA . I - I, rm —-——--I-th-ffl’q:y-—-I --I.’rr[C??]-+J(-(,T“-J;i L——--——I —I —&4I—-I I —-.‘1 IExample 4.7b is also significant in terms of roots because the C# substitutioncreates chords whose roots — C#, E and A respectively — collectively suggest an A tonic.Only the second chord in R40+4 has any resemblance to a C-rooted sonority, and thisreference is ambiguous because the chord is an augmented triad.22The reference to A, which is caused by the unexpected roots in the passage, isimportant in immediate tonal connections because it prepares the next tonic. A is generatedin R43ff. by the repeated progression <I, IV, Vll, v, I>, by the A-Mixolydian collection,and by the termination of the repeated four-measure phrase with the melodic gesture <A4,22The reference to an augmented triad, which most likely has an E root, foreshadows the ending sonority ofthe suite, the chord {E, Off, B, C}.145‘ .. n I r I I I fl----—---Roots: C# E146E4, A3>. The C-C# tonal opposition returns at R44, only to lead once more to thecontrasting A tonic at R45-2. This mimics the tonal structure of the second and thirdmovements, which also alternate tonics related by minor thirds. The use of new materialfor the second A tonic recalls the similar thematic differentiation of the G tonics in the“Mexican Dance” and the subsequent “Finale” in the second half of the second movement.That is, when G returns as a tonic in the second half of the second movement it isassociated with the theme of the “Finale.” A is generated at R45-2 by the repeateddescending-fifth pitch motion <E4, A3> above an ostinato, <{C2, C#4}, Al, {C#2, C4},Al>., that incorporates pcs C and C# as chromatically opposed representatives of the thirdscale-degree. A is confirmed as a tonic by the ending of the first four-measure phrase(R45+3) and by the A-major collection in the melody.At R46 a restatement of the material in R42ff. transposed to Eb interrupts theprogression from A to the bitonal C/C# texture that we have been preconditioned toexpect.23 This texture resumes four measures later. The sixth movement ends with thechords {G#l(2), D4, F#4, A4, D5} and {C#2(3), C4, EM, AM, C5}. This chordsuccession, originally a subordinate phrase ending at R48, is incessantly repeated to form afour-measure phrase-extension at R48+4.24 It strengthens the opposition between the Cand C# tonics (see Example 4.8). If we view the bitonal texture of this movement as analteration of an essentially C-major texture then the closing two-chord gesture in R48+4ff.represents an altered <V, I> progression in C. However, the roots of these chords suggest23R4, is also striking formally because the material of section p changes its function: at R43 this materialis used to introduce another contrasting segment in a different key (segment C in the rondo); but at R46 itis used to seguc into a reprise of the opening material in the original bitonal texture of the movement(segment A in the rondo).24Because the drama of the next movement dwells on the fact of Billy’s death it is natural to identify theemphatic repetition of these chords as symbolizing the final gun battle in which Billy is mortally woundedfollowing his prison escape. Obviously, such a view is not tenable if one considers the original context ofthe ballet because the movements of music where Billy was incarcerated, etc., have been omitted. However,the similarity of this material to that in the fourth movement and in R27A to R28 is highly suggestive of astruggle of some sort. If we consider the ending of the “Celebration” in this manner then the tonalopposition betwecn C and C#, which is the focus of the entire movement, inherently contains within it thegerminal seed of what is eventually associated with Billy’s death. This is appropriate symbolically becauseit suggests that Billy’s death, like his life, is shaped by his society.147that we understand this two-chord gesture as a <V, I> progression in Cl: GI and D are theroots of the first chord;25and Cl is the root of the second chord. The resulting oppositionbetween C and Cl is reinforced when it is pc C, and not pc Cl, that is sustained by itselffollowing the last statement of this gesture. This effectively crystallizes the oppositionbetween the C and C# tonics that was introduced at R40.Example 4.8 Concluding Gesture of Bitonal CJC# Texture ([] if.)The fifth movement makes numerous references to the seminal voice-leading modelunderlying R27+4ff. (Example 4.3). For example, the main theme of the bitonal texturebegins with the ascent <G4, A4, B4>, and, in the phrase repetition at R4lff., uses thesame ascent in a transposition down a fourth (within the C referential collection) as theupper portion of the accompanimental pattern. This transposition, <D4, E4, F4>, recallsthe descent (<F, E, D>) that characterized the lowest voice and implied root progression ofthe brass motive at R36-t-6 (shown in Example 4.6). The change of span in this motivefrom a major (<G, B>) to a minor third (<D, F>), which results from this transposition,foreshadows a similar shift between minor and major thirds that culminates in the arrival ofthe final tonic of the suite.25G# is considered as a root of the first chord because of the predisposition toward continuing a texturedivided into two sireams, and the noted similarity to a <V. 1> gesture in C#.148The references to the voice-leading model in Example 43 are continued in the firstA tonal area (R43ff.) by a similar incorporation of an ascending major and minor third,<A5, B5, C#6> and <B5, C#6, D6> respectively, in the melody and by the curiousharmonization at R46-6ff. of the melody in the second A tonal area (R45ff.).26 The latter,which results in a simultaneous statement of the theme beginning on A5, F#7 and G#7respectively, recalls the sonority {F3, G3, E4}, which was introduced in the bass inR25Aff. and was similarly subjected to parallel motion.At R49 a G tonic is melodically generated by repetition of the ascending bass line<G 1, B], D2>. G is supported by the G-major collection, and by the harmonicprogression <IV, (III), V6/4, 1> (R49+2 to R49+4).4.3.6 Sixth MovementAt R51 the first theme of the suite is recapitulated above a Gl(2) pedal. The Ctonic, which we are predisposed to hear, is generated when this pedal tone becomes theroot of the chord {G 1(2), D3, F3, Bb3, D4} and resolves to the C-rooted chord {C2, A3,C4, E4, C5, G5} in R51+6. R52 recapitulates R4 and generates an F tonic in the samemanner. Unlike that in the opening movement, this F tonic is not followed by a C tonic.The suite ends, instead, on an E tonic which is generated in the same way C was generatedin the first movement.4.3.7 Aspects of Resolution in the Final Tonal AreaThe E tonic ending the suite has a programmatic function. Copland apparentlyintended it as a “different coloration to convey the idea of a dawn breaking over theprairie.”27 It is dramatic because it produces a higher, more triumphant, sound and allowsfor a fuller orchestration of the “open range” material than the original pitch level.2&rhe opening gesture of this melody — <C#7, 86, A6, G#6> — is similarly related to the seminal voice-leading model in Example 4.3.27Copland and Penis, op. cit., p.285.149However, the move to E at the end can also be understood as a culmination ofseveral processes in the suite. On one hand, it is the ultimate formal realization of themodal mixture which characterizes the C tonic in the first movement. Eb is related to Cwhen it delays the resumption of the bitonal texture in the fifth movement; E is related to Cat the end because the recapitulation of the first two tonal areas of the first movement (Cand F) in the sixth movement preconditions us to understand E as a substitution for the Ctonic that we expect. Further, the opposition between pcs Eb and E is underlined at twoimportant points in the suite — R6- I and R27A — by the statement of pc Eb aloneimmediately following passages where pc B has been emphasized: at R6-1 Eb is stated afterpc E is established as the third scale-degree of C in the emphatic last statement of the “openrange” material in the first movement; and at R27A Eb is stated after pc E has beenemphasized as the sixth scale-degree of G.The material at R28 is important because it helps to establish a connection betweenC and E. For example, the emphasis on pcs B and C at R28 (as different representatives ofthe third scale-degree of Ab) is recalled in different ways in the C tonic at R4Off. and in theE tonic at R54÷5ff. At R40 there is an the insistent emphasis upon pc B in the melody ofthe C tonal strand, and at the end of the suite pcs B and C are both included in the finalsonority of E.The opening material of the fifth movement strengthens a connection between C andE because the bitonal setting introduces pc E as a root of two chords (recall Example 4.7b)— a minor-major chord ({G#l, E4, G4, B4} at R40-f-1, R40+2 and R40÷3) and anaugmented triad ({G#l, C4, E4} at R40-i-4) — that foreshadow elements of the final Etonic. For example, the minor-major chord anticipates the modal mixture (two differentthird scale-degrees) that, inherent to the “open range” material, manifests itself at R54 ofthe concluding E tonal area (R53ff). The augmented chord {E, G#, C} anticipates theending sonority of the suite — {E, G#, B, C) — because it contains three of the pcs of that150chord. It might also be understood as a reflection of the modal mixture of the “open range”material of the beginning because it is Ti-related to the previous augmented triad — {Eb, G,B} — that is formed by the outer voices in R27A to R28-2 as a result of the alternationbetween pc Eb and the G-eleventh chord.E and C are also related through an important ascending step-progression in thestrings, <FI6, G1t6, A#6, C7>, that is superimposed over the repetition of an E-majorchord at R54ff. (see Example 4.9a). This links the ending E tonic to the material at R28because the highest note of the B-major chord in the melody, Fit, is the starting pc of theascent. However, the implicit emergence of pc Fit from pc E in R54 parallels the earlieremergence of pe Fit in R28 from a texture that emphatically emphasized pc E. Thissuggests PC E is the ultimate origin of this line. Thus, the step-progression in the strings inR54ff. presents a microcosmic motion between pcs E and C that recalls the macrocosmictonal motion of the suite as a whole.The final two pcs of this line, Bb and C respectively, are also important in the long-term connection of C and E (see Example 4.9b). They provide the voice-leadingresolution, albeit in a different context, of the lowered seventh scale degree (Bb) of C.This resolution was avoided in the first movement of the suite by punctuating the end ofphrases with a chord having the fifth scale-degree (pc G) in the soprano. The use of Bb(Alt) is also, in itself, significant because that pc is a not a member of the established Ereferential collection, and it prepares a C that sounds simultaneously with B. This recallsthe opposition between major and minor modes that characterized the C tonic of the firstmovement.151Example 4.9 Step-Pro ression Linking C and E A Aa) Step-ascent in 54 if. b) Resolution of C: ? E: #4 q6g [C:9 1]___I!127A1 [] +3 +4 +5 -3 -2 +4 -i-S__ _________•Roots: C G C Ec) <G, A, B> Ascent C I E I‘— —‘ ifi—; t,JJ__- m2-3 -2+44 IIThe step progression in R54ff., however, also brings our attention to an importantmotive in the soprano voice of the chords that end the first and last movements of the suite(see Example 4.9c). For example, the most striking thing about the opening C tonic is thesuccessive transformation of the chord ending each phrase, a transformation that results ina shift from pe G to pc A in the soprano. The E-major chord sustained in R54ff., alreadyemphasized by the superimposed step-progression, has the fifth scale-degree (pc B) in thesoprano. The resultant soprano line of these chords, <G, A, B>, restates the ascendingline which has increasingly predominated the motivic structure sinle R27+4ff. Thus, thefinal sonority of E becomes the goal of a larger process that becomes increasingly moreevident following the crucial denial of C at R28.1524.3.8 Minor-Major Third Complexes in the Tonic SuccessionThe tonic succession in the suite also contains an opposition between major andminor thirds. For example, the crucial G tonic at R24 (the “Finale” of the secondmovement), which created the expectation of a return to C, is framed by the tonics Bb andB in R23 and R28 respectively. The implicit contrast between the minor and major thirdsof G, which is suggested by this tonic succession, is strengthened by the initial reference toa G tonic (R22) within a larger Bb tonal area and by sustaining pc G as a pedal when themelody expressing B is stated in R28.The tonic succession in the third, fourth and fifth movements also creates minor-major third complexes but about pcs F and A: the third and fourth movements contain thetonic succession <Ab, F, Ab, A>; and the fifth movement contains the tonic succession<CIC#, A, C/Cs, A>. These complexes might be construed to suggest another relationshipbetween C and E. For example, the succession <Ab, F, Ab, A> is associated with Cbecause the opening tonic (Ab at R29) sounds like C:bVI. However, the succession<C/C#, A, C/C#, A> is associated with both C and E: it occurs in a movement where C is avery important tonic; and the bitonal texture C/Cit is permeated by references to E as achord root. Thus, we might understand the first complex <Ab, F, Ab, A> as orientedtoward C and the second as marking a shift toward E.4.4 Pc Continuity153Figure 4.2 summarizes the pc-scale-degree design of the suite. Most of the changesfrom one tonic to the next are marked by several connecting streams, emphasizing a highdegree of connectivity in the suite. The abundance of common pcs between collectionsassociated with successive tonics compensates for the disruptive sectional nature of themusic that results from the use of many different themes. The motives which link primaryconnective streams are shown in Example 4.10.iiiii ‘ ‘—t.L.. 3 J L 3 ..J L.. 3 _J 1.3 J L.. 3 _J L.. 3 .JExample 4.10 Motives Identified in the Pc-Scale-Degree DesignMl (mm.lff.) (W+5ff.)Al I. I&M3 +2ff.)AI1 HM2 (-3ff.)- I i LJ —=-tt 1’... . -- --‘)+-1-——-——LL • I • I I • II-- ft_. . -. --JJj,.‘‘ II II I!I,LI—j---— .1:):U)r 4 I —— —. .——— r . I —lp1pIv, ,ip1vl4(ff.). I I\ I III .I I.....— EEL_3_J L3..JMS (ff.)Alk________ __________&- ;.;;i Sf is-i ;;;i1544.4.1 Stream GenerationStreams in the suite are sustained over long periods of time, and tend to a greatnumber of tonics. Very often when a tonic returns after being briefly displaced by anothertonic in the suite the same pcs are emphasized throughout. Thus, in the tonic succession<C, F, C> of the first movement a focus is maintained on the pcs G, Bb and C. Similarly,in the tonic succession <Ab, F, Ab> in the third movement a focus is maintained on the pcsF and C. Further, streams in Billy the Kid are particularly obvious in that they are oftencreated by registral connections (i.e., the repetition of particular pitches) or by a commonpc acting as the first pe of a theme which interrupts a previous melody.Registral connections generating a primary stream can be seen in the connection ofthe Bb and G tonics in R23 to R24. The melody at the end of the Bb tonal area emphasizesD5 in the repeated gesture <D5, Bb4>; the melody of the subsequent G tonic places agogicaccents on D5. The F and Ab tonics in R30 to R3 1+2 are similarly connected by the pitchC6, which is prominently sustained in the highest voice.Primary streams are frequently generated in the suite by using an expected(collectional) pc as the first note of a theme that interrupts another theme. For example,when the twelve-measure phrase in Bb is repeated at R2lff. the expected ending gesture,<D5, Bb4., is replaced by the gesture <D4(5,6), C4(5,6)>, which is the opening gestureof a new G tonal area, where pc D assumes a new scale-degree function as the fifth.28Often, as in the fifth movement, this technique of connection results in fairly strikinginterruptions. For example, at R45-2 an A tonic interrupts the concluding phrase of a Ctonic, replacing the expected final measure of a repeated two—measure sub-phrase (themelodic gesture <C5, E4, C4>) with new material. We expect pc E at R45-2 to sound in28The actual phrase before G an-ives is, in fact, twelve measures, but this results from an internalexpansion caused by the repetition of the eighth and ninth measures of the twelve-measure phrase. Thephrase symmetry allows the arrival of G as a tonic to simultaneously sound as a regular interlude, and notsimply as an interruption._,_sA.-‘1-2—5—5—2-U--M2-I2-IIIIA.A.A.A.A.A.A.A.A.-‘--P661-2-1—612-i—4—4—1--P-i-3IUM2-?c2I)3.7_3_3_7.-7F1iIA.A.IsA.A.5b7-P1-b7-5b7-JUII-c______________s-I—-fS-b7—4—4—6—[----Figure4.2Pc-Scale-DegreeDesignofBillytheKid(OrchestralSuite)R:m.iI11121+4131141151161171+4+8I83181+1191+41101Movements:I.“OpenPrairie”(variations)11.1“StreetinaFrontierTown”(rondo)Sections:aala2a3a4a5a6bbl(ant.)c(ant.)bi(cons.)c(cons.)cib2b3(ant.)Rondo:A[AlB!AlB]BA[ATonics:CFCAbFAbFCCWFDbS-b6-b3-A Ab --F-.E--Eb--C--B-Bb-A.A.A.1-52—5-1I1-----•11----A.A.A.A.P-i5—1—S—i—-1-b7a—b--U’Figure4.2(cont.)R:Movements:Sections:Rondo:Tonics:1101+41111-41111112111411151+21161+511711181(‘91-41191(201[11.1]11.2b3(ant.)c2b3(cons.)c3c4d(trans.)efelc5b4g(trans.)h[A/B!A]BBtrans.CDCBAtrans.DbFDAAXbDSS7—4—P-4:6I3,4M3,4-?1-2—5—5—2IUM12Iv2--‘,.,..,%_,-‘_..I1-61-—p2-1—4—4—1——P-i‘3?çI2p3-7—3—3—7—BbA Ab0--F#-F E Eb-C#C--B BbFigure4.2(cont.)IIII__sFSs6—1-P2—1—6-P1-6—1—[UM5-.‘_%,—‘iF7_5-P2-5—I7U-P-b6—3-1-3—5___MP.3R:1201121112211231I24j125A1126A1127A1I281291-313011311-31311+21331Movements:11.2“MexicanDanceandFinaleifi.“CardGameatNight”(ternary)TV.Sections:hhiih2jjij2k(trans.)a71m11nRondo:Tonics:BbGBbGBBXAbAbFFXAbAbAA AbG F#-.F E--Eb-.D C#-.C-.B Bb-..-‘,,__‘_--P.6—1—1—66-S-6—UP-b7—5—I.‘_%.,\-,.5—5——33— L-H -I -J---&1-S-----S-55Figure4.2(cont.)R:13311351+2+81361÷71371+51381-41381+213940114111421143114411451-21461+41471Movements:IV.“GunBattle”(variations)V.“Celebration”(rondo)Sections:nnin2n3n4nSn6n7n8oolpqo2rp1o3o4Rondo:AABCADBAATonics:ACACAEbCC#C#C#A AbF#-F Eb-1]-Ss-----I-4H[1,ri[1--I ‘-S.C- --JB Bb--S 7,I-----2-5-i-52--2-2——3-I•-I-I--Mi--Mi-—I—_.‘-‘-‘_%EEz;-E-EZ-i-4-1_5—--S-S----L:I 6—i---M1-b7_4LS4Figure4.2(cont.)R:1481+4149115011511152115311541+5Movements:(V.)VI.“Billy’sDemise”(variations)Sections:(o4)ssiaaSa8Rondo:(A)EETonics:CGCFEC#A AbG F#-F--E--Lb-D C#-C--B-Bb—LIb2160the context of C because of the preconditioning of the lop voice of the accompanimentalpattern in R44+2ff. — the alternation of F4 and E4 in this voice predicts the arrival of pc Eat R45-2. However, pc E begins an accompanimental pattern in A.Other important methods that generate primary streams of connection includeconnection by a common soprano note in chords that are successive over the point of tonalchange, the continuation of an accompanimental motive from one tonal area to the next atthe same pitch, the use of a characteristic recurrent dyad, and incessant reiteration of a pc asa dissonance.Connection by a common soprano pc is best shown in the single primaryconnective stream at R14. Pc F, the soprano pc of the Db-major chord ending the Db tonalarea, is the soprano pc of the first chord of the F tonal area (F:”IV”).Connection by the continuation of an accompanimental motive is best demonstratedin two motivically analogous areas, R8+l to R9+7 and R18 to R19-4. Theaccompanimental patterns <F3, E4, G4> and <D4, C#5, E5> respectively are continued asostinatos in the lowest voice while a new theme, generating a tonic a fifth away, issuperimposed. This forces the listener to focus on the changing meaning of the pcs in therepeated accompanimental pattern.Generating a pc stream by the use of chords which feature a recurrent dyad isparticularly important at the end of the suite. For example, primary streams are created onthe pcs C and Cit at R44 to R46+4 because of the emphasis on chords that contain boththese pcs in the C/Cit and the A tonal areas.29 The chords on the downbeats of R44-i-3 andR44+5 in the C/Cit bitonal texture — the A minor-major chord, and the C-major triad aboveC# in the bass respectively — contain pcs C and Cit in a prominent (outer voice) position.2hc Eb tonic, while generating a primary and secondary stream of connection on its own, is parentheticalto the streams connecting the C/C# and A tonal areas. The streams connecting Eb only temporarilysuspend the continuation of a primary connective stream on pc C#.161The placement of these chords on the downbeat of every other measure establishes a patternthat is continued at R45-2 when the first chord of the A tonal area also prominently containspcs C# and C. Pcs C and C# are made particularly conspicuous in R45-2ff., however,because they appear in the bass within a one-measure ostinato that alternates the dyads{C2, C#4} and {C#2, C4} on beats 1 and 3 respectively. The next CIC# area (R46+4)first emphasizes C# and C by re-articulating a C-major triad above the C# bass line, butlater repeats a closing melodic figure (R47+5ff.) such that a chord containing C# in thebass and C in the soprano appears on the downbeat of every other measure.The recurrent dyad {G, D) is particularly important at the end of the suite. Startingas a simple continuation of the primary stream on D at the end of the G tonic in R51-3, {G,D} is emphasized because pc D is given a special timbre — it is played by the harp.3° TheG pedal in the bass which connects the G tonic to the following C tonic resolves to a C-rooted sonority only after pc D is sounded as the soprano pitch (R51+5). {G, D}reappears a measure later as the expected ending gesture of the phrase in the highwoodwinds. The {G, D} fifth recurs between the highest voices in the first three measuresof the F tonal area (R52ff.). (Because this involves all three pcs of the woodwind gestureending the C tonal area — pcs D, G and C — Figure 4.2 shows that an additional primarystream on pc C is related to the streams on D and G that connect the C and F tonics.) Thisconnection is reinforced because the C tonal area does not end with the dramatic Bb-rootedchord of R4-4, which connected the C and F tonics earlier in R3 to R5. The climax of thisset of pc streams occurs when the fifth {G, D} becomes the highest two voices of the firstsonority of the E tonal area (R53). The final transformation of the {G, D} fifth issatisfying, in part, because we hear pe D as the strongest pc connector between the F and Etonics. This focus on D realizes a change in function of that pc that is projected in the30Thc stream on pc D was originally generated by a similar kind of prominence at the end of the first andthird measures of four-measure phrases, a prominence which was emphasized by stating D over harmoniesin which it was not consonant (i.e., D is stated above the subdominant in R49+2, and sustained above Dbmajor, B-major, and A-major triads in R49+4 to R49+5).162opening movement of the suite. For example, pc D originally appears as the highest noteof the woodwind motive that ends section al and a3, and then becomes the root of aD-major triad superimposed upon a C-ninth chord at the end of next section (a4).4.4.2 Pc-Scale-Degree DesignThe music projects characteristic ways in which prominent pcs change scale-degreefunction when the tonics change. These characteristic changes are repeated, even when thepc materials and tonics are different, and different movements characterized by similarchanges in scale-degree function sound similar on this account.Table 4.2 demonstrates how the pc-scale-degree design in Figure 4.2 reflects theAAinteraction of two important abstract groupings of pc streams of continuity — {<5,2>.,A A AA AA AA AA AA A A AA<b3.b7>. <1,5>, <b7,4>, <1,4>} and {<b3,5>, <1,3>, <5,b7>, <6,1>} — by chartingthe timepoints at which these streams are initiated on particular pcs. Many of the streamslisted in this table involve only primary streams. These are indicated by a box around therespective pcs. Table 4.2 treats streams that contain different representatives of the samescale-degrees as the same. That is, the table ignores the relatively superficial differencesAA A Abetween, for example, the stream <1,3> and the stream <1,b3>. Streams have been listedin Table 4.2 by the first form in which they appear in the pc-scale-degree design of thesuite. Table 4.2 includes retrogrades of streams, which are indicated by brackets, becausethese occur at almost every significant repetition of a part of each group in Figure 4.2. ForAA Aexample, the stream on pc G which is initiated in m. 1 — <5.2,5> (the first stream of GroupAA AA1)— contains both <5,2> and its retrograde <2,5>. Similarly, the stream on pc F which isAAAAAAA’ AAinitiated at R6 — <6,1.1,6,1,1,4,4 1...> — contains both <6,1> (the fourth stream ofAAGroup 2) and its retrograde <1,6> and <1,4> (the fifth stream of Group I) and itsAAretrograde <4,1>. However, Table 4.2 lists retrogrades only when they illustrate a contrastbetween successive combinations of streams or show a formal parallel between differentparts of the pc-scale-degree design. Thus, Table 4.2 shows the retrogrades of the streamsCl(IC4-CC(4163C.’CDt’)CoiC)_Th91165<> and 4.1> at R31-3 because they coincide with the statement of third retrogradedAt’stream from Group 2 (the stream <b7,f,> on pc Eb) which was absent at R29-3. Similarly,At’ A A AATable 4.2 shows the retrogrades of the streams <h3,5>, <5,b7>., and <6,1> at R7+4 andR22 because this shows that the pc-scale-degree design takes on a similar form at thebeginnings of the two halves of the second movement (“Street in a Frontier Town” and“Mexican Dance and Finale”). Retrogrades are particularly significant for the perception ofGroup 2.The two groups of streams shown in Table 4.2 are derived from the repetitions ofstreams in Figure 4.2. Group 1 is relatively easy to derive from Figure 4.2 because all fiveAt’ A A AA At’ At’streams —<5,2>, <b3.b7>, <1.5>, <h7,4> and <4.1>— are initiated at R9+4: we hear pcsA AA A A AG, E. C. Bb and F change scale-degree functions respectively from 5, b3, 1, b7 and 4 to 2,b& . and 1. Group 2, however, is more obscure than Group 1. It is the sum of thestreams that are initiated at R20 and R28 respectively. That is, at R2Off. the first, third andfourth streams of Group 2 occur when we hear pcs D, F and G change scale-degreeAA t’ A A t’functions respectively from 3. 5 and 6 to5, b7 and 1 at R28ff. the first, second and thirdstreams of Group 2 occur when we hear pcs Eb, B and F# change scale-degree functionsA A A A A Arespectively from 3, 1 and 5 to5, b3 and b7. Group 2 is similarly suggested by thenumerous simultaneous statements of three of its constituent streams. For example, asdiscussed above, the retrogrades of the first, third and fourth streams of Group 2 are statedin streams that are initiated at R3 1-3. Similarly, the second, third and fourth streams ofGroup 2 are present in streams that are initiated at R40 and R42 (in the tonic succession<CIC#, A>). That is, we hear pcs C#., C, G and A change scale-degree functionsAt’ t’ A A A A Arespectively from [1/1, 1/[ I, 5![ I and 6/I I to 3, 3, 7 and 1. I Group 2 is more elusivethan Group I because we never hear a simultaneous statement of its four streams.31The square brackets signify that a given pc has a scale-degree function in only one part of a bitonaltexture.166The purpose of Table 4.2 is to show the interaction of streams from Groups I and2. These groups of streams are clearly distinguished by behavior. Those of Group I arelargely static. Most of the repetitions of streams from this group result from either thetransposition or literal recapitulation of thematic material. For example, the streamsinitiated at RI 9-4 are T9 of those initiated at R9+4 because both involve the material ofsection b. More importantly, however, the streams initiated at R51, which could beconsidered as a support for the cyclic form, result simply from the literal recapitulation (T0)of the thematic material that generated the streams at m.l. In Table 4.2 these thematicrecapitulations are marked by curved lines labeled asT9 and TO respectively that connectcircled rehearsal numbers.However, repetitions of Group 1 streams are not entirely constrained to thematicrecapitulations. For example, the first two statements of streams from this group, at m. Iand R9+4 respectively, do not result from passages with obviously related thematicAA AAmaterials. These statements have four streams in common — the streams <5,2>, <1,5>,A A AA<b3,b7> and <b7,4>. However, even this relatively striking correspondence possesses astatic aspect because the streams at m. I and R9+4 result from the same tonic succession —<C, F>. Thus, three of the four common streams occur on the same pcs. That is, in bothpassages we hear the pcs G, C and Bb change scale-degree functions respectively from 5,A A A A A A A1 and h7 to 2, 5 and 4. Only the fourth common stream — <h3,h7> — occurs on twoA Adifferent pcs: at m. 1 Pc Eb changes scale-degree function from b3 to b7; at R9+4 pc EA Achanges scale-degree function from 3 to7.In contrast to the mostly static repetition of streams from Group 1, however, therepetition of streams from Group 2 is much more flexible and dynamic. The pc-scaledegree design in Figure 4.2 employs many different combinations of its constituentstreams. Sometimes, like at RIO, it is fairly difficult to infer the presence of streams fromAAGroup 2 because only one of its streams — <1,3> on pc F — is present. What is revealed by167Table 4.2, however, is the consistency between the pc-scale-degree designs within the twohalves of the second movement and between the second and third movements. Forexample, at the beginning of the first part of the second movement (R6) we hear theAA A A A Adifferent pcs F, Eb and C change respectively from 6,5 and 3 to 1, b7 and 5 and then revertto their former functions. The initial change is then repeated. When the second half of thismovement begins (R20) we hear an almost identical pc continuity structure but the changesfrom 6, 5 and to 1, 7 and now occur on the pcs G, F and D respectively. The streamsAA A A<3,5> and <5,b7> are then repeated at R28 as part of a group of three streams thatarticulate the third movement. Thus, at R28ff. we hear pcs Eb and F# change scale-degreeA A A A AAfunction respectively from 3 and 5 to Sand hi. The stream <6,1> is replaced by the streamA A<1,h3> that occurs on pc B. The repetition of these groupings at the beginning of 11.1 andover most of [1.2 respectively unifies the two disparate halves of the second movement.The specific grouping of streams which occurred at R20 then becomes the focus of theAAthird movement. However, the second stream of this particular group — <5,b7> — enterslate and, therefore, appears oniy in its retrograde form. Thus, at R29-3ff. we hear the pcsA A A AF and C change scale-degree functions from 6 and 3 respectively to 1 and 5. The streamAA<b7,5> on pc Eb enters (R31-3) when these changes are reversed.The ending streams on pcs G and C, however, contain retrogrades of two of theAA AAfour streams from Group 2—the streams <b3,5> and <1,6>. We hear these streams fromGroup 2 because of preconditioning, that is, when E is substituted at R53 for the C tonic,which is forecasted by the large-scale recapitulation, the change of scale-degree function inthese connective pcs between R5lff. (when C is the tonic) and R53ff. (when B is the tonic)is emphasized.32 Thus we hear a broader change in the respective scale-degree functionsA A A Aof pcs G and D from 5 and 1 (at R51) to 3 and 6 (at R53). The accentuation of streamsfrom Group 2 within streams from Group I at R5lff. suggests that the final E tonic32This process is unique to this context. Without the substantial preconditioning of this context we wouldnot hear the streams included for Group 2 at RS1 in Table 4.2.168synthesizes the two groups of streams into a single whole and, thereby, provides asatisfactory conclusion.Table 4.2 also indicates a form for the suite that confirms the thematic form that wasshown in Figure 4.1. The pc-scale-degree design focuses first on streams from Group 1.In the second movement it contrasts these streams by using them in a quasi-rondo structurethat is initiated by the streams from Group 2. Group 2 streams then become the sole focusof the third movement, but are contrasted by new streams when the fourth movement isAAarticulated. With the exception of the stream <2,7>, most of these other streams are notincluded in Table 4.2 because they are of relatively little importance in terms of streamrepetition over the suite. However, they are apparent in Figure 4.2. Streams from Group2 retain their importance in the fifth movement. However, streams from the first groupAAstart to reappear. This is first suggested by the return of the stream <b7,4> in a modifiedAAretrograde form (<4,7>) on pc D in R45-2. Streams from the first group then appear toregain priority toward the end of this movement (R4.8-i-4ff.), and are used to articulate thefinal movement of the suite. Far from being eliminated, however, the streams from Group2 are actually synthesized into streams whose orientation seems to be toward Group 1. Thesynthesis of streams from groups 1 and 2 joins the most static streams in the pc-scale-degree design — the streams of Group 1 with the most dynamic streams — the streams ofGroup 2. This synthesis is supported by the only stream shown in Table 4.2 — the streamAA<2,7> — that does not belong to either groups 1 or 2. (Table 4.2 identifies this stream bythe label “Other”.) This stream, which occurs on pc B at R35+2 and at R43, is also heardat R5 1ff. in the stream on pc D for the same reason (preconditioning that makes us expect aC tonic at R53) as the streams from Group 2. Thus, at R5lff. we hear a broader change inthe scale-degree function of pc D from (R5 1) to (R53). In this way the ending alsosynthesizes a significant stream that is introduced in the fourth movement when onlystreams from Group 2 are present.1694.4.3 Aspects of Resolution in the Pc-Scale-Degree DesignThe pc-scale-degree design suggests a reason why pcs D and G are the last primarystreams to be heard in the suite. Looking at the long-term pc streams in the suite, weobserve a kind of bipartite form articulated at R27A. This two-part division is caused by alarge-scale repetition of successive pc streams <Eb, F, D, D+G>. Figure 4.3, whichisolates the most important stream lines of Figure 4.2, shows this repeated pattern. Theprimary stream shifts from an initial 0 to Eb in R5, which is paired with, and eventuallyfollowed by, a longer primary stream on pc F. A secondary stream on pc C is also present.The stream on pc F overlaps with a stream on pc D in R14; the stream on D is subsequentlypaired with a stream on pc G (R19-4). The broader movement between the focal pcs ateach end of this series in the first half— Eb (R5ff.) and D+G (Rl9ff.) — is emphasized byrepeating the Group 2 streams of R6ff. (on pcs F, Eb and C) at R2Off. (on pcs G, F andD). Continuity between the focal pcs F and D is suggested by the repetition of the Group 1streams of R8+ 1ff. (when F is the long-term focal pc) at Rl7ff. (when D is the long-termfocal pc).The sequence of pc streams repeats starting at R27A, where a stream on pc Eb isintroduced. At R29-3 this stream is again paired with, and followed by, a stream on pc F.The stream on pc F is again paired with a stream on pc C. The relationship to the openingAA AApart is made explicit at R29-3 by the recapitulation of the same streams <6,1>, <b7,5> andAA<3,5> which occurred on pcs F, Eb and C respectively at R6ff. Each of these two groupsis prefaced by a dramatic statement of pc Eb. The parallelism between mm. 1ff. andR27Aff. leads us to expect a focus upon pc D and its eventual pairing with pc G.However, they do not appear at R35. Rather they are delayed until just before the end ofIIIIPsPsfP.PsP.AI•--P4---6-1-6-1—2-1-6-1-6—1A:U-F1---1,M5-I,M5-I,1M5-M15IIIIr,IAP.P.AP.P.PsAP.AAAP.Iip.11I-‘PsAAlAA-P&-l-?2-l—6——l-rP14—P-l-3l-2-1-j3[J----P2547-1-h7-5-T’2-547L_JIU...:U----I-IF-43,4--M3,4--1r—liiiP.AAAp5—b7-P1-b7—5——b7--[LIAAP.Ii,..AAp.P’.P.—6—1—P21-4—4—1Ph—3—5—S-5—3—P-3—5-l-._____j•Figure4.3SummaryoftheMostImportantFocalPcsinFigure4.2R:m.114151I6171+4+8I81-3191‘110111411171I18!11911201122112311241Movements:I.11.111.2Sections:aa5a6bcbicb2b3dc5b4gihih2j(ant.)(cons.)_(cons.)(ant.)_(trans.)Tonics:CFCAbFAbFCDbFDABbGBbGA AbG F# F E Eb D C#C B BbPb—P.AAA-P-i—5—1—S—i—Ii)_sI.—5—-jIII_‘_‘326•--Figure4.3(cont.)R:127A11281291-313011311-31311+2:rMovements:(11.2)ffl.IVSections:ka71m(11)nTonics:(G)BBXAbAbFFXAbAbA484149151I15211531(V.)VI.(o4)saaSa8£0CFEC#A Ab0 F# F E EbD C#C B Bb,\—‘,,_d\P-6—1—1—6—6-S-6U—5f---.P-b7—5——5--“‘s,c%---P.3-5—5—3—3—L,‘P-b6—3-P1-3—5—P.3—i—i—b3Iii)r‘1—1- LI2,\-p5-2-5-b2-J172the suite — R49.33 Pc D, appearing as the ending primary stream in the suite, is paired withpc G in R50. This is a satisfactory close not only because of the repetition of the largescale pattern <Eb, F, D, D+G>., but also because we end on the same pc that was the focusof the opening.4.4.4 The Importance of Major and Minor ThirdsThe pc continuity structure supports the cyclic form of the suite independently ofthe thematic design because it ends with the same focus it begins on. But it also suggeststhat we hear the suite as divided into two large parts at R27A. These parts can be heard asexpressing a metaphor for an opposition between Eb and E as the third of C because pc Ebsounds like the goal of the first half and an E tonic is the goal of the second half. Theopposition between these two pcs as different representatives of the third scale-degree in Cis crystallized at the end of the first movement where a cadence in C major is negated by aheld Eb. On the other hand, this movement from a minor third to a major third could beconstrued as a metaphor for the intervals in the “open range” theme. For example, in thefirst six pcs of this theme Bb is first involved in a minor third (<G, Bb>) and then in amajor third (.<Bb, D>). The implied succession from minor to major thirds in this themeprovides a metaphor on a microcosmic level for the large-scale chromatic oppositionbetween pcs Eb and E in the C tonic which governs most of the suite. The pc relationshipsin the “open range” theme also account for the static repetition of the streams in Group 1 atR19-4, which results from a transposition of the thematic material of R6 down a minor33This suggests a disjunction in the form of the suite that emphasizes the contrasting nature of the fourthand fifth movements already established by their unique tonal structures (i.e., the fourth movement is theonly movement to employ long-term tonal ambiguity, while the fifth movement is the only movementwhich divides the texture into two separate tonal strands). However, the underlying similarity between thetwo parts of the bipartite form suggested by successive focal pcs is emphasized by using a single primarystream to connect successive tonics only at R6and R33 respectively. That is, at R6 the C and Ab tonicsare connected by a single primay s ream — <b3,5> on pe Eb; and at R33 the Ab and A tonics are connectedby a single primary stream — 3, 3> on pc A. The parallel is reinforced by other similar features of thesestreams. For example, both streams arc generated by sustaining a pc when the tonic changes, and bothbegin on a representative of the third scale-degree.173third, because it is followed in the third and fourth movements by an implied T4 of twostreams of Group 2 — <3,5> and <6,1> — from pcs C and F respectively to pcs E and A.34This implied T4 prepares the crucial large-scale substitution at R53 when E, substituted inplace of C, is the tonic.The ultimate superiority of the major third in a cadence is implied by the way pc Ebis heard as the third scale-degree at the beginning of each respective half. For example, atR6 pe Eb is striking because it is the lowered third scale-degree, emphasized by thecompletion of the ascending motive in the brass (i.e., <C3, G3, Eb4>), within material thathas already cadenced on the major third. However, when pc Eb is sounded by itself atR27A, the initial correspondence of Eb with the minor mode of G, which similarly followsa passage firmly rooted in the major mode, is displaced when Eb becomes the third scale-degree of B. This alludes to the final choice of the major third at the end of the suite. Thischoice is dramatically confirmed in the last few measures of the suite when the brassmotive, which similarly concluded the first part, is restated (R54ff.) but now has the thirdscale-degree of E-major as its final note (i.e., <E4, B4, G#5> in the third trumpet).4.5 SummaryWe can summarize the material of the above analysis on the orchestral suite of Billythe Kid and answer the foremost question of this thesis: what function do Copland’s tonicsserve — how do these tonics and their successions relate to form. On the most basic level,tonal shifts in Billy the Kid occur at the beginnings of all of the movements and many ofthe sections in the form shown in Figure 4.1. Contrasts in thematic material, thus, areusually supported by contrasts in tonics. In some cases, such as the third movement and,to a lesser degree, the fifth movement, the tonic succession seems to conform closely toclassical tonal designs. That is, the ternary form of the third movement is reflected in an34This transposition is partially obscured, however, because pcs E and A present the retrogrades of thesestreams(<5,3> and <1,b7>).174Ab-F-Ab tonal design; the rondo form of the fifth movement is reflected by a tonal designwhere the “A” segment remains in its original key (C/C#) and all other segments, with thesingle exception of the first “B” segment, have different tonics. The strikingly differentthematic structure of “Gun Battle” is complemented by the fact that it is the only movementin the suite that has a single tonic.The tonic successions in the suite, in themselves, do not seem to support a C globaltonic by prolongation. Rather, Copland reminds us of C by more abstract means — hecreates thematic materials in the successive tonal areas which continually refer to the step-progression that is shown in Example 4.3. Ultimately, Copland uses this seminal step-progression to link the ending E tonic to the C tonic that guides most of the suite (as shownin Example 4.9). Tonic successions within movements, however, might also be construedto be important with regard to the connection between C and E. This is suggested in thethird to fifth movements by the association of the successive minor-major third complexesabout F and A respectively with pcs C and E.The tonic successions in the suite articulate a separate structure of pc streams, thepc-scale-degree design, that traces changes in the scale-degree functions of emphasizedpcs. This pc-scale-degree design contains valuable information. It confirms certain aspectsof the thematic design. For example, it offers a compelling reason for us to understand R6to R29-3 as a single unified movement. The two apparently distinct parts participate in anongoing quasi-rondo form, begun in the first half and mimicking its thematic design, thatresults from repetitions of streams from groups I and 2. The pc-scale-degree design alsosuggests a unity of expression in the suite because repetitions of streams from Group 2occur in all six movements. Most importantly, however, the pc-scale-degree design offersus three separate reasons to understand the ending E tonic as a satisfactory conclusion, andnot simply as an arbitrary programmatic device. At the simplest level E is satisfactory as aconclusion because its collection allows a continuation of the focus on pcs D and G that is175begun at R50. These pcs mark the end of a repetition of the <Eb, F, D, D+G> successionof focal pcs that is started at R27A. However, E is also satisfactory as a conclusion formore significant reasons. For example, the transpositional levels among repetitions ofstreams from the two groups suggests, like the minor-major third complexes betweensuccessive tonics, a succession of minor and major thirds that has E as its goal. Thissuccession, which probably represents the first intervals of the “open range” theme itself, isconfirmed motivically by the triumphant brass motives that conclude the first and last partsof the suite. The E tonic also generates the simultaneous recapitulation and, therefore, asynthesis of the two groups of streams around which the entire pc-scale-degree designrevolves.176Chapter 5Short Symphony, First Movement5.1 IntroductionIn the previous chapter we saw a pc-scale-degree design that offered severalimportant ways in which to hear the final E tonic of Billy the Kid as resolutive and notsimply as a programmatic device, and to hear the suite as a unified whole. In the presentchapter we will analyze the first movement of one of Copland’s most “serious” pieces — theShort Symphony. In this movement pc connectors are particularly emphasized. This isperhaps due to the nearly complete lack of chord progressions on the surface of the musicin this movement. We shall find that the pc-scale-degree design of this movementincorporates one of the features of the pc-scale-degree design of Quiet City — a palindromicstructure — in a much more central way. The palindromic structure in the Short Symphony,like that in Quiet City, is permeated by references to another (concurrent) pattern.However, in the Short Symphony this second pattern is a large-scale alternation betweenfocal pcs. These focal pcs are emphasized on the surface of this movement in a way thatparallels the emphasis of the fifth scale-degree on the surface of Quiet City. The pc-scale-degree design of the Short Symphony also incorporates one feature of that of BilIy the Kid— the order of focal pcs — to make apparent the relationship between Large (thematicallyrelated) sections.5.2 FormThe form of the first movement of the Short Symphony is best represented by atripartite A-B-Al scheme. Figure 5.1 gives an analysis of the form, showing formaldivisions at the top, motivic content in the middle, and local tonics at the bottom. The twomajor sectional divisions of the form are at R8 and RI 2. Parts A and Al have similarFigure5.1MotivicandTonalSummaryoftheFirstMovementoftheShortSymphonyR:18111+2121+1+4131+6141151-2161171-3181-4-2181191-4Parts:ABSections:aala2bSubsections:abala2ca3bia4ddl(trans.)eelMotives:1,211[1]1,213,l,[lJa332,3Tonics:1)GABbKkBdir.B!?BbXGdir.0EII0R:19[i-2I1O4liol+3liii11211131-411311141+1/2+31151-311511161-4Parts:(B)AlSections:(b)a3a4aSbiSubsections:e2e3aSffla6g(trans.):a7a8d2(trans.)e4hMotives:2,32,31[2],[3][2],[3]1,2211332,3[1]Tonics:C#AC#EGBbCAbAb/CDDIGGC#R:11611171-31171+4Parts:(Al)Sections:a6Subsections:da9alOallMotives:3,[1]111Tonics:Bdir.B/DGCTable5.1SummaryofTn-RelatedPassagesSectionsSubsectionsa2T7aa2T5a1(bass)aST2a4dlT4drn-21[T8d]178internal structures insofar as both present variations of section a. However, the structure ofpart Al differs from that of part A because it interpolates an additional section, which doesnot vary the material of section a, between the last two variations.Sections a 1 and aS subdivide into two variants of subsection a followed by acontrasting subsection. Part B differs from parts A and Al in that it divides into only twosections, b and a3 respectively, each of which varies new material, that is, subsections eand f respectively.5.2.1 Motivic AnalysisA motivic analysis is included in Figure 5.1 because it provides ajustification forthe tonics in the summary. It recognizes three motives within the first movement. Thesemotives, which will be labeled 1, 2 and 3, are reproduced in their original forms inExample 5.1. Motives 1 and 2 are initially perceived as overlapping members of a single,unified phrase member. As the movement progresses, however, they become moredistinct; first, motive I is heard without motive 2 (R 1+1), then motive 2 is heard withoutmotive I (R8).1‘The dyads in R8 are nearly identical to those which result from the mcifications to motive 2 in R3+3,that is, the succession <{B2, E4}, {C#3, D4}, {A3, A3>, {B3, E5},{C#4, D5}> in R3+3 to R3+4 issimilar to the succession <{B3, E5}, {C#4, D5, {A3, F#5, {C#4, D5).> in R% to R8-i-1. The onlysubstantive difference between motive 2 in R3+3 and in R8 is the new rhythmic profile of the latter, whichis borrowed from motive 3.Example 5.1 Summary of Motives in the First Movement of the Short SymphonyMotive 1 (mm. 1-2) Motive 2 (m.2)jii179In Figure 5.1 special symbols indicate how these motives are combined. A commabetween motive labels, as in “1,2”, means two motives are active within a section. Squarebrackets around a motive label, as in “[21”, mean a recognizable fragment of the motive isembedded in the texture. One motive label listed above another, as in”!”, means two2motives are simultaneously active but one appears in the high register while the otherappears in the low register.The motivic analysis of the movement reveals another way in which part B differsfrom the framing parts: part B incorporates some kind of interaction between motives 2 and3 in all but one of its subsections, while parts A and Al feature an interaction betweenmotives I and 2 or motives 3 and 1. Copland subjects all three motives to ongoingvariation, which often emphasizes the relationship between tonality and form. The locationof special variants of motive 1, in particular, will be seen below to provide importantindicators of tonal direction.The motivic analysis suggests an important reason why this movement should beconsidered as a ternary form and not a sonata form as Quincy Hilliard suggests.2 Thedistinction between the two schemes rests on whether the so-called “second theme” isrecapitulated. Hilliard identifies the second theme as the material starting at R9-4. But atthe location he identifies as the recapitulation of the second theme (RI 5), we do not hear arecapitulation of R9-4ff., but of R8, the introduction to that theme. The R9-4 theme itselfnever reappears.Even though the materiaL at R8 is recapitulated, there are important motivic reasonsnot to consider it as the second theme. Motivic contrast to the A section material isprovided not by R8, but by R9-4, which presents motive 2, stated within an inner line,2Quincy Hilliard, “A Theoretical Analysis of the Symphonies of Aaron Copland” (Ph.D. dissertation,University of Florida, 1984, pp.100-101. Julia Smith also considers this movement as a sonata form inAaron C’opland: His Work and coniribution to American Music (New York: E. P. Dutton and Company,Inc., 1955), p.151.180simultaneously with motive 3, which is embedded in the counterpoint between bass andsoprano. The embedding of motive 3 is shown in Example 5.2 by brackets: arrowsconnect brackets in R6 to R7-2 to their counterparts in R9-3 to R9+2. Further, the motiviccontent defines the material at R8 and R15 as transitional. Example 53 shows that a seriesof T2 transpositions begins at R5-2. At R8 the restatement of motive 3 at its original pitchlevel (i.e., a <D, E> motion in the soprano above a <G, A> root movement as in R5-1)terminates this cycle of transpositions. At R15 the soprano moves similarly from pc D topc E and a specific variant of motive 1 foreshadows the arrival of the original tonic ofmotive 3. Because this variant is consistently linked in each of its three appearances to aprocess of transition in which the next tonic gradually emerges, it will be addressed underthe section “Motivic Correspondences” (see below, p.l95).Example 5.2 Embedding of Motive 3 in [J-3 toa) Motive 3 in [] to [] -2 (upper tonal strand)rr- -(7zJw.I. IJ I ( 14cy— liii I‘I’ 14ar, —..4 ._J 7w’a14 ,.‘,c,Ab) Motive 3 Embedded in-#.I1r1_ II I,•I Ir,,I.—-— -I II—.—1LIJi- I -.LI. — Iii I[I “—Tt’T8‘r r•1 I,..a.—-P--_h --I -.. I.,I I I - - ifJ7 J ij i r •—I. II,ifL IILø 0_j.’” Tr-t--.I I I181Example 5.3 Transpositions of Motive 3 in -2 toa) Parallel Triads b) Octave Ascent By Whole-ToneThe most compelling reason to adopt a ternary interpretation of the form, however,is the tonal structure of the movement. The tonal character of sonata form — that the secondtheme is recapitulated in a different key (eventually the main key of the movement)— is notapparent here because R15 simply restates material from R8 at the same pitch level.53 TonalityThe following discussion gives a detailed reading of the tonality in each part.Special techniques will be noted. Several of the tonics are clouded by ambiguity; however,unlike the other works studied in this thesis, this ambiguity most often results from thepreparation of the next tonic.5.3.1 Part AThe movement begins with a tonal ambiguity between D and G. The openingmelodic motive, partitioned into a D-rooted seventh chord anacrusis and an agogicallyaccented G4, weakly asserts a G tonic. However, this interpretation is contradicted by theharmonization of pc G as a dissonant minor ninth above the bass note of a D-major six-three chord.3 In the measure before Ri PC G is eliminated, leaving the D-rooted harmony.3Hiniard asserts that this verticality should be considered as a polyharmony of tonic over dominant becausehe wishes to prove that a G tonic is present. Hilliard, op. cit., p.107. The lack of a fifth above G4,however, makes it unreasonable to hear 0 as a root, let alone a root of equal strength to D. We wouldperceive a G root above a D root in the manner asserted by Hilliard only if the sonority of mm.2 and 7182At the end of the section an ascending line from G3 terminates on an accented D5 in R1+1,which subsequently becomes the root of a major third. This directed motion furtherconfirms D as tonic. So the <Ft, D, F, C> anacrustic motive of m. I takes on, at leastretrospectively, a tonic function. In R2+ I we do hear G briefly tonicized, but it is mainlydue to the transposition of the initial <D, F, C> motive, which we are predisposed to hearas asserting D, toG. The G-rooted harmony in R2+1, like the D-rooted harmony in m.2,is also clouded by a dissonant pc — Ab. However, Ab contradicts the G tonic not by animplied dominant-tonic progression of a different tonic but by introducing a large variety ofpossible chord factor interpretations of the pcs in the transposed bass motive that do notsupport the expression of a G tonic. These include making pc F sound as the root of aminor triad, and pc B as the third of an Ab-rooted harmony.In R2+4ff. PC A is generated as a tonic by the repetition of the A-rooted verticality{C#2(3), A3, D4, A4, E5} such that the pitches of the inherent A-major triad are elaboratedby neighbor-tone motion — <C#2, D2, C#2> in the bass in R2+5, <E5, F5, E5> in thesoprano and <A3, G#2, A3>, <A3, A#3, A3> in the inner voices in R3-3. This A tonicremains in effect until R4. At R3 the material of mm.lff. is transposed up a fifth,reinforcing the A tonic. However, the conflict between A and D, which we expect becauseof the conflict between the D-major six-three chord and pc G in the original passage, ismanifested in a different way in R3ff. than in mm.lff. D as tonic is suggested at R3+1 bythe return of the minor ninth {F#3, G4} familiar from mm.2 and 7, and by the samemelodic gesture in R3+3 that suggested G in the first two measures of the movement.Unlike m.2, however, no chord harmonizes the D at R3+3; pe D is not heard clearly as adissonance until the next measure when it sounds as a seventh above pc E, and it resolvesin the normative manner to pc C# (Db). D is also suggested as a tonic in R3ff. when theincluded all the pcs of the 0-major and D-major triads in a registrally discrete ordering (i.e., {F#2, D3, A3,G4, B4, D5}) or if it included a significant doubling of the interval of a fifth above 04 (i.e., {F#2, D3, A3,04, D5, 05, D6}). Copland uses a similar sonority, {D3, G3, A3, D4, A4, D5, F#5, A5}, at R6 of “Hoedown” in Rodeo. However, despite the timbral emphasis there Ofl PC 0, which results from stating it in thetrombones, this sonority also sounds like it has a single root, pc D.183material of RI-i to Ri, including the crucial directed motion line, is recapitulated at thesame pitch level in R4-2 to R4-l. These references to D, however, are not sufficient todisplace the A tonic of R2+4ff. for several reasons. The A-rooted sonority emphasized inR2+4ff. does not resolve to a strong D-rooted sonority after R3. To the contrary, the onlyD-rooted sonority around R3, {F#3(4), G4, A4, D5, A5, E5} in R3— 1, resolves to the A-rooted harmony in R3 as in a plagal cadence (see Example 5.4). Further, in R3+l therestatement of the minor ninth {F#, G}, which implies a return to a D tonic, occursbetween two A-rooted harmonies, suggesting again a plagal extension of an A tonic. Thefinal statement of the {F#, G} minor ninth (R3+6 to R4-2) is also framed by two A-rootedharmonies (R3+5 and R5- 1 respectively). However, the plagal extension here is moreobscure because the resolution to A (R5- 1) is interrupted by the interpolation of a Bb tonicat R4, and because the root of the minor ninth shifts from D (R3-l and R3+l) toG (R5-2ff.).Example 5.4 Minor Ninth (F#, G} as “Plagal Extension of A-rooted Harmonies in []-1ff.±N[Interruption]yi “; E—-1 ] +1 +2 +3 +4 +6 -2 +3 [.i -2,-•• .. — —#. S. III h.IA: IV I “1V’ I “IV? [Bb Tonic] Vll I“Vll?”Bb is melodically generated as a tonic in R4 by the appearance of a transposedvariant of motive I (T8 of Rl÷ 1ff.) above a pedal Bb3. It is supported as a tonic by thecollection {Bb, Db, Eb, E, Ab}. A close approximation of the pc collection that Bbinterrupted returns in R5-2. The material of R5-2ff. initially recalls the previous A tonicbecause the root movement <G, A> recalls the <G, A> alternating second of motive 2 in‘4L—,-—-q - U L_ L_184R3+ 1 and because the registration of the first chord allows us to hear the minor ninth {F#,G} continuing to function as subsidiary to an A-rooted harmony. The persistent intrusionof pc Bb into this progression, which causes an alternation between pcs A and Bb, reflectsin a pc microcosm the tonic succession <A, Bb, A> in R2+4 to R5-2.Surprisingly, the progression in R5-2ff. is ultimately directed toward a B tonic,4causing a retrospective reevaluation of the function of the pcs in the passage and generatingwhat is best described as a tonal overlap. (This is notated at this point in Figure 5.1 byconnecting the A and B tonics by overlapping phrase marks.) The shift of the referential pcin the collection from A to B in this passage is alluded to at R5-2 when the root associatedwith the connective minor ninth {F#, G} changes.At R6 Copland executes the first of several elisions of tonic. Motive 3, whichcharacterizes the B tonic, is now supplanted by a return of motive I in the bass, generatinga G tonic. Once again, however, 6 is undermined as a tonic. Here the G tonic isundermined by dividing the texture into two tonal strands that use different motives (i.e.,motive I appears in the low strand and motive 3 appears in the high strand). The highertonal strand is characterized by a transpositional conflict: two different (simultaneous)transpositions, Ti 1 and T4 respectively, generate the soprano line and the parallel five-three chords (see Example 5.5). These different transpositions suggest different tonics.For instance, if we hear the soprano establishing the tonic then the pitch level of motive 3 atR6 implies an A# tonic. However, if we hear the parallel five-three chordal motion as thebasis for establishing the tonic then its pitch level at R6 also implies an Eb tonic. We cannot resolve this (transpositional) conflict and assign a tonic to this strand because the finalchord of motive 3 at R6ff. is withheld. What is abundantly clear at R6ff. is that thetransposition of motive 3 initiates a movement away from the B tonic. This departure isonly strengthened at R7- I when motive 3 returns at its original pitch level (i.e., that of R5-‘1This cadence was discussed earlier. See Example 1.28, pp.49-51.2ff.) but is similarly modified so that it creates an unresolvable ambiguity between theimplications of different tonics. The omission of the final chord of motive 3 at R7- 1ff.results in a conflict between an F# tonic, which is suggested by the pitch level of thesoprano, and a B tonic, which is suggested by the pitch level of the parallel five-threechordal motion.185Example 5.5 Conflicting Transpositions of Thematic Material at if.1) Soprano Til>11)Soprano1j I• I• •1 _JF( • -II— I. —- —.———5.3.2 Part BAt R8 the next transposition of motive 3 closes properly to generate the G tonicbeginning the second part of the form. Three measures before this close, however, thereare references to a Bb tonic: the prominence of the fifth {Bb, F} moving to the triad {F, A,C} in the highest voices of R8-3 suggests Bb; and the pc collection is that of Bb-major.The references to Bb result in a tonal overlap between Bb and G in R8-3ff. which is similarto that earlier heard between A and B in R5-2ff.When references to Bb are eliminated at R8, however, the G tonic is thenchallenged to some degree by references to A, effected through the chord {C#4, A4, D5,. .. I I - —-+ ,—-U-—I I1t_.u__and 2)_Parallel Triads 2) Parallel T iads9:5‘flI I Tonic: A# or D#186E6} in R8+2. This A-rooted sonority is T7 of the opening chord in m.2 and is voiced likethe chord that was emphasized when A was a tonic in R2+4 — {C#2(3), A3, D4, A4, E5}.One reason to hear a major formal articulation at R8 is the subsequent move at R9-3to a tonic and collection — E — that is very different from the preceding ones. Coplandgenerates the E tonic in R9-3ff. in a characteristic way. An inner melodic voice (FirstViolin/Heckeiphone) repeatedly accents the pitch 134 throughout a melody that ends on pcG# following a repetition of the descending fifth <B4, E4>. E is supported as a tonic bythe E-major collection and by an implied dominant-tonic root progression that is repeatedtwice (see Example 5.6). The chord in R9-4 to R9-l and R9+l is the dominant seven-four(or the jazz harmony A/B); it resolves to a first inversion tonic chord in R9 and R9+2.Example 5.6 Dominant-Tonic Progressions in []-4ff.- A A A A [A]0 0 00 0 0 0 0, E-4to-1 +1 +20 0 0 SE: J 6” ‘‘V” 16(Jazz A ..A)B BA Cl tonic is melodically generated in the soprano in R9+3ff. by a differentrhythmic setting of a transposition (T9) of the motive that melodically generated E in theprevious section. Here agogic accents are placed on pcs Cl, El, and Gil, and each shortphrase ends on pc Cl. This C# tonic is anticipated in R9+2 because the two (incomplete)neighbor-tone motions, <B5, C#6> and <E6, F#6> respectively, allow us to(retrospectively) hear the sonorities on beats I and 3 of this measure as a Cl-minor six-four187chord followed by a G#-rooted minor seventh instead of as a contrapuntal continuation ofan E-major six-three chord.Four measures before RiO the texture divides into two tonal strands. The upperstrand contains another variation of motive 2, which melodically generates an A tonic. Thelower strand continues the previously established CII1Db tonic. Both strands are supportedby their respective pc collections: the upper strand uses a subset of the A-major collection{E, F#, G#, A, B, C#}; the lower strand uses the lower pentachord of the Db-majorcollection {Db, Eb, F, Gb, Ab}. At RiO the implications of the A tonic are eliminated andDb again sounds by itself. Here Db is generated as tonic by a statement of motive 1transposed to C# above a sustained C#-major six-three chord. An F# added to thissonority makes it a transposition of the first chord in m.2 and, therefore, related to the A-rooted chord in R8+2. This establishes a unity of harmonic character between parts A andB.Underlying R9-3 to RiO-i is a step-progression, like that in the texturallyanalogous R6ff. (recall Example 53), which connects the point of tonal divergence to thestable tonics that frame it. The voice-leading underlying the passage, which is shown inExample 5.7, involves contrary motion between two voices using two different collections:a soprano voice falling by step within the E-major collection; and a bass voice rising bystep within the C#-major collection.188Example 5.7 Two-Voice Model of -3ff.J _I JJ-3 +1 +2 4 -1‘__________________The association of E and C# that this model posits is subsequently affirmed whenthe C# tonic of RiO gradually merges into an E tonic at R1O+3. E is generated as tonic inR lO+3ff by the alternation of B- and E-rooted chords (see Example 5.8). The transitionfrom C# to E is effected in RlO+3 by a subtle reinterpretation of the progression from the Amajor-major four-two chord to the B-rooted sonority. Initially, this chord progression isreminiscent of the one that harmonizes the first statement of motive 3, because it is similarto T2 of R5-2ff. However, Copland deflects the progression away from the C#-rootedchord that such a transposition leads us to expect by reinterpreting the A- and B-rootedchords as a subdominant-dominant progression in E. This passage illustrates how subtlyCopland can alter the fundamental tonal identity of his material, in this case changing amotive from a linear to a functional harmonic progression.1..Roots: B E B E BE: “V” I add6’V6”“J6” Iadd6 “V6”3 T1-31:J -.-— 112 2ac,-I•.-Example 5.8 Dominant-Tonic Progressions in [fl -3ff.—0______ _ _ _ _ _1189Other elements confirm E as a tonic at RlO+3. For instance, the only rhythmicallyactive line in this texture embeds a restatement of motive 2 at the same pitch level thatmelodically defined E as a tonic back at R9-3 (see Example 5.9). The rhythmic placementof the successive pcs F#, E, G# and E in this line approximate the rhythm that is associatedwith motive 2 in R8 and R9-2. Further, the soprano line above the dominant-tonic rootprogression in R1O+3 recalls the ending of the previous E tonal area in R9+2: the cadentialE-major chord is similarly colored by an added sixth in the soprano that is introduced by anascent from pc B to C#. E is again supported by the E-major collection.Example 5.9 Embedding of Motive 2 in []+3ff.+1ff. (G tonic)i: , 1 =(E tonic))J44jI IJ÷3ff. (E tonic) JJdpt)4JA I I IL(EE7zEFr‘‘- -J .-hut I -- IiT •— 1ry=J)JJ)4. • I —l-IIIAt Ri 1 the three-chord progression of RI O+3ff. is transposed up three semitones togenerate a G tonic. The material in Ri 1ff. is similar to the previous passage in its emphasison tonic-rooted sonorities and the embedding of motive Part AlAt R12 Copland interrupts the final repetition of the three-chord progression ofRi 1ff. by restating motive 1. Since we expect the first note of R12 to be pe B, completingthe last repetition of the <B 1, D2, B2> bass gesture, the pc Bb sounds like a substitution190for B, as the minor third of G. The implied relation of Bb to a G tonic is immediatelydispelled, however, when it becomes clear that Bb is the first tone of a transposition ofmotive 1 that melodically generates a Bb tonic. The fourth scale-degree of the referentialcollection in this passage — pc Eb — has a lesser role in this tonal area than in previousstatements of the opening material of the movement. Pc Eb functions merely as a nonessential dissonant tone within a Bb-major six-three chord; it does not have sufficientstrength to induce tonal ambiguity (between Bb and Eb tonics) in the same way as itscounterpart pc G did in m.2.Bb connects to the next tonic, C, by a transitional passage where a series oftranspositions (Ti) is performed upon pairs of notes in a variant of motive 2. In R13-2these transpositions result in a restatement of the minor ninth interval between bass andsoprano and the leap of a minor sixth in the bass that characterizes the beginning ofmotive2. Copland does not, however, confirm the tonal implications of this restatement (i.e.,allow it to generate either a B or an E tonic) but treats it simply as an internal point withinan ongoing cycle of transpositions. This transitional passage becomes importantharmonically in generating the following C tonic because its last verticality, {D4, G4, B4,C5, D5(6)}, presents a G root just prior to the statement of a C-rooted minor third on thedownbeat of R13. C, generated in this manner by the descending-fifth root motion <G,C>, is confirmed as a tonic melodically by a transposition of motive 1.The following Ab tonic is not clearly generated until R14, when motive I fromR13, transposed to <Ab3, AM, Ab3, CM, GM>, emphasizes Ab3 above an Eb2 pedal inthe bass. Ab is, however, foreshadowed as a tonic iii the three measures before R14 by the-‘Taking the bass figure in the fourth and seventh measures after R12 — <D2, Bb2, Eb3, F4> — to bemotive 2 and allowing a slight modification in R13-4 — <D2, Bb2, Eb3, Bb3, E4, F#5> — one can trace aseries of transpositions of pairs of notes up a semitone (i.e., transposing the third and fourth notes up asemitone in R13-3; the first, second, fifth, and sixth notes up a semitone in R13-2; and the third and fourthnotes up a semitone again in the measure before R13).191continued references to that pc as a root of the minor-major third {B2, AM, C5} and themajor-major four-two chord {G3, Eb4, AM, C5}.The first verticality of R14+3, {Ab2, G3, C4}, in some senses culminates thepreceding Ab tonal area because its lowest tone, which is the root of the verticality, is thegoal of an ascending directed motion created by a special registration of the second half ofmotive 1 (i.e., <Ebi, Gbl, Db2, Ab2>). However, because of an elision, this verticalitysounds as both an ending point for the Ab tonic and a beginning point for a new C tonic. Cis weakly generated as a tonic by the accent placed upon the soprano C4 as the starting, andthe most often reiterated pc of a short, repeated phrase that contains pcs from the C-majorcollection in the high register.The C tonic is quite severely weakened, however, because an incomplete version ofmotive 3, similar to that in R6ff. and R7-lff., engenders two other, non-C, tonalinterpretations of the material in RI 4+3ff. (see Example 5.10). If, as at R6 and R7- 1, thesoprano melody determines the tonic, then E is the tonic of R14+3ff.; if, however, theparallel five-three chords determine the tonic, then A is the tonic of R14+3ff.192Example 5.10 Conflicting Transpositions of Thematic Material at []+3ff.+3ff.Tonic: E or AC is further weakened as a tonic by the anticipation of elements from the next tonalarea (D). For instance, the dyads {F2, Bb2} and {E2, C#3} in the low register in R14+4reappear within full triads in the low register in R15-3ff. Similarly, the A-rooted chord{E2, C3, A3, D4} in R14+3 forecasts the A major-minor four-three chord that isemphasized in the D tonal area by its registration (i.e., it is the only chord where the bassand soprano have the same pc — E). These anticipations of a D tonic are confirmed at R15-3 when a D-rooted sonority — {D2, B2, D3, A4, Cl5, E5} — terminates the four-measurephrase that began in R14-i-3. D is subsequently melodically generated as a tonic in the nextthree measures in the same manner as the preceding C tonic in R14÷3. This generationentails a restatement of the soprano of motive 3 at its original pitch level — <D4, E4>. D is,however, also confirmed as a tonic in R15-3ff. by two simultaneous root progressions,<D, A, D, A, D, G, D> and <Bb, A, Bb, A, D, Bb, A, Bb, A, D>, that result from thealternation of multiple rooted chords with A- or D-rooted chords (see Example 5.11).-pA5or 2) Parallel Triads(9:Example 5.11 Multiple Root Progressions Confirm D as Tonic in []-3ff.193Ay”- s •t . s_.____2I4g$! Lth 1ERoots: D D ABbTonic: DD DD D AD GDBbA Bb BbAR 15 is a recapitulation of R8 at the same pitch level, so we are predisposed to hearthe tonic as G. Indeed, pc G sounds prominently as the lower of two roots in the chordthat punctuates the ending of motive 2.6 However, G has already been foreshadowed as atonic in the types of verticalities Copland uses in the six measures before R15. The finalverticality of R15-1 and the first verticality of R15, {E2, A2, C#3, G4, B4, D5} and {D2,B2, D3, D5, F#5, A5} respectively, are similar, but not identical, to T9 of the twoverticalities in R8-3,7 so they articulate a G tonic,just as the previous chords articulatedB b •86This sonority contains both a G root and a D root because of the registration: 0 is a root because thelower half of the sonority is characterized by the doubled tfth {G, D} and reminds us of the 0 major-majorlour-two chord which initiated motive 3 at R5-2; D is a root because the outer pitches — {F#, D, F#, A, E}— form a D-ninth chord familiar from the measure before R3. The former is a particularly importantreference because it recalls the process where the root associated with the minor ninth {F#, G} graduallyshifts from D in m.2 to 0 in R5-2, and also because it recalls the sonority at R8+2.7Neither chord is a proper transposition of the chords in R8-3: the first verticality has an extra pc, pc B; thesecond verticality is missing a pc, pc 0. The absence of the latter is important because it allows Coplandto maintain a sense of D as a tonic on the downbeat of R15. 0 only emerges as a tonic after this pointbecause the material is recapitulated at its original pitch level. The transpositional relationship between thechords in R15-1 and RS-3 is anticipated to a degree in the fourth measure after R14: the second verticality ofthis measure, {F2, Bb2, C4, E4, 04}, contains all of the pcs of the first verticality in R8-3 but texturallyinverted; the third verticality of this measure, {E2, C#3, 04, B4, D5}, is the final sonority of R15-1 and is,therefore, also related, albeit more distantly, to the first chord in R8-3.8One might conceivably hear the chord on beat 4 of R14+3 ({E2, C#3, A3, D4}) as a foreshadowing of theG tonic at R15 because a similar chord ({C#4, 04, A4, D5, E6}) was prominent the last time we heard Gas a tonic (at R8ff.).194RI 6 marks the return of material from R5-2ff. at the same pitch level. A B tonictherefore similarly emerges when the same B-rooted sonority appears in R 17-3 as theterminal chord of the section. B is foreshadowed in the four measures before R16 inseveral different ways. For instance, the only chord which has G as its root in this passage— the chord {A#2(3), B4, D5, F#5, G5, B5, G6} at R16-4 (an altered G minor-majorchord) — is framed by two chords — {F#3(4), B4(5), D5(6)} and {A1(2), B3, D4, F#4,D5} in R16-4 and R16-3 respectively — that are B-rooted. When pc G is omitted in arepetition of this chord at R16-l we hear pc B, and not pc G, as the chord root. As aresult, all of the sonorities in R16-1 (the measure before we hear a B tonic) have pc B astheir root. Further, a move away from G is alluded to in R16-4 because the alternating B-and G-rooted sonorities are accompanied by different transpositions of the first three notesof motive 1 (i.e., <F#5, D6, D5> and <B4, G5, G4> respectively). Finally, the shiftaway from the G tonic is emphasized by the F#-minor-major tetrachord formed by the pcsFit, A, A# and Cit in the bass.The material at Rl6ff. shares an important characteristic with that of R5-2ff.: thecadence in R17-3, like that in R6, becomes the beginning of a new tonal area because ofelision — at R17-3 the B tonic is supplanted by a D tonic that is melodically generated bymotive 1. The tonics following rise by fourth as motive 1 is successively transposed: Dmoves (at R17) to G; G, in turn, moves (at R17+4) to the C tonic that ends the movement.The starting note of the motive at each new pitch level also has a dual function as the lastnote of the preceding statement.9 The elisions in R17-3ff. point out an interesting change9Hilliard does not acknowledge the final C k)flic of this movement because he hears the correspondingpassage as a transition to the second movement and, therefore, as tonally subordinate to the 0 tonic whichprecedes it, and because a C tonic at this point in the form contradicLs his conception of the movement ashierarchically organized around G. Hitliard, op. cit., p. 107. However, such a perspective distorts themanner in which these tonics are generated in the first place; pc C is, in fact, the final pc of motive 1 at thepitch level which melodically generates 0. Further, the statement of pc C at Rl7+4 is as striking as thestatement of pc G at R17, although for different reasons: at R17 the statement of pc G is underlined by achange from an imitative polyphonic to a monophonic texture; at R17÷4 pc C is accented by duration,contour (as the lowest pitch in the movement), dynamics (sff), and a severe registral displacement fromF4(5,6,7) to C 1(2,3). Pc C at R17 is also where the driving rhythm of motive I (the “bounding line”) isallowed to disintegrate. My analysis also reveals, however, that the starting tonic of the movement is notin the nature of motive 1: at the beginning of the movement its last note had a dissonant,disruptive function, but at the end of the movement the last note is stable.5.3.4 Motivic Correspondences195Motive 1, in fact, is crucial to the tonal form of the movement. Some of the tonicsuccessions and individual tonics in Figure 5.1 are intricately associated with intervallic andrhythmic variants of motive 1. For instance, three important cases of tonal foreshadowingin the movement employ a unique intervallic variant of motive 1 (see Example 5.1 2a). Thisvariant is initially stated in the first and second measures after RIO where an E tonic isbeing foreshadowed within a C# tonal area. It reappears in R13 to R14 to foreshadow anAb tonic within a C tonal area, and within Rl6-4to R16 to foreshadow a B tonic in a Gtonal area. Associated with this variant in all three cases is the trichord 10,2,5], which isusually associated harmonically with a minor-minor seventh four-two chord.1+1—,I I •.)‘ I,, I I’ —•i) ii) i) ii)G, as Hilliard claims, but D. This removes the need for Hilliard’s hierarchical tonal explanation of the endof the movement and allows a more consistent approach to its tonality.Example 5.12 Variants of Motivea) IntervaflicAIii 2-y a I+1 +2-,.-ø— —L/ , — —a . a i’— i’— 1’—IFLii IT SIL —-1b IT24.,2-LJ Li[0,2,5](C#mm7 in )[0,2,51Bmm7 inb) Rhythmic[] +2ff. -I-4ff.A A-—--—.— .1:1. I 221 I I II .iC .—i. -r r k 11.1 —--—-—-—— 1.1 II iiJI • l- V I II II I ....-..-. .) . — I I I I III .F L Cd I (FV I IL I I LI I 1P’ IVF’II196A rhythmic variant of motive 1, shown in Example 5.1 2b, is used only at twocrucial points in the form: at R1+2ff. where D is established; and at R17+4ff. where C isestablished. This reinforces a large-scale change in the scale-degree function of pc C —from the (lowered) seventh scale-degree of D to the first scale-degree of C — over thecourse of the movement that is emphasized by certain features of the surface of the music inthe beginning of the movement. For instance, this pc is emphasized from the outset of themovement in motive I as a dissonant seventh that never resolves down by step in aconvincing manner (recall Example 1.36, pp.63-65). Further, Copland alludes to thisparticular transformation of the scale-degree function of pc C in R 1+6 when the minor third{C, Eb}, which has a C root, appears in the D tonal area in a rhythm that mimics theclosing gesture of the preceding section (Rl+l). The shift in mode from major (in R1+1)to minor (in R1+6), which precludes hearing an exact transpositional relationship here,foreshadows the minor mode in which the C tonic is ultimately expressed in the movement(i.e., at R13 and R17+4). Copland also alludes to this transformation of the scale-degreefunction of pc C in the second tonal area of the movement (G at R2+ 1ff.) by setting pe Fmelodically as the (lowered) seventh scale-degree of G and harmonically as the root of aminor triad (a metaphor for F as the first scale-degree).’° This correspondence suggests asimilarity of function between the D and G tonics (i.e., foreshadowing a long-term event)that will be shown to be important later (see below, pp.209-210).The use of a special variant of motive 3 is also formally significant. The firstsoprano pc of the motive (i.e., pc G at R6- 1) is heard as the first scale-degree only twice inthe movement: at R14+3 (C tonic); and at R15-3 (D tonic). We might construe theplacement of this variant in successive C and D tonal areas in the final part of the form toallude to the reinterpretation of the scale-degree function of pc C that, occurring over thepiece as a whole, was forecasted in the first tonal area.‘The functional parallelism I have inferred between pcs C and F is reinforced at R2-1 by the manner inwhich we first hear pc Ab together with pc F: the rhythmic setting of the minor third {F, Ab}, like that ofthe minor third {C, Eb}, is clearly modeled after the concluding gesture of Rl+1.1975.3 .5 Formal Function of Successions of Third-Related TonicsThe tonic succession within individual parts reinforces the thematic design. Forexample, successive tonics in parts A and Al are related primarily by the intervals of aperfect fourth or a major second (or their inversions), while successive tonics in part B aresolely related by major or minor thirds (or their inversions). This unifies parts A and Aland clearly differentiates part B. Part A does contain third-related successive tonics atR6ff., when a transition to part B is begun (i.e., the succession <B, ?/G, Bb G>).However, these initiate a large-scale retrograde that guides the successive tonics in R8-4 toR12, that is, the tonic succession in R8-4 to R9+2, <Bb, G, E, C#>, is retrograded in RiOto R12. This retrograde has an important influence on the pc-scale-degree design that willbe discussed later.The third-related tonics at the end of part A are also significant because they can beunderstood as a composing out of motive 1. We can understand the tonic succession <B,?IG, Bb> in R6 to R8-4 as another statement of the truncated version of motive I (cB#,G#, B>) that occupies the bass line of the C# tonic at RiOff. This suggests that we hear Band Bb as the major and minor third of G, functions that have significance in the pc-scaledegree design.5.4 Pc ContinuityFigure 5.2 shows how the twelve pcs are given various scale-degree functionswithin the first movement of the Short Symphony. The pc-scale-degree design in Figure5.2 is permeated by references to related simultaneous primary streams, that is, streams thatresult from the recurrence of a specific dyad, or a motive that remains active over a longtimespan.1985.4.1 Stream GenerationThe pc streams are initiated in a myriad of ways in the first movement. Oneimportant way of establishing a pc connection involves continuing motives. Motivicassociations of common pcs is most obvious where motive 3 connects the B tonic of R5-2to the G tonic of R8 and the G tonic in R15 to the B tonic in R16.A second important technique of generating primary streams in this movement isthrough an emphasized dyad that recurs in successive tonics. This technique is evident inthe first streams generated in the piece — the paired primary streams on pcs Ab and F. PcAb, by far the most striking connective pc in R1+2ff., is consistently paired with pc Finthe first three tonal areas of the movement; that is, the dyad {F, Ab} appears at R2- 1 andR2 in the D tonal area, at R2+2 in the G tonal area, and at R3-3 in the A tonal area. Thebeginning and ending points of this stream in Figure 5.2 is demarcated on the surface by acorrespondence between the rhythmic setting of the dyad at R2-1 and R3-3: the rhythm andcontour of both versions of {F, Ab} are modeled after the closing gesture of the firstsection (Ri + 1). ‘ What is unusual about this particular dyad is that it is a focal point forintroducing new, and unexpected, chord factor interpretations. For instance, pc F,emphasized by its incongruity as the melodic (lowered) third scale-degree of D following acadence on a D-major harmony, sounds like a root when it is repeated in R2- 1 because therhythmic setting of the Ab octave mimics the concluding gesture of the first section (R1+1).Similarly, the sustaining of pc Ab in the G tonal area forces a new chord factorinterpretation upon pc F (i.e., as the root of a minor triad) when it is finally statedsuggesting that we hear it both melodically as the (lowered) seventh scale-degree of G, and1 1n R3-3 pcs F and Ab are registrally inverted: pc Ab appears in the bass; and pc F appears in the sopranoand is given the rhythmic profile and contour that pc Ab had in R2- 1.Figure5.2Pc-Scale-DegreeDesignoftheFirstMovementoftheShortSymphony--P1—IbJ—b2—7z,%_%3S-66---—6—551/_[11-P2h3h7—I6L6IIP-S5-h4—5—4—1—4—1-?L---Mi3--------=zIzzR:18l1i-2121+1+413I-i131141151-2161171-1181-481I93Parts:ABSections:aala2bSubsections:abala2c:a3a4ddl(trans.)eelTonics:DGABbAXBdir.Bf?BbXGdir.GEGAbG F#-F E Eb-D C-B Bb-A-6-j-P-6-1H_,P-3-5II.z.z.z 7JP-‘-4-iS-1-b2jj[-J-P-1—b3-b3•r---I5IS1jVj[Figure5.2(cont.)II4,sI,%.psI’P2-3—5--f1-3-b2j----UI:I1jM3-M31116A./aIA.P1—2—4jP/A.;4S2-2—7U_-rS—6—l-P-i/IR:81191-3191+21101-4liol+3liii12111311141+31151-31151Parts:BAlSections:ba3a4:a5blSubsections:eele2e3aSffia6a7a8d2(trans.)eTonics:GEC#AC#EGBbCAbAb/CDGc#Ab0-•F#--F Eb-c#C--B Bb2 A-I ;zJP-3/F—ILA.[b3]L_aaFigure5.2(cont.)202harmonically as a root. Finally, the registral inversion of the dyad {F, Ab} in R3-3 alsogenerates as host of new chord factor interpretations. These conflict with the implicationsof the bass line and with the tonic pc itself. For example, pc A# (Bb) tends to shift the{G#, F} dyad toward a Bb root and away from the G# root that might be inferred (i.e.,hearing {G#, F} as an incomplete version of A:viio7). However, the bass G# also makesa C#-minor triad sound in the lowest voice of this measure, allowing a fragment of motiveI — <C#2(3), E2(3), B2(3), F#3(4)> — to become more prominent in the following twomeasures (R3-2 to R3-1).’2There is one unique set of primary streams in Figure 5.2 that are simultaneouslyrelated by both of the techniques described above. Pcs E and D, which connect the D andG tonics of R15-3 and R15, are related both by a continuing motive — E and Dare thesoprano pcs of motive 3, which continues in an attenuated form in the soprano when thetonic changes to G — and by a recurrent dyad, {D, E}, which is prominent in each tonalarea (i.e., R15-3, R15+l, R15+3, and R15+5).’3Another important technique of establishing a pc stream in this movement is byconsistently sustaining the same pc in the soprano at the endings of phrases and sections.This method establishes the primary stream on pc E which runs from R2+4 to R8. Forinstance, pc E, first heard as the soprano pitch of the repeated A-rooted sonority in R2÷4,is the final soprano pc of the section al. The D-rooted chord which ends this section givespe E a new chord factor meaning as a ninth. The timbre of the harmonics in the highstrings emphasizes pc E in its next appearance in the soprano in R4- I, at the end oft2This reference is important in tonal foreshadowing because the same transposition (i.e.,T11(Ml)) laterinterrupts motive 3 in R5+2ff., and eventually generates a tonic in RiO.13n her analysis of this movement Smith points to the repeated dominant four-three chord in R15-3ff. as a“lapse of style” and a “poor choice of harmony” because it is “at variance with the harmonic language of therest of the movement.” Smith, op. cit., p.151. The striking context of this familiar chord, however,serves an important function in my analysis because it emphasizes pc E (as its outer pitches) in a passagewhere that pc is a primary connector between the collections of successive tonics. Thus, the “out of place”dominant seventh chord represents a deliberate compositional emphasis upon a structurally important pc.203subsection a3, drawing our attention to the way it is sustained over into the interrupting Bbtonic. Following this interruption, pc E is the soprano note on which the music pauseswhen the tonic of motive 3 is emerging (R5-2ff.), and when that tonic is subsequentlydenied (R7-3ff.). E is the soprano pc that ends the short, repeated phrase in R8+2 andR8+4. The continuation of the stream on E past this point involves a change of character,because pc E is no longer emphasized as the ending pc in the soprano but as the starting,ending, and most repeated pc in the short melodic cells of an inner line.Soprano pcs in cadential sonorities are frequently involved in streams of continuityin this movement. For instance, the primary stream on pc B in R8 is initiated because ofthe emphasis placed upon the terminal sonority of motive 3. The soprano pc B here isunexpected because the collection which prepares G has pc Bb and not B as its third scale-degree. Further, the severe change in texture at this cadence gives the {G, B} third adistinct profile. In the next tonal area (E), pc B is both the most prominent pc in thesoprano, and the most accented pc of all.Some pcs in the bass gain prominence as primary connectors because of theirchanging meaning within different, but temporally proximate, harmonic entities. Forinstance, in R10±l pc B sounds as the bass note of a C#-minor-minor four-two chord. Itis emphasized by an agogic accent and a chromatic opposition (pc B#, the otherrepresentative of the seventh-scale degree of C#, precedes pc B). At the next statement ofpc B in the bass (R10+3) it sounds as the root, and not the seventh, of the chord {B1(2),A3, E4, F#4, B4}; B is emphasized as the outer voices of this chord. The change in scaledegree function of pc B is underlined motivically because both statements of B in the bassconclude the motive 1 fragment <B#1(2), G#2(3), 81(2)>. In Ri 1+2ff. pc B returns inthe bass under a third, G-rooted, chord in the G tonal area. This chord begins and ends athree-chord gesture that, through repetition, becomes the motivic basis of the rest of the Gtonal area.204A similar process establishes the primary stream on pc D at R12-I. Because thefinal chord of the bass gesture emphasizing pc B is removed, pc D sounds as the bass noteof the final chord in the G tonal area. The next chord, which begins the Bb tonal area(R12-i-1), also has pc Din the bass. However, the repetition in the bass, like the earlierrepetition at Rl0+3, is not the only way pc D is emphasized as a common tone between thecollections of the G and Bb tonics. D is also emphasized within the G tonic as the goal ofneighbor-tone motions in the soprano at RI 1+2, when pc B was being emphasized in thebass, and within the Bb tonic as the starting pc of a variant of motive 2 at R12+3, R12+5,Rl2+8, and R13- Suspended StreamsFigure 5.2 includes a very striking example of suspended streams in the pairedprimary streams on pcs E and D that are initiated at R5-2. These streams, which aregenerated by the striking restatement of the (parallel five-three) chordal motion of motive 3at its original pitch level in R7- 1ff. and R8ff., create a large-scale shift in the scale-degreefunctions of pcs E and D respectively from sand 3 to and 5. The continuation ofmotive 3 is interrupted twice, at R6 and R8-4, by interpolated tonics (?/G and Bb) thatgenerate their own streams. At R7-3 when the phrase repetition in the bitonal texture ?/G isitself interrupted at R7-3 by a restatement of motive 3 at its original pitch level. The senseof a larger continuity from R5-2 to R8 is also reinforced motivically because the thematicmaterial of the interpolated passages is derived from motive 3. The streams on pcs E and Dare temporarily suspended at R6 because neither pc is stated in a strand of the bitonal ?IGtexture. The return of motive 3 at its original pitch level in R7-1 is unusual in the pc-scaledegree design because there is no recognizable tonic. Indeed, all we can specify about thepassage in R7-lff. is that B is no longer the tonic. (For this reason the streams on pcs Eand D show the symbol “?“at R7- 1 instead of their scale-degree functions at R5-2.)However, in the second interpolated tonal area at R8-4 only the stream on pc E is205suspended, because pc D belongs to the new referential collection, and is also stronglyaccented in the bass.5.4.3 Pc-Scale-Degree DesignThe pc-scale-degree design in Figure 5.2 corresponds roughly to the thematicdesign. Part A begins in Rl+2 with motivically paired primary connective pcs then shiftsto non-related primary and secondary streams, the latter of which is suspended at R4. Thepc-scale-degree design of part A gradually becomes more complex starting in R5-2. Thiscomplexity first arises from the addition of secondary streams to the primary connectivestream on E. The stream on pc E is then paired with a second primary stream on D. Thesetwo streams connect the B tonic at R5-2 and the G tonic at R8. But this connection isinterrupted by two other connections involving primary and secondary streams on 1C5-related pcs (R6 and R8-4 respectively). The second of these interruptions forces areinterpretation of the scale-degree function of pc D in the primary stream, a reinterpretationwhich will be shown below to be crucial to the form.The pc-scale-degree design of part B differs from that of part A: the pc-scale-degreedesign of part A increases gradually in complexity in a manner that mimics a crescendo; thepc-scale-degree design of part B incorporates several important symmetries, mostnoticeably the paired primary and secondary streams on pcs F# and G# at R9-3 and Ri0+3respectively. Simultaneous primary streams at the beginning of part B (on pc E and pc B)are not paired together (by membership in a recurrent dyad or a continuing motive) and partB ends with a primary stream (<5,3>) on pc B (Rl0+3) that is repeated on pc D (Ri 1).Part Al incorporates elements of the pc-scale-degree design of part B. Forinstance, the beginning and ending of part Al, like the ending of part B (RiOff.), ischaracterized by a single primary connective pc (i.e., R12 to R14+3, and R17-3ff.).Similarly, at Rl3ff., like R10+3ff., two secondary streams of connection accompany a206primary stream that ends on (b)3 followed by an arrow.14 Further, both parts B and Alend with a repeated stream in successive primary streams: part B ends with the successivestatement of the stream on pcs B and D respectively; and part Al ends with theA Asuccessive statement of the stream <(b)3,(bJ7-> on pcs F and Bb. That is, at RI I weA Ahear pc B change scale-degree function from 5 to 3; and at R12 we hearpc D change scale-A Adegree function from 5 to 3. Similarly, at R17 we hear pc F change scale-degree functionA A A Afrom 3 to 7: and at R17+4 we hear pc Bb change scale-degree function from b3 to b 7.The pc-scale-degree design in part Al at first appears to be only superficially related to thatof part A because it begins with different primary streams that are stated on different pcs.Part A focuses on pcs Ab and F(RI+2ff.) as they change scale-degree functionsA A A A A Arespectively from b5 and b3 to b2 and b7 and to 7 and b6, and on pc E (R2+4ff.) as itA A A Achanges scale-degree function from 5 to 4 to 5 to 4. But part Al focuses first on PC EbA A(Rl2ff.) as it changes scale-degree function from 4 to b3, then on pc B as it changes scale-degree function from to b, and finally on pc C as it changes scale-degree function from3 to 1. Despite this initial difference, however, the second halves of parts A and Al areclosely related. For example, both parts use motive 3 near their end to generate streams onthe pcs E and D. Further, the order of successive primary streams at the end of part Alresembles the order in which interpolated streams interrupted the primary streams on pcs Eand D in part A (i.e., <E+D, F’+B, F+Bb>). The respective endings of parts A and Alboth inherently contain the succession of focal pcs <E+D, F#, F, Bb>: in part A we hearthe paired primary streams on pcs E and D (R5-2ff.) to be interrupted by streams on pcs F#and B at R6 and by streams on pcs F and Bb at R8-4; and in part Al we hear the pairedprimary streams on E and D (Rl4+3ff.)to be followed by successive streams on pcs F#(R17-3), F (R17) and Bb (R17+4).A A AA14The secondary streams on pcs Ab and Eb at R1O+3ff. and Rl3ff. (i.e., .3,b2> and <b3,5.) share thischaracteristic: both streams begin on (b)3.207The similar ordering of focal pcs in the endings of parts A and Al is reinforcedthematically in R 16ff. by the recapitulation of R5-2ff. at its original pitch level. The streamOfl pc F# at R17-3 of part Al, which is heard to follow the streams on pcs E and D, alsobegins on as did the stream on pe F# at R6 of part A. That is, at R6 we hear pc F#change scale-degree function from to an unknown quantity (?/[ D and at R17-3 we hearA Apc F# change scale-degree function from 5 to 3. Further, the pc-scale-degree design of partAl ends with two statements of the stream <(b), (b)7>, the first of which occurs on thesame pc, F, that occurred at the outset of part A. That is, in both R1+2ff. and R17-3ff. wehear pc F change scale-degree function from 3 to Motive 1 as the Basis of the Pc-Scale-Degree DesignThe analysis reveals the important role that motive 1 plays with respect to the pcA Astructure of the movement. Often when the third scale-degree. 3 or b3. is emphasized as aPC of connection there is modal mixture — a strong reference to the opposite representativeA Aof the same scale-degree function, b3 or 3 respectively. The perception of this chromaticopposition is particularly strong when a stream of pc continuity either begins or ends with aAstatement of the third scale-degree. A stream starting from 3 manifests itself from theoutset of Figure 5.2: Pc F, asserted as a primary pc of continuity in the shift from a D to aG tonic in R2+ 1, is preceded by statements of pc F#.15 A stream featuring a chromaticopposition between different representatives of the third scale-degree can be seen mostclearly at R12. Pc D, asserted as the primary pc of continuity when the tonic shifts from Gto Bb, is similarly challenged by the initial association of the tonic pc Bb with pc Db, theminor third scale-degree. Only three streams of continuity beginning with the third scale-degree in the movement are prefaced by a different primary stream ending on the oppositerepresentative of the same scale-degree. These pcs are pc B at R8, pc C at R14+3, and pcF at R17-3. The first and last of these pcs relate to an ongoing dialogue of alternation1-The implicit competition between pcs F and F# to become the unchallenged third scale-degree of D isinherent within motive 1. The emphasis on this competition in R1+2ff. has already been discussed.208between pcs F and F# and pcs B and Bb, a dialogue that informs the pc structure of themovement. The use of the pattern Ofl pc C is another allusion to the importance of PC C inthe movement.5.4.5 Focal PcsThe succession of primary pcs in Figure 5.2 can be characterized as a series ofalternations between members of the focal sets {F, F#} and {B, Bb} that culminates in thestatement of <(b)3, (b)> in successive streams on pcs F and Bb; that is, we hear streamson pcs F and Bb to alternate with streams on pcs F# and B. These alternations are oftenpunctuated by streams on pcs E and D. Pcs F and F# are first incorporated into the pcscale-degree design by two different chromatic oppositions that are embodied in theprimary stream on pc F (R1+2ff), and in the following secondary stream on pc F#(R2+4ff.). That is, when F is the connective pc we hear pcs F and F# as differentrepresentatives of the third scale-degree; and when F# is the connective pc we hear pcs Fand F# as different representatives of the sixth scale-degree. The shift from pc F to pc F#at the end of the second section of part A is marked by a concurrent primary stream on pcE. This primary stream eventually incorporates the same chromatic opposition that colorsthe stream on pc F# (i.e., at R8-4 pc Eb will temporarily displace pc E as the sixth scale-degree of G). At R5-2 pcs E and D become focal pcs before a primary stream on pc B isinitiated (R6). The shift in focus away from the chromatically opposed pcs F and HI,however, introduces a new conflict of scale-degree function in the pc-scale-degree designbetween pcs Bb and B. This conflict becomes apparent in primary streams on pcs B andBb in R6 and R8-4 respectively. The primary streams on pcs B and Bb are accompaniedby secondary streams on their respective counterparts within the other focal set — pcs F#and F.The pc-scale-degree design of part B focuses primarily on pcs B and HI: streams onpc B first alternate, and then sound simultaneously with streams on pc F#. In some ways209the simultaneous sounding of streams on pcs F# and B in part B can be said to “resolve”the curious lack of definition of pc F# at R6 (where F# becomes an unknown quantity) thatmakes the secondary stream on that pc so striking. We can hear the first primary stream onpc Fl (R9-3ff.) as clearly related to the first primary stream on pc F (R1+2ff.) becauseboth of these streams are paired (by a recurrent dyad) with a stream on pc Ab (G#). Theprimary stream on pc B near the end of part B is followed by a primary stream on pc D.The last part, Al, focuses first on pc D, and then moves briefly to focus on pc Bagain before pcs E and D are reasserted as paired primary streams. But instead of leadingto a focus on pc B as at R6, the E-D pairing is first expanded at R15 by an additionalstream on pc Fl. The stream on pc Fl is then redefined as the sole primary stream at R16prior to the final assertion of pc F as primary in R17-3.The direct progression between {F, F#} and {Bb, B}, is suggested in three waysin the pc-scale-degree design: by the simultaneous use of streams on pcs Fl and B in R6,and F and Bb in R8-4; by the alternation of primary streams on pcs Fl and B in part B; andby the succession of the stream <(b)3, (b)> on pcs F and Bb. The broader movementof the entire pc-scale-degree design also suggests motion between the focal sets {F, F#}and {B, Bb} because it begins with a focus on pc F and ends with a focus on pc Bb.The analogy between the focal sets {F, F#} and {Bb, B} in the pc-scale-degree design isreinforced by some important surface features of the movement. For instance, thestatement of a variant of motive I at two different pitch levels, D and G (R2-4 to R2+3),results in precisely the same kind of pc alternation in the bass where pcs F and Bbrespectively are heard to prevail. Motive I in D results in the alternation <F, Fl, F> in thebass; motive 1 in G results in the alternation <Bb, B, Bb> in the bass. These alternationsare also reinforced by other contextual means such as the immediate substitution of one pcfor another. For example, pc F is substituted for pc Fl in section a!; pc Bb is perceived as210substituting for pc B at R4 because both pcs sound in relation to pc E; and pc Bb similarlysounds initially as a substitution for pc B at R12 for reasons discussed earlier.16The analogy of function between pcs Fl and B and pcs F and Bb can be traced bythe repetition of particular streams on these pcs in the pc-scale-degree design. For instance,A AAthe stream <(‘ )7,5,3> appears on pcs B (RiO to Rl2-1) and Fl (R15 to R17-3). That is,at RiOff. we hear pc B change scale-degree function from to to 3; and at Rl5ff. weA A Ahear pc Fl change scale-degree function from 7 to 5 to 3. Similarly, as discussed abovethe stream <b(b)3,(b)7> occurs in successive streams on pcs F and Bb at the end of themovement. A strong relationship is also implied by the two sets of streams that interruptthe connecting streams on pcs E and D at the end of the first part. These sets pair nearlyA Aidentical primary streams on B and Bb (i.e., <1,?/3> Ofl PC B and <1 b3> on pc Bb) withsimilar secondary streams on their analogous counterparts Fl and F respectively (i.e.,A A-7cA<5.?II j> on pc Fl and <5 7> on pc F). That is, at R6 we hear pcs B and Fl changeA A Ascale-degree functions respectively from 1 and 5 to ?13 and an unknown quantity (?I[ 1);A Aand at R8-4 we hear pcs Bb and F change scale-degree functions respectively from 1 and 5to b3 and . Such an analogy of function is also manifested in R15-3 when the pairedstreams on 13 and D occur between the stream <3,1> on pc B (R14-i-3) and the streamAA<5.3> on pc Fl (R17-3). This is explicitly suggested at R15-3 on the surface of the musicwhen the beginning and ending chords of the repeated gesture, {F2, Bb2, D3, A3, D4}and {D2, B2, D3, D5, F#5, A5}, create an alternation between pcs Bb and F and pes Band Fl in the context of the same tonic, D, that opened the movement. The analogy isagain explicitly suggested in R17-3 when the cadence of the nearly pitch-identicalrecapitulation of subsection d does not result in a reinterpretation of the scale-degreefunction of the bass pc, B, but instead that of the soprano pc, Fl. The differing treatmentsof these identical cadences underlines the relation between pcs B and Fl immediately beforethe final repetition of the stream <(b)3,(b)7> makes apparent the analogous relation16Sec pp.189-190.211between pcs F and Bb. The cadence at R17-3 is also important in that the resulting streamAA A,’cA<5,3> on pc Fl, like the stream <5 7> n pc F at R8-4, also offers an interpretation ofthe undefined <,?/1 1> stream on pc Fl at R6. The two ending functions of these streams,A A3 and 7, are the two functions in the following stream which ends the pc-scale-degreedesign in the movement.The pc-scale-degree design suggests that the pairs {F, Fl} and {Bb, B} areAAanalogues in other ways such as, for example, by the variations on the stream <2,7>. TheA Astream <b2, 7> on pc Ab (R2+lff.) reappears on pc Bb (R5-2). (Pc Ab has already beenidentified as important to this analogy because it is paired with the primary streams on pcsF and Fl (mm. 1ff. and R9-3ff.) in the first two parts of the movement.) A similar stream,<2, is heard in the primary stream on pc B (R1O-4), which sounds simultaneouslywith a primary stream on pc Fl. That is, at R5-2 we hear pc Bb change scale-degreeA A A Afunction from b2 to 7; and at R 10 we hear pc B change scale-degree function from 2 to 7.AAThe stream <2,7> then appears in a secondary stream on pc Fl (RI 0+3). This anticipatesA AAthe long term connection between pcs B and F#, which is implied by the <( )7, 5,3>correspondence.5.4.6 Palindromic StructureThe pc-scale-degree design of the movement presents a structure that is palindromicaround RIO within the second part. Arrows in Figure 5.3 show this palindromic structure.The Fl sustained at RIO is framed locally by four different patterns. The first of thesepatterns involves the return of a focus on specific pcs, but not the actual retrograde of scaledegree functions within those streams. For example, paired streams on pcs F# and GIoccur before and after RiO, but these involve different scale-degree functions: the primary--‘-(P1).6—,-4-Figure5.3PalindromicStructureinthePc-Scale-DegreeDesignofFigure5.2LP-:-—JAbG F# F E EbD c# C B BbA—P2-35-F4’Erzzzr3F______________----P-1/;\III3?c________t::z:zzz4i1-tE1centerofsymmetry213AA AA AA I’ Astreams <2,4> and <3,5> before RIO, and the secondary streams <2,7> and <3,b2> afterRIO. The second of these patterns involves the order of successive primary and secondarystreams on a given pc. Only twice in the movement are a primary and a secondary streampresented successively on the same pc — the stream on C# in R9-3 to R1O-4 (S to P), andthe stream on Eb in R12 to R14 (P to S) — and both respective primary streams sound bythemselves (i.e., are not accompanied by other primary or secondary streams).’7The othertwo patterns, however, involve exact retrogrades of the changes in scale-degree function inspecific pc streams. For example, the secondary stream <6,1> on pc C# before RIO isAAstated in retrograde (<1,6>) in a secondary stream on the same pc after RIO. Similarly, theAA . . AApnmary stream <3,5> on pc B before RIO is stated in retrograde (<5,3>) in a primarystream on the same pc after RiO. That is, at R8 we hear pc B change scale-degree functionA A A Afrom 3 to 5; and at R1O+3 we hear pc B change scale-degree function from 5 to 3. Theretrograde of this particular stream also affects both major articulations of the form throughAA AAprimary streams on pc D — the primary stream <3,5> into R8 and the primary stream <5,3>into R12. That is, at R8-i-4 we hear PC D change scale-degree function from 3 to 5; and atA ARi 1ff. we hear pc D change scale-degree function from S to 3. Thus, the palindromicstructure within part B is reinforced by a larger process of retrograde of two statements ofAAthe primary stream <3,5> successively on pcs D and B, which begins in part A and ends inpartAl.The pc-scale-degree design in parts A and Al also reinforces palindromic structure.AAFor example, the streams resulting from the E-D pairing in part A, the streams <4,6> andare reversed in Al by the final two scale-degree functions in the E-D pairing atR16. That is, in R5-2 to R8 we hear pcs E and D change scale-degree functionsA A A Arespectively from 4 and 3 to 6 and 5; and in R15 to R16 we hear pcs E and D change17This correspondence confirms a relationship between the C# tonic of R9+2 and the C tonic of R13 thatis suggested by the use of a variant of motive 1 and, more generally, by the use of an imitative texture.See the discussion of Example 5.11 on p.192.214scale-degree functions respectively from 6 and 5 to 4 and 3. Similarly, the primary streamA A AA<1,?13> on pc B at R6 is retrograded in the primary stream <3,1> on pc C at R14±3. Thepalindromic structure established by all of the above correspondences is framed in R17-3by the recapitulation of one of the pc streams, <3,> on pc F, which began themovement in Rl+2.5.5 SummaryLet us summarize the main features of the above analysis and focus on the centralquestion of this study: what function do tonics serve — how do tonics and their successionsrelate to form. Figure 5.1 clearly shows that most of the divisions in the thematic design —the two major divisions (R8 and R12), and all of the lowest level divisions in parts B andAl — are supported by a change in tonic. Indeed, the only divisions in the form that are notconsistently reinforced by changes in the tonic occur in part A at sections al and a2, andsubsection b. This suggests a contrast between parts A and B that is also establishedmotivically. The only two subsections in the form that contain more than one tonic —subsections dl and d2 in parts A and Al respectively — are thematically related and functionas a transition to the material of section b. This reinforces the thematic unity between partsA and Al. The intervals between successive tonic pcs also reinforces the form.Successive tonics in parts A and Al are related primarily by perfect fourth and majorsecond. However, successive tonics in part B are related exclusively by major or minorthird.Tonics in this movement are quite often obscured or ambiguous. A characteristictype of ambiguity arises between 1C5-related tonic pcs (i.e., in the first tonal area).Another type of ambiguity between successive tonics is that caused by tonal foreshadowing(i.e., when B is foreshadowed at R16-4 at the end of the G tonal area). Foreshadowing isconsistently associated thematically with a particular variant of motive I. The ending ofpart A, however, is marked by an ambiguity that, created by simultaneous transpositions215with different tonal implications, can not be resolved. This helps to further differentiatepart A from part B, because the tonics of the latter are not inflected by ambiguity.The interaction of the motivic materials in this movement generate a pc-scale-degreedesign that reinforces the form. This design establishes the similarity between the endingsof parts A and Al in terms of successive focal pcs, and it emphasizes the differencebetween parts A and B by using different structures, which are respectively crescendo-likeand symmetric. The pc-scale-degree design incorporates a palindromic structure that,although centered on the middle of part B, clearly links parts A and Al. The beginning andA Aending of the movement is signaled by the statement of the same stream (<3, 7>) Ofl PCF. However, the pc-scale-degree design can also be understood as a working out ofmotive 1.18 It contains numerous references to streams that incorporate differentrepresentatives of the third scale-degree, and uses {F, F#} and {B, Bb} as analogous setsof opposed pcs that are alternately focused upon. Both of these characteristics areemphasized on the surface of the music around R2+ I when the tonic changes for the firsttime in the movement.18Copland alluded to this feature in his statement that all melodic figures (in the first movement of theShort Symphony) result from a nine-note sequence — a kind of row — from the opening two bars.” He alsoalludes to it by his alternate choice of a title for this piece — “The Bounding Line.” Aaron Copland andVivian Penis, Copkmd: 1900 Through 1942 (New York: St. Martin’s/Marek, 1984), 209.216Chapter6Piano Sonata, First Movement6.1 IntroductionIn the previous chapter we saw how a large-scale retrograde became one of thecentral ideas behind the pc-scale-degree design of the first movement of the ShortSymphony. In the present chapter we will discuss the first movement of the PianoSonata,which is another characteristic example of Copland’s “serious” music. We shall see thatthe pc-scale-degree design of this movement, like that of Billy the Kid, features therepetition of streams on different pcs and, like that of Quiet City, imbues certain streamswith a formal (recapitulative) function.6.2 FormCopland has described this movement as a “regular sonata form with two themes, adevelopment section characterized by disjunct rhythms and a playful mood, and a clearrecapitulation in which the opening idea is dramatically restated.” Neil Butterworth goesso far as to claim that this movement has “a basically classical sonata form.”2 Authors suchas Julia Smith and Neil Butterworth, have fleshed out Copland’s terse summary of theform by making the location of the second theme explicit (i.e., mm.58ff.), by adding a fewcursory references to tonality and by defining the thematic structure in more detail .3 Takingthese analyses as a point of departure the top four lines of Figure 6.1 analyze the firstmovement of the Piano Sonata as a modified sonata form. Although the large-scalethematic design of a traditional sonata (i.e., Exposition-Development-Recapitulation-Coda)‘Aaron Copland and Vivian Penis, Copland: 1900 through 1942 (New York: St. Martin’s/Marek, 1984),p.33 I.2Neil Butterworth, The Music fAaron Copland (Gloucester: Toccata Press, 1985), p.84.3JuIia Smith, Aaron copiand: His Work and contribution to American Music (New York: E. P. Duttonand Company, Inc., 1955), pp.231-232 and Butterworth, op. cit., pp.84-85.217is discernible, there is a different and unexpected character to the overall form. At the mostbasic level, there is an unusually high degree of similarity between the thematic materials.For example, Smith, among several other authors, notes that the second theme is anembellishment of the first and that the recapitulation of the second theme acts as anaccompaniment to a theme which is derived from the original idea.4 The different sectionsof the form, however, also acquire unexpected characters. For example, an unusualallusion to a rondo form is made in mm.33 and 50 by the dramatic restatement of theopening chordal gesture. These measures are identified in Figure 6.1 by the bracketed term“motto.” Similarly, the development section, which usually divides into several shortersections in a traditional sonata form, is strikingly divided into two very disparate halves atm. 123 by changes in texture and tempo. From the perspective of thematic developmentthis division is logical because these two parts focus respectively on the first and secondthemes and are connected by a transitional passage whose material is derived from both theearlier transition (i.e., mm.44-47) and the second theme. However, the second part isunusual because its emphasis on rhythm is manifested in a dance-like character that is morerepresentative of the second movement than of the first, in which it never recurs. As aresult, this passage sounds within the sonata form more like an interlude or hiatus thatforeshadows the next movement than like the continuation of the development sectionbegun at m.96.Other departures from traditional sonata practice, which are reinforced by the tonicsuccession, include highlighting the variations of the second theme in the Exposition by theunconventional technique of giving each variation a different tonic. (The transpositionalrelationships between second theme subsections in Figure 6.1 are identified in Table 6.1.)This gives the second theme a far different character from that which is expected. In atraditional sonata the second theme prolongs a single tonic as a contrast to the fluctuating4Smith, op. cit., p.232.Figure6.1SummaryofThematicandTonalDesignsintheFirstMovementof thePianoSonataMm.:1ii26333538445053586774808693—Parts:Exposition—Sections:FirstThematicAreatrans.1(motto)(motto)fSecondThematicArea—Subsections:aalba2cda3eele2e3e4—Tonics:BbBbkFFF)Cdir.CGDFCEGdir.—III1L,1)2)13)]Mm.:96104106112115118123127133141162169175189Parts:Development—Sections:PartI(onTheme1)trans.2(ontrans.i,Theme2)PartII(onTheme2)—Subsections:a4aSa6cieSe6e7e8e9elOf—Tonics:GAbA1XEbdir.EbBBbDF#Fi?cDA-Mm.:196204211223234237Parts:RecapitulationCodaSections:FirstThematicAreatrans.3ThemeISecondThematicAreaSubsections:a7a8a9elialOTonics:BbDbBbdir.BbTable6.1SummaryofTn-RelatedSubsectionselT7eciT3ce2T3e1e9T4e7e3T7e2a9T3a1e4T4e3eliT9e4aST1a400219tonality of the transition. However, in the first movement of the Piano Sonata the secondtheme assimilates tonal fluctuation into its character. Since inherent characteristics of thefirst theme are explored in the second thematic area, one might hear the latter as adevelopment section.The recapitulation also differs from that in a traditional sonata form because, asindicated by Smith, it places more emphasis upon the first theme than upon the second.For example, the first theme is recapitulated with a new thematic and tonal structure: thetwo halves of the first theme (mm. I and 11) have different tonics and are connected by aninterpolated transition. The omission of the original transition which connected the firstand second themes make the arrival of the second theme in the recapitulation more subtle,and reinforces the dramatic predominance of the first theme. Thus, the recapitulation of thesecond thematic area is uncharacteristically understated and sounds more like anothervariation of the first theme.The recapitulation of the second theme in a tonic other than that which begins andends the movement is not unusual in itself, especially in light of the sonata forms in lateRomantic and early twentieth-century music. However, this recapitulation is logicalbecause it concludes an intervallic series that is derived from a descending minor third inthe first theme, and permeates the tonic succession in the movement. Only a few of theelements of this process are indicated in Table 6.1, by the various transpositionalrelationships which are shown between corresponding subsections. The full scope of itseffect will be apparent only when we comprehend the tonic succession of the entiremovement. Therefore, this process will be discussed only at the end of the section ontonality below.22063 Tonality6.3.1 Exposition — First Thematic AreaA Bb tonic is generated in mm.lff. by the opening chordal gesture. This gestureemphasizes pc Bb as the root of three different sonorities and presents the Bb-minor triad inthe soprano and an incomplete Bb-major triad in the bass. In mm.3-5 Bb continues to besupported weakly by the modified Bb-Aeolian collection {Bb, C, Db, D, Eb, F, Gb, Ab}5but more clearly by an underlying voice-leading pattern that is shown in Example 6.1. Thelast Bb-rooted chord in Example 6.1 is what would result if the contrary motion establishedin m.3 between the outer voices were maintained. The gesture notated in Example 6.1would also support a Bb tonic as it contains a directed motion in the bass that terminates onBb3, which is the root of the final chord. The last three pcs in the soprano of this gesturecreate an intervallic motive, <-2, -1>., that will be reflected in the tonic succession of themovement, as we shall see. Copland obscures the “resolution” to Bb at m.5, however, bysubposing pc G beneath Bb and withholding pc Db thereby transforming the held chordinto a transposition (T1 j) of the chord which preceded it. This challenges our expectationof the Bb root because not only is the characteristic contrary motion disrupted but also theresulting accent on pc G in the bass raises the possibility of a new G root.6 The “wrongnote” quality to G is enhanced by the fact that it does not even belong to the underlyingreferential collection of Bb.‘This is a version of the diatonic octad” (i.e., a modified diatonic collection with two representatives of thethird scale-degree) similar to that discussed earlier with regard to Example 1.1. See pp.8-9.6The resultant chord, {G2, 8b2, C4, F4}, is similar to other jazz-related (four-two) chords used by Coplandwhere the bass tone is, in fact, the root. See, Ibr example, the sonority {B2, A3, D4, E4} at R3+1 ofQuiel City where the bass pc sounds like the root.4;._.___#3mm.:3 4-3* • EEEE----<-3, +1, +2>Our hearing is directed toward the arrival of the Bb-rooted sonority in m.12 becausethe soprano line of mm.3-5 — <F, Ab, Gb, F> — reappears in mm.11-12 transposed (upfive semitones) so that pc Bb is the melodic goal. However, the removal of Bb in the basswhen this two-measure phrase is repeated (mm. 13-14) reduces the strength of the Bb rootand allows other tonal implications to emerge. The first of these occurs when the samemelodic cell is again transposed up five semitones in m. 16, making Eb the terminal pc.However, an Eb tonic is denied when the concluding note of the cell is relegated to an innervoice, so that pc Eb is not the root or lowest tone of the supporting chord. Instead, theharmonization of this cell with parallel five-three chords emphasizes Ab as the final root.The resultant voice leading in the bass, which is very similar to the directed motion shownin Example 6.1, suggests an Ab tonic. Ab does receive some further support as a tonic bythe presence of the pcs Cb and Fb, which are foreign to the established Bb referentialcollection.Ultimately, we do not hear Ab as a tonic because of the continued presence of themelodic cell <Bb, Db, Cb, Bb> and because the return of the opening chordal gesture inm.23 makes us hear the bass line of mm. 13-23 as a step ascent from F to Bb (see Example6.2). The fourfold repetition of the ascent <F, G, Ab> is marked by the gradual accretionof parts from a three- to a five-voice texture. The completion of this ascent to Bb isobscured by placing Bb in a higher register in m.23.221Example 6.1 Contrapuntal Model of mrn.3-5<+3, -, -1>A Ii —I222Example 6.2 Bass Step-Progression in min.13ff.We expect a Bb tonic to emerge from the minor third {Bb, Db} at m.26 becausethis would allow us to hear a more satisfactory conclusion of the bass ascent from pc Fwhich begins in m.13. The first two chords of m.26 seem to support Bb as a tonic becausethey are familiar as the first and last sonorities respectively of the opening phrase of themovement. However, it is F, and not Bb, which emerges as the tonic of the chordaltexture at mm.26ff. This ambiguity is acknowledged in Figure 6.1 by a tonal overlapbetween Bb and F tonics.In mm.26-27, F is generated by a chord progression that resembles <iv, [i], i7, V6,i> in F minor.7 This relatively traditional progression, however, is obscured because anunconventional registration moulds the gesture into the shape of a directed motion. Theresulting bass line contains a directed motion which similarly predicts an F tonic: adescending motion from Bb2 terminates on an accented Fl, which is the bass pitch of theminor third {F, Ab}. The unusual registration becomes particularly important in therepetition of this gesture in the following three measures when the insertion of a Bb-majorsix-three chord between the two last chords obscures the crucial dominant-tonicprogression. Although confusing to the underlying conventional harmonic progression,7j do not hear 0 as the root of the second chord in m.26 because pc 0 behaves, like the G in m. 10, as aneighbor tone to pc F. For this reason I hear the second chord as having an F root which is delayed.II I_____IJI(IV)number of voices: 2 lowest 4 lowest all 5 voicesand highest223this change actually helps in the generation of an F tonic by directed motion because thechange of the penultimate chord when the gesture is repeated allows us to hear the {F, Ab}dyad as the most accented chord in the passage. As a result, the F tonic suggested by theroot succession in mm.26-27 is most clearly generated by directed motion in mm.26-30.The proximity of a Bb tonic in this passage is suggested by the ease in which themotto of the first theme resurfaces at m.33. The tonal impetus of this motto, however, isnegated at m.34 when F, and not Bb, is heard as the final root. This arrival is prepared,albeit abstractly, by the phrase structure and voice-leading of mm.26-32. The phrasestructure in this passage is based on a double repetition of the two-measure phrase inmm.26-27. Each repetition of this phrase is extended by adding one chord after thepenultimate chord of the previous phrase. That is, mm.28-30 adds a Bb-major six-threechord after the C-major six-three chord of the previous phrase; mm.3 1-32 adds a C-majorfive-three chord after the Bb-major six-three chord of the previous phrase. The metricaland dynamic accents on the penultimate chords of the first and second phrases of thepassage, in mm.27 and 30 respectively, suggests a step-progression that is explicitly statedin the voice-leading of the third phrase in m.32 (see Example 6.3a). However, thejuxtaposition of the accented C-and Bb-major six-three chords to the crucial {F, Ab} dyadsuggests that we hear a similar step-progression over a much longer timespan — mm.26-34— between the accented sonorities (see Example 6.3b). Example 6.3c presents a tonalinterpretation of the step-progressions in Examples 6.3a-b. It posits a progression in F,<V6, 1V6, V, IV> — supporting a linear inner-voice motion above the sustained tonic pedaltones {F, Ab}.8 The gradual registral expansion of the original two-measure phrase intothis step-progression recalls the gradual accretion of voices around the incomplete ascent<F, G, Ab> in the preceding step-progression in mm. 13-26. Although attractivetheoretically the tonal interpretation in Example 6.3c is very difficult to hear because thej hear pc Gb in the chord on the downbeat of m.33 as a neighbor tone to F, and not as a root, because therecapitulation of the first theme makes me expect a Bb root here and because Gb sounds as a dissonanceagainst PC F in the next chord, which does have a Bb root.224ending of the step-progression is obscured in the context. For example, the bass of thethird phrase (mm.3 1-32) does not terminate on pc F like the earlier phrases of this passage.Further, when F finally does arrive in the bass (m.34) it is stated in the wrong register(i.e., two octaves higher). This breaks the most fundamental aspect of the step-progression in Example 6.3 — the fixed register of pc F in the bass — which is establishedby the directed motions in mm.26-30.Example 6.3 Bass Step-progression Between Metrically Accented Sonorities in mm.27-34a) Successive chords in mm.32ff. b) Accented Sonorities in mm.27ff. c) Tonal Interpretation of mm.27ff.‘ - I- I I N IE• I L.’jF:V6 w6 V iv iIpedalIn the following repetition of the motto at m.36, however, the crucial ending chordis obscured by the neighbor tones {Gb, Db}. The subsequent denial of repose which thiscreates extends this repetition into an ascending directed motion which has C4 in m.38, theaccented bass pitch of a C-minor triad, as its goal. The tonic succession in Figure 6.1reflects this transformation by showing the passage as an overlap between the F and Ctonics.C is confirmed as a tonic in mm.38-40 by the harmonic progression <i, iv, v, i>.The parallel voicing of these chords results in the linear intervallic pattern 5-5-5-5. Theharmonic progression in mm.38-40, like that in mm.33-34, is also transformed uponrepetition into a directed motion (mm.4Off.) that similarly treats C as a goal.-—qg-...—.. —‘-v-r,-.a-’.®---__L lp— I._ —--—-,-l- 11p: --®@€®L I—-----------...iD-‘——225The return of the first theme in m.50, which so forcefully directs our attention awayfrom C, initiates a passage of tonal ambiguity. By the simple recapitulation itself we arepredisposed, as in m.33, to hear a Bb tonic. The nearness of Bb is suggested by the wayin which the C tonic dissipates: the Bb-major triad, which is so prominent at mm.44ff., isfollowed by an implied F-root in m.49, suggesting that F is Bb:5 and needs to resolve to aBb-rooted sonority in m.50. However, an F tonic is equally near because the bass pcs C,Bb and D in mm.48 and 50 respectively are identical to those which prepared the F-rootedtonic chord in mm.32-33.Copland avoids both Bb and F by the simple expedient of substituting a new chordat the end of m.50, which is a pitch transposition up two semitones of the F-rooted chordin m.34, for the expected Bb-rooted concluding chord. The resulting G root, whichinitially sounds strikingly out of place, recalls the unexpected chord in m.5 with G in thebass. Like the earlier treatment of m.34, the root of this final chord eventually proves to bean accurate indicator of the forthcoming tonality. However, the new G tonic, unlike the Ftonic at m34, is introduced very abruptly and largely without preparation. Onlyretrospectively can we hear how the motto at mm.50-51 incorporates the melodicpresentation of the G-minor triad in the bass and perhaps implies a dominant-tonicprogression in G between its second and third sonorities.96.3.2 Exposition — Second Thematic AreaThe apprehension of G is further obscured when it becomes apparent that all of thematerial in mm.36-38 has been similarly transposed up a tone in mm.52-57. This results ina directed motion toward D where the terminal D-minor triad is placed under a fermata.Unlike the C tonic at m38, however, D is not confirmed as a tonic by another technique atmm.58ff. and so we tend to hear the D-minor chord, at least from mm.58-63, as the9When interpreted in 0 the second chord in m.50 is not heard as the Bb-major six-three chord with addedminor sixth that we are preconditioned to expect but as an altered dominant of G that has a raised fifth andboth minor and major thirds.226dominant of a G tonic. A G tonic is suggested in these measures by the melodicpresentation of the G-major triad in the bass. This bass line contradicts and overshadowsthe orientation of the melody which, when taken by itself, suggests Bb as a tonic.° Thisrecalls mm.33ff. and 50ff. where Bb was similarly hovering. G is reinforced as a tonic inmm.58ff. by giving pc G a metrical accent each time it is stated in the bass in mm.58-62and by associating the corresponding dyad, {G, Bb}, with G-rooted sonorities.11 G isweakly supported by the modified G-Aeolian collection {G, A, Bb, B, C, D, Eb, F},which is a transposition of the Bb referential collection in mm.lff.The implication of G as tonic is, however, weak because G is not established by adirected motion or a chordal progression unlike all of the other tonics so far in themovement. Indeed, a G tonic is contradicted by references to a D tonic starting as early asm.63. For example, in mm.63 and 66 it is D and not G which is metrically accented as aroot in the bass. These D-rooted chords are not heard as subordinate to the G-rootedchords because the only time D and G appear in successive root position triads (mm.66-67)the progression sounds like the beginning of a <i, iv, i> progression in D. Coplandemphasizes the relative weakness of the G root in m.66 by the intervallic structures of thechords: the D-rooted sonority is a complete minor triad but the Grooted sonority is only adoubled minor third. This suggests that we retrospectively hear a similar (hierarchical)relationship between the root position D-minor triad and the doubled minor third {G, Bb}in mm.57-58. The implication of D in the opening of the second thematic area is alsostrengthened retrospectively at m.67 when T7 of the theme generates the D tonic which wasforeshadowed by the directed motion into m.57.It is possible to hear D as a tonic throughout mm.58-73 because the G tonic isrelatively weakly generated when compared to the (transposed) directed motion whichnearness of a Bb tonic in the material of the right hand is demonstrated by the way a simple pitchsubstitution in the harmony voice — substituting either D5 or 8b4 for G5 in m.66 — results in a muchstronger sense of that tonic.‘Some of these sonorities, like the chord on the downbeat of m.61, are obscured by neighbor tones.227preconditions us to hear D. However, to analyze this passage simply as a D tonic would beto risk inconsistency in the analysis. For example, if we take mm.67-73 outside of thecontext, as we did mm.58-66, we find that D is established as a tonic by the same elementswhich earlier suggested G. It does not make sense to place such an emphasis on thedirected motion into m.57, which, at any rate is not immediately confirmed, because thetransposition of the actual theme itself proves to be what guides the tonic succession in thesecond thematic area. That is, successive transpositions of this theme result in F, C and Etonics at mm.74, 80 and 86 respectively. Figure 6.1 therefore represents mm.53-66 as atonal overlap between G and D tonics.The G and D tonics become the first “leg” of a larger sequence of tonics. Themotion from G to D is replicated down a tone, thus creating a second “leg,” when F(mm.74ff.) is succeeded in m.80 by C. The sequence is broken in the next “leg” becausethe E tonic at m.86 is never succeeded by a B tonic. The “legs” of this sequential tonicsuccession begin on G, F and E respectively. This series of transpositions corresponds tothe interval series <-2, -1>., which spans the soprano line <Ab, Gb, F> in mm.3-5.One of the more interesting aspects of this sequence is that it underlines thedependency of the second theme on the first theme, which was already noted with regard tothe thematic materials. The tonic succession is modeled after a central intervallic motive —<-2, -1>— and adopts the single tonal principle — the motion to tonics that are a perfectfourth lower — that was explored in the transition.The perception of this sequence is enhanced by the manner in which these tonics areconnected. For example, the use of metrical accent in mm.66-67 to announce the firstsonority of the D tonal area at the end of the preceding G tonal area is paralleled in mm.79-80 where the first chord of the C tonal area, {C, Eb}, also appears on the downbeat of thelast bar of the preceding F tonal area. Similarly, the linear ascent of a third in mm.73-74,when D is succeeded by F as the tonic, is paralleled by a similar ascent in mm.85-86 when228C is succeeded by E as the tonic. However, these connections are parallels in only asuperficial sense because each omits the expected functional harmonic connection betweentonics. For example, the functional <i, iv, i> progression that connects the G and D tonicsat mm.66-67 is wholly lacking at the corresponding place (mm.79-80) when F issucceeded by C as the tonic. Similarly, the functional progression which connects the Dand F tonics at mm.73-74, the <vi7, 1V6, viiø7, i> progression in F minor, is absent at thecorresponding place (mm.85-86) when C is succeeded by E as the tonic.The lack of functional harmonic connection between parallel tonic successions isimportant because it underlines the emphasis on the relative major in the soprano. Thisemphasis becomes particularly noticeable when the melody is no longer harmonized inthirds at the beginning of the second “leg” of the sequence (mm.74ff.). By the time that theE tonic arrives the implication of the relative major is so strong that we can almost hear atexture that has been divided into two separate tonal strands: a lower strand in E and ahigher strand in G.6.3.3 Development, Part IThis emphasis on pc 0 in the melody of the E tonic is largely responsible for theease in which the expected B tonic, which is suggested in m.93 by the doubled minor third{B, D}, is transformed, by a different incorporation of the triadic bass line of the secondtheme, into a 0 tonic. However, this tonic does not become clear until at least m.97.Example 6.4 provides a sketch of mm.93-103. Initially, we are predisposed to hear thetonic as C, at least in mm.93-96, because preconditioning suggests that the bassarpeggiation of a C-major triad is tonic-defining. A C tome even seems to be confirmed inm.96 when the opening measure of the development section appears to introduce T2 of thefirst theme. However, m.97 does not continue this transposition because the goal of thisthree-chord gesture is a strongly accented root position G-ninth chord. Thus, m.96actually introduces T2 of mm.33-34 where the soprano has been modified and, therefore,229suggests a G tonic. The extremely wide leaps in the lowest sounding voice of mm.96-97 —the line <C4, E2, G 1> — confirm G as a tonic by making it the goal of a descendingdirected motion. This small-scale directed motion is nested within a larger-scale directedmotion from B3 in m.93 that also terminates on G 1 in m.97. The motto of the first themeat m.96 obscures but does not negate the tonic-defining effect of the larger-scale directedmotion. This motion from m.93 also contains the germinal plagal progression whichconstitutes the harmonic basis of mm.96- 103.“iv 6’ iv “jT 6” i 9 “iv” “iv 6”The G tonic at mm.96ff. is much stronger than the previous G tonic at m.58.Although both are obscured by references to another tonic pc — C at mm.96ff. and D atmm.58ff. — there is no doubt in m.97 that G, which seemed to be hovering over mm.50-66, has solidly arrived. A relationship between these two instances of G is alluded to inmm.94-95 when the only G-rooted sonority is the same minor third — {G, Bb} — whichbegins the second thematic area proper (i.e., m.58).’2 The G tonal area at mm.97ff. is alsointeresting because it reprises the plagal harmonic setting that was introduced at mm.33-34and thereby suggests a long-term T2 relationship between the transition (mm33ff.) and the121 will not address the possibility of a prolongation of G over the entire second thematic area because it isnot germane to the present discussion.directed motion 0 tonicII LJG: [16] IV3b3 j 1V3b3 i J”.J 3b3 iv ‘IV 6” i 9 “IV”230Development (mm.97ff.). This presents a macrocosmic version of the microcosmic T2relationship between the terminal chords of the first theme motto at mm33 and 50. Themost curious aspect of this long—term connection is that it further minimizes any leftoverindependence we perceive in the “second theme,” suggesting rather that the entire secondthematic area is an extension of the first thematic area.The two-measure phrase in mm.102-103 is transposed up a semitone in thefollowing two measures. Instead of an exact transposition of the bass, however, Coplandinterpolates a transposition of the bass line from the directed motion that is shown inExample 6.1. The resulting bass ascent from Bb to Db recalls a similar ascent from F toAb in mm.l 1ff. The bass ascent in mm.104-105, like that in mm.llff., does not representa directed motion (which generates a Db tonic): the T1 transposition makes us hear the Dbninth chord in m.105 as Ab:iv9. The harmonic basis of mm.104-1 15, like that of mm.93-103, is also an extended plagal cadence (see Example 6.5). The last subdominant chord(m. 114) resolves to a root position Ab-minor triad that is inflected by two neighbor tones(Bbb and Fb). Like m.35, these neighbor tones transform what would otherwise be agesture of harmonic resolution (i.e., Ab:<”1V6”, i>-) into a directed motion which is atransposition (up a minor third) of the material in mm.36-43. This striking use of neighbortones makes the parallel between the first two tonal areas of the Development section andmm.33ff. even more apparent and thus confirms the Ab tonic retrospectively.Example 6.5 Plagal Progressions Defme Ab as Tonic in mm.104-1 15Ab: “iv 6” iv9 jb7[jv4Jj 9 jb7[jv6]j9jv93 b7 4‘iv6 “iv ‘,1V6” iv 9 “IV6”231The arrival of G and Ab as tonics at the beginning of the Development also suggestsretrospectively that the second thematic area is a development of the first thematic areabecause they are the second and third members of an inversion of the <-2,-I> intervallicseries (i.e., <+2, + I>) that is formed by successive transpositions of the first theme. Thatis, a <+2,+l> series is generated by the F, G and Ab tonics that result from thetransposition of the first theme in mm.33ff., mm.97ff., and mm.IO4ff. respectively. Thecontinuity of this series is reinforced on the surface of the music by the harmonic setting ofthe motto of the first theme: in all three passages the underlying harmonic progression ofthe motto is a plagal cadence. This series links the transition to the Development.The directed motion which is initiated in m. 115 generates an Eb tonic from Ab inm.1 17 in the same manner in which a C tonic was generated from F in m.38. Like theearlier passage, the second diverted tonic points strongly toward an accented Eb tonic atm.123. This impression is a result of preconditioning: we expect a continuation of thelarge-scale transposition such that m.123 will be the transposition of m.44. However, theexpected Eb-minor triad with PC Eb in the bass does not materialize in m. 123 and we get anew passage and a new tonal area where there is a significant amount of ambiguity.At least four different tonics — pcs Eb, G#, F# or B — could be ascribed to thematerial of mm. 123ff. Although the last of these — pc B — is eventually heard as the tonicof the entire passage, B is by no means clear as a tonic at the beginning of the passage.Therefore, let us discuss the evidence for each possible tonic in turn. Pc Eb is suggested inm. 123 because of the preconditioning invoked by the large-scale transposition (asdiscussed above) and because the highest voice of the first two dyads in this measure —{D#2, B5} and {F#2, AI5} respectiveLy — sounds like a b6-5 neighbor-tone motion overan Eb root. Pc G# is also, however, suggested as a tonic in mm.123-124 because themelody is Ti-related to the original melody in the second theme (i.e., mm.58ff.). We canalso hear references to an F# tonic in mm.123ff. because the step-related parallel fifths in232m.l23 — {B2, F#5} and {C#3, G#5} respectively — recall the subdominant and dominantchords within the linear intervallic pattern of the preceding Eb tonic (i.e., in mm. 117-119).The referential collection at mm. 123ff. helps in evaluating these first three possibilities forthe tonic. For example, the collection makes Eb unlikely as a tonic because it contains pesA and E, which are not members of the established Eb referential collection (mm. 117ff.).Similarly, the collection of mm. 123ff. makes G# unlikely as a tonic because it is not Ti-related to the collection at mm.58ff. However, the collection could support an F# tonicbecause an ordering from F# results in a collection with two different representatives of thethird scale-degree, which is familiar from the first and second themes. Ultimately, we donot hear F# but B as the tonic of this passage. We hear B as a tonic primarily because a B-major triad begins the ascending line in the bass and the pcs B and F are the beginning andending notes of the melodic line repeated in mm. 124-126. If one accepts the pcs E, A, Band C# as constituting a single A-rooted harmony then the bass line could be construed tomelodically realize a neighbor-tone motion around the pcs of the B-major triad. (Thismotion becomes more obvious if we place all the pcs of the bass line into the sameregister.) B is also suggested as a tonic by the new concordances that result when the bassand soprano motives shift their relative metrical positions. For example, the first and onlystatement of an octave in the passage, which occurs on the second beat of m.124, results ina sonority — {B1(2), A4, B5(6)} — that has a B root. Similarly, the succession of threedyads in mm.125-126, <{B3, F#5}, {C#4, B5}, {E4, A#5}>, is suggestive of theharmonic progression <I, ii7, V4/2> in the key of B major. This leads us to expect thedyad {D#4, B5} on beat 2 of m.126. The direction of this progression, however, isconfused because the leading tone, pc A#, is immediately contradicted in the bass byaccenting the other representative of the seventh scale degree, pc A.On the downbeat of m.127, like that of m.123, Copland similarly retains pc D# inthe bass but again substitutes an entirely new collection. Initially, it seems that D willemerge as the tonic of this collection for three reasons: pc D receives three successive233agogic accents in the two highest voices (mm.127-128); the agogic accent on D5 in m.128suggests that the dyad {F2, D5} is a goal and pcs F and D, which are prominent in thebass, are emphasized by a double voice exchange in m.129. A C tonic is also weaklysuggested because of the agogic accents on pc C in the bass and because the bass motive<F, D, G, C> is a restatement of a (soprano) motive that was introduced at mm.44-47when C was a tonic. However, the tonic of this passage is eventually defined as Bb.’3Example 6.6, which gives a verticalization of the melodic texture, posits an underlyingdominant-directed progression in Bb. This interpretation is suggested most strongly by thecurious dyads at the end of m. 129 and the beginning of m.130 which, when juxtaposed tothe bass {F, D} sixth, sound like a variation of Bb:ii6/5. The bass sixth, which representsan incomplete version of a Bb six-four chord, never resolves. Bb is supported as a tonicby a subset of the Bb-major collection — {Bb, C, D, Eb, F, G}.’413This is a very unusual transitional passage in Coplan&s music because the relatively clear change incollection at m. 127 is not accompanied by a clear change in tonic. We might easily posit Eb instead of Bbas the tonic for this same passage, or even hear the passage as based on an underlying chromatic step-progression with descending lines in the soprano and bass (i.e., <B (m. 123), Bb (m. 132), A (m. 133)> inthe soprano, and <D# (m.123), Eb (m.127), D (m.132)> in the bass). Either an Eb or Bb interpretationdoes not produce a significant change in the pc-scale-degree design and following analysis.14Pc E is heard as a non-collectional tone because it is constrained to the repeated neighbor-tone gesture inmm. 127-128 and occurs in less registers than the collectional pc Eb (i.e., pc E occurs in Iwo registers whilepc Eb occurs in four).Example 6.6 Verticalized Two-part melodic texture in mm.129-132Bb: J6 jj 6 I 6_ [ii 6] J6 [ii 614 5 4 4 5NC NC2346.3.4 Development, Part IIWe are predisposed to hear an A tonic at mm. 133ff. for three reasons: thefamiliarity of the opening melodic cell, <A5, E5, F#5, A5>, as ajazz gesture in A major;the emphatic accentuation of pc A throughout the first eight-measure phrase; and thetranspositional relationship (T2) between these same four notes and the first, third, fourthand fifth notes respectively of the second theme (mm.58ff.). However, the third of thesereasons is weak because the tonal ambiguity of the second theme could also suggest an Etonic. Despite the predisposition toward A we hear the passage as, ultimately, generating aD tonic even though this is delayed at least until m. 140. D is generated as the tonic becausethe melody as a whole tends to revolve around notes from the D-major triad: bothstatements of pc F# are punctuated by rests and pc A is associated with pc D on threedifferent occasions.The ambiguity between the A and D tonics, which is suggested from the outset ofthis section, recalls the ambiguity between G and D tonics at mm.58-66 and the ambiguitybetween G and C tonics at mm.93-103. One of the more striking aspects of this part of theDevelopment is how the later repetition at mm. I 70ff. of the material of mm. 133ff. weightsthe ambiguity between D and A heavily toward A just before A becomes the final tonic ofthis section (mm.175ff.).The return at m.141 of the eighth-note motive of mm. 13 1-132 as an introductionfor the repeat of the opening phrase presents a pared down retake of the material in the Bbtonal area at mm.127-133. This suggests that we hear a similar change in tonic to Bb atm.141 followed by a return to D in mm. 146ff.The recasting of the material from Bb in mm.l4Iff. suggests a further reason whywe should hear a D tonic at mm. 133ff. and also at mm. 146ff. This repetition reinforces thesense that the soprano line of the preceding transition, particularly mm.127-129, is235interwoven into the melody of mm.133-140. This is shown in Example 6.7. If this is thecase, the prominent accent on pc D in mm. 127-128, in a passage ostensibly generating aBb tonic, can be perceived as another example of tonal foreshadowing.The D tonic becomes more substantial in mm. 151-161 when pc D starts to becomemore accented than pc A in the high register and a second voice, which gradually emergesfrom the large leaps between the notes of a single melodic line, gives us grounds to infer aharmonic progression that revolves around a D-major six-four chord (see Example 6.8). Ifwe posit a final chord that has D as its root at m. 162 then the resulting <V, I> cadencereceives a conventional metrical setting with the dominant in a weak position (i.e., at theend of m.161) and the tonic in a strong position (i.e., on the downbeat of m.162).However, in m.162 the expected “resolution” of this progression — the return of the melodyof mm. 133ff. at its original pitch level — is denied when that melody is transposed (up amajor third) to begin on pc C#. This substitution allows the A root at the end of m.161 tosound over into the following measure suggesting, briefly, that pc C# is its major third.236This passage recalls similar uses of substitution elsewhere in the movement withintransitional sections (i.e., mm.33 and 50). It also parallels the most recent substitution,m. 123, because it similarly results in a shift between tonics related by a major third.Because of its transpositional relationship to mm. 133ff. the melody in mm. 162ff. alsogenerates an ambiguity between pcs a fourth apart. However, our tendency to focus on pcC#, which results from the lingering A root of m.161, does not expand into a sense of atonic because the opening cell is twice punctuated by an F# minor-major six-three chord.The lack of a C#-rooted chord to counteract and “resolve” the accented F#-rooted chordreorients our hearing away from C# toward an F# tonic.15 F# is supported by the pccollection {F#, G#, A, A#, B, C#, D#, E}, which is familiar from the first and secondthemes.In m.169, pc C# again initiates a change in tonic because it marks the return of theinitial collection from mm.133ff. We are predisposed to hear a D tonic here because atruncated version of the original melody is prefaced (mm. 171-174) by a D minor-major six150ne might also hear a B tonic for this passage for two reasons: B is emphasized as a chord root inmm. 158-160 near the end of the D tonal area (recall Example 6.8); and the F#-rooted sonority in m.163 hasthe same pitches in the lowest register — A2 and F#3 respectively — as the D-major six-four chord thatprepares the B-rooted sonorities in mm.158ff. The pe collection — {B, C#, D#, E, F#, G#, A, A#} — mightalso be construed as support for a B tonic because it is identical to that in mm. 127ff. when B was last atonic.Example 6.8 Tonal Interpretation of Verticalized Two-voice Melodic Texture in mm.15 1ff.D: 16 V4 /1V”IV6 “16 J6 “1V6”[V] 16 vi J6 vi IV V4 3 4 4 4 4237three harmony. However, the D tonic is almost overshadowed by an A tonic that is impliedin the first two measures. The A-major triad which introduces the original collection of thissection makes F# sound like a neighbor tone to pc E, as in the jazz melodic gesture <A, E,F#, A>, and consequently suggests that the D minor-major six-three chord is not a tonicbut, in fact, a subdominant harmony.The increasingly strong references to A in the thematic material of the D tonicforeshadows the arrival of an A tonic at mm. 175ff. The sense of flow from D to A here isstrengthened motivically in m. 174 when the final two-note motive of the original melody,<B5, A5>, is transformed into an ostinato in the highest voice in the next eight measures.The progression is also satisfying motivically because the respective materials ofmm. 133ff. and mm. 175ff. explore a different, but complementary, aspect of the secondtheme: the material in mm.133ff. explores the pc relationships within the melody of thesecond theme while that in mm. 175 explores the pc relationships within the bass of thesecond theme.The A tonic of this passage is generated by the melodic presentation of an A-minortriad as a descending line in the bass below the rearticulated pitches C5, ES, AS, and B5.’6At mm. 183-187 this texture is subtly altered: the bass line changes directions and adds pcG while the re-articulated pcs in the right hand are melodically combined to form a longer,ascending line — <C4, E4, B4, A4, C5, G5, D5, E5, B5>. The underlying repetition ofmelodic cell <C, E, B, A> in this line is obscured by interpolating two additional notes, pcsG and D, and omitting the final tone. A is supported as a tonic by the A-Mixolydiancollection.At mm. I 89ff. the D minor-major six-three harmony, which was implied earlier inm.170, becomes the harmonic basis for an entire phrase through simple repetition. A D16Not all of these pcs arc present in every measure because the trichords {C5, ES, B5} and {C5, AS, B5}alternate in mm. 175-178.238tonic is weakly suggested in these measures because the pcs used in the passage — {D, E,F, F#, G, A, B, C} — form a collection that contains, like the referential collections of boththe first and second themes, two representatives of the third scale-degree. D is alsoimplicated as a tonic because the composite soprano line, which results from successivelysuperimposing a trichord and two different dyads (i.e., the verticalities {E.5, F#5, A5},{G5, C6} and {85, E6} respectively) above a sustained D-minor chord, associates PC Awith pc D and states D-tonic motivic gestures that are familiar from jazz. Example 6.9acontains all the pcs of mm.189ff. and shows the soprano line by upward stems; Example6.9b extracts the composite soprano line to show the pc association between A and D andthe D-tonic motivic jazz gestures. The latter, which are related to the <A, E, F#, A>melodic cell in mm.133-134, are other familiar figures from jazz. They are slightlyobscured in the context because pc D appears in the wrong register.However, the lack of a harmonic progression supporting D suggests that the Atonic of mm.175ff. is not displaced and that the D-rooted sonority sustained in mm. 189ff.is A:iv6 (cf. m.178). An A tonic is also suggested by conventional practice — it is moretypical for a D-minor chord to function as A:iv than for an A-minor sonority to function asD:v.17 Because there is no tonicizing technique at mm.189ff., outside of the relativelyminor consideration of pc collection, which supports D as a tonic Figure 6.1 shows an A17n typical fashion, however, Copland does use precisely this progression — <v, I> — in the cadence thatdefines Bb as the tonic in the Coda. This cadence was discussed on p.33.Example 6.9 Composite Melodic Line in mm.189-1941” ‘rPC A associated with pc D239tonic for the passage. This casts a new perspective on the chromatic opposition betweenpcs F and Fl as thirds of a D harmony by shifting our understanding of these pitches fromthe third to the sixth scale-degree.6.3.5 Recapitulation — First Thematic AreaAt mm. 196ff. the first theme is recapitulated beginning with the motto at its originalpitch level. The framing chords of the motto are reasserted as tonic-rooted sonorities. Thisresults in a Bb tonic for the same reasons as in mm.lff (see pp.220-221). However, adifferent emphasis is cast upon this familiar material because pcs F and Ab are added aspedal tones below the final chord. This makes the final chord sound like a variation of thesonority which was heard on the first two beats of m. 11. A summary of this passage isshown below in Examples 6.lOa and b. These examples, unlike Salzer’s,’8do not attemptto show prolongation but merely to summarize the voice leading.The way these pedal tones are introduced mimics the directed motions which wereso prominent in establishing the F tonic in the beginning of the expositional transition. Forexample, mm.196-197 parallels mm.26-27 in that both begin on the dyad {Bb, Db} andend with an emphasis on the dyad {F, Ab}. Similarly, the cadence upon C-major and Bbmajor six-three chords in mm. 199 and 201 respectively, which are linked to the originalBb-rooted sonority in m.197 by the {F, Ab} pedal tones in the bass, parallels therelationship between the same chords in the transition in mm.27 and 30 respectively.Ultimately, these references facilitate the emergence of a transition to a secondrecapitulation of the first theme which has a tonic other than Bb. However, this role doesnot become apparent until much later in the passage.The growing implication of an F tonic, which is suggested by the parallel to thetransition of the Exposition, is negated in the next repetition of this gesture (mm.203-204).18Felix Salzcr, Structural Hearing: Tonal Coherence in Music (New York: Dover Publications, Inc., 1962),Vol. 1, p.194 and Vol. 2, pp.182-187.240Here the transposition of the second and third chords down a tone results in an unexpectedcadence on an Db-major six-three chord in m.203 beneath which is placed the equallyunexpected trichord {A, C, Db}. As the second half of the first theme emerges inmm.204ff. this bass A descends by step to F. The resulting definition of pc F as a goal inthe bass suggests that we hear the entire passage as a series of chords above the sustaineddyad {F, Ab}. This is shown in Example 6.lOa.Example 6.10 Summary of Voice-Leading in mm.196-210a)1s4L!44 -..-p—A AM —.--- >p—The voice-leading model in Example 6.1 Ob suggests that the purpose of theharmonies which successively end the repetitions of the motto is to bring out the centralchromatic opposition between pcs D and Db. This is achieved in two ways: by alternatingpcs Db and D within different harmonies above the F pedal — Db (m.197)-D (m.201)-Db(m.203)-D (m.208) — and by framing the entire passage by two Bb-rooted chords such thatPC Db is replaced by pc D as the third. Only the harmony in m.199, which functions as ab) Accented Sonorities241neighbor chord to the framing Bb-rooted sonorities in Example 6.lOb, does not containeither pc Db or D.The ultimate definition of the {F, Ab} pedal tones in terms of a Bb root (mm.208-209) is important because it suggests the continuation of the Bb tonic. However, this Bbroot, paradoxically, seems to be directed not to a Bb but to an Eb tonic. Our predispositionto hear this chord as a dominant seventh of Eb, because of the presence of pc D, isreinforced in the context because it is prepared by a chord — {F, Ab, Cb, Eb} — that couldbe understood as iiO7 in Eb minor. The resulting ambiguity between Bb and Eb tonicsrecalls the similar tonal ambiguity between 1C5-related tonic pcs that was introduced in thesecond thematic area.However, Copland avoids an Eb tonic when the expected ending of the motive inmm.207 (beat 3)-208 is transposed up a minor third upon being repeated in mm.209 (beat3)-210. This results in a major-minor seventh chord built above Db. A Db tonic is thengenerated in the following measures by recapitulating the second half of the first theme —mm. 11ff. — in a transposition up a minor third. This transposition also, however, makesreferences to a Cb tonic for the same reasons as it did an Ab tonic in mm.l6ff. (see p.221).Cb does not become the tonic essentially for the same reasons as those regarding Ab: thecontinued presence of the transposed melodic cell <Db, Fb, Ebb, Db>; and the return of themotto of the first theme in m.221.63.6 Recapitulation — Second Thematic AreaThe step-progression in the bass line of this transposed passage, the ascent from pcAb to Db corresponding to that of mm. 13-23, is concluded when the first theme isfollowed in m.223 by a similar transposition of the second theme to Db. Db is generated asa tonic in mm.223ff. in the same manner as those tonics in mm.58-86. The transpositionof the second theme to Db emphasizes how the original third scale-degree of Db, pc Fb (in242the first theme), is challenged at m.223 when pc F appears in the bass and at m.230 whenF6 becomes the melodic climax of the first crescendo in this passage. The inherent motionfrom Fb to F as the third scale-degree of Db mimics the underlying motion betweendifferent representatives of the third scale-degree of Bb (i.e., a motion from pc Db to pc D)that was shown in Examples 6.lOa-b (see p.240).At m.223 Copland superimposes what appears to be a new melody above thesecond theme. However, this melody is really a compilation of fragments from the firsttheme (mm.3-5), the transitional material (mm.36-44) and the second theme (mm.58-73).We return to the original Bb tonic by a directed motion that begins in m.234 andincorporates in mm.235-236 a transposition (down a tone) of the directed motion whichended the second thematic area in the Exposition (mm.93-95). This is shown in Example6.11. Like the earlier directed motion there is a delay in reaching the terminal chord; thegoal pitch, BbO, does not arrive until m.239. However, the root movement underlyingmm.235-236 mimics a <V.1> progression (as shown in Example 6.11) and not a <IV, I>progression like that of mm.93-95 (cf. Example 6.4). Because m.234 is ostensibly theorigin of the directed motion to Bb, we can posit two harmonic interpretations of thismeasure. It is not only understood as a clear continuation of the Db tonic (i.e., aneighboring motion around a Db six-three chord) but also as the embryo of a <v, i, v>progression in Bb. In fact, the transition from Db to Bb is dependent upon our hearing thechange in the function of the pcs F and Ab. The emphasis on these pes in mm.23 1-238recalls a similar emphasis on F and Ab at the beginning of the transition in the Exposition.EExample 6.11 Directed Motion Defines Bb as Tonic in mm.234-239Ii .0Au I -.Tr.—bL1 e.-S’.,..—.-.—. — IfL,4— I-I,-—J2* tdirected motion Bb tonicDb: I 6 vi”I 6”Bb: [v i vJ “J6” jb7[j4] Jbs VJ6 v 1b8 v i6.3.7 CodaThe intrusive {F, Ab} pedal tones, which so characterized the recapitulation of thefirst theme, are resolved in the final section of the movement when F and Ab appear as aseparate sonority that progresses to a Bb octave in m.239. This results in a descending-fifth root motion that recalls the implied progression in beats 1 and 2 of m.234. Themovement ends, appropriately enough, with the recapitulation of the element thatsymbolizes the first shift in tonics, the motto of the first theme. The final chord of thismotto, which was transformed in the expositional transition and the first part of theDevelopment section, now becomes a held chord below which is repeated the resolutivegesture of m.239.’919The fermata on this particular chord is significant because it can be understood as a metaphor for thechromatic opposition between pcs D and Db that is inherent in the referential collection of the Bb tonic andthat inlorms several important points in the form. For example, the only time a fermata is used on a nonBb-rooted sonority in the movement is in m.57 on the D-minor chord. This chord follows a section(mm.5Off. when the tonal direction shifts unexpectedly from Bb to G) in which Db and D are heard in astriking chromatic juxtaposition. The D-minor chord emphasized in m.57 plays a central role in acharacteristic ambiguity between A and D tonics at mm. 189ff. This passage of ambiguity is followed by aRecapitulation of first theme material that is modified to accentuate the alternation between pcs Db and D(ci. Example 6. lOa-b).24324463.8 Tonal-Thematic InterrelationshipsThe tonic succession of the first movement is unusual in Copland’s works in that itrepresents a significant layering of smallcr successions that follow the pattern <-2,-I>, itsinversion <+2,+ 1>, or its retrograde inversion <+ 1, +2>. This complex of patterns,which are derived from the voice-leading model of mm3-5 shown in Example 6.1,governs both the tonic succession of an entire individual section and the most significantarrivals in the form including the recapitulation of the second theme in a tonic other thanBb.Perhaps the most obvious manifestation of one of these patterns is in the tonicsuccession of the second thematic area. For example, the entire second thematic area isbased on the series <-2, -1> because the sequence draws our attention to the large-scaletonic succession <G, F, E>. However, these patterns also occur in much subtler ways inthe tonic succession of the movement. For example, the inversion of this series — <+2,+ 1>— is present in the successive transpositions of specific material over the course of themovement. For example, the series <+2, + 1> is implied when the successive transpositionof the directed motion in mm.36-38 — first up a tone in mm.53-57 and then up a semitonein mm.l 15-117 — suggests a connection between the tonics C, D and Eb. This successionis, however, obscured in the context because the striking ambiguity (between D and G)which shrouds the first transposition is removed only after a significant delay. Similarly,the series <+2, + 1> also results from transpositions of the subdominant-tonic harmonicversion of the motto of the first theme; this links the tonics F (m.33), G (mm.96ff.) and Ab(mm. 104ff.). This occurrence is particularly striking because the first transposition of theseries is foreshadowed by the T2 relationship that obtains in the transition between the Fand G-rooted sonorities which are substituted (at mm.33 and 50 respectively) for the finalchord of the first theme motto.245Both the Bb and Db tonics of the Recapitulation mark the conclusion of one of theserelated intervallic series. For example, the Bb tonic concludes the series <+1, +2> becauseit follows transpositions of the first theme which generated the G and Ab tonics inmm.96ff. and mm.lO3ff. respectively. The Bb tonic is also, however, predicted by a <+2,+ 1> series suggested by the transpositions of the second theme that generate the G and Atonics in mm.58ff. and mm.175ff. respectively. This series would account for the specialemphasis placed on an A tonic in the characteristic ambiguity at the end of the Developmentsection by identifying it as a preparation for Bb. However, this series is not literallypresent in the motivic-tonal design because the second theme is never transposed to Bb inthe Recapitulation. The Db tonic which replaces Bb in the recapitulation of the secondtheme also concludes a series: the successive transpositions of the second theme materialthat generate the tonics E(m.86), D (m.133) and Db (m.223) make Db the goal of theoriginal series <-2, -1>. This particular series gives added significance to the E tonic thatends the second theme: E is simultaneously the ending and beginning points of twoseparate statements of the <-2, -1> series.206.4 Pc ContinuityFigure 6.2 summarizes the pc-scale-degree design of the first movement. Thisdesign emphasizes a high degree of connectivity. All of the important articulations of thesonata form, mm.58, 96, 133, 1% and 237 respectively, are marked by at least twoprimary streams. Indeed, with the single exception of the shift from B to Bb in mm.123-127 every tonic succession in the movement emphasizes two or more primary streams ofconnection. Most commonly these streams are paired either by a recurrent dyad or, less20E is also highlighted in a more abstract way by the referential collections associated with the tonics ofthe second thematic area. Only three collections, those associated with the tonics D (m.67), F (m.74) and E(m.86) respectively, are missing the fturth scale-degree. By changing the order of these tonics we couldnormalize them into either the series <+2, +1> (i.e., <D, E, F>) or the series <-1, -2> (i.e., <F, E, D)which are, respectively, the inverse and retiograde of the pattern discussed above. The latter inference isparticularly important because the inverse of this pattern, the series <+1, +2>, links the Developmentsection to the recapitulation of the first theme. This suggests that the second theme foreshadows thestructure of the rest of the piece in an entirely unexpected and unconventional way.246often, by the continuation of a motive. The strategic use of simultaneous primary streamsthat are not paired in these ways, such as at the end of the transition and the second part ofthe development, stands in contrast to the use of paired primary streams in the two thematicareas within the Exposition and Recapitulation.The pc-scale-degree design in Figure 6.2, like that shown for Billy the Kid, showsa fair number of secondary streams. In several cases, these were chosen because they arerelated to other nearby primary streams. Different secondary streams, which other listenersmight hear at some of these points, are not included in Figure 6.2 to prevent its becoming asimple, and highly abstract summary of all the common tones present at any one tonal shift.The numerous streams in Figure 6.2 include many repetitions of streams. Transpositionlevels between such successive statements give the form an unconventional aspect. Thiswill be discussed below.6.4.1 Stream GenerationThe single most common method of generating primary streams in the firstmovement is by emphasizing a dyad that is common to the collections of successive tonics.For example, the first primary streams of the movement are generated by stating the dyad{Bb, Db}, which is emphasized at the beginning (m.l) and ending (mm.23, 25 and 26) ofthe initial Bb tonic, as the first sonority in the successive directed motions in the followingF tonic. The stream on pc Bb is the most important because the step-progression in thebass in mm. 13-26 focuses our attention on this pc. In Figure 6.2 these streams are labeledas also resulting from a reference to the first theme, which is indicated by the label “Ml”,because of the inclusion of the beginning and ending sonorities from the initial fivemeasure phrase as the first two sonorities in the directed motions.The second thematic area is permeated with examples of this type of streamgeneration in that every primary stream within it except one, the stream <2,7> on pc DFigure6.2Pc-Scale-DegreeDesignoftheFirstMovementof thePianoSonataI_sfss• 1—1:1—4—4—-S-b7-b3‘-I__5__‘,sfs‘1-b7-rb7—b3b3rxirci-‘---j6[----s2151S2-5—’—S—l—l—1-14—fELz-‘2-53 b3-i-tIIHF-1i3----II-5 3-Ss•1-b7b3I2-5—i—-Mm.:1112633353844505358677480Parts:ExpositionSections:1stT.A.trans.1(motto)(motto)2ndT.A.Subsections:aalba2cda3eele2e3Tonics:BbB?cFFikiDdir.CG—ThFCB--Bb-- MA Ab-G-F#--F--E--Eb D-Db-C--2-51--S 5—5-1—5—1—-Figure6.2(cont.)Mm.:(80)869396104106112115118123127133141146Parts:(Exposition)DevelopmentSections:(2ndT.A.)PartI(onTheme1)trans.2(trans.1,Theme2)PartII(onTheme2)Subsections:(e3)e4a4a5a6ci:e5e6e7e8Tonics:(C)EGdir.GAbEbdir.EbBBbDBbDB--Bb--A-Ab--0--F#--F--E--Eb--Db-C214-------—i.—’—p-I-s---1-4ii---b65‘1-51--P-i—3—4-f-s—Fp S-2Figure6.2(cont.)Mm.:(146)162169175189196204211223234237Parts:(Development)RecapitulationCodaSections:(Part11)1stT.A.trans.311stTheme2ndT.A.Subsections:(e8)e9elOfa7:a8•a9elialOTonics:(D)F#Fi)ABbDb(Db)Bbdir.BbB--BbA-Ab-G-F#--F--E--Eb--Db-C-,,1-6—21%.,-?c,.‘_-P-3—11—3---S-3—6\?IIIs-----i-2—4—••%-P-7—55—7-4—N__--——I—-b6- I—5—I 3—P13 I.’b3-b3I-I-II_%,‘>2—5b7—UIf—i-P1-f3—5-------b33--‘S-S-Ib3‘.5-b7—-—--I--S—5—--S-3-‘-Sb3-‘Sb2—---‘S.1250connecting the C and E tonics, is based upon a similar redefinition of a minor third. Whatchanges as the second theme is varied is the clarity of the articulation of this interval. In thefirst tonal shift (mm.65-66) the dyad {D, F}, which is common to the collections of the Gand D tonics, sounds by itself when it receives successive metrical accents. However, laterconnections, such as those between the tonics F, C and E in mm.74-86, obscure theplacement of the common minor third in the lowest two voices by sounding different notesabove it. Because this pattern relies on our perception of the bass, the lowest tone of thethird is considered to be the most important primary stream of the pair.Paired primary streams are crucial in the articulation of the Recapitulation and theCoda. For example, the main sense in which the end of the Development “prepares” thereturn of the first theme is by anticipating the special sound of the trichord formed by thepcs D, F, and F# (Gb).2’ This trichord is present as the most important notes of the Dminor-major chord, which forms the harmonic basis of mm.189-194, and as the lowestthree notes of the second sonority of m. 196. The stream on pc F is considered to be themost important because it is accented in the bass in both the D and Bb tonics (i.e.,mm. 189-194 and 197, 199, and 201 respectively). The stream on pc D is the secondstrongest because it is the soprano note of the chord stated on the downbeats of the D tonalarea and is the lowest tone of the second sonority of the Bb tonal area. Using thisparticular sonority to establish a pc connection between the D and Bb tonics recalls the waythe second chord of the opening gesture was (retrospectively) reinterpreted in mm.5Off. asan altered dominant in G.2 demonstrates how different Copland’s tonal procedures are from those in earlier tonal music. Herethe end of the Development section does not prepare hamionically as V for the following tonic or eventhematically for the firs theme as expected in a traditional sonata but rather by re-announcing a specificchromatic opposition between two pcs — F and Gb. This recalls how pes F and Gb were put into strikinglydifferent relationships when the motto of the first theme was stated in the expositional transition. The Atonic makes us consider pcs F and F# as different thirds of a subdominant harmony and, therefore, recallsthe G and Ab tonics of mm.96ff. and 104ff. which had a similar emphasis on different thirds in thesubdominant harmony. This reminds us of the first theme just before the Recapitulation begins.251This technique is also responsible for generating the two primary streams that endthe pc-scale-degree design of the movement. For instance, the connecting dyad {F, Ab},which is emphasized as the lowest two voices of a constantly shifting four-voice chord inthe last three measures of the Db tonic, is also accented as a dyad in the bass of the Bb tonalarea (m.237). The primary stream on pc F is considered to be the most important becausepc F, as the lowest note of the common third, occurs prominently in the bass in both tonalareas. The resolutive force of the reinterpretation of this particular dyad will be discussedlater.The technique of continuing a motive from one tonal area to the next also plays arole in this movement, albeit a much less significant one than the use of a recurrent pcdyad. The motives which are referred to in Figure 6.2 are shown below in Example 6.12.The use of motive I (the first theme) in mm.96- 114 emphasizes that the pcs E and Eb arecommon to the collections of the G and Ab tonics. In G they are different representativesof the sixth scale-degree, which are alternately focused on in the bass in mm.96, 99, 100and 103 respectively; in Ab they are emphasized as the outer tones of the first chord and asmembers of the sonority {Db, Fb, Ab, Bb, Eb} which ends the first gesture. The streamOil PC Eb is considered to be the most important in the pair because pc Eb is stronglyaccented in the bass and soprano voices around the timepoint of transition (i.e., mm.102and 105 respectively).22 Pcs Eb and E are made more apparent as connectors in m.104when pc Bb, which is also common to the bass lines <EM, Bb3, Eb3> and <Fb3, Bb2>,suggests that we hear pc Fb as a substitution for pc Eb. This mimics the initial chromaticopposition of Eb and E (i.e., as different representatives of the third scale-degree of C inmm.96 and 101) which established primary streams on these pcs in the first place.22TheT1 relation between identical chord-types in mm. 103-104 partially obscures pc Eb as a connector.252Example 6.12 Summary of Motives Referred to in Pc Continuity GraphMl (rini.1ff) M2(m.174)•214Other techniques which generate separate streams in the first movement of the PianoSonata include agogically accenting a pc in the outer voices and accenting the same pitch inthe bass. An example of the former can be seen in mm.33-38 where the primary streamAA<6,2> on pc D is generated by agogic accents on that pc in the bass of the F tonal area(mm.33-36) and in the soprano of the following C tonal area (mm.39, 41,44 and 45respectively). This stream is important in the immediate context because the substitution ofPC G for pc F as the tone which melodically follows pc D foreshadows a similarsubstitution involving the second and third chords of the first theme at the two statementsof the motto. When the F-rooted sonority of m.34 is replaced by a transposition up a tonein m.50, the end of the bass line shifts from <D, F> to <D, G>.Generating a primary stream by accenting the same pitch in the bass can be seen inmm.151-165. Here the primary stream on pc A is generated by consistent dynamicand registral accents upon A2 in the D and F# tonal areas (i.e., mm.151, 154, 156, 157,159 and mm.163 and 165 respectively).6.4.2 Unusual Techniques of Stream GenerationOne unusual technique Copland uses in the first movement of the PianoSonata isconsistently inflecting a common pc by different chromatic oppositions in successivecollections. This is used in only a single stream in the movement, the secondary streamA AA<b6,b2,7> Ofl PC Gb, which spans the first fifty measures of the movement. This stream is253generated because the unusual recapitulation of the opening gesture in mm.33 and 50makes us concentrate on the shifting function of pc Gb. Each of the three functions in thisstream are involved in chromatic oppositions with the other representative of the respectivescale-degree. That is, pc Gb is opposed by pc G as the sixth scale-degree of the Bb tonic(mm. 1ff.), and the second scale-degree of the F tonic (mm.33ff.) and pc Gb (understoodenharmonically as F#) is opposed by pc F as the seventh scale-degree of the G tonic(mm.5Off.). However, the second and third oppositions differ from the first, which ischaracteristic of the first twenty-five measures of the movement, in that they are constrainedto the measures which recapitulate the motto of the first theme.Another unusual technique Copland uses in this movement is emphasizing a pccommon to the collections of adjacent tonics by consistently stating it within the same voiceA AA1(Aand following it by a rest. For instance, at mm.133-174 the primary stream <3,1,1 3> onpc F# is generated when the statement of that tone in the soprano is consistently followedby a rest around the two points of tonal shift, mm. 162 and 169 respectively (i.e., mm.154,156, 158, 159, 163, 165, 170, 171 and 173).6.4.3 Pc-Scale-Degree DesignThe majority of streams shown in Figure 6.2 prominently incorporate a chromaticopposition at their beginning and/or ending points. The chromatic opposition in many ofthese streams involves different representatives of the third scale-degree. The prominenceof chromatic oppositions inflecting the third scale-degree functions in Figure 6.2 suggeststhat we understand the referential collection of the opening Bb tonic, which similarly hastwo representatives of the third scale-degree, as the ultimate origin. The second themebecomes a development, or working out, of ideas inherent within the first theme when thisopposition becomes the single most important focus of the streams in the second thematicarea.2546.4.4 Repetitions of StreamsThe pc-scale-degree design of the first movement is permeated by repetitions ofstreams that contain two or (at most) three scale-degree figures. These repetitions ofteninvolve a change in the status of the stream from primary to secondary, or vice versa, and aA Achange in the representative of a particular scale-degree (i.e., exchanging 6 for b6 or viceversa). This focus on repetition is made apparent from the beginning of the Exposition.AAFor instance, the primary stream <1,1 4,4> on the pc Bb that opens the piece isimmediately restated in an adjacent secondary stream on pc F. That is, at mm.lff. we hearA APC Bb change scale-degree function from 1 to 4; and at mm.33ff. we hear pc F changeA A AAAscale-degree function from ito 4. Similarly, the primary stream <2,5,1> on pc G(m.33ff.) is overlapped with its own repetition in a primary stream on pc D (mm.38ff.).A A AThat is, at mm.33ff. we hear pc G change scale-degree function from 2 to 5 to 1; and atA A Amm.38ff. we hear pc D change scale-degree function from 2 to 5 to 1. Finally, the pairedA A AAsecondary streams <b7,b3> and <5,1>, on pcs Ab and F respectively (mm.lff.), becomethe focus of the pc-scale design in the first half of the second thematic area through primarystreams on pcs D and F (mm.58ff.) and pcs C and Eb (mm.74ff.). That is, at mm. 1ff. weA A A Ahear pcs F and Ab change scale-degree functions respectively from b7 and 5 to b3 and 1.These changes are replicated in streams at mm.58ff. and 74ff.: at mm.58ff. we hear pcs Fand D change scale-degree functions respectively from 7 and to and 1; at mm.74ff.A A Awe hear pcs Eb and C change scale-degree functions respectively from b7 and 5 to b3 andA1.Repetitions of this nature also reinforce particular part and sectional articulations ofthe form. For example, the paired primary streams that connect the E and G tonics atmm.86-96 (over the beginning of the Development) — the streams < 75> and <> onpcs D and B respectively — are repetitions of the paired primary streams at mm.67ff. whichoccur on pcs C and A respectively. That is, at mm.67ff. we hear pcs C and A changeA A A Ascale-degree functions respectively from 7 and 5 to 5 and 3; and at mm.86ff. we hear pcs255D and B change scale-degree functions respectively from and . to and . Similarly,two of the three primary streams and the single secondary stream which articulate theRecapitulation section — the streams <6,5>, <6.b6> and <3,> on pcs F, F# and Crespectively — are repetitions of the three streams which connect the G and Ab tonics inmm.96-104 — the paired primary streams on pcs Eb and E and the secondary stream on pcBb. That is, at mm.96ff. we hear the pcs Eb, E and Bb change scale-degree functionsAA A A A Arespectively from b6, 6 and b3 to 5, b6 and 2; and at mm. 175ff. we hear pcs F, F# and CA A A A A Achange scale-degrees respectively from 6 and b3 to 5, b6 and 2.The repetition of streams also reinforces the sense that the Development section isdivided into two halves which are based on the first and second themes respectively. Forexample, the streams initiated at mm. 106ff. (on pcs Eb, Bb, Ab and F) that connect the AbAA AA AA AAand Eb tonics — the streams <5,1>, <2,5>, <1,4> and <6,2> — are repetitions of thestreams initiated at mm.33ff. (on pcs C, 0, F and D) respectively that connect the F and Ctonics in mm.33ff. This shows how deeply the first theme material affects the pc-scale-degree design of the first part of the Development. Similarly, the pc-scale-degree design ofthe second part of the Development reflects the thematic focus on the second theme materialby a repetition of streams that were introduced in the second thematic area. For example,AA AA AAthe streams <7,5>,<5,3> and <3,1>, which were first stated on pcs C (mm.67ff.), A(mm.67ff.) and E (mm.8Off.), are prominent in the beginning of Part II of theAADevelopment: <3,1> appears in the primary stream on pc D (mm. 127ff.) that articulatesAA A APart II of the Development and is immediately repeated in mm. 141ff.; <7,5>, <5,3> andAA<3,1> connect the D and F# tonics (at mm. 146ff. and mm.162ff.) in primary streams onpcs Db, A and F# respectively. That is, at mm.133 and 146 we hear pc D change scale-A Adegree function from 3 to 1; and at m. 162 we hear pcs Db, A and F# change scale-degreefunctions respectively from , and 3 to , 3 and 1.256On the other hand, however, the Development is also made distinct from theExposition by the initial Lack of repetition of previous streams which is caused by theintroduction of several new streams. For example, Part I of the Development begins withAA A Atwo primary streams that are new — the streams <b6,5> and <6,b6> on pcs Eb and E. Anew stream, <3,4> Ofl pc Eb, is also introduced at mm.123-127, which is the only place inthe pc-scale-degree design of the movement where only a single stream connects successiveAAtonics. The secondary streams also contain a new stream — the <4,6> on pc Ab(mm.l 18ff.). Mm.127-169 in the Development is also the first place in the pc-scale-degreedesign of the movement where streams contain the retrogrades of their beginnings. That is,AAAA A AA Athe second and third functions in the streams <3,1,3,1:>, <2,7,2,7> on pcs D and C inmm.127ff. are retrogrades of the first and second functions; similarly, the third and fourthA A ,XAAA AAP<AAAA A AAA)(Afunctions in the streams <5. 5,5,1>. <3,1,1 3,3,6,6,b6- and <7,5,5 7> on pcs A,F# and Db in mm. 141ff. are retrogrades of the first and second functions.The repetition of streams suggests another important way in which the end of thesecond part of the Development section prepares for the Recapitulation. For example, theAA AAstreams <62> and <5,1>, which occur in mm.33ff. in streams on pcs D and Crespectively, are restated in primary streams on pcs B and A near the end of the second partof the Development (mm. 169ff.). That is, in mm.33ff. we hear pcs D and C change scale-A A A Adegree functions respectively from 6 and 5 to 2 and 1; and at mm. 169ff. we hear pcs B andA A A AA change scale-degree functions respectively from 6 and 5 to 2 and 1. At mm.169ff. theseAAprimary streams are accompanied by a secondary stream — the stream <3,6> on pc F# — thatis also a repetition of a primary stream from the first thematic area, the stream on pc Db inA Amm.lff. That is, at mm. 1ff. we hear pc Db change scale-degree function from b3 to6; andat mm.l69ff. we hear pc Fit change scale-degree function from to . Together theserepetitions abstractly suggest the return of the first theme. However, because of the clearassociation of each respective part of the Development with the pc-scale-degree design ofthe material on which it is based we can infer a second, more abstract way in which the first257theme is prepared. For example, as mentioned above, the three streams which connect theAA A A AAfirst two tonics of Part I of the Development — the streams <b6,5>, <6,b6> and <b3,2> onpcs Eb, E and Bb respectively — are repeated in the streams on pcs F, F# and C respectivelythat articulate the Recapitulation. These repetitions confirm the arrival of the first thematicarea because they restate the streams the first theme acquires in Part I of the Development.They also suggest one way in which Copland’s focus on the transformation of his materialsis reflected in the pc continuity structure of the piece. The Recapitulation and Coda alsoincorporate the process of retrograde that was introduced in the second part of theAADevelopment by a repetition of the stream <3,1,1 3>011 pc F#(mm.l4lff.)in the streamAAA A<b3,1,1,b3> on pc Db (mm.196ff.).Repetition of streams in the pc-scale-degree design shown in Figure 6.2 alsoreinforces some other aspects of the unconventional sonata form used in the movement.For example, the first streams used in the second part of the Exposition are restatements ofthree of the four streams which open the first part: the primary stream <b,b> on pc DbA A AAand the secondary streams <b7,b3> and <5,1> on the pcs Ab and F respectively. That is,at mm. 1ff. we hear the pcs Db, Ab and F change scale-degree functions respectively fromA A A A A Ab3, b7 and 5 to b6, b3 and 1; and at mm.58ff. we hear the pcs Bb, F and D change scale-A A A A A Adegree functions from b3, q7and 5 to b6, 3 and 1. Even the slight modification of theA Astream <b7,b3>, which results from including a chromatic opposition on the terminal thirdscale-degree, is anticipated in the secondary stream on Bb (mm.44-58) which ends the firstpart. The use of different combinations of these three common streams with new streamswithin the second part of the Exposition reinforces the sense that the second theme is, insome respects, a development or recasting of the first theme. Similarly, the recapitulationof streams from the first thematic area in mm. 133-189 helps us to hear this passage as acontinuation of the Development and not as an hiatus in the form, as might be inferred fromthe similarity of its radically different rhythmic profile to the materials of the secondmovement. Finally, the repetition of streams suggests that the pc-scale-degree design of258the Recapitulation and Coda function as a kind of analogue to traditional Recapitulationsand Codas, which resolve the tonal instability created by the second thematic area and theDevelopment, in several important ways: streams that are associated with either the first orsecond thematic areas appear in the first thematic area of the Recapitulation; and streamsthat are associated with both the first and second parts in the Development are repeated toarticulate the Coda. For example, three of the streams that articulate the Recapitulation —AA A A AA<6,5>, <6,> and <3,2> on pcs F, Gb and C — are repetitions of the streams on pcsEb, E and Bb (mm.96ff.) that are introduced at the beginning of the first part of theDevelopment. The introduction of these streams at mm.96ff. makes us associate them withthe first thematic area. The primary streams on pcs Db and D which follow — the streamsAA A A<b3,1> and <3,b2> in mm.196ff. — are repetitions of two secondary streams on pcs G andAb (mm.86ff.) that connected the end of the second thematic area of the Exposition to theAA A Aopening of the first part of the Development. Thus, the streams <b3,1> and <3,b2> areassociated with the second thematic area. However, the immediate (modified) repetition ofA Athe stream <3,b2> in mm.96ff. (on pc Rb) also associates this stream with the firstthematic area. Similarly, the streams which articulate the Coda are associated with both thefirst and second parts of the Development and, consequently, with the first and secondA A A Athematic areas. For example, the streams <5,b7> and <1,b3> on pcs Ab and Db atmm.223ff. are repetitions of streams on pcs Bb and Eb at mm. 118ff. of the first part of theA A AA A ADevelopment and all three of the streams at mm.223ff. — <5,b7>, <3,5> and <1,b3> onpcs Ab, F and Db respectively — are present at m.169 in streams on pcs Db, A and Gb.The presence of streams from the Development to articulate the Coda suggests arelationship between these sections that mimics that between Developments and Codas intraditional sonata forms.2596.4.5 Transpositional Relationships Between Stream RepetitionsBecause there are so many repetitions of streams in Figure 6.2 it is possible toderive an abstract diagram that shows how different levels of transposition characterize thetwo sections of the Exposition and the Development (see Figure 6.3). To make these levelsclearer Figure 63 does not include the transpositional relations between streams that appearin different sections of the Exposition or between the large parts of the form (i.e., betweenthe Exposition and Development or the Development and Recapitulation) except to showrecurrences of two special transpositions (T7 and T2) that forecast the arrival of theRecapitulation. Special symbols have been adopted in Figure 6.3 to characterize differentfunctions. Arrows labeled as “Tn” represent the repetition of streams between contiguousor widely separated streams. For the sake of simplicity Figure 6.3 ignores anymodifications in the repetitions of streams (i.e., where either one or both of the scale-degrees are replaced by their opposite representative). Two brackets connected by anangled line with the letter “R” indicate streams that contain a retrograde of their beginnings.A circle around the “Tn” qualifier indicates that the transpositionally-related streams occurin different parts of the form.The abstractions in Figure 63 provide us with an unconventional means ofperceiving the form of the movement. The two parts of the Exposition are clearlydifferentiated in that the first is predominated by repetitions that are related by T7 while thesecond is predominated by repetitions that are related by TiO. Both differ from thebeginning of the Development section which focuses on the repetition of streams that arevariously related by T3, T4, T6 or Ti 1.---4----\H/-4_7/_•-- --PS—P3s4---iP26T4LJSFigure6.3TraispositionalRelationshipsBetweenRepetitionsofStreamsinFigure6.2Parts:ExpositionDevelopmentRecapitulationCodaSections:1stT.A.2ndT.A.PartIPartII1st T.A2ndT.A.B-Bb-AbF#-F-E-Eb-.Db-C--P1---SI:4 Si—_P2\ ri-fP1P2-4IILIpredominantly17P1-P2-4-F-—F--predominantlyTiOvarious(T3,T4,T6,Ti1)-JIT2andT7forecastarrivalofFirst ThematicArea261The Recapitulation and Coda do not contain any stream repetitions withinthemselves and, thus, can not be characterized by a predominant transposition level like thefirst and second thematic areas and the Development. However, the transpositional levelsof streams that occur between the Development and the Recapitulation can be understood toforecast the arrival of the first thematic area of the Recapitulation in that two transpositionallevels present in mm.1-50 —T2 and T7 —obtain between streams stated in the Developmentand Recapitulation sections. These transpositions account for almost all of the importantstreams in the Recapitulation and Coda. For example, the streams on pcs F, F# and Cwhich articulate the Recapitulation and <3,2>) are T2-related to thestreams on pcs Eb, E and Bb that are present at the beginning of the first part of theDevelopment.23 T7-related streams follow these T2-related streams in mm. 196ff.: theAAA Astream <b3,1 .1,b3> on pc Db at mm.196ff. is T7-related to the stream on pe Gb atA Amm. 146ff.; and the stream <5,b7> on pc Ab at mm.223ff. is T7-related to the stream on pcDb at m. The First Thematic Area as a Source of StructureIn some ways the pc-scale-degree design of the movement as a whole reflectsimportant characteristics of the first part of the Exposition. On one hand, this designreflects the three oppositions that inflect the referential collection of the opening Bb tonic —the presence of two representatives of the second, third, and sixth scale-degrees in mm. 1-25. This is reflected in the pc-scale-degree design by the substitution of the oppositerepresentative of one of the scale-degrees in a stream when it is repeated. For example, thealternation of opposite representatives of the third scale-degree can be seen in thetransformation of the stream 4,> on pc A (m.67) into the stream on pcs GAA(m.80) and A (m.141) and the transformation of the stream <3,1> on pc E(m.80) into the23Thus it is not only the stream repetition itself but also the specific transposition level betweenstatements of these streams that makes that makes them forecast the return of the first thematic area.262stream <b,i> on pc Db (m.196). Similarly, the alternation of opposite representatives ofA Athe third and sixth scale-degrees can be seen in the transformation of the stream <b3,b6>AAon Db (m.l) into the stream <3,6> on pc F# (m.169). Finally, the alternation of oppositerepresentatives of the second and third scale-degrees can be seen in the successivetransformations of the stream <,b2> cm pc Ab (m.86) into the stream <b(,2> on pcsA AEb (m.96) and C (m.175) and the stream <3,b2> on pc D (m.196). It is precisely therelationship of two of these pairs of pes, the pcs Db and D, and Gb and G respectively,which strongly colors the first transition: pcs Db and D are strikingly opposed in thedirected motions of mm.26ff. and at the second statement of the first theme motto(mm.SOff.); pcs Gb and G are similarly opposed at mm.33ff. and 50ff. However, thecompetition between the remaining pair, pcs C and Cb, as the second scale-degree of theBb tonic in mm. 1-25, becomes explicitly related to the opposition of pcs D and Db in theRecapitulation because the transposition of the second half of the first theme makes pc D(Ebb) sound as the lowered second scale-degree of Db.The pc-scale-degree design also, however, reflects the first part of the Expositionby the primary pc streams which begin and end the pc continuity structure. For example,the outer points of this design, like the voice leading of the first phrase, are also demarcatedby a focus upon the dyads {Bb, Db} and {F, Ab} respectively. The importance of pcs Fand Ab to the broader structure is foreshadowed in the opening of the pc-scale-degreedesign because the streams that open the second thematic area occur first on these pcs(mm.1 1ff.). The significance of the {Bb, Db} and {F, Ab} dyads to the larger pc-scaledegree design is alluded to on the surface of the music in the expositional transition by theappearance of these particular dyads as the framing sonorities of the successive directedmotions (mm.26 and 28). This motion is explicitly restated in the pc-scale-degree designwhen the final two pairs of primary streams that end the movement (those initiated atmm.196 and 223) involve the pcs Db, Bb, F and Ab. The ultimate emergence of streamson pcs F and Ab at the end of the movement is strikingly suggested in the Recapitulation263when the dyad {F, Ab} uncharacteristically intrudes as a pedal in the lowest two voices atthe beginning of the Recapitulation (mm. 196ff.) and the Coda (mm.223ff.).The preeminence of the minor third to the overall design of the movement is alsoreflected in a more general way on the surface of the music by the emphasis on the intervalof a minor third in the two lowest voices. This focus, which is directly responsible for thechromatic opposition between different representatives of the third scale-degree, permeatesthe texture in the entire Exposition. It dissipates gradually in the beginning of theDevelopment and does not reappear until the Recapitulation. As a result, the interval of aminor third becomes a symbol of resolution. This suggests that we hear the Db tonic in theRecapitulation as a large-scale manifestation of the minor third of the Bb tonic that opensand closes the movement. Essentially, such a consideration brings us full circle becausethe sonority that opens the movement — the dyad {Bb, Db} — proves to be a microcosmicrepresentative of the interval that defines the broader macrocosmic tonal movement.6.5 SummaryLet us summarize the processes in the first movement of the Piano Sonata to answerthe central question of this thesis: how tonics and their successions are related to the form.The tonic succession of this movement supports a thematic design of sonata form in severalways. For example, the most important articulations in the form — the Development andRecapitulation in mm.96 and 196 respectively — are clearly demarcated by tonal shifts.There are also some contrasts between sections in the level of tonal fluctuation, as, forexample, between the Development and Recapitulation sections, which mimic traditionalpractice. The Development has many tonics and tonal changes occur fairly rapidly.However, there are also contrasts expected in a sonata form that are missing. For example,although the expositional transition is marked by the onset of tonal fluctuation as in aclassical sonata form, this fluctuation actually continues into the second thematic area.Effectively, this obscures any difference between the ending of the transition and the264beginning of the second thematic area. It also reinforces that the second theme is adevelopment or recasting of the first theme. The tonic succession in this movement is alsosomewhat unusual in Copland’s works because of how it is organized. All of the mostimportant arrivals in the sonata form, including the curious Db tonic in the Recapitulation,are involved in a statement of one of several related intervallic series that are derived fromthe voice-leading motive <-2,-i>, which is introduced in the first phrase of the movement(mm.3-5). The widespread use of this series suggests that the first theme is the progenitorof the structure of the entire movement.The tonic succession in this movement produces a pc-scale-degree design that has asignificant layering of repetitions of short two- and three-function streams. Theserepetitions help to define the form. They show the derivational status of the second theme;they also define the focus of the disparate parts of the Development (on the first and secondthemes respectively) and integrate these parts into a unified whole. Most importantly,however, these repetitions demonstrate the unconventional manner in which the end of theDevelopment prepares for the recapitulation of the first theme. This is important becausethe Recapitulation is not prepared harmonically by the tonic succession or motivically bythe thematic design.265Chapter 7ConclusionWe have seen that the analytical literature on Copland’s music strongly suggests adichotomy between “popular” and “serious” works, especially in 1930-1950. Indeed,these two styles are distinguishable by the differing complexity of their thematic materialsand harmonic structures. At a more fundamental level, however, Copland’s “popular” and“serious” works are consistent. This consistency is revealed by a detailed study of tonalitythat addresses two central issues: the generation of tonics, and the function of tonics — howtonics and their successions relate to form.Chapter 1 discussed the most basic consistencies between Copland’s “popular” and“serious” works — a common set of tonicizing techniques that are used to establish tonicand to modulate from tonic to tonic. These techniques are: isolated descending- andascending-fifth motion of roots; triadic melodic structures; arpeggiation of special pc-setclasses in the lowest voice; “directed motion;” textural and thematic articulation of a rootedchord; pedal tones; reiteration of a root; and neighbor-tone motion.Chapters 3-6 demonstrated these consistencies and others by analyzing two“popular” works (Quiet City and Billy the Kid) and two “serious” works (the firstmovements of the Short Symphony and the Piano Sonata). These analyses focus on thefunction of tonics — the relationship of tonics and their successions to the thematic design.They demonstrate several important correspondences. Some of these involve obvioussurface characteristics of short passages. For example, the “popular” and “serious” workshave passages where an overlap obtains between successive tonics. An overlap occursbetween F and Ab tonics at R3 1-3ff. of Billy the Kid, between Bb and G tonics at R8-4ff.of the first movement of the Short Symphony, and between Bb and F tonics at mm.26ff. ofthe first movement of the PianoSonata. Similarly, one work in each style — Billy the Kid266and the first movement of the Short Symphony — contains a passage having a bitonaltexture. These works also use specific motivic materials to foreshadow future tonics and,thereby, to establish both small- and large-scale coherence. Coherence in Billy the Kidrevolves around the repeated references to a seminal voice-leading model articulated at thesingle most important place of the suite; coherence in the first movement of the ShortSvmphony is created by the consistent use of motive 1. Consistency between the twostyles is also evident within individual tonal areas because of a characteristic ambiguitybetween 1C5-relatecl tonic pcs. This type of ambiguity, which permeates most of the tonalareas in Quiet City, is particularly striking in the opening of the first movement of the ShortSymphony and in the Recapitulation of the first movement of the PianoSonata. In at leastone case (motive 7 in Quiet City and motive I in the first movement of the ShortSymphony) this characteristic ambiguity arises from the conflict between a melodicallygenerated tonic and those generated by other (contextual) means.The “popular” and “serious” works studied also contain similar manipulations ofimportant motivic materials, manipulations that change the tonal meaning — the scale-degreefunction — of those materials. Changes of scale-degree function in motivic materials caneasily be traced in Quiet City and in the first movements of the Short Symphony and thePiano Sonata. For example, in part C of Quiet City the first note of motive 6 changesA Afunction from D: 1 to D: 2 when the opening phrase is repeated, and the first note of motiveA A7 shifts from D:5 to D: 1 at the end of the D tonal area. Similarly, all three motives in theopening movement of the Short Symphony are reinterpreted: the last note of motive 1changes over the course of the movement from a dissonance at the beginning to aAconsonance at the ending; the second (accented) soprano pc of motive 2 changes from 4(m.2) to (R8); the first soprano pc of motive 3 changes from a defined scale-degree atR6-l (ba) to an unknown quantity at R6ff. (?); and the second bass pc of motive 3 changesA Afrom b7 (R6- 1) to 5 (R1O+3). Finally, the harmonic underpinning of the first theme in thefirst movement of the Piano Sonata is changed from a succession of varied tonic harmonies267(mm. 1ff.) to a <IV, I> harmonic progression (mm.33ff., and the opening of theDevelopment section).The placement of tonics within respective forms is also consistent betweenCopland’s “popular” and “serious” works. Virtually all of the important divisions in thethematic designs of the works studied are supported by a change in tonic. Furthennore,tonal change is only withheld at very strategic points and this withholding reinforces thethematic design. For example, the lack of a change in tonic in part A of the first movementof the Short Symphony, and at the recapitulation of the varied theme (part Al) in QuietCity, reinforces the form in each case. In the first movement of the Short Symphony, itestablishes the tonal unity of part A, which is thematically diverse, and distinguishes itfrom part B; in Quiet City, it unifies widely spaced variations (of section b), which havedifferent formal functions, by giving them the same tonic.The rate of change in the tonic is also of importance in Billy the Kid and the firstmovement of the PianoSonata. For example, in Billy the Kid the complete lack of tonalchange in “Gun Battle” helps us to distinguish it from the surrounding movements becausethis makes it the only movement in the suite that maintains a single tonic throughout.Similarly, in the first movement of the PianoSonata the rate of tonal fluctuation heLps todefine the sonata form: it delineates the beginning of the transition and it differentiates theDevelopment and Recapitulation sections.Consistency is also demonstrated between the “popular” and “serious” worksstudied in that tonic successions in three of the works studied — Billy the Kid, and the firstmovements of the Short Symphony and the Piano Sonata—are organized by a consistentpatterning. For example, the tonic successions in the second to fifth movements of Billythe Kid are guided by minor-major third complexes and these help to define the large-scalemovement from C to E. Similarly, the tonic succession in part B of the first movement inthe Short Symphony is organized by a palindromic structure and this links parts A and Al.268Finally, all of the important tonal arrivals in the first movement of the PianoSonataparticipate in some unfolding of the intervallic series <-2,-i> or a related series.The tonic successions in transitional passages are also treated in similar waysbecause they are guided by step-progressions in every one of the four works studiedabove. For example, in Quiet City parts A, B and C, which contain the first, second andthird variations of section b, are linked by a step-progression employing a linear intervallicpattern of 5-5-5-5-5. Similarly, in Billy the Kid the most crucial passage in the form,R27A, is guided by a step-progression. Step-progressions here also establish a logicbehind the large-scale motion from C to E. Step-progressions similarly inform thetransitional passages of the two “serious” works studied: they establish the coherence of themost significant transitions in the opening movements of the Short Symphony (R5-2 to R8-1), and the PianoSonata (mm.26ff.). Step-progressions also inform individual tonal areasin these works as they do in Billy the Kid.The most immediately recognizable consistency in the tonic successions ofCopland’s “popular” and “serious” music is the emphasis on pcs that are common to thecollections of successive tonics. These common pcs are represented in the analyses by pcstreams on graphs; these graphs help us to perceive a consistency between the twoapparently distinct styles. At the simplest level we can observe that pc streams aregenerated in all of the works by similar means. For example, all of the works generatestreams by agogic accents in the outer voices and by literally sustaining a pc (or pcs) overthe point where one tonic is succeeded by the next. All four works use recurrent dyads andthree of the four (Billy the Kid, the first movements of the Short Symphony and the PianoSonata) use a continuing motive to generate paired primary streams. All four works alsoemploy suspended streams, albeit at much different levels of prominence.The larger pc-scale-degree designs that emerge from graphing the individual pcstreams of connection also provide us with useful information that confirms and reinforces269the thematic designs. For example, the pc-scale-degree design of Quiet City expresses thefundamental unity of the piece because each part is articulated by a primary stream that endson . Further, it reflects the conflict of formal function between variations of section b byAshowing a palindromic structure that overlaps with a series of streams that begin with 7.The pc-scale-degree design of Billy the Kid reinforces the six-movement form, andparticularly the unity of the sprawling second movement, by the interactions between twolarge groups of streams. It also reinforces the unity of the entire suite because streamsfrom Group 2 occur in every movement. The pc-scale-degree design of the first movementof the Short Symphony establishes a significant similarity between parts A and Al (by theorder of focal pcs at the end of each part), differentiates part B, and establishes a large-scaleretrograde that unfolds over the course of the movement. The pc-scale-degree design of thefirst movement of the Piano Sonata reinforces sonata form by establishing the unity of theDevelopment section, by defining how the end of the Development acts as a preparation forthe Recapitulation, and by creating a context in which the Recapitulation and Coda serve aresolutive function. It also reflects the close relationship between the first and secondthemes by emphasizing that primary streams in the second thematic area are derived fromsecondary streams in the first thematic area.There are also more specific correspondences we can observe between specific“popular” and “serious” works on the basis of the pc-scale-degree designs. For example,palindromic structure is important to both Quiet City and the first movement of the ShortSymphony: in Quiet City, it unifies the second and third variations; in the first movement ofthe Short Symphony it links parts A and Al. One work in each style — Billy the Kid andthe first movement of the Piano Sonata — have pc-scale-degree designs that are permeatedby repetitions of short streams. Further, one work in each style — Billy the Kid and thefirst movement of the Short Symphony — has a pc-scale-degree design that uses therepetition of an ordered series of focal pcs to define the form. The pc-scale-degree designsalso provide us with compelling reasons to hear certain tonics as resolutions, such as, for270example, the E tonic ending Billy the Kid or the Db tonic in the Recapitulation of the firstmovement of the Piano Sonata.One other significant correspondence that emerges from the four analyses is themanner in which aspects of the opening motive informs the overall structure of a work.Although the motivic basis of form can be traced to varying degrees in all four of the worksstudied, it is most obvious in the structures of QuietCity and the first movement of thePiano Sonata. For example, the emphasis on the fifth scale-degree in the first twomeasures of QuietCitv can be heard as a microcosmic realization of the most significantcharacteristics of the rest of the piece: the step-progression that, featuring successive perfectfifths, unifies parts A, B and C; and the succession of primary streams that end on . Thepc-set type [0,2,5], which is also manifest at the outset of the piece, figures prominently inthe pc-scale-degree design through simultaneous primary pc streams and the generalsuccession of focal pcs throughout the work. Similarly, the tonal structure of the firstmovement of the PianoSonata is informed by aspects of the first theme in several ways.One obvious example is the confirmation of the thematic derivation of the second themefrom the first theme in the pc-scale-degree design: streams from the first thematic area arerepeated in the second thematic area. But the first theme affects the structure of themovement more fundamentally as well: its opening phrase states an intervallic series, <-2,-1>, that permeates the tonic succession and informs every significant tonal arrival in theform. The same process can be traced in Billy the Kid and the first movement of the ShortSymphony. For example, the opening movement of Billy the Kid contains one version ofa step-progression that later becomes seminal to the motivic materials of the followingmovements of the suite. It also contains a pitch-class opposition between pcs Eb and E (asdifferent representatives of the third scale-degree of C) that is reflected by the goals of thetwo halves defined within the pc-scale-degree design. Similarly, the opposition of themajor and minor thirds in the opening motive of the first movement of the Short Symphonyis manifested in the tonic succession at the transition to part B, and in the pc-scale-degree271design through the conflicts between different representatives of the third scale-degree atthe beginning or ending of streams that connect successive tonics.The concept of tonality and the method of analysis adopted in this thesis would beuseful in analyzing Copland’s other major works of the 30’s and 40’s — AppatachkLnSpring, Rodeo, the ClarinetConcerto, the Piano Concerto and the Piano Variations —because these pieces use the characteristic textural devices of the four works studied in thisthesis. That is, in each of these works we can find many passages where Copland usescharacteristic techniques — sustaining a pc when the tonics change, or placing agogicaccents on a pc in the outer voices of successive tonal areas — to connect successive tonicsin the absence of functional harmonic progressions.’ Step-progressions are also present inthe transitional areas, especially in the ClarinetConcerto (I, mm.48-77), the PianoConcerto (1, R10-3 to RiO and Ri 1-2 to Ri 1+6) and “Buckaroo Holiday” from Rodeo(R15-3 to R20). The Piano Concerto also employs other techniques that are found in thefour works which were analyzed: the first movement begins with a tonal area that employsthe characteristic ambiguity between IC5-related tonic pcs (between B and E tonics), andcontains at least one example of a transformation of the tonal meaning of a motive (at R7-2ff. the neighbor-tone motive of Ri, which was discussed in Example 1.35, is transformedinto a functional <IV, V> progression at the end of an F tonal area). These similaritiesreinforce the essential unity of Copland’s works from 1930-1950.These analytical techniques would be less useful for works by Copland’s mostsignificant American contemporaries — Roger Sessions, Roy Harris and Walter Piston.The music of these composers does not have those characteristic textural phenomena thatsuggest that specific pcs are used to connect successive tonics. Further, their music doesnot consistently employ large-scale transpositions of thematic material, which is soof these passages were discussed earlier in Chapter 1. See Examples 1.19, 1.33, and 1.37 on pp.39-40, 56 and 68-69.272characteristic of Copland’s music from this time period, and they do not use step-progressions in such a prominent role.This method of analysis is also not very useful for either the music of Copland’stwo main European contemporaries — Hindemith or Stravinsky. Hindemith’s music, unlikeCopland’s music, uses all twelve pcs in every tonal area, and connects successive tonalareas with long, contrapuntally-oriented transitions. These characteristics of Hindemith’smusic make it exceedingly difficult to hear tonal boundaries and to extricate referentialdiatonic collections. The method of analysis proposed in this thesis is also not successfulfor Stravinsky’s music because Stravinsky’s music, like Hindemith’s music, is alsofundamentally different from Copland’s music. In Stravinsky’s music we are focusedupon the different tonics that a single collection can support.2 Usually the resultingambiguity of tonics is of global importance to his pieces. However, in Copland’s music anew tonic is characteristically supported by a new referential collection. Tonal centers inCopland’s music, therefore, are normally clearly demarcated in a way that is atypical forStravinsky’s music. Further, in the rare passages when Copland does change the tonic butretains the same collection ( for example, in the succession <Ab, F, Ab> at R30-lff. ofBilly the Kid) this type of invariance results in only an overlapping between successivetonics and not in the polarization of tonal centers, and is always constrained to a smallsegment of a piece. There are also obvious surface differences between Stravinsky’s andCopland’s music. For example, Stravinsky’s motives are far more fragmented and atomicthan Copland’s; only on very rare occasions (such as in “Gun Battle” of Billy the Kid) isthere a strong similarity between Copland’s and Stravinsky’s motivic practices. Further,many of the changes in tonic in Copland’s music of this period are also reinforced by direct2Paul Johnson, “Cross-Collectional Techniques of Structure in Stravinsky’s Centric Music,” in StravinskyRetrospectives (Lincoln: University of Nebraska Press, 1987), pp.55-56; and William E. Benjamin,“Tonality Without Fifths: Remarks on the First Movement of Stravinsky’s concertoJor Piano and WindInsirumeni’s,” In Theory Only 2/11-12 (1977): 53-70 and 3/2 (1977): 9-31.273transpositions of thematic material, a characteristic that is noticeably lacking in Stravinsky’smusic.There are, however, works of various other American composers where it appearsthat this type of analysis might be useful. For example some of the works by VirgilThomson (i.e., the suite from The Plough that Broke the Plains and parts of the SecondSymphony), Leonard Bernstein (e.g., On the Town) and David Diamond (i.e., theConcertofor String Quartet, and the Concertofor Small Orchestra), and some of the earlymusic of Paul Bowles (i.e., Sonatina for Piano, and Musicfora Farce) and Irving Fine(e.g., Musicfor Piano) have a close resemblance to Copland’s music suggesting that thistype of analysis might be informative. Potentially the largest application of this analyticalapproach, however, lies in tonal minimalist music. Certain pieces by minimalists such asJohn Adams (i.e., Fearful Symmetries and “Wild Nights” from Harmonium), and SteveReich (i.e., Sextet) feature sudden shifts in key and collection that are frequently blurred bycommon tones. The sudden shifts in these pieces are very reminiscent of similar passagesin Copland’s music.Certain aspects of this analytical approach might also be applied to a wide range ofcomposers with regard to specific forms. For example, it is possible that applying thisanalytical approach to the analysis of sonata forms of various composers would beinformative because the recapitulation of this form is predicated upon the listener hearingthe repetition of particular scale-degree functions.The analyses of this dissertation place a very important role upon pitch classes. Wemight speculate that for Copland this effectively constituted the point of his departure intothe twelve-tone method. Instead of simply following a recent trend that had become passé,Copland’s adoption of the twelve-tone method can thus be seen as a logical outgrowth ofhis previous compositional concerns. It continues the focus on the function of pitch classesbut defines function in terms of position within the row, rather than intervallic relation to a274tonic. Note also the use of retrograde in the pc-scaLe-degree designs is consistent withclassical twelve-tone operation.3 Copland believed that the Piano Variations began hisinterest in serial writing.4 He stated that the twelve-tone method was attractive because hecould hear chords that he “wouldn’t have heard otherwise,” and because it offered a “newway of moving tones about.”5 One might infer from Copland’s statement that serialwriting “freshened up one’s technique and one’s approach”6that he also perceived anunderlying continuity between his works of the 1930’s and his later adoption of the twelve-tone method. One might also speculate a connection between these stylistic periods inCopland’s artistic career because of the continuing significance of melody: melodies arecrucial for the generation of tonics in both his “popular” and “serious” works and,according to Copland, are the origin of rows in his twelve-tone pieces.7 The connection ofCopland’s music in the 1930’s to his (much later) use of the twelve-tone method allows usto posit a more fundamental consistency of method in all of Copland’s works. Hisincorporation of tonality, like his incorporation of folk song materials and, much later, ofthe twelve-tone method, is made on his own artistic terms; Copland transforms andindividualizes every style that he assimilates. Thus, although the generation of tonics inCopland’s music is clearly based on traditional practice, the clearest function of those tonicsis much different from traditional practice.3The relationship between the intervallic series that guide different portions of the first movement of thePiano Sonata is reminiscent of the operations of transposition, inversion, and retrograde in twelve-tonemusic.4Edward T. Cone, “Conversation with Aaron Copland,” Perspectives ofNew Music 6/2 (1968), p.66. Inthe same passage Copland refers to a song he wrote in 1927, which was published in the 1960’s under thetitle “Poet’s Song,” that shows he was thinking in twelve-tone terms.5lbid., p.67.7lbid., p.68.275BibliographyMonographsAn Anthology ofLetters ofComposers. Compiled and Edited by GertrudeNorman and Miriam Lubell. New York: Alfred A. Knopf, 1946.Baker, James. The Music ofAlexander Scriabin. New Haven: Yale UniversityPress, 1986.Berger, Arthur. Aaron Copland. With a New Introduction by Leonard Burkat.New York: Oxford University, 1953. Reprint. New York: Da Capo Press,1990.Butterworth, Neil. The Music ofAaron Copland. Preface by Andre Previn.Gloucester: Toccata Press, 1985.Clurman, Harold. The Fervent Years: The Story ofthe Group Theatre and theThirties. New York: Hill and Wang, 1957.Copland, Aaron. The New Music 1900-1960. Revised and Enlarged Edition.London: MacDonald, 1968.____________What To Listen For In Music. New York: McGraw-Hill BookCompany, Inc., 1939.Copland, Aaron, and Vivian Perlis. Copland: 1900 Through 1942. New York:St. Martin’s/Marek, 1984.Forte, Allen. Contemporary Tone Structures. New York: Bureau ofPublications, Teacher’s College, Columbia University, 1955.Hilliard, Quincy. “A Theoretical Analysis of the Symphonies of AaronCopland.” Ph.D. dissertation, University of Florida, 1984.Hindemith, Paul. Craft ofMusical Composition. Books I and II. Fourthedition. English translation by Arthur Mendel. Mainz: B. Schotts Söhne,1970.Machlis, Joseph. Introduction to ContemporaryMusic. Second edition. NewYork: W.W. Norton, 1979.Mellers, Wilfrid. Music in a New Found Land: Themes and Developments inthe History ofAmerican Music. London: Barrie and Rockliff, 1964.Neumeyer, David. The Music ofPaul Hindemith. New Haven: YaleUniversity Press, 1986.Reti, Rudolph. Tonality, Atonality, Pantonality: A Study ofSome Trends inTwentieth-Century Music. New York: The MacMillan Company, 1958.Richard Wagner: Prelude and Transfigurationfrom “Tristan and Isolde.”Norton Critical Score. Edited by Robert Bailey. New York: Norton, 1985.276Salzer, Felix. Structural Hearing Tonal Coherence in Music. 2 vols. With aForeword by Leopold Mannes. New York: Dover Publications, Inc.,1962.Schoenberg, Arnold. Theory of Harmony. Translated by Roy E. Carter.London: Faber and Faber, 1978.Shnayerson, Michael. Irwin Shaw: A Biography. New York: G. Putnam’sSons, 1989.Smith, Julia. Aaron Copland: His Work and Contribution to American Music.New York: E. P. Dutton and Company, Inc., 1955.Straus, Joseph. An Introduction to Post-Tonal Theory. Englewood Cliffs:Prentice Hall, 1990.ArticlesBaker, James. “Scriabin’s Implicit Tonality.” Music Theory Spectrum 2(1980): 1-18.____________“Schenkerian Analysis and Post-Tonal Music.” In Aspects ofSchenkerian Theory, 153-188. Edited by David Beach. New Haven: YaleUniversity Press, 1983.Berger, Arthur. “Copland’s Piano Sonata.” Partisan Review 10 (1943): 187-190.Benjamin, William E. “Tonality Without Fifths: Remarks on the FirstMovement of Stravinsky’s Concertofor Piano and Wind Instruments.” InTheory Only 2/11-12(1977): 53-70 and 3/2(1977): 9-31.Cinnamon, Howard. “Tonal Structure and Voice-Leading in Liszt’s Blume undDuft.” In Theory Only 6/3 (1983): 12-24._____“Tonic Arpeggiation and Successive Equal Third Relations asElements of Tonal Evolution in the Music of Franz Liszt.” Music TheorySpectrum 8(1986): 1-24.Cone, Edward T. “Conversation with Aaron Copland.” Perspectives ofNewMusic 6/2(1968): 57-72.Johnson, Paul.”Cross-Collectional Techniques of Structure in Stravinsky’sCentric Music.” In Stravinsk’’ Retrospectives, 55-75. Edited by EthanHaimo and Paul Johnson. Lincoln: University of Nebraska Press, 1987.Lewis, Christopher. “Into the Foothills: New Directions in Nineteenth-CenturyAnalysis.” Music Theory Spectrum 11/1(1989): 15-23._“Mirrors and Metaphors: Reflections on Schoenberg andNineteenth-Century Tonality.” Nineteenth Century Music 11/1(1987): 26-42.277Morgan, Robert P. “Dissonant Prolongations: Theoretical and CompositionalPrecedents.” Journal ofMusic Theory 20(1976): 49-91.Oster, Ernst. “Re: A New Concept of Tonality (?).“ Journal ofMusic Theory4(1960): 85-98.Shackford, Charles. Review of Ubungshuch fur den Dreistimmigen Sazz byPaul Hindemith. Journal ofMusic Theory 16(1972): 238-265.Straus, Joseph N. “The Problem of Prolongation in Post-tonal Music.”Journal ofMusic Theory 31 / 1 (1987): 1-22.Thomson, Virgil. “American Composers VII: Aaron Copland.” Modern Music9/2 (1932): 67-73.Travis, Roy. “Directed Motion in Schoenberg and Webern.” Perspectives ofNew Music 4/2 (1966): 85-89.____________“Toward a New Concept of Tonality?” Journal ofMusicTheory 3/2 (1959): 257-284.Wilson, Paul. “Concepts of Prolongation and Bartok’s Opus 20.” MusicTheory Spectrum 6(1984): 79-89.


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