Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

John Weinzweig’s Woodwind quartet : a study in compositional development and serial methods Lind, Stephanie Kathleen 2003

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-ubc_2003-0450.pdf [ 6.24MB ]
JSON: 831-1.0091027.json
JSON-LD: 831-1.0091027-ld.json
RDF/XML (Pretty): 831-1.0091027-rdf.xml
RDF/JSON: 831-1.0091027-rdf.json
Turtle: 831-1.0091027-turtle.txt
N-Triples: 831-1.0091027-rdf-ntriples.txt
Original Record: 831-1.0091027-source.json
Full Text

Full Text

JOHN WEINZWEIG'S WOODWIND QUINTET: A STUDY IN COMPOSITIONAL DEVELOPMENT AND SERIAL METHODS by STEPHANIE KATHLEEN LIND B.Mus., Wilfrid Laurier University, 2000 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (School of Music) We accept this thesis asxonforming to the required Standard THE UNIVERSITY OF BRITISH COLUMBIA July 2003 © Stephanie Kathleen Lind, 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my writ ten permission. Department of Ur.J o9 M ^Su r The University of British Columbia Vancouver, Canada Date UZS^f / ^ a o O * ? DE-6 (2/88) 11 Abstract John Weinzweig was the first Canadian composer to use techniques of serial organization in his compositions. Through his teaching, composing, and promotion of Canadian music, he has been influential in the development of Canadian music. Because of this, it is of interest to study one of his significant works, the Woodwind Quintet (1963/64). This work exemplifies Weinzweig's serial techniques, including the use of row forms that share common segments (such as dyads, trichords, tetrachords, and hexachords), as well as an allusion to octatonic sounds. This thesis approaches Weinweig's work first from a serial standpoint, and then examines how the composer approaches the idea of motivic development within his work. Thorough analysis of twelve-tone relationships, themes, textures, and rhythms reveals how Weinzweig focuses not just on serial materials, but also on other aspects of composition. Following a brief introduction about the composer and the piece, Chapter 1 examines the properties of the row used in the Woodwind Quintet. The discussion continues, in Chapters 2, 3, and 4, by examining each movement from a different analytical perspective, giving an overview of the work as a whole. Texture and instrumentation are the focus of the discussion of the first movement; segmentation is examined in the second movement; and rhythmic motives are studied in the third movement. Rotation, inversion, and other serial techniques are examined in the work as a whole. This thesis attempts to give an overview of Weinzweig's compositional style Ill while discussing specific passages from the Woodwind Quintet and their unique manner of development. iv TABLE OF CONTENTS Abstract Table of Contents List of Tables List of Figures List of Row Diagrams Introduction CHAPTER I: Properties of the Row CHAPTER II: The First Movement and its Characteristic Textures CHAPTER III: The Second Movement and Segmentations of the Row CHAPTER IV: The Third Movement and its Rhythmic Motives 1 Conclusion 1 Bibliography 1 List of Tables Table 1.1: Dyads in the accompaniment instruments, bars 40-45, first movement 41 Table 1.2: Subsets of the octatonic collection within the Woodwind Quintet (and their order positions within P) 53 Table 2.1: A brief overview of the first movement 59 Table 2.2: Order positions of T0(P) in bar 73, first movement 72 Table 3.1: A brief overview of the second movement 77 Table 4.1: A brief overview of the third movement 137 vi List of Figures Figure 1.1: Bars 1 -14, first movement 6 Figure 1.2: Bars 15-37, first movement 7 Figure 1.3: Tone row matrix using P as the prime form row 12 Figure 1.4: Bars 1-4, second movement 13 Figure 1.5: Bars 71-83, first movement 15 Figure 1.6: Bars 131-134, third movement 18 Figure 1.7: Bars 135-143, third movement 20 Figure 1.8: Bar 24, second movement 22 Figure 1.9: Bars 37-45, first movement 29 Figure 1.10: Bars 1-8, third movement 31 Figure 1.11: Bars 182-191, third movement 32 Figure 1.12: Bar 201, third movement 33 Figure 1.13: Bars 5-8, second movement, with segmental trichords 34 Figure 1.14: Bars 5-8, second movement, with order position set class trichords 37 Figure 1.15: Bars 37-52, first movement 39 Figure 1.16: Bars 131-134, third movement 43 Figure 1.17: Bars 1-14, first movement 44 Figure 1.18: Bar 1, first movement, with annotations 46 Figure 1.19: Bars 30-33, second movement 48 Figure 1.20: Bars 117-130, third movement 50 Figure 1.21: Bars 192-198, third movement 52 V l l Figure 1.22: Bars 19-24, second movement 55 Figure 2.1: Rhythmic variations in the oboe, bars 1-7, first movement 63 Figure 2.2: Rhythmic variations in the oboe, bars 7-13, first movement 63 Figure 2.3: Bars 37-52, first movement 65 Figure 2.4: Bars 15-37, first movement 67 Figure 2.5: Bars 71-83, first movement 71 Figure 2.6: Bars 88-92, first movement 75 Figure 3.1: Bars 1-4, second movement 82 Figure 3.2: Bars 5-8, second movement 83 Figure 3.3: Bars 9-15, second movement 85 Figure 3.4: Schoenberg's Fourth String Quartet, first movement, bars 1-6 87 Figure 3.5: Bars 16-23, second movement 89 Figure 3.6: Bars 22-27, second movement 91 Figure 3.7: Bars 25-31, second movement 94 Figure 3.8: Bars 30-33, second movement 96 Figure 3.9: Bars 33-40, second movement 98 Figure 3.10: Bars 40-44, second movement 101 Figure 3.11: Bars 43-49, second movement 103 Figure 3.13: Bars 50-56, second movement 106 Figure 4.1: Bars 36-41, third movement 115 Figure 4.2: Bars 60-62, third movement 116 Figure 4.3: Bars 106-116, third movement 117 Figure 4.4: Bars 117-130, third movement 119 V l l l Figure 4.5: Bars 1-8, third movement 120 Figure 4.6: Bars 9-24, third movement 121 Figure 4.7: Bars 42-50, third movement 123 Figure 4.8: Bars 51-59, third movement 124 Figure 4.9: Bars 68-80, third movement 125 Figure 4.10: Bars 81-85, third movement 126 Figure 4.11: Bars 154-174, third movement 129 Figure 4.12: Bars 175-181, third movement 130 Figure 4.13: Bars 182-191, third movement 132 Figure 4.14: Bars 192-200, third movement 134 Figure 4.15: Bar 201, third movement 135 ix List of Row Diagrams Row Diagram 1.1 5 Row Diagram 1.2 9 Row Diagram 1.3 10 Row Diagram 1.4 10 Row Diagram 1.5: Hexachordal and dyadic segmentation of To(P) and Ii(P) 16 Row Diagram 1.6: Intervals between consecutive pitch classes of To(P) 21 Row Diagram 1.7: Segmental trichords of To(P) 22 Row Diagram 1.8 27 Row Diagram 1.9 30 Row Diagram 1.10: Swapped trichords between two rows sharing the same unordered first hexachord 34 Row Diagram 1.11: Distribution of order position set class trichords within P 36 Row Diagram 1.12: Intervals between consecutive pitch classes of To(P) 37 Row Diagram 1.13 47 Row Diagram 1.14 56 Row Diagram 1.15: To(P), interval classes between members of segmental dyads, and cycles of the I] transformation 57 Row Diagram 2.1 69 Row Diagram 2.2 74 Row Diagram 3.1 92 Row Diagram 3.2 95 Row Diagram Row Diagram 1 Introduction John Weinzweig has often been called "the dean of Canadian composers," an apt title, in my view, for his strong devotion to the development and propagation of Canadian music. Born in 1913 in Toronto, Weinzweig studied music at the University of Toronto and then at the Eastman School of Music in Rochester. He was interested in contemporary music from his early days of study, but opportunities to study recent music were limited at the University of Toronto when Weinzweig studied there. The music of Berg, Stravinsky, and others was more easily accessible at Eastman, which Weinzweig also found to be a more favourable environment for composing. In a 1975 interview, he remarked that "At Eastman I found, for the first time, a climate of creativity that was encouraged. It was the first time I had any composition guidance and that was from Bernard Rogers, a marvelous man."1 Weinzweig studied both composition and conducting at Eastman. Weinzweig returned to Canada in 1938 after completing his studies at Eastman. Over the years he has composed for the C B C and the National Film Board of Canada, has taught at the Toronto Conservatory of Music (now the Royal Conservatory of Music) from 1939-1943 and 1945-1960, and at the University of Toronto from 1952-1978, and has promoted his works and those of other Canadian composers. The latter two occupations were those in which he most distinguished himself: at the University of Toronto he taught many influential composers of the next generation, such as R. Murray 1 John Weinzweig, "Interview!," interview by Jane Champagne, The Canadian Composer, no. 100 (April 1975): 24-33. 2 Richard Henninger and John Beckwith, "Weinzweig, John," in the Encyclopedia of Music in Canada, 2 n d ed., 1391-1394. 2 Schafer, Harry Freedman, Harry Somers, Murray Adaskin, Norma Beecroft, and Brian Cherney. Weinzweig helped to establish the Canadian League of Composers in 1951, and was a co-planner in the creation of the Canadian Music Centre in 1959. Weinzweig has been an active writer on Canadian music, with articles/editorials published in The Canadian Composer, Canadian Review of Music and Art, NOTATIONS, and the Canadian League of Composers Newsletter? Weinzweig was the first Canadian composer to use serial compositional techniques, and he imparted this knowledge and experience to his students upon his return to Canada. He wrote the first Canadian twelve-tone work, the Suite for Piano no. 1, in 1939.5 The Woodwind Quintet, composed in 1963/64, is a relatively late work in his serial style. Other features of the Quintet characteristic of Weinzweig's style are an emphasis on rhythm, and a "tight motivic organization, usually but not slavishly controlled through a personal application of serialism."6 These traits will be discussed in the following document, along with the various means by which Weinzweig develops his source material in each movement and in the work as a whole. This thesis presents an assessment of the Woodwind Quintet in the four following chapters: Chapter 1 examines the source material of the work (its twelve-tone row) to show its first appearances in the work, and to explore its properties of segmentation and interval content. In Chapter 2, Chapter 3, and Chapter 4, each of the three movements of 3 "Dr. John Weinzweig," Canadian Music Centre's Directory of Associate Composers [on-line], Canadian Music Centre; available from; Internet (last accessed 10 July 2002). 4 For a list of his writings, see Elaine Keillor, John Weinzweig and his Music: The Radical Romantic of Canada (Metuchen (NJ): Scarecrow Press, Inc., 1994), 287-288; in addition, several of Weinzweig's writings are collected in Richard Henninger, ed., "Writings of John Weinzweig," Les Cahiers canadiens de musique/The Canada Music Book 6 (1973). 5 Henninger and Beckwith, "Weinzweig, John," 1392. 6 Ibid. 3 the Quintet will be discussed in terms of a specific musical feature emphasized by the composer. For each movement, the corresponding chapter will present an overview of each movement and its features, discuss selected passages, and examine the form. A table will indicate the overall form of each movement, the serial derivation of its subsections, and a brief description of each section. Several notational conventions are used in this thesis. Pitch classes are indicated by their letter names, not by integers. Order positions (in the row) are often used to identify subsets, row rotations, and other kinds of serial information. Order positions will always be indicated by integers mod 12, with / = 10 and e = 11; order integers will be italicized within the document text (but not the figures). Order position sets and set classes will also be set in italic type. As is conventional, ordered sets will be indicated by angled brackets < >; unordered sets will be indicated by curly brackets { }. Because order positions are used throughout this thesis and identified in score excerpts, the derivations and direction of row forms are easily seen. For this reason, retrograde row forms are generally not identified with a separate label from the regular forms. Two means of labeling retrograde row forms are used: on musical examples, the regular row form label is indicated and order numbers show that it is in retrograde: <e, t, 9, 8 ... 1, 0>. In the text, commenting on such places, the (parenthesized) symbol (R) is sometimes included before the row-form label to indicate, without listing order integers, that the row in question is being retrograded. Pitch-class sets (and set classes) will be labeled in the following way: a sequence of integers indicating the normal order of the set will be preceded by a parenthesized lettername indicating the pitch class in the "0" position of the normal order; a 4 parenthesized (I) is inserted if the set is to be read as "inverted," descending from the "0" pitch class. Thus (C#) 014 = {C#, D, F} while (A)(1) 014 = {A, G#, F}. Both are representatives (or members) of SC (014). Forte labels are not used in this thesis. Transformation and inversion operations are labeled according to Babbitt's convention: In(x) = n-x (mod 12) where x is a pitch-class integer, with the pitch-class C fixed as 0. Octatonic collections will be referred to later in this document. The label OCT(x, y) will be used to indicate a specific octatonic collection, where x and y represent two adjacent pitch classes within that collection. From this information, the octatonic collection in question can easily be reconstructed by the reader. Figures, tables, row diagrams, and transformational networks are included in the body of the document. All of these examples are numbered by a number representing the chapter, followed by another number indicating the order of appearance within each chapter. For ease of reading, some figures have been repeated (this is usually indicated within the text). All musical excerpts provided are in C-score: the transposing instruments, clarinet and horn, have their parts listed as heard, not as originally written for the musician. This has been done in order to more easily observe the pitch-class relations examined in this paper. 5 Chapter 1: Properties of the Row All three movements of this work are based upon a single twelve-tone row, henceforth labeled P, and its derivations. P is shown in Row Diagram 1.1 with its order positions identified by integers mod 12 (with t = 10 and e = 11): Row Diagram 1.1 ^ r d < I r 0 1 2 3 4 5 6 7 8 9 t e Position: C Eb E A Bb C# G# B G F# F D The first fourteen bars of the work, provided in Figure 1.1, are derived from To(P) in an interesting but somewhat complex way. For the present we can observe from the ordered integers on Figure 1.1 that the oboe uses only the last tetrachord of P — (8, 9, t, e} -- in various different orderings and rhythms. The other four instruments state the complementary octachord, consistently divided into two different tetrachords occurring as alternating simultaneities that are labeled X and Y beneath the music: X = order positions {0, 1, 3, 4} = (A) 0136, while Y = order positions {2, 5, 6, 7} = (G#) = (E)(1) 0358. Because tetrachords X and Y are not segmental order-position tetrachords, it is difficult to determine the row from this opening passage alone. We shall return to this interesting passage later to analyze it in the detail it deserves. For the present we shall move on to examine passages where P and its transformations are presented more clearly. 7 While order positions on F i g u r e 1.1 show how bars 1-14 can be derived from To(P), they hardly offer proof that P is in fact the referential row for the movement. To help confirm this assertion, bars 15-37 are examined in F i g u r e 1.2. Figure 1.2: Bars 15-37, first movement Flute Oboe Clarinet Horn Bassoon 8 9 The first clearly-ordered form of the row is the retrograde of Lj(P) played by the flute in bars 16-18, which also plays a rotation of the retrograde in bars 2 2 - 2 4 . 7 Row Diagram 1.2 provides TQ(P) and IsfP) for comparison. Row Diagram 1.2 0 1 2 3 4 5 (5 To(P): f c E b ~ | ! _ l j E A | A# C# G# I 5(P): j~F D ! C# G# G E A 7 5 B G F# ~^F D ! ! i A# B I C I Eb | I Row Diagram 1.2 helps us to observe that Is(P) and its retrograde share some consecutive dyads with T 0 (P): {F, D } = I 5(P) (0, 1} = T 0 (P) ft, e}; {C, Eb} = T 0 (P) (0, 1} = I 5(P) ft, e}; {C#, G#} = I 5(P) {2, 3} = T 0 (P) {5, 6}; and {E, A } = T 0 (P) (2, 3} = I 5(P) (5, 6}. In general the pitch classes that compose these dyads have been heard together in bars 1-14: {F, D } was prominent in the oboe tetrachordal melody; {C, Eb} was found in the simultaneous tetrachord X ; and dyad {C#,G#} appeared in the simultaneous tetrachord Y . The invariant segments do not necessarily stand out as independent entities, but it is interesting nonetheless that they are all preserved. Boxes shown on Row Diagram 1.2 highlight these shared dyads. In addition to the rotated-retrograde statements of Is(P) in the flute on Figure 1.2, the clarinet and bassoon each present melodies of six pitch classes which also confirm P as the prime-form row. R o w labels and order positions on the figure show how the 7 Throughout this thesis, order positions are given only for "forward" forms of the row and its transformations. Retrograde forms of the row are therefore indicated when those order positions appear in retrograde. 10 bassoon and clarinet figures are derived from the complementary hexachords of tyP). This row form is given along with TQ(P) in Row Diagram 1.3: Row Diagram 1.3 0 1 2 I7(P): G JE Eb ! To(P): C jEb E | A# 5 6 7 5 9 F# B G# C C# C# G# B G F# F D ! i l7(P) also preserves many of the consecutive dyads of Tn(P): both row forms have {Eb, E} in order positions {1, 2}, {A, Bb} in positions {3, 4} (these two dyads produce the tetrachord {E, Eb, Bb, A} in order positions {1, 2, 3, 4} of both row forms), {G#, B} in positions {6, 7}, and {D, F} in positions {t, e}. This last dyad was also a common segment between Tn(P) and the flute's Is(P). In fact, by comparing Is(P) and I?(P) (Row Diagram 1.4), we can find their common segments (the appearance of these in the actual music will be discussed at a later point): Row Diagram 1.4 0 1 2 3 4 5 6 7 8 9 t Is(P): F D C# G# G E IA F# Bb B I C Eb I7(P): G E Eb j Bb A F# B j G# C C# D F 11 I5(P) and I7(P) also have segments in common: {G, E} = I5(P) {4, 5} = I7(P) {0, 1); {A, F#, Bb, B} = I5(P) {6, 7, 8, 9} = I7(P) {3, 4, 5, 6}; {F, D, C#} = I5(P) {0, 1, 2} = I7(P) /9, t, ej. The interaction between the three instruments emphasizes the latter of these: because the flute presents its row in retrograde, {F, D, C#} occurs at the end of both (R)I5(P) and I7(P) in the ordering <C#, D, F>. In particular, the <D, F> dyad is emphasized since it occurs at the end of the first flute statement (bar 18), and at the end of every clarinet statement (bars 22, 27-28, and 36-37). The C# is separated from the D by two other pitch classes (repeating in the clarinet). The observations made in connection with Figure 1.2 help confirm our assertion of P as the appropriate row for the movement. Indeed, To(P) is the only row form derived from the unambiguous twelve-tone ordering in bars 16-18 of the flute that has the tetrachord {G, F#, F, D}, played by the oboe in bars 1-14, as one of its segmental tetrachords. The accompanimental tetrachords of bars 1-14 are not segmental; we will see later how the dyads of these tetrachords are segmental. For reference, the complete list of derived row forms can be found in Figure 1.3, a tone-row matrix created from P. 12 Figure 1.3: Tone row mat r i x using P as the p r ime f o r m row c Eb E A Bb C# G# . B G F# F D A C C# F# G Bb F G# E Eb D B G# B C F F# A E G Eb D C# Bb Eb F# G C C# E B D Bb A G# F D F F# B C Eb Bb C# A G# G E B D Eb G# A C G Bb F# F E C# E G G# C# D F C Eb B Bb A F# C# E F Bb B D A C G# G F# Eb F G# A D Eb F# C# E C B Bb G F# A Bb Eb E G D F C# C B G# G Bb B E F G# Eb F# D C# C A Bb C# D G G# B F# A F E Eb C To indicate further that P is used in all three movements, Figure 1.4 shows how bars 1-4 of the second movement are also derived from To(P). This strictly "linear" sequential statement of P helps confirm it as the prime-form row for the work as a whole. The passage also shows an explicit segmentation of the row into trichords, a matter which will be examined a bit later. 13 Figure 1.4: Bars 1-4, second movement Oboe 6 , 3 8 0 1 2 ^ £—^ ' Row P and its transformations have interesting properties of symmetry, interval content, and segmentation that Weinzweig explores in the Woodwind Quintet. The following discussion will examine several properties of the row and its transformations, and give an initial indication of how these are exploited within the Woodwind Quintet. The transformations of P are often partitioned into two hexachords. A notable case in point is the clarinet/bassoon duet texture from the first movement, already shown in Figure 1.2, where it accompanies rotated statements of (R)Is(P) in the flute. Another example of this kind of texture occurs in bars 71-83 of the first movement, where the oboe and horn now present the hexachords of Io(P) against a three-voice canon built from canonic rotated statements of (R)To(P) in the flute, clarinet, and bassoon. This passage, to be further discussed in Chapter 2, is provided in Figure 1.5. For the present we can observe how the oboe uses (e, t, 9, 8, 7, 6} from Io(P), and the horn uses its complement 14 {5, 4, 3, 2, I, 0} from I0(P). Those two instruments also play in isorhythm;8 the other three instruments will be discussed in Chapter 2.9 The term 'isorhythm' is used throughout this discussion; although the term can indicate successive exact repetitions of duration series, I am using 'isorhythm' in this thesis to indicate two or more instrumental parts that share the same rhythm. 9 The pitch-class sets and set classes brought out by the isorhythmic segmentation here are interesting. For example, in bars 71-73: {e, 5, t, 4} = (G) = (D)(1) 0347 and {9, 3, 8, 2} = (Eb) = (Ab)(I) 0235; these are both octatonic subsets. We also see {8, 2, 7, 1, 6, 0} = (C) = (E) = (Ab) = (C#)(I) = (F)(1) = (A)(1) 014589; this is commonly referred to as a 'hexatonic' collection. It is also interesting to observe that 6-related order positions are always paired isorhythmically (i.e. e with 5; t with 4; and so forth). These properties could be discussed at length; unfortunately there is not enough space to address these issues in detail in this document. The hexachords of P (and its transformations) share several interesting features. The first hexachord of P belongs to SC (013467); with two degrees of symmetry, each form of this hexachord will map onto itself under some inversion operation. This 16 property is shared, necessarily, by its complement, which belongs to SC (012369). These complementary hexachords each map onto themselves under the same inversion operation. On T0(P), the respective hexachords (A) = (E)(1) 013467 and (F) = (G#)(I) 012369 are each invariant under Ii. Row Diagram 1.5 shows this invariance on To(P) and Ii(P). In fact, the first hexachords of Tn(P) and of I](P) are retrogrades of one another. Although this is not true of the second hexachords of these rows, there is another property that is true of both hexachords: the consecutive dyads in the row each map onto themselves or onto another consecutive dyad in the same hexachord, under the inversion operation in question. Therefore the dyadic partition of To(P) involves the same pitch-class dyads as the dyadic partition of Ii(P): Row Diagram 1.5: Hexachordal and dyadic segmentation of T0(P) and I](P) Order position: 0 1 2 3 4 5 6 7 8 9 t e To(P): C Eb E A Bb C# G# B G F# F D Ii(P): c# Bb A E Eb C F D F# G G# B Hexachord A Hexachord B These properties of To(P) and Ii(P) are true of other transposition levels, and thus hold for any Tn(P) and I„+i(P). Therefore generalizations can be made from the relations observed in Row Diagram 1.5; they are formulated below as strict relations among ordered sets of order positions on the row forms Tn(P) and In+i(P), and then among the unordered membersets of the dyadic and hexachordal partitions of those row forms: 17 For any index number n, Tn(P) <0, 1, 2, 3, 4, 5> = In+i(P) <5, 4, 3, 2, 1, 0>, and Tn(P) <6, 7, 8, 9, t, e> = In+,(P) </, e, 9, 8, 6, 7>. Let D be the dyadic partition of T„(P) and H be the hexachordal partition of Tn(P). Then D and H are both invariant under the inversion In+i. Consequently, D is also the dyadic partition of In+i(P) and H is also the hexachordal partition of In+i(P).10 The dyadic property in particular can lead to ambiguity about which row form is being used when the row dyads are presented as simultaneities. This occurs, for instance, in the third movement, bars 131-134 (Figure 1.6) and 135-143 (Figure 1.7, given shortly). In bars 131-134, the oboe and clarinet play in isorhythm and present (and repeat) the simultaneous dyads < { G , Bb}, { F # , Db}, {A, C } > ; these dyads correspond to the first hexachord of either T 9 ( P ) or Iio(P)- Analytically, one is likely to conclude that this is the first hexachord of Iio(P), since the dyads of the first hexachord of Iio(P) correspond, in order, to the simultaneous dyads of the oboe and clarinet hexachord. However, the cyclic repetition of the dyads casts some doubt on their first-to-last order, and it is also possible that the composer was using a retrograde of the first hexachord of TQ(P). The horn and bassoon do not clarify this ambiguity because they do not play the complement of the oboe/clarinet hexachord. The horn and bassoon instead present material treated in a similar manner: their dyads <{D#, C } , { E , A}, { C # , Bb}> 1 0 There is a significant body of work dealing with these issues. For a broader discussion on aggregate formations, set structure, and other twelve-tone issues, see the following works: Milton Babbitt, "Set Structure as a Compositional Determinant," Journal of Music Theory 5.1 (1961): 72-94; Donald Martino, "The Source Set and its Aggregate Formations," Journal of Music Theory 5.2 (1961): 224-273; David Lewin, "A Theory of Segmental Association in Twelve-Tone Music," Perspectives of New Music 1.1 (1962): 89-116; Richard B. Kurth, "Mosaic Isomorphism and Mosaic Polyphony: Balance and imbalance in Schoenberg's twelve-tone rhetoric," (Ph. D. diss., Harvard University, 1993). 18 correspond to the first hexachord of either To(P) or Ii(P). These simultaneous dyads correspond, in order, to those of To(P), but the possibility that they might actually derive from Ii(P) is not completely discounted without further collaboration from the complementary hexachord. Another ambiguity arises as a result of these properties: it is not clear whether the horn/bassoon duet is to be heard as an inversion or as a retrograde transposition of the oboe/clarinet duet. Registral parallelisms between the two duets probably incline one to hear their relationship as an inversional one, but some ambiguity in the matter nonetheless persists. The oboe/clarinet and horn/bassoon duets also have common pitch-class material in bars 131-134 (Figure 1.6). From their collections <{G, Bb}, {F#, Db}, {A, C}> and <{D#, C}, {E, A}, {C#, Bb}>, several things can be observed. Firstly, the two ordered collections of dyads map onto each other under Iio: in fact, the pitch classes {A, Bb, C, 19 C#} occur in both collections, forming (A) = (C#)(I) 0134, also invariant under Iio.11 This tetrachord is reiterated at the end of the excerpt (and is also sustained across the bar line in bars 132-133), and is also a subset of the octatonic collection OCT(A, Bb). Indeed, the combination of the oboe/clarinet and horn/bassoon collections results in {F#, G, A, Bb, C, C#, D#, E}, the entire OCT(A, Bb) collection. Octatonic materials are often incorporated into the twelve-tone materials of this work; the composer seems to have intentionally chosen sets incorporating octatonic materials. The use of these materials is discussed later in this chapter. Figure 1.7 shows bars 135-143, in which the same pitch classes are presented in a similar manner, but in a different instrumentation. In bars 136-138 the flute and oboe present <{G, Bb}, {F#, C#}, {A, C}>, while the clarinet and bassoon present <{Eb, C}, {E, A}, {Db, Bb}>. In bars 141-143 these associations are reversed: the flute and oboe now present <{Eb, C}, {E, A}, {Db, Bb}>, while the clarinet and bassoon present <{G, Bb}, {F#, C#}, {A, C}>. The same arguments hold true as in the discussion of bars 131-134: the dyads of each hexachord correspond best to the unordered dyads of the first hexachord of Iio(P) and To(P). Again the two hexachords combine to create an octatonic collection, and again the complement of neither hexachord is to be found in the texture. Indeed, the horn material in Figure 1.7 heard (in bars 138-141) between the two statements of the flute/oboe and clarinet/bassoon hexachords derives from l4(P), not from any of the row forms that might correspond to the hexachords in question. 1 1 The oboe/clarinet duet and the horn/bassoon duet both present instances of SC (013467); these also map onto each other under I10. This set class is a subset of the octatonic collection. 20 Red boxes: <{G, Bb}, jF#, C#[, {A, C}> Blue boxes: <{Eb, C}, (E, A), {Db, Bb}> Dotted lines indicate that the contained pitches form a single hexachord. As previously mentioned, the first hexachord of each row form belongs to SC (013467), a set class with two degrees of symmetry. As we have seen, its ordering in row is also symmetrical. Row Diagram 1.6 examines TQ(P) to show this property: 21 Row Diagram 1.6: Intervals between consecutive pitch classes of T0(P) Order position: 0 1 2 3 4 5 6 7 9 t e To(P): C Eb E A Bb C# G# B G F# F D Directed interval from previous pitch class: +3 +1 +5 +1 +3 -5 +3 -4 -1 -1 -3 The first hexachord, shown in To(P), is ordered as a palindromic sequence of intervals: <+3, +1, +5, +1, +3>. For an inversion of the row, the direction of the intervals will be the opposite, <-3, -1, -5, -1, -3>, but the palindrome is maintained. The first and last pitch classes of this hexachord map onto one another under Ii; because of this relation, the first hexachords of any two rows Tn(P) and In+i(P) (in other words, any two row forms related by Ii) will be retrogrades. Although Weinzweig does not exploit this property overtly, he does seem to be conscious of the interval direction required to create this palindrome. Bar 24 in the second movement (Figure 1.8) presents a melody in the flute created from the first hexachord of To(P), with several repeated pitch classes. This melody is strictly ascending, and any repeated pitch classes remain in the same register. The melody within this bar also does not move by any interval larger than 5 semitones (between the E and A); the smallest possible intervals between consecutive pitch classes are used, thus producing the exact palindromic sequence of intervals listed above. This melody therefore displays the symmetry just discussed. 22 Figure 1.8: Bar 24, second movement 2 3 4 5 Also common within this work is the segmentation of row forms into trichords. The opening four bars of the second movement (see the discussion above accompanying Figure 1.4) emphasize this segmentation by presenting the four trichords of To(P) melodically, each in a different instrument. This segmentation is interesting because the composer has designed the row so that all of the segmental trichords belong to SC (014). Trichordal segmentations and the use of SC (014) will now be examined. The discussion will begin by examining To(P) and its segmental trichords, given in Row Diagram 1.7: Row Diagram 1.7: Segmental trichords of T0(P) Order positions: 0 1 2 3 4 5 6 7 8 9 t e To(P): C Eb E A Bb C# G# B G F# F D Labels: (E)(1) 014 (A) 014 (G) 014 (F#)(I) 014 Trichord 1 Trichord 2 Trichord 3 Trichord 4 23 Since the four segmental trichords all belong to SC (014), the unordered trichords can be mapped onto each other under various transformations.12 The transformations which map the segmental trichords onto one another in To(P) are shown in the following transformational network: More generally, for the transposed row forms Tn(P) the transformations will be as follows: 1 2 The use of segmentation and transformations between segments of twelve-tone rows (especially in respect to Webern and the derivation of twelve-tone rows) is discussed extensively in Milton Babbitt, "Twelve-Tone Invariants as Compositional Determinants," Musical Quarterly 46, no. 2 (April 1960): 246-259. 24 For the inverted row forms In(P) the transformations will differ. The transposition and inversion operations mapping trichords to each other are listed below: for the transpositions, the index number is the complement of the corresponding transposition for To(P) in Transformational Network 1.1; for the inversions, the index number is the complement of the corresponding inversion for To(P) in Transformational Network 1.1 plus 2n: trichord 1 to trichord 2: I(12-l)+2n _ Ill+2n trichord 1 to trichord 3: 1(12-1l)+2n = II + 2n trichord 1 to trichord 4: T(i2-2) = T, 0 trichord 2 to trichord 3: T(12-10) = T 2 trichord 2 to trichord 4: I(12-3)+2n = I9+211 trichord 3 to trichord 4: I(12-l)+2n = Ill+2n 25 Although the inversion operations within the transformational networks above differ depending upon n, the transposition operations within each network are not affected by n. Several relationships can be observed when the transformational networks for In(P) and Tn(P) are compared: In+2n and Ii+2n swap places from Transformational Network 1.2 to Transformational Network 1.3 between trichords 1 and 2, 3 and 4, and 1 and 3; Tio and T2 also swap places from trichords 1 to 4 and 2 to 3. In fact, because Tio and T2 are inverses, both these two operations relate the relevant pairs of trichords, depending on the direction of relationship; for example, in Transformational Network 1.2 Tio maps trichord 2 onto trichord 3, while T2 maps trichord 3 onto trichord 2. This emphasizes Tio and T2, and indeed those are the only two transpositional relationships among transpositionally-related trichords in any row form. A simpler form of the transformational networks provided above gives the transformations between adjacent trichords; these are given below as Transformational 26 Network 1.4 and Transformational Network 1.5. These new networks call attention the symmetries found in P and emphasize the T2 and In_n , transformations that will later be examined within the three movements of the Woodwind Quintet. Transformational Network 1.4: Simplified trichord mapping for Tn(P) T2 Transformational Network 1.5: Simplified trichord mapping for I„(P) T2 27 Weinzweig invokes T2 and Tio relationships within the Woodwind Quintet by using them in recapitulatory material (such as the relationship of the clarinet material in bars 1-8 and 182-191 of the third movement, to be discussed shortly) and also in the interaction between two seemingly unrelated melodic streams (such as the relationship between the flute and clarinet/bassoon material in bars 15-37 of the first movement, also to be discussed shortly). Why would the use of these particular transformations be an effective compositional tool? To answer this question, a pair of T2-related row forms are examined in Row Diagram 1.8. Row Diagram 1.8 Order position: 0 1 2 3 4 5 6 7 8 9 t e To(P): ' C Eb ; E A Bb C# G# B G F# F D T2(P): D F# B ( c D # ; Bb C# A G# G A pair of T_-related row forms were previously examined in Row Diagram 1.4 l5(P) and I?(P), the row forms used by the flute and clarinet/bassoon in bars 15-37; a different pair of T_-related rows are presented in Row Diagram 1.8. Both row forms share an unordered tetrachord, trichord, and dyad among their segments; these are indicated in Row Diagram 1.8 by the use of matching boxes and ovals (similar - and 28 analogous - to those used in Row Diagram 1.4). When rows related by T2 (or Tio) are used, they will present corresponding segments containing the same pitch classes. Several passages in which this occurs will now be examined. Bars 1-14 of the first movement (as already discussed in Figure 1.1) present an oboe melody with accompaniment in the remaining instruments, all drawn from To(P). This material returns in bars 37-45, shown in Figure 1.9. The instrumentation and texture remain the same (a tetrachordal melody in the oboe with accompaniment in the other four instruments) but the pitch material differs: in bars 37-45 the oboe presents {B, D, F, F#} = (F#)(I) 0147, whereas in bars 1-14 the oboe presented {G, F#, F, D} = (G)(1) 0125: the use of B instead of G arises because T2(P): (0, 1, 2, 3} is presented instead of To(P): (8, 9, t, ej. These two tetrachords represent different set classes, but still share the trichord {D, F, F#}. The variation used here involves maximal - i.e. trichordal - pitch-class overlap (short of identity) between the two oboe tetrachords, and a switch in serial derivation from the last tetrachord of the row form to the first. It is an example of the manner in which T2-related rows share pitch-class material: the third tetrachord of To(P) (heard in bars 1-14) shares three of four pitch classes with the first tetrachord of T2(P) (heard in bars 37-45). The accompaniment materials follow a similar process. In bars 1-14 the accompaniment involved two alternating chords, X = {A, Bb, C, Eb} = (A) 0136, and Y = {G#, B, C#, E} = (G#) = (E)(1) 0358. In bars 37-45 the accompaniment also alternates two chords, {C, Db, E, G#} and {D#, G, A, Bb}. These two chords each share three of four pitches with one of the accompaniment chords of bars 1-14 and therefore will be labeled X' = {D#, G, A, Bb} = (Bb)(T) 0137 and Y' = {C, Db, E, G#} = (C) 0148. 1 3 The transformational networks previously discussed demonstrated how T2-related trichords mapped on to one another; the tetrachord indicated in Row Diagram 1.8 could be interpreted as a segmental trichord with an added pitch class. 29 Again, although none of the accompaniment tetrachords are segmental tetrachords, three of four pitch classes from each tetrachord of bars 1-14 are retained in the tetrachords of bars 37-45. Figure 1.9: Bars 37-45, first movement In bars 15-37 of the first movement, previously discussed in connection with Figure 1.2, there is another T_-relation. In this passage the flute presents rotated row 30 forms derived from (R)I5(P) while the bassoon and clarinet present the two hexachords of l7(P). These instruments are rhythmically independent, alternating with one another (each plays solo while the other two instruments rest), but the pitch-class materials between the flute and the bassoon/clarinet are remarkably similar: Row Diagram 1.9 f "\ (R)I5(P): Eb C B A# F# A E G G# C# D F r I7(P): \ G E Eb Bb A F#| |B G# C C# D F | As illustrated in Row Diagram 1.9 with solid boxes, two corresponding locations within each row present the same trichord, in the first case differently ordered and in the second case identically ordered. These do not occur simultaneously in this passage, but it is easy for the listener to hear that both row forms end with the same trichord, <C#, D, F>. The trichord {A#, F#, A} is also a common segment in the flute and clarinet parts during this passage. In fact, {B, A#, F#, A} is a common segment of both row forms (see also Row Diagram 1.4 above; on Row Diagram 1.9 it is shown with braces), but the clarinet and bassoon subdivide (R)I?(P) into hexachords, thus breaking up the tetrachordal segment, but nonetheless preserving the trichord. There do not seem to be any TVTio-relations in the second movement, but the third movement presents several instances. The third movement begins with a passage in which the clarinet plays rhythmicized repetitions of the first trichord from Tio(P), as heard in bars 1-8 (Figure 1.10). 31 Figure 1.10: Bars 1-8, third movement J = 116 Flute Oboe Clarinet Horn Bassoon FI. Ob. Cl Hn Bsn The rhythmic motive used here (to be discussed in detail in Chapter 4) returns in bars 182-191, again in the clarinet, this time presenting the first trichord of To(P). This passage is given in Figure 1.11. Unlike Figure 1.10, bars 182-191 present accompaniment played by the oboe, horn, and bassoon which each present one of the remaining trichords of To(P). The two row forms that present the clarinet's rhythmic motive in both passages, Tio(P) and To(P), are related by T_; Row Diagram 1.8 and the accompanying discussion have already established that rows related by T2 and Tio share 32 several segments. In this case, the second trichord of To(P) (heard in the horn in bars 182-187 and the clarinet in bars 188-189) shares {Bb, C#} with the first trichord of Tio(P) (heard in the clarinet in bars 1-8). Figure 1.11: Bars 182-191, third movement 182 The T2-relationship between TK)(P) and To(P) is continued by the clarinet into the last bar of the work, bar 201 (Figure 1.12). Here the flute, oboe, horn, and bassoon present Ti(P) as accompaniment while the clarinet plays the first hexachord of T_(P). The row form presented by the clarinet is, at first, ambiguous: the <D, F, F#> heard at 33 the beginning of the bar in the clarinet is a segmental trichord of both To(P) and T2(P). One might assume To(P) is being continued from the previous passage until hearing order positions <3, 4, 5> of the clarinet's final hexachord. The switch to T2(P) in the clarinet emphasizes the T2-relation previously discussed. This, in addition to the return of opening material from both the third movement (the clarinet motive) and the first movement (the row form, To(P)), effectively concludes the work. Figure 1.12: Bar 201, third movement Shared trichords also occur in row forms related in other ways. As we have seen, two row forms that share the same unordered first hexachord can also map their trichords onto one other; Row Diagram 1.10 gives one example of such a pair, TQ(P) and Ii(P). 34 Row Diagram 1.10: Swapped trichords between two rows sharing the same unordered first hexachord To(P) C Eb E A Bb C# G# B G F# F D Ii(P) c# Bb A E Eb c F 0 F# G G# B The inversion swaps the first two trichords of these rows and strictly retrogrades them; the inversion also swaps the last two trichords as unordered sets. This process does not manifest itself directly in Weinzweig's music, but may be reflected by other means. Bars 5-8 of the second movement (Figure 1.13) stimulate an interesting discussion in this regard. Figure 1.13: Bars 5-8, second movement, with segmental trichords T0(P) Flute Oboe Clarinet Bassoon s f 0 r T3-nr r-0 3 5 7 • 5 7 5 1—3-_7|y t e id 1 \ e i e 0 2 4 i -a _s. . m 3 4 —1 r 1 —-al 4 y f • . u 1= _4 6 1 4 • 1 1 9 1 :"H~ 7 jh I \ It 1 rr~ . r 1-4. This passage presents two isorhythmic duets: flute with clarinet, and oboe with bassoon. In combination these instruments present TQ(P) as a series of simultaneous 35 dyads. Figure 1.13 considers this passage from a trichordal perspective (trichord 1 is indicated in red, trichord 2 in blue, trichord 3 in green, and trichord 4 in purple). Trichordal segmentation is not the most apparent analytical means for this passage (consecutive dyads seem more obvious) but it does allow us to see more easily the relation to Row Diagram 1.10 above. Specifically, segments of the row form are repeated before the entire row is completed. In bar 5 of Figure 1.13 the following occurs: <trichord 1, trichord 2, trichord 1>. Compare this to Row Diagram 1.10, above: by repeating trichord 1 after trichord 2, both the first hexachord of To(P) and the retrograde first hexachord of Ij(P) are presented. If Weinzweig was making use of exchanging trichords within Ii+2n-related rows, this is the most likely location. The melodic formation of trichords brings out another relationship. Examine the flute and clarinet melodies in Figure 1.13: trichords occur in the first bar as order positions <1, 2, 5> in the flute and <0, 3, 4> in the clarinet. The associated pitch-class trichords, {Db, Eb, Fb} in the flute and {A, Bb, C} in the clarinet, both belong to SC (013), a set class that contains icl and ic3, significant intervals from P. More generally, other order-position trichords sometimes show a similar relationship: for instance, the pitch-class trichords corresponding with order positions (0, 1, 3} and {2, 4, 5} both form trichords of SC (036) (which contains two instances of ic3); likewise, the pitch-class trichords in order positions (6, 7, 9} and {8, t, e} both represent SC (025) (which also contains ic3). The latter two set classes discussed above, (036) and (025), result from the same pattern of order positions within each hexachord; one could call this an "order position set class" (OPSC), specifically OPSC (013) since this set involves two adjacent order positions and another order position separated by one intervening order position. It 36 is also interesting that the corresponding pitch-class sets in each hexachord are consistently related by a single inversion: In +i on Tn(P), and In+i on In+i(P). Row Diagram 1.11 shows To(P), with brackets indicating four representations of OPSC (013) and the set class of each corresponding pitch-class trichord. Row Diagram 1.11: Distribution of order position set class trichords within P SC(036) SC(025) OPSC(013) OPSC(013) Order 0 1 2 3 4 5 6 7 8 9 t e positions: T0(P): C Eb E A Bb C# G# B G F# F D SC(036) SC(025) OPSC(013) OPSC(013) Figure 1.13 illustrated the segmental trichords found within bars 5-8; Figure 1.14 illustrates how the order position set class (013) trichords just identified occur within this same passage: a dyad of the trichord occurs simultaneously in two instruments, with the third pitch in either the previous or following attack in one of the two instruments. In bar 6, for example, OPSC(013) is formed by order positions <{0, 1}, {3}> in the flute and clarinet on the first and second triplet-eighth notes, and also by order numbers <{2}, (4, 5}> in the same instruments on the second and third triplet-eighth notes (creating two SC (036) trichords). The same process occurs in the oboe and bassoon when they enter: OPSC(013) is formed by order numbers <{6, 7}, {9}> on their first and second triplet-eighth notes in bar 6, and <{8}, {t, e}> on their second and third triplet-eighth notes in bar 6 (creating two SC (025) trichords). This process continues throughout this passage, and 37 is shown on Figure 1.14 by coloured boxes: red indicates order positions (0, 1, 3}, blue indicates order positions {2, 4, 5}, green indicates order positions {6, 7, 9}, and purple indicates order positions (8, t, ej. Figure 1.14: Bars 5-8, second movement, with order position set class trichords Toff) Clarinet Horn Bassoon 5 i : 5 1 2 o : 5 2 5 7 5 1 — » 1 ^ 7 n 8 t T— 1 6 8 e 9 i—:ii = r L U ! 0 / / r - C 4 1 • 5 U 1 4 6 II r " 4 6 Ii J9 t i • 7 9 i 1 C i r~i 5 t s 0 j J * The Woodwind Quintet also emphasizes particular interval classes. Row Diagram 1.12 replicates Row Diagram 1.6, listing the intervals between consecutive pitch classes of TQ(P): Row Diagram 1.12: Intervals between consecutive pitch classes of T0(P) Order 0 1 2 3 4 5 6 7 8 9 t e position: T 0 ( P ) : C Eb E A Bb C# G# B G F# F D Directed +3 +1 +5 +1 +3 -5 +3 -4 -1 -1 -3 interval from previous pitch class: 38 From this, we can see that icl and ic3 occur most often between consecutive pitch classes of the row, specifically four times each. Interval classes 5 and 4 also occur in the row, ic5 occurring twice, and ic4 occurring once. Several passages within the Woodwind Quintet emphasize the most frequent intervals, both consecutively in the row form and in other places where the pitch classes are not consecutive. These will be examined now. Bars 37-52 of the first movement (Figure 1.15) present a tetrachordal oboe melody accompanied by two isorhythmic duets played by flute/clarinet and horn/bassoon; the four accompanying instruments present the remaining octachord out of row-form order. The passage is derived from T2(P), the row form corresponding to the oboe's tetrachord. We briefly examined the simultaneous accompaniment tetrachords X' and Y' earlier in connection with Figure 1.9. Now we will examine the individual instrumental voice leading in bars 37-45; a discussion of the entire passage will occur later in Chapter 2. 39 Figure 1.15: Bars 37-52, first movement T2(P) Y ' X ' Y ' X ' Y ' Y ' X ' Y ' X ' Y ' 40 Figure 1.15, con't. 2 7 4 7 4 4 8 Alternating flute/clarinet and horn/bassoon pairs In bars 37-39 each accompaniment instrument plays a dyad: the flute plays the ic3 dyad {Db, Bb}, the clarinet plays the ic5 dyad {C, G}, the horn plays the icl dyad {G#, A}, and the bassoon plays the icl dyad {E, D#}. As noted in the last paragraph, these are three of the four interval classes that occur between adjacent members of P. In this passage, however, the clarinet and bassoon materials are not formed from adjacent members of the current row form: in T2(P) the clarinet's {C, G} occur in order positions (4, tJ, while the bassoon's {E, D#} occur in order positions {e, 5}. The following bars, shown below in Table 1.1, by and large continue this sort of pattern: 41 Table 1.1: Dyads in the accompaniment instruments, bars 40-45, first movement Bar: ••/. 40 41 "43 ;5l4v'" 45 Flute {C, G} {C,Bb} {Db, Bb} {C, G} {Db, Bb} {Db, Bb} Interval class: ic5 ic2 ic3 ic5 ic3 ic3 -Order positions: {4,0 {4,6} {7,6} {4,0 {7,6} {7,6} Clarinet {Db, Bb} {Db, G} {C, G} {Db, Bb} {C, G} {C, Gj Interval class: ic3 ic6 ic5 ic3 ic5 ic5 Order „ positions: {7,6} a o {4,t} {7,6} {4,0 {4,0 Horn {E,A} {G#, A} {G#, A} {E,A} {G#, A} {G#, A} Interval class: ic5 icl icl ic5 icl icl Order '< positions:-1 {e,8} {9,8} {9,8} {e,8} {9,8} {9,8} Bassoon {G#, D#} {E,D#} {E, D#} {G#, D#} {E, D#} {E,D#} Interval class: ic5 icl icl ic5 icl icl Order positions: {9,5} {e,5} {e,5} {9,5} {e,5} {e,5} As indicated along the right side of the first staff on Figure 1.15, the flute and clarinet both use the (unordered) tetrachord Q = {C, Db, G, Bb} = (Db) 0136. The horn has the (unordered) trichord {E, G#, A} = (A)(1) 015, while the bassoon has {D#, E, G#} = (D#) 015; the horn and bassoon trichords share the dyad {E, G#} and combine to form R = {D#, E, G#, A} = (D#)=(A)(I) 0156. None of these is a segment of T2(P). The intervals created in this passage nonetheless reflect those found consecutively in P: ic5 occurs most often (9 times) and is played in every instrument; icl occurs 8 times, only in 42 the horn and bassoon; ic3 occurs 5 times, only in the flute and clarinet. Ic2 and ic6, which do not occur between consecutive pitch classes of P, each occur only once, ic2 in the clarinet and ic6 in the flute. Again, the most common intervals in this passage are those which are most common within P. Of course, as noted earlier, the simultaneous tetrachords labeled X' and Y' are also not row segments. Bars 131-134 of the third movement, previously discussed in Figure 1.6 and recreated as Figure 1.16, also emphasize common intervals within P. As Figure 1.16 shows, the oboe and clarinet form an isorhythmic duet, as do the horn and bassoon. Each instrument melodically plays a (013) trichord, forming icl, ic3, and ic2 as consecutive intervals. The order trichords are {0, 3, 4} and {1, 2, 5}; these are both of OPSC (014) and will always yield a pair of SC (013) trichords. The simultaneities within the isorhythmic duets are adjacent dyads within either To(P) or Iio(P) in the oboe and clarinet, and To(P) or Ii(P) in the horn and bassoon. The specific intervals formed from these simultaneities are ic3, ic5, and ic3 in the oboe and clarinet duet (dyads {G, Bb}, {F#, Db}, and {A, C}), and ic3, ic5, and ic3 in the horn and bassoon duet (dyads {Eb, C}, {E, A}, and {C#, Bb}). Interval classes 3 and 5 are thus emphasized as simultaneities, while interval classes 1, 2, and 3 are emphasized as melodic intervals; ic2 is the only one of these intervals that does not occur consecutively in P. Interval classes 1, 3, and 5, however, occur most often between the consecutive pitch classes of P. 43 The beginning of the first movement (originally provided as Figure 1.1 and replicated here as Figure 1.17) also emphasizes the use of these interval classes. In addition, this passage provides a good example of the use of tetrachords within the work and the process by which dyads are manipulated, which will now be examined in relation to this passage. The first two bars of the accompaniment (flute, clarinet, horn, and bassoon) are a good passage in which to examine the interval content. Each accompaniment instrument 45 presents two different icl dyads melodically, but also combines with the other accompaniment instruments to produce the simultaneous tetrachords labeled X and Y on Figure 1.17. The four accompaniment instruments play isorhythmically, but two duets can be seen by comparing the pitch-class content. In bar 1 the flute and clarinet play the same two dyads, {D#, E} and {A#, B}, in total playing the collection {A#, B, D#, E} = (A#)=(E)(I)0156, labeled V on Figure 1.17. The horn and bassoon likewise both play {A, G#} and {C, Db}, to share the four-note collection {A, G#, Db, C} = (G#)=(Db)(I)0145, labeled W on Figure 1.17. The use of dyads is significant in this passage because the dyads are swapped between the instruments of each duet; this process is notated on Figure 1.17 in red. Materials in bars 1-14 are derived from To(P); their distribution within the accompaniment material, however, does not correspond to the segmental tetrachords (as does the oboe melody, as discussed earlier). Order positions and coloured boxes on Figure 1.18 show how the first and second tetrachords of To(P) are distributed within the accompaniment material. Two dyads - one melodic, the other simultaneous - pair consistently to create the segmental tetrachords of To(P). The first tetrachord is shown by dyads <1, 2> and (0, 3} in red boxes; the second tetrachord involves the dyads <4, 7> and {5, 6} in blue boxes (two separate statements of these two tetrachords are divided by a dotted green line). 46 Figure 1.18: Bar 1, first movement, with annotations J = 120 T0(P): 1 2 Flute Oboe Clarinet Horn Bassoon 4 7 0 5 4 7 m 1 2 3 6 Red = tetrachord 1 of T0(P) Blue = tetrachord 2 of T0(P) Although non-consecutive tetrachords are used in the opening, segmentation into consecutive tetrachords is fairly common elsewhere in the Woodwind Quintet. This is especially prominent in the first movement in the oboe and isorhythmic accompaniment texture, to be examined in Chapter 2. Weinzweig's use of this segmentation is interesting because he uses not only the segmental tetrachords of P, but also tetrachords whose set classes are not represented by segments of P. We have seen instances of both types in the preceding figures. We will now explore these two types of tetrachords a bit further. The set classes of the three segmental tetrachords of P are SC (0147) in order positions {0, 1, 2, 3}, SC (0235) in order positions {4, 5, 6, 7}, and SC (0125) in order positions {8, 9, t, ej. Set classes (0147) and (0125) have one degree of symmetry, while set class (0235) has two degrees of symmetry. These set classes occur in To(P) as shown on Row Diagram 1.13: 4 7 Row Diagram 1.13 Order positions: To(P): Labels: 0 8 C Eb Bb C# G# B G F# D (E)(1) 0 1 4 7 Tetrachord 1 (G#) = (C#)(I) 0 2 3 5 Tetrachord 2 (G)(1) 0 1 2 5 Tetrachord 3 Given the low degree of symmetry, these specific tetrachords will not generally occur as segments in any other row form; however, they do recur in other contiguous order positions in row forms of P . Specifically, SC ( 0 1 4 7 ) occurs in order positions (0, 1, 2, 3} and {2, 3, 4, 5}; SC ( 0 2 3 5 ) occurs in order positions {4, 5, 6, 7} and {t, e, 0, J}; SC ( 0 1 2 5 ) occurs in order positions {8, 9, t, ej, (3, 4, 5, 6}, and {6, 7, 8, 9}. SC ( 0 1 4 6 ) is the only other set class that occurs more than once in adjacent order positions of P : it occurs in order positions (5, 6, 7, 8} and (9, t, e, 0}. Because of their frequency within P , these set classes are emphasized. Does the composer accentuate these tetrachords within the Woodwind Quintet? Bar 3 2 of the second movement and bars 1 1 7 - 1 3 0 of the third movement make use of these tetrachords as segmental tetrachords and will now be examined. Bar 3 2 (given in Figure 1.19) acts as a transition between two different textures. In bar 31 the oboe and bassoon each present a dyad on the fourth quarter-beat; these dyads are continued into bar 3 2 . The oboe and bassoon combined form {F#, A, A#, B}, tetrachord 3 of T ^ P ) . The other two instruments, flute and horn, each play a four-note melody constructed of two dyads, {C, Eb} and {D, F}, in alternation. Interestingly, these two dyads occur as the first two and last two pitch classes of Is(P) and TQ(P), two row 48 forms that have previously been discussed.14 In this context, however, these four pitch classes in combination form {C, D, Eb, F}, tetrachord 2 of T4(P). The missing tetrachord 1 of T4(P) occurs as part of a melodic hexachord in the bassoon in bars 30-31. Figure 1.19: Bars 30-33, second movement 30 Specifically, <C, Eb> = T0(P) <0, 1> = I5(P) <t, e>, and <F, D> = T0(P) <t, e> = I5(P) <0, 1>. 49 Bars 117-130 of the third movement (Figure 1.20) also present segmental tetrachords, in this case as isorhythmic accompaniment material derived from Te(P). The tetrachords occur as simultaneities played by the oboe, clarinet, horn, and bassoon, while the flute plays a melody derived from Is(P). The segmental tetrachords of Te(P) are presented in alternation in the following sequence, as observed on Figure 1.20: <1, 2, 3, 2, 3, 1, 2, 3, 3, 1, 2, 3, 1, 3, 1>; the different tetrachords are indicated on Figure 1.20 with coloured boxes, red for the first tetrachord, blue for the second tetrachord, and green for the third tetrachord. Consider this parsing of the sequence just presented: [123J[23123][31231][31]. Although this parsing does not correspond well to the chord rhythms, it presents an interesting ordering. This sequence could be interpreted as a series of overlapping rotations: the second group, for example, overlaps tetrachords 2 and 3 from the first group and rotates through the tetrachords, with the first tetrachord following the third; the third group overlaps tetrachord 3 and rotates through tetrachords 1, 2, 3, and 1; the fourth grouping overlaps tetrachords 3 and 1. Also of note are the fixed instrumental trichords occurring as the alternating tetrachords are reiterated: the oboe presents (E)(I)015, the clarinet presents (C)(I)025, the horn presents (Ab)(I)016, and the bassoon presents (F#)(I)015. In the last bar, however, the oboe and clarinet swap their usual pitches on the second quarter-note beat. In bar 124 the flute has (C)(1) 025, a collection previously heard in the clarinet. No other collections repeat within this passage. '» t 4 In Ob (E)(I)015 (C)(I)025 (Ab)(I)016 (F#)(I)015 (oboe and clarinet are swapped here) Non-segmental tetrachords also occur prominently within the Woodwind Quintet. Two examples will be briefly discussed. 51 Bars 1-14 of the first movement have recently been examined in the analysis of dyad presentation and prominent intervals. At this point I will remind the reader that the simultaneous accompanimental tetrachords are non-segmental tetrachords, created by joining members of melodic and simultaneous dyads. Bars 192-198 of the third movement, shown in Figure 1.21, also present non-segmental tetrachords, here also derived from To(P). In this passage the flute, oboe, and clarinet play isorhythmic accompaniment, while the horn plays a combination of melody and accompaniment and the bassoon plays a leaping bass part. The flute, oboe, clarinet, and horn alternate two tetrachords, labeled J and K on Figure 1.21: J = order positions {0, 1, 7, 8} = {C, Eb, B, G} = (B)0148; K = order positions {2, 4, 5, 9} = {E, A#, C#, F#} = (F#)(I)0258. These simultaneous tetrachords create sonorities for the listener that are not directly derived from melodic statements of To(P), but rather formed mostly from segmental dyads of P: J contains two segmental dyads of To(P), {C, Eb} and {B, G}, while K contains one segmental dyad of To(P), {A#, C#}, and two other pitch classes. There are also two instances of SC (0236): the flute and oboe pair creates (C#)(I) 0236, while the clarinet and horn pair create (F#)(I) 0236. The flute/oboe pair maps onto the clarinet/horn pair under T 5 , interesting since these two sets are derived from the same row form. 52 Figure 1.21: Bars 192-198, third movement J K J J K Apart from recurring hexachords, tetrachords, trichords, and other subsets of P, octatonic collections are also alluded to throughout the Woodwind Quintet, a result of the 53 composer's structuring of P. Octatonic subsets often emerge; for instance, the first hexachord of P represents set class 013467, a subset of the octatonic collection, SC (0134679t). Table 1.2 illustrates how a number of octatonic subsets occur within P; shaded cells identify the order positions that correspond with the octatonic subsets in question. Table 1.2: Subsets of the octatonic collection within the Woodwind Quintet (and their order positions within P) Set class Derivation 0 1 3 4 5 6 7 9 e 013467 First hexachord of P 1 1 I 0147 First tetrachord of P (also {2, 3, 4, 5}: see page 47) 1 1 0235 Second tetrachord of P (also {t, e, 0, 1}: see page 47) 1 1 1 1 0136 Bars 37-45, first movement, flute and clarinet tetrachord 1 1 014 Segmental trichords of P 1 1 1 1 1 0137 Bars 37-45, first movement, simultaneous tetrachord (T2(P)) 1 1 1 1 0358 Bars 1-14, first movement, simultaneous tetrachord 11 1 0258 Bars 192-198, third movement, simultaneous tetrachord 1 013 Bars 131-134, third movement, melodic trichords 1 1 1 1 1 1 036 Chapter 1 discussion, page 36, OPSC(013) trichords 1 1 I 54 025 Chapter 1 discussion, page 36, OPSC(013) trichords 1 1 1 These octatonic subsets are distributed throughout the work; several passages present especially clear octatonic sounds. Some passages, such as those in Figure 1.6 and Figure 1.7, have already been discussed; others will now be examined. Bars 19-24 of the second movement (see Figure 1.22) provide another instance of the kind of "octatonic sound" one sometimes hears in the piece. These bars present an interestingly florid flute melody accompanied by two isorhythmic duets in the oboe/clarinet and horn/bassoon. The accompaniment material in bars 19-23 consists of order positions {2, 3, 4, 5} of I3(P): the resulting set {F#, F, D, B} = (F#)(I)0147 is drawn from the first hexachord of this row, and must therefore be an octatonic subset, in this case of OCT(F, F#). The melody material in bars 19-23 in the flute is formed from the remaining pitch classes of l3(P), order positions {6, 7, 8, 9, t, e, 0, 1}. These pitch classes, {A, Bb, C, C#, D#, E, G, G#}, form a collection closely related to the octatonic scale OCT(A, Bb): if G# were replaced with F#, that octatonic collection would result. {G#} appears as a lower neighbour note to {A} in this passage (the only exception being bar 22, in which {G#} precedes {A} but is an octave below its neighbour position), and as such could be treated as an ornamental note rather than an actual member of the collection. Six of the eight pitch classes presented in the flute, {A, Bb, C, C#, D#, E} (which form a subset of the octatonic collection OCT(A, Bb)) are also the pitch classes of the first hexachord of TQ(P). In fact, in bar 24 the flute plays the first hexachord of TQ(P), 55 and therefore reinforces the sense that the flute in bars 19-23 was octatonic - or very nearly so. Figure 1.22: Bars 19-24, second movement Flute Oboe Clarinet Horn Bassoon To(P) and l3(P) are related by significant shared material, as shown in Row Diagram 1.14. 56 Row Diagram 1.14 Order positions: 0 I 2 3 4 5 6 7 8 9 t e I3(P): ( Eb c )B F# F D G E G# A Bb C# To(P): ( C ) E A Bb C# G# B G F# F D Two ordered trichords are found in both row forms, in order positions <3, 4, 5> and <9, t, e> of each row. Weinzweig makes use of this fact in bars 23 and 24: the last three pitch classes in each bar are the same (pitch classes <A, Bb, C#>) even though they are taken first from I3(P) <9, t, e> and then from To(P) <3, 4, 5>.15 The first unordered dyad of each row form is also the same: {C, Eb}. The similarities between I3(P) and To(P) are exploited to make bar 24 transition material between those two row forms. Octatonic sounds are also created within the work through the use of dyads: the segmental dyads of P often present intervals common within the octatonic collection. Interval class 3 is especially prominent here due to a previously-examined property: the hexachords of the row map onto themselves under l\. This is shown on Row Diagram 1.15, below. 1 5 This is the same relationship as discussed in connection with Transformational Network 1.1, 2,3,4, and 5 (pages 23 through 26). 57 Row Diagram 1.15: T0(P), interval classes between members of segmental dyads, and cycles of the I t transformation To(P): C Eb E A Bb C# G# B G F# F D Interval class between dyads: As shown in Row Diagram 1.15, {C, Eb} maps onto {Bb, C#} and {G#, B} maps onto {F, D} under Ii (and vice versa). The segmental ic3 dyads are therefore maintained under the inversion in question. Several previously-discussed passages make use of segmental dyads of P, and therefore feature ic3 as a prominent interval. These include bars 131-134 of the third movement (Figure 1.6), bars 135-143 of the third movement (Figure 1.7), bars 1-14 of the first movement (Figure 1.1, Figure 1.17, and Figure 1.18), and bars 19-24 of the second movement (Figure 1.22, although its dyadic accompaniment was not examined in detail in this chapter). Several properties of the tone row P have been examined in this chapter. Weinzweig uses the intervallic and segmental properties of the row to unify the pitch material in this work. In the upcoming chapters, numerous passages will be discussed in further detail to give an overview of the important features of each movement. 58 Chapter 2: The First Movement and its Characteristic Textures In the first movement of the Woodwind Quintet, form is often established through differences in texture and instrumentation in addition to differences in the melodic and pitch-class materials employed. Table 2.1 presents the structure of the first movement from this perspective. The table gives several types of information: the location of each section in the score; a label for each formal division; an overview of the texture, instrumentation, pitch-class distribution, and row forms; and a brief description that elaborates the information provided in the previous columns. The formal division labels A l , A2, BI, B2, and so forth distinguish two broad kinds of music, with upper-case letters indicating (repeating) material and numbers indicating which statement occurs (i.e. "2" means it is the second occurrence of that particular material); this is in correspondence with the information given in the "Specific Instrumental Components, " "Number of pitch classes, " and "Row forms " columns. The legend for the table also identifies the characteristic textures in the movement: TET(x) signifies a texture in which a segmental tetrachord occurs as the melody in instrument x, often with simultaneous tetrachords that are not segmental tetrachords of the row in the other four accompanimental instruments; ISO(xy...) signifies a texture in which the instruments x, y play an isorhythmic accompaniment; ROT(x) signifies a melodic texture involving one or more rotations of a row form; HEX(xy) signifies a texture in which two hexachords that are complements of each other occur interact in instruments x, y; and D(xy) signifies a texture in which instruments x, y play in isorhythm, forming a duet. 59 43 ii > © e 0> o 'E o 45 H s 41 OS O) o 43 o 03 i i c o c o 03 43 O 43 O ni is 3 O I 6 .c 'I x" c <L) E .s . G _o E 43 o o o ^_ G « E 2 fi .S CD S a I OD JJ &ft 03 G 03 SX 6 P o X o •s & o <S C_> l-H s a is -3 <a o -4-> ll 43 x G H | H S O 43 o 03 is 0) <L> 43 T3 <L> '3 p-c <G o G <D s G 03 A . E o o o 03 E3 G 03 0^ T3 <u T3 3 43 G a> I o o * .s T3 o 13 E u o o o 2 T3 OJ -*-> 03 O T3 13 E u ts +^  o •a G <l> E 43, o 43 o 03 G o E j> "a. E o o •G 43 C +-* 03 i2 on ^ (-! 03 03 33 O 43 O 03 x 43 G O 03 1-4 .s "o3 T3 o 43 o 03 X <U 43 X >< D 3 T3 03 00 G -s O CU G 03 X G at 1 <L> 3 T3 43 G o o 03 X> II e o 43 /-^ a .3 o 43 O .22 5? E K K O b Q III « J s -a 1 c 03 •+-» <u G M . & 43 6 .S O 43 O H 03 X OJ 43 G O o &o 03 CQ S3 o o O P3 >< W PQ Pi •G -t3 C on 03 CL> G V « 42 .5 S O 03 o QQ G 43 60 c o s 1 2* OS fe H • b a a I 8 5 S a o u « .2 I £ Q ,1 CN < CN i .2 c a § 1 s 2 s C2 .SH •_ S o j 3 £ £ u ° £ £ gig t\i *-1 j_* o c a x <L> o . cn Crt s i •a 5 ca + n O . X ! on m ^ " c 3 cn e < u c a m i x i c a C B o o o o cn cn cn cn c a c a X> X> S3 -X> _ §1 H H H O CQ >< o < 2 cn C .2 S c a * - » a « •5 o CO <U s §1 o g CO c c a T3 o X ) o <D X5 H . o CU O cn *7t cn 2 T3 X3 <U o S -a s " 5 cn 0> O 3 X> •S ts cn ^ ^ s cn 3 .a in o IS T 3 | > c a o 2 g £ 6 <+H o O X3 o CN CN u s CQ + H MTH — o o „ c S § I! fe i o H D . cn e o o cn t5 cn 2 c a 6 00 c d e g * O X J O D CX CQ O cn 1.1 JS g H O H e - i T3 >H O X I o c a x D X ) o c c a I 3 < r-H c a S >. 2 ^ S O 60 <D g E * g "2 x > < u o -a fe o H CQ X o o CD 61 Table 2.1 shows the two families of material, labeled A and B. Family A includes material in which a melodic tetrachord is heard with isorhythmic accompaniment, presenting a single row form; family B includes material in which a melody drawn from a rotated row form occurs in alternation with two hexachords from a different row form. The interaction between these two families is reminiscent of both sonata and rondo forms: rondo form is suggested in the alternation between A and B families; sonata form is alluded to by the manner of thematic exposition and development. Specifically, material introduced in bars 1-37 is varied and developed in bars 37-83, with fragments of the opening material returning to close off the movement (bars 83-92). In spite of these qualities, the overall form is neither sonata nor rondo, but involves alternation and variation of the A and B material. Bars 1-14 present the first thematic material of the movement (see Figure 1.17). As previously explained, the oboe repeats its tetrachord in various orderings, while the other four instruments play isorhythmic accompaniment chords derived from the complementary octachord; this instance will be labeled A l . This characteristic texture returns in two places: in bars 37-52, in a varied form labeled A2 on Table 2.1; and in bars 88-92, labeled A3 on the table. This type of instrumental interaction is listed as TET(O), ISO(FCHB) on Table 2.1, and the corresponding partition components are shown as 4 and 42. As we have seen in Chapter 1, the accompaniment uses two distinct types of tetrachords: two distinct, alternating simultaneous tetrachords X and Y, involving order positions fO, 1, 3, 4} and (2, 5, 6, 7} respectively; and two distinct instrumental tetrachords V (in the flute and clarinet) and W (in the horn and bassoon), involving order positions (1, 2, 4, 7} and {0, 3, 5, 6} respectively. V and W appear in two 62 different orderings in their respective instrumental parts up through bar 9: V appears as <1, 2, 4, 7> in the flute and (rotated) as <4, 7, 1, 2> in the clarinet; W appears as <0, 5, 3, 6> in the horn and (rotated) as <3, 6, 0, 5> in the bassoon. These can be considered rotationally complementary since the first dyad of the flute is the second dyad of the clarinet, and vice versa, and the same relation obtains between in the horn and bassoon. Bars 1-14 also present an interesting rhythmic development in the oboe solo. Figure 2.1 shows three of the oboe statements (bars 3-4, 5, and 6-7), aligned vertically to show their rhythmic relationships. In the music, these statements are separated by rests, and each are differently aligned against the notated metre, as shown by the bar lines on the figure. Each statement presents the third tetrachord of Tn(P), {G, F#, F, D}, but in varying lengths and with different rhythms. When aligned as in Figure 2 . 1 , each variant of the original motive can be seen as an overlay and variation of the original presentation: the rhythm of the motive is basically the same as in the original occurrence, but is developed first by truncation, and then by anticipating and lengthening certain rhythmic values, and by extension. However, the pitches in the second and third occurrences present essentially the same rhythms (attack points) as those of the first statement in bars 3-4 even though their metric placement may differ; the one exception is the D in bar 6, which anticipates the D's from the first two statements, but is sustained into its "original" position, and is similarly terminated by the entrance of an F4. 63 Figure 2 . 1 : R h y t h m i c var iat ions in the oboe, bars 1-7, first movement i l l - > ^ ^ P5*" d 7 S-1 ^ J l l j ^ w This sort of process is continued in bars 7-11; Figure 2.2 shows the oboe in bars 7-13, rhythmically aligned. The tetrachord {G, F#, F, D} is still used, but its ordering and rhythm is varied even further. Again, for ease of comparison, the three oboe statements in bars 7-13 are vertically aligned on Figure 2.2 to show their rhythmic relationships. Like bars 1-7, the three oboe statements vary the melody and rhythm (bar 7-8, 9-11, and 11-13). The statements of bars 9-11 and 11-13 each present a palindromic melody: the pitches are <G4, F#4, F4, D4, F4, F#4, G4>. Figure 2.2: Rhy thmic var iat ions in the oboe, bars 7-13, f i rst movement 64 This material is varied and developed beginning in bars 37-52. This is shown in Figure 2.3, a duplication of Figure 1.15. In this variant of A l , called A2, the oboe again has the melody and the remaining instruments accompany with simultaneous tetrachords. The developmental variation occurs here in two ways. First, there is shared pitch-class material between the oboe in A l and A2 (the two oboe tetrachords share 3 of 4 pitch classes, specifically {F#, F, D}) as well as between the accompaniment chords in A l and A2: X and X' share {A, Bb, Eb}, and Y and Y' share {G#, C#, E} (previously examined in Chapter 1 in the discussion of T2/Tio-related materials). Second, and more important in the context of the previous formal discussion, the texture within the accompaniment changes in bars 37-52. Here the accompaniment alternates between isorhythmic tetrachords and dyads in two isorhythmic duets. In bars 41, 44, and 46-50, the flute and clarinet isorhythmically play {4, 7} then {6, t}, while the horn and bassoon isorhythmically play {9, e} then {5, 8}; the duets are in rhythmic opposition to the other, unlike A l , in which four instruments were isorhythmic. Instrumental dyads also occur in each duet fragment; the order position dyads {7, 6}, {4, t}, {9, 8}, and {e, 5} are heard in each of the flute, clarinet, horn, and bassoon, swapping between these instruments. As well, these dyads also swap members; in bar 41, for example, the dyads {7, 6} and {4, tj each swap one of their members to become {7, tj and {4, 6} in the flute and clarinet. The same process occurs with the other two dyads: {9, 8} and {e, 5} become {9, 5} and {e, 8} in the horn and bassoon of bar 43. 6 5 Figure 2.3: Bars 37-52, first movement Alternating flute/clarinet and horn/bassoon pairs 66 Figure 2.3, con't. 2 7 4 7 4 4 8 Alternating flute/clarinet and horn/bassoon pairs The rhythmic variation of the melody used in bars 1-14 is not as clear in bars 37-52: the tetrachordal oboe melody repeats, this time with variation in the order of its pitch classes. This, in turn, affects the metric placement: unlike bars 1-14, the same pitch classes do not occur in the same metric positions. There are emphasized intervals within this tetrachord; the melody often leaps from B4 to D4, an interval of 9 semitones, leaps up 3 semitones from D4 to F4, leaps up 4 semitones from D4 to F#4, and moves by semitone from F4 to F#4 (and vice versa). A texture contrasting to bars 1-14 appears in bars 15-37, shown previously in Figure 1.2 and duplicated in Figure 2.4. This texture is labeled BI on Table 2.1. In bars 15-37, the flute plays rotated forms of (R)l5(P), while the bassoon and clarinet each play a complementary hexachord from I?(P). The three instruments alternate with one another, creating a succession of solo phrases. This texture is labeled ROT(F); HEX(BC) on Table 2.1, and its associated partitions identified as 12 and 6 . 23 8 7 6 5 4 3 2 1 0 e 68 Figure 2.4, con't The flute plays three rotated statements of (R)Is(P) in this passage. Each rotated row-form statement begins one order position ahead of the previous rotation of (R)Is(P): 69 the first statement begins with order position {e}, the second with order position {tj, and the third with order position {9}. The first statement occurs in bars 16-18, presenting the twelve pitch classes of (R)Is(P) once: <e, t, 9, ..., 1, 0>. The second statement occurs in bars 22-24, and is rotated by one position: <t, 9, 8, ..., 0, e > , again with each pitch class occurring only once. The third statement, bars 28-30, presents eight different pitch classes, rotating to start from order position 9: <9, 8, 7, ..., 3, 2>; in this statement pitch classes E, G, G#, and C# are repeated (order positions {5, 4, 3, 2f). When development and variation of this material first occur in bars 52-71 (labeled B2 on Table 2.1), it presents fragments of rotated rows and complementary hexachords. This section presents material similar to BI except that the row form used by the flute has changed: in BI the flute presented rotations of (R)Is(P), while in B2 it presents rotations of To(P). Row Diagram 2.1 examines the relationship between these two rows. Row Diagram 2.1 (R)Is(P): Eb C B Bb F# A E To(P): C Eb JE A | Bb C# G# G# m D F# D As Row Diagram 2.1 illustrates, the two row forms share four dyad segments. In fact, when the non-retrogrades of both row forms are examined, the relationship is even more striking: order positions <0, 1> in one row form have the same pitch classes as order positions <t, e> in the other row form (and vice versa); and order positions <2, 3> in one row form have the same pitch classes as order positions <5, 6> in the other row form 70 (and vice versa). These correspond to the cycles of I5. The row forms are closely related because of this property; and in particular, To(P) begins and ends with the same unordered dyads as (R)Is(P). This is similar to the material involved in the T2-relation of (R)I5(P) and I7(P), discussed in Chapter 1. The next development of B material presents several new developmental processes. Bars 71-83 (labeled B3 on Table 2.1) vary the B idea in several ways: all instruments play simultaneously, with the flute, clarinet, and bassoon presenting rotations of (R)To(P) and the oboe and horn presenting complementary hexachords of (R)Io(P). This passage, previously examined as Figure 1.5, is duplicated in Figure 2.5. BI, on the other hand, presented the flute, clarinet, and bassoon in alternation with one another. The flute in bars 15-37 presents rotations of (R)Is(P) while bars 52-71 and bars 71-83 present rotations of (R)To(P). In all three passages, rotated statements of one row form are accompanied by hexachords of a different row form. In B3, however, the 72 rotated row material is presented by the flute, clarinet, and bassoon in canonic imitation, while the complementary hexachords occur isorhythmically in the oboe and horn. Moreover, a different transformational relationship is observed between the rotated row form and the accompanying hexachordally-treated one. And in B3, unlike in BI, the two complementary hexachords do not occur in alternating phrases, but are now played isorhythmically. The canonic treatment of the rotated row forms in bars 71-83 (Figure 2.5) also creates an interesting feature: because of the way in which the composer has aligned the flute, clarinet, and bassoon, simultaneous trichords formed from adjacent order positions result. These can be heard in bar 73, bar 75, bar 78, bar 80. Let us examine the first occurrence in bar 73: the second, third, and fourth eighth durations of the bar each present a simultaneous trichord, involving order positions {3, 4, 5j, {2, 3, 4}, and {1, 2, 3}. Each trichord shares two pitch classes with the previous trichord, creating a sense of overlap. Table 2.2 illustrates the order positions of To(P) in the flute, clarinet, and bassoon (with empty cells indicating rests) in order to show the resulting simultaneous trichords. Table 2.2: Order positions of T0(P) in bar 73, first movement eighth-note position: 1st 2nd 3rd 4th 5th 6th 7th 8th Flute: 4 3 2 1 Clarinet: 5 4 3 2 1 0 e t Bassoon: 5 4 3 2 1 0 e Orderposition {3,4,5} {2,3,4} {1,2,3} trichords: 73 This process is reminiscent of the overlapping tetrachords of the third movement discussed on page 49 of Chapter 1. Bars 71-83 are climactic in textural density, and in other ways that are visible from Figure 2.5: it is the only section in which all instruments play simultaneously; it presents continuous eighth-note motion, and is therefore the most active section of this movement; and it contains the highest pitch of the movement, D6 in bar 77 of the flute. It also occurs approximately three-quarters of the way through the movement; this is not necessarily climactic, but there is a sense that this passage is leading toward the end of the movement. All of these traits combine to emphasize this passage more than any other in this movement. This is therefore the climax of the movement. Weinzweig concludes the first movement by reiterating material from the beginning of the work, repeating the textures, pitch-class distribution, and motives. This decreases the intensity created by the climax and leads to the conclusion of the movement. This concluding process begins in bar 83 and continues until the end of the movement, at bar 92. Bars 83-87, labeled B4, present a fragmented variation of BI and will not be discussed in detail except to illustrate the relationship between the two row forms used: Row Diagram 2.2 (replicating Row Diagram 1.3 of Chapter 1) gives these two row forms, T0(P) and I?(P). 74 Row Diagram 2.2 To(P): C Eb E A Bb C# G# B G F# F D MP): G E Eb Bb A F# B G# C C# D F As shown by the boxes above, there are four dyads that retain the same order positions within both row forms: in fact, each dyad is found in retrograde in the second row form (as noted in Chapter 1, the dyads {Eb, E} and {A, Bb} combine to form the tetrachord {E, Eb, Bb, A} in order positions {1, 2, 3, 4} of both row forms). This is similar to the relation noted earlier between the rotated rows of the flute in BI and B2. Bars 88-92, labeled A3 (given as Figure 2.6), also present a fragmented variation of A l : the accompaniment material is a truncated restatement of A l , constructed by piecing together earlier fragments from the opening. Bars 88 and 89 correspond to bars 1 and 3 (respectively), bar 91 is slightly modified from bar 1 (the last attack is missing and the rhythm is changed for the third attack), and bar 92 is an enharmonically-respelled and rhythmically-modified variant of bar 10. There is no accompaniment in bar 90, which makes the single oboe statement stand out. The oboe in this passage plays material from bars 7-8 (see Figure 2.2) but with the first note elongated. This variation of A l is an effective way to remind the listener of the opening by concluding the movement with the same materials and developmental processes as the opening passage. The movement ends with semitone motion in all four isorhythmic instruments in bar 92, suggesting a final cadence. 75 Figure 2.6: Bars 88-92, first movement | T o ( P ) : Oboe The first movement effectively emphasizes contrasts in texture and instrumentation that appear throughout the movement. The second movement, while still using concepts of texture introduced in the first movement, uses solo melodic material more frequently. The use of certain segmentations of the twelve-tone row is also emphasized, as will be seen in the following chapter. But there has been no unambiguous melodic statement of To(P) within this movement; the listener must wait until the opening of the second movement to hear this. 76 Chapter 3: The Second Movement and Segmentations of the Row The second movement is more texturally uniform than the first; while the first movement had significant changes in instrumentation from one subsection to the next, the subsections of the second movement lead into one another, often retaining a similar texture type but changing the instrumentation. For example, bars 9-15 present a solo horn melody accompanied by a duet in the clarinet and bassoon, which leads into bars 16-18, where a solo flute melody is heard accompanied by two duets: one of oboe and clarinet, and the other of horn and bassoon. Both passages contain a solo melody and an accompanimental duet. The second movement will be analyzed more from the viewpoint of segmentation (what types of segmentation are used in each subsection). Table 3.1 presents an overview of the second movement, similar to that provided in Chapter 2 for the first movement. 77 41 E ii > O E ii JS ii t > © 42 — x S J H c (L> E x T3 4) O _o "3 4) -*-» -a o o C/3 6 33 o o T3 4) 43 O 6 o «S ca o 4> 4> & 00 •3 4) O 4) X ) CS 43 u •3 .a u. O O R •2 b Q s fe « J s -a b , q fe o H fe O -a 2 CN CQ >, T3 O o e J— o 43 4» £ » X j 43 *t s c ^ s § ~ C O m -a ^ 43 •S £ '£ S-OO fe 4-» ^ 13 0 0 4) ^ cn 4) ^ 53 CO T3 CCS <£ c n CO -a X i- J8.S o o S3 00 o SB 4) 4) ,—, "is .3 D .s fe o H CQ O a 4) 4) X S S .§ te E « o o cd ~ J . s .s-S g l O T3 cn O CO Q C3 PH fe O O 78 K O b Q 3 X > CU g ° T3 & , >- cu g X J XS C3 -5 t n CD » H cA « CU CU XJ 2 * 0 f-H ti> cu 2-> oo CJ CU c , v j^fe [ca _£> cu cu ca £ a s o c3 6 .2 X J " H .23 cu x j .S T3 O < x> cu £ B & eg o _ •S .S2 •C ca X J « S "B § « 3 C H a <u 0 3 3 XJ d r=J +J o w 1 1 ^ a . <u e o o cn cn ca X ) CU o X l O o § X J s ca cu x i ea . g cn oo C . o >-. H cu " £ cu ca co 3 oo CT 3 « o a •5 -a CU CU o XJ O JO X J o c S—1 H M-H M H o o C N m -a T S C3 a . o cn S e CB X J cn .£> XJ g S St cu » CU 1 o o .s C H 2 cu -4-» CU t o o .s 00 H cu j u " a S o o C cu cu "a . fe H fe 00 H C N s ca SJ o u o •a I s .a co <N CQ O Q O P- CQ X o PH Q CQ O Q 3 3 K •SJ SC , o K O •B-b I "2 <; a. s -a l £ 3 0 t-1 8 s l CO ca 4= CO £.3 cn f—1 CO 3 on •° "a S o O 43 CS 43 C3 . ° ° .a o i CT) .5 icr • S3 cn CO x> 3 ^ X o CO - r ; 33 CO ca cn 23 o .2 4 3 £ H cx £ o 5S ' o CO a. cn O z o ca 23 cfa I D o 4 3 33 _2 fe a H CO C w C o « . oo E CO W cfl c3 £ « ^ ca c/3 cfcl C i i . I o o .s fe o cu -»-» CO 1 o o .s en 80 Although there are fewer types of textures, the changes between these textures occur more often than in the first movement: seven changes of texture occurred in the first movement (listed in Table 2.1), whereas eleven occur in the second movement (listed in Table 3.1). In addition, there are a greater number of row forms used in the second movement: the first movement uses five transformations of P: To, T2,15,17, and Io. The second movement uses seven: To, T i , T 4 , T 5 , Tg, Io, and I3. Of these seven transformations, four were not heard in the first movement: T i , T 4 , Tg, and I3 (the transformations To, T 5 , and Io are used in both movements). The second movement mostly uses transpositions of P, while the first movement used inversions of P to a relatively greater degree. T 3 and T 4 relationships occur frequently among these row forms, and will be discussed at a later point. Formal divisions are determined by a combination of textures, instrumentation, and row segmentation. There are four prominent textures within this movement: multiple melodies (often interacting contrapuntally); two isorhythmic duets; or solo melody accompanied by an isorhythmic duet; a texture related to the latter involves solo melody accompanied by two isorhythmic duets. These four textures generally correspond to the formal labels A , B, C, and D, respectively, although there are a few exceptions in cases where the pitch materials are obviously related to a different formal section. One such example occurs in bars 41-42. This is labeled D3 on the table even though the texture consists of two solo instruments: the pitch material in this section anticipates the next section, bars 43-49, which does depict the D texture. A l l textures involve some combination of solo and duet passages, but some texture types return in sections corresponding to different labels (D(CB), for example, occurs in C l , D4, and 81 A3). The formal labels refer to the combinations of textures, not the individual texture types themselves. To clarify, examine BI and B2 on Table 3.1: both consist of two isorhythmic duets; however, the instrumentation in BI is D(FC), D(OB), whereas the instrumentation in B2 is D(FH), D(OB). Texture type and segmentation type are not always consistently associated, but segmentation type does help define sections. In fact, change in segmentation is often used to contrast adjoining sections. Segmentations of the aggregate used in this movement are segmental dyads (often used as accompaniment), segmental trichords, and segmental tetrachords. Hexachords are also used, but more sparingly than the other segmentation types. The second movement begins with the quintet's first strictly linear presentation of To(P). In bars 1-4, this row form is segmented into melodic trichords, each presented by a different instrument (clarinet, flute, oboe, and bassoon, respectively), as shown by Figure 3.1 (a duplication of Figure 1.4). These four bars act as an introduction to the movement and a similar texture reappears in bars 24, 25-31, and 50-56, to be discussed shortly. Bars 1-4 present the first occurrence of A material, a texture in which solo melodies occur without accompaniment. Section A l is defined by the solo melody texture, the use of To(P), and the use of trichordal segmentation (as illustrated on Table 3.1). 82 Figure 3.1: Bars 1-4, second movement TQ(P): i - ^ 4 5 6 1 — 3 — p 0 1 2 ^ — 3 — i Figure 3.2 shows how bars 5-8 are characterized by counterpoint between two isorhythmic duets, corresponding to formal type B on Table 3.1. The duets create a 'complementary' rhythm: when one duet is rhythmically active, the other is not (see bars 6, 7, and 8). The resulting pattern of triplet eighths alternating with longer notes (quarter notes, half notes, or dotted half notes) allows for a nearly continuous presentation of triplet eighth-notes in this passage. The first quarter-note beat of bar 7 creates a break in this rhythmic continuity: all four instruments hold their pitches for the first quarter duration, subsequently tied to the next triplet eighth note. Shorter disruptions to the rhythmic continuity occur in bar 6 (beat 2), bar 7 (beats 2, 3 and 4), and bar 8 (beats 2 and 3). The simultaneous tetrachords that occur during these disruptions are forms of SC (0347), as shown below Figure 3.2. In fact, the two different SC (0347) tetrachords that occur are related by T2 and Tio, the common transpositional relationship first discussed in Chapter 1. 83 Figure 3.2: Bars 5-8, second movement nro(PJl {Bb, Db} {Bb, Db} {Bb, Db, D, F} = {Ab, B, C, Eb} = (Bb) = (F)(1) 0347 _ J A b ) = (Eb)(l) 0347 j {Bb, Db, D, F} = (Bb) = (F)(1) 0347 The analysis accompanying Figure 1.13 and Figure 1.14 demonstrated how two different types of trichords could occur in bars 5-8. Figure 3.2 presents the same four bars without these annotations. In this context, we see the consecutive dyads of To(P) presented as simultaneities, contrasting with the trichordal segmentation of the same row form in bars 1-4. In bars 5-8 the order position dyads {0, 1}, {2, 3}, {4, 5}, {6, 7), {8, 9}, {t, e} are heard. Each isorhythmic duet presents these dyads, although the members of the duets play either member of the order position dyad. Note, for example, that the flute plays order positions {1, 2} as its first two notes in bar 5. These occur in bar 6 in the clarinet; the clarinet in turn plays order positions {0, 3} as its first two notes in bar 5, 84 which occur in the flute at the beginning of bar 6. The only exception to the use of the specific order position dyads listed above occurs in the bassoon in bar 7 and is indicated on Figure 3.2 with an asterisk: here the order position dyad {0, 2} occurs in the oboe and the bassoon. This creates the simultaneities <{0, 1}, {2, 0}, {4, 5}> in bar 7 within the oboe and bassoon parts. If the order position {3} was used instead of {0}, a hexachord would be presented by the oboe/bassoon duet in bar 7: <{0, 1}, {2, 3}, {4, 5}>. It is possible that the {0} at this location is an error by the composer; {3} = A is only one ledger line away. The C material occurs in bars 9-15; this passage is shown in Figure 3.3. This material is closely related to the D family: material from the C family involves a solo melody accompanied by one isorhythmic duet, whereas material in the D family involves a solo melody accompanied by two isorhythmic duets. In the Cl statement of bars 9-15, the clarinet and bassoon play an accompanimental isorhythmic duet while the horn, in its first entry of the movement, plays a melody. As in the previous A l and BI sections, To(P) is still the only row form used. The isorhythmic duet might suggest a dyadic interpretation, as in bars 5-8, but in fact the consecutive trichords of To(P) are reappearing from bars 1-4. The first two trichords appear first in the accompaniment as two trichords (order positions {0, 1, 2} in the clarinet and {3, 4, 5} in the bassoon) then the second hexachord is played by the horn in bars 10-12 (order positions {6, 7, 8} and {9, t, e}). In bar 12, the clarinet switches to the trichord {6, 7, 8} while the bassoon continues with (3, 4, 5}, and the horn now substitutes {9, t, e} and {0, 1, 2} for {6, 7, 8} and {9, t, e}. Effectively, the clarinet and horn have exchanged {0, 1, 2} and {6, 7, 8}. Another possibility is that the composer mis-read the clef: C4 occurs in the same position on the bass clef as A5 does on the treble clef. 85 The circulation of trichords in this passage is reminiscent of the opening of Arnold Schoenberg's Fourth String Quartet, given in Figure 3.4. The twelve-tone row used in that work is given below with order positions: 0 1 2 3 4 5 6 7 8 9 t e D C# A Bb F Eb E C Ab G F# B 86 In the Schoenberg quartet the first violin presents a melodic statement of the row while the second violin, viola, and violoncello present isorhythmic accompanimental material. Each attack of the accompaniment presents one of the segmental trichords of the row; in the first bar, for example, the three attacks present {Bb, D#, F}, {Ab, E, C}, and {F#, G, B}, trichords 2, 3, and 4 respectively, while the first trichord occurs in the first violin in bars 1 and 2. This process is repeated in bars 2, 3, and 4-6: the first violin presents the next melodic trichord in the row while the accompaniment instruments present the other three trichords. This is indicated in Figure 3.4 through the use of coloured boxes. Weinzweig's circulation of trichords in the quintet passage is not as strict as Schoenberg's: in bars 9-13 (Figure 3.3) Weinzweig has the first trichord in the clarinet, the second trichord in the bassoon, and the remaining two trichords in the horn melody. The first trichord returns in bars 14-15 of the horn (also in Figure 3.3), but the process of circulation does not continue beyond this point: the next section, bars 16-23, is based upon a different segmentation. 87 = trichord 1 (order numbers {0, 1,2}) = trichord 2 (order numbers {3, 4, 5}) = trichord 3 (order numbers {6, 7, 8}) = trichord 4 (order numbers {9, t, e}) 88 Bars 16-23, shown in Figure 3.5, present the first occurrence of D material (labeled Dl), in which three components now occur simultaneously: a duet between the horn and bassoon, another duet between the oboe and clarinet, and a solo melody in the flute (essentially a flute melody with accompaniment). This section is based upon dyadic segmentation, but sometimes smaller equal segments are combined into multiples, as in bars 16-17, where one finds four dyads and a tetrachord (two consecutive dyads). Two different but related segmentations occur in this passage: bars 16-18 segment the aggregate into four dyads in the duets and two tetrachords in the solo flute, while bars 19-23 segment the aggregate into two dyads in the duets and one octachord in the flute. The accompanimental duets occur mostly as isorhythms, with exceptions in bar 17 (oboe) and bar 23 (clarinet); they present the consecutive dyads of ^ (P), played simultaneously as indicated by order positions and coloured boxes on Figure 3.5. This is similar to the BI material of bars 5-8, as previously discussed in association with Figure 3.2, which also used simultaneous consecutive dyads - in that case dyads of To(P). Both passages use the order position dyads {0, 1J, {2, 3}, {4, 5}, {6, 7}, {8, 9}, {t, ej as simultaneities in their isorhythmic duets. The D family combines aspects of A, B, and C: solo melodic material from A, simultaneous dyads as previously heard in B, and the "solo melody with isorhythmic accompaniment" texture heard previously in C. 89 Figure 3.5: Bars 16-23, second movement 1 7 X (continued from bar 19) (exactly repeated) = order numbers 0, 1 = order numbers 2, 3 order numbers 4, 5 order numbers 6, 7 order numbers 8, 9 order numbers t, e 90 Bars 16-23 also present rhythmic and melodic repetition in the accompaniment; this is illustrated on Figure 3.5 with brackets below the staff and the labels 'x' and y'. These represent the repetition of smaller ('y') and larger ('x') segments in bars 19-21 and 21-23. The literal repetition of the accompaniment and the independent solo flute implies a 'vamped' accompaniment to an improvised solo such as one might see in jazz. In bars 16-23 the flute melody is virtuosic, presenting segments of 13(F). It presents the first segmental tetrachord in bar 16 (order positions {0, 1, 2, 3}), a second tetrachord from order positions {6, 7, 8, 9} in bar 18, and an octachord from order positions (6, 7, 8, 9, t, e, 0, 1} in bars 17-23. The flute and accompaniment combine to present the aggregate: the accompaniment plays order positions {4, 5, 6, 7, 8, 9, t, e} in bars 16-17; order positions {e, t, 0, 1, 2, 3, 4, 5} in bars 18-19; and order positions (2, 3, 4, 5} in bars 20-23. The transitions between sections and individual themes are smoother in the second movement than in the first; one reason for this is the repetition of row forms between sections. This can be seen from Table 3.1: in the Row Forms column all but two sections contain a row used in the previous section (the two exceptions are bars 16-23 and bars 33-40). Transitions between sections in this movement are also smoothed by the use of related thematic material. One example occurs in bar 24: to discuss this passage portions of the previous section (bars 16-23) and the following section (bars 25-31) must also be examined, and so bars 22-27 are given in Figure 3.6. 91 Figure 3.6: Bars 22-27, second movement The same pitch classes occur in two different row forms, in the same register' 4 S 4 5 3 4 The transitional material in bar 24 contrasts with the material in the previous section. In bar 24 only six pitch classes are presented, in the solo flute. To(P) is used in both the first section and the transition; there are also similarities in the melodic material. The flute melody (continued from Figure 3.5), is still using the octachord (6, 7, 8, 9, t, e, 0,1} of I3(P) in bars 22-23. In bar 24, the last gestures of the melody are derived from 92 the first hexachord of To(P), making an echo of the melody in bars 19-20, which also started with <C, Eb> and which shares the same contour. There are other similarities, however, between the row forms used in each passage. I3(P) and To(P) are given in Row Diagram 3.1, with boxes indicating shared dyads and trichords. Row Diagram 3.1 I3(P): To(P): Eb C C Eb B ! F# F D G E G# A Bb Db A Bb Db G# B G !F# F D Two ordered trichords occur as segments in both l3(P) and To(P): <A, Bb, Db> and <F#, F, D>. The first of these trichords is used to forge the transition between bars 23 and 24 (because bar 24 only presents the first six pitch classes of T0(P) the latter trichord is not heard there). The relationship of <A, Bb, Db> between bars 23 and 24 is quite striking: these pitch classes occur in the same register and are also rhythmically similar. The first hexachord of To(P) neatly summarizes aspects of the preceding l3(P) music, making bar 24 sound both cadential (due to the use of repeated material and sparser instrumentation) and liquidative in respect to the previous passage. In respect to the following passage, however, it acts as a transition by introducing the first six pitch 2 1 These four pitch classes are also presented in the second quarter-beat of bar 23, with order positions {8, 9} one octave higher and {t, e} reversed. The repetition of order position {e} one octave lower in the clarinet helps to orient the listener to the new register. The repetition in the flute is indicated on Figure 3.6 in red. 93 classes of To(P) in the flute, thus preparing for their repetition, at T 4 , in the oboe in bar 25. Before discussing the passage that begins at bar 25, a few comments will be made about the overall form of the second movement. The musical material from bars 25-56 contrasts with the previous material in several ways, and therefore bars 1-23 and 25-56 will be analyzed as two larger sections, with bar 24 acting as a transition. In bars 25-56 multiple row forms occur simultaneously, whereas in the first section no row forms were presented simultaneously. Aggregates do not occur in bars 32 or bars 41-42, in contrast with the aggregates presented in every subsection of the first section. The construction of aggregates differs as well; in the first section there was a greater use of dyads, trichords, and tetrachords, while in the second section segmentations such as decachords (seen in bars 43-49) and collections in which pitch classes are repeated (such as bars 33-40, in which five different tetrachords occur in.the accompaniment). Like the first section, however, the second section begins and ends with unaccompanied melodic material labeled as type A on Table 3.1: in bars 25-31 the solo oboe and bassoon interact contrapuntally; in bars 50-56 the flute, oboe, and horn present solo material accompanied by a duet in the clarinet and bassoon. This differs from other occurrences of A material because of the isorhythmic duet, but retains its A character because four different parts (one being the combination of clarinet and bassoon) are still heard. The formal divisions of the second section will now be discussed with these properties in mind. In bars 25-31, shown in their entirety in Figure 3.7, there is a contrapuntal interplay between the oboe and bassoon. Like the transition in bar 24, the material here consists of solo melodies, a texture labeled A2 on Table 3.1. One might consider 94 classifying this material into a different family (the texture differs significantly from A l in bars 1-4); however, the use of solo melodies and the counterpoint created by these has a distinct sonority that is easily heard. The A l material (which plays melodic fragments in alternation instead of simultaneously) is, in my view, a variation of the A material heard later in the movement; it has been labeled A l because it is the first occurrence of this material in this movement. 29 95 In this passage the oboe plays a complete statement of T4(P) while the bassoon plays a complete statement of (R)To(P), and later also plays T4(P). This is the first point in the second movement at which two different row forms occur simultaneously; two different aggregates are presented. These two row forms also share pitch-class material, as shown on Row Diagram 3.2: Row Diagram 3.2 To(P): C Eb A Bb JC# G# I B G F# j F D 1 T4(P): E G G# C# I i D F C Eb B i Bb A | F# To(P) occurs in retrograde in this passage, which means that there are three ordered dyads and one unordered dyad in common: <G#, C#>, <Bb, A>, <D, F>, and {C, Eb}. By placing these two rows in counterpoint the same dyads are heard between the oboe and bassoon, creating an echo effect. A second instance of transition material occurs in bar 32. Specifically, the pitch material is carried over from bars 25-31 and an increase in the number of voices prepares the listener for bars 33-40, where all instruments play. The oboe and bassoon repeat the pitches they had played in the last quarter-beat of bar 31 (forming the third segmental tetrachord of T4(P)), while the flute and horn enter with the second segmental tetrachord of T4(P), {C, Eb, D, F}, in isorhythm. The flute and horn play this tetrachord as two ascending ic3 dyads, the flute as <C, Eb, D, F> and the horn as <D, F, C, Eb>. Figure 3.8 shows bars 30-33. Interestingly, this dyadic alternation is reminiscent of bars 1-14 96 (especially bar 1) of the first movement, previously examined in Figure 1.1 , Figure 1.17, and Figure 1.18, in which the accompanimental instruments similarly swap their melodic dyads. Figure 3.8: Bars 30-33, second movement 30 pitches continue from bar 31 to bar 32 97 This transition also presents a brief moment of liquidation: order positions {8, 9} and (t, e} of T4 (P) are repeated in the last quarter beat of the bassoon and oboe, respectively, in bar 31. The interval classes formed by each of these, ic3 by the oboe and icl by the bassoon, occur prominently within the row forms of P (previously discussed in Chapter 1). The repetition in both the flute/horn duet and the oboe/bassoon duet emphasizes this bar and presents a cadence (through repetition), as was the case in bar 24, the previous transition. This would be the recapitulation in a sonata form; in the Woodwind Quintet bars 33-56 conclude the work by a return to D and A material, soon to be discussed, which could also be interpreted as a recapitulation. The movement continues with a break in bar 33 in the flute, oboe, horn, and bassoon, while the clarinet begins a solo melody leading into a completely new texture. In bars 33-40, shown in Figure 3.9, there is a return to the D material. In this variant, labeled D2, the flute and oboe create an accompanimental isorhythmic duet, as do the horn and bassoon. Here it is the clarinet that plays a virtuosic melody, with large leaps, extremes of range, and a rapid tempo (much like the DI flute melody in bars 16-23). These features can be seen in bar 34. The leap of 11 semitones between Gb5 and F6 is large with the upper pitch, the F6, in the clarinet's altissimo register, a pitch difficult to leap to and hard to tune on the Bb clarinet. A higher pitch occurs in bars 37-38: F#6, another pitch approached by a difficult leap of 11 semitones and hard to tune. These elements of texture are similar to those of bars 16-23 with the exception of the instrumentation: in bars 33-40 the clarinet plays the virtuosic melody instead of the flute. Bars 33-40 are based on a single row form, (R)IQ(P); the clarinet melodically presents a 98 complete aggregate of this row form, while the accompaniment instruments present simultaneous tetrachords. Figure 3.9: Bars 33-40, second movement Leap of icl 1 to F6 F#6, highest pitch in the 0 5 4 2 3 0 1 0 3 0 3 6 5 4 3 3 f#H q I,,,. 1J " I ••••[•'••na -V 1 1 I — • • •«? • —• L J7 '/ ' ' * 9 1 0 e 3 - 4 * " ~ i — 3 — i r - : -j: ^ 1 > » = 3 1 Uv 1 3 99 Due to these similarities between bars 16-23 and 33-40, it is worthwhile to compare their row forms. Row Diagram 3.3 gives (R)Io(P) and MP). Row Diagram 3.3 (R)Io(P): Bb G Gb F Db E B D Eb I3(P): Eb C B F# F D G E Ab A G# A Bb Db There are two ordered dyads in common between these two row forms: <Gb, F> and <Ab, A>. These row forms do not share as many common segments as other rows compared so far, but their common dyads do belong to the same interval class, icl. The two large leaps discussed in the previous paragraph involve the <Gb, F> dyad (the leap in bar 34 leaps between the two pitch classes of this dyad, whereas the leap in bars 36-37 leaps to the F#, then falls by semitone to F). The second dyad, <Ab, A>, is not emphasized within this passage. In bars 16-23, however, the <G#, A> is emphasized through the octatonic relation discussed in Chapter 1 (the G# always relates by semitone to A and is not a member of the octatonic collection being used), while the <F#, F> dyad occurs repeatedly in the oboe as accompaniment. Overall, however, the relationship between (R)Io(P) and I3(P) is weak. Bars 41-42 begin a process of build-up that continues to the end of the movement. This passage can be seen in Figure 3.10, which gives bars 40-44. The clarinet and bassoon begin the build-up in bars 41-42 by presenting motives that each begin with Ab, 100 the last pitch class of the previous section; they also each present the first segmental trichord of a row, Tg(P) in the clarinet and Io(P) in the bassoon. In(P) is the row form used in bars 33-40, while Tg(P) occurs in the clarinet and bassoon from bars 43-56 (the end of the movement). Because of the solo melody texture in this passage, one might consider this a member of the A family; however, since this passage introduces material that is continued through bars 43-49 to the end of the movement (namely, the clarinet motive), this acts as an introduction to the D material of the next section. As such, it is labeled D3 on Table 3.1. The clarinet is joined by the bassoon in isorhythm from bar 43; they each present a segmental trichord of Tg(P) (bars 43-49 are presented in Figure 3.11). In a sense this is reminiscent of the opening bars of the second movement, but there are significant differences between the two passages: in bars 43-56 only two segmental trichords are presented, while in bars 1-4 all four segmental trichords were heard; in bars 43-56 the 102 two segmental trichords of Tg(P) occur simultaneously, whereas in bars 1-4 the segmental trichords of To(P) each occurred as a melodic solo; in bars 43-56 the clarinet and bassoon repeat the first pitch class of their motives, while in bars 1-4 the trichordal solos did not repeat any pitch classes. These differences are significant enough that the listener would not hear the relationship between bars 1-4 and bars 43-56; other passages, to be discussed shortly, have stronger similarities to bars 43-56. 103 isorhythmic Although bars 43-49 are labeled D4 because of their texture (solo melody accompanied by two isorhythmic duets), there are several similarities between the bars 43-49 and bars 9-15, seen previously in Figure 3.3. Bars 9-15 present a horn melody with clarinet and bassoon accompaniment, while bars 43-49 present a similar texture with 104 the addition of the flute and oboe. As previously discussed, the clarinet and bassoon in bars 43-49 present a repetitive and isorhythmic accompaniment consisting of the first and second trichords of Tg(P) (order positions {0, 1, 2} in the clarinet and {3, 4, 5} in the bassoon). This is similar to the first statement in bars 9-16 where the clarinet and bassoon present the first two trichords of To(P). The pitch-class relationship between these two passages is not very strong, however: the first hexachords of To(P) and Tg(P), share only two of their six pitch classes, {C, A}. The horn presents melodic material in bars 43-49, a similar texture to bars 9-15, while the addition of flute and oboe is unique to bars 43-49. The flute and oboe present accompanimental material that alternates between isorhythmic dyads and short independent melodies: isorhythmic dyads occur in bars 44, 45, and 48, while independent melodic material occurs in bars 46, 47, and 49. The flute and oboe isorhythms interact with the horn materials in places such as the second eighth duration of bar 44, the second eighth duration of 45, and the second and fourth quarter durations of bar 48 where they together present trichords of Ti(P). The melodic materials of the horn are also derived from T)(P), although bar 47 presents a possible error in the score (see footnote 19): in bar 47 the horn trichord is not an ordered trichord from Ti(P), as expected, but rather Te(P), a row form that has not yet occurred in this movement. The pitch classes found at this point would occur if one were to forget to transpose the third trichord of Ti(P) for the French horn. The pitches involved are marked with asterisks in bar 47 on Figure 3.11. The build-up discussed in conjunction with bars 41-42 increases here: all instruments are playing, presenting two different row forms, Tg(P) and Ti(P). 105 Bars 50-56 in Figure 3.12 begin to disintegrate the process begun in bar 41. The clarinet and bassoon continue their pitch materials throughout bars 50-56 and are the two instruments that conclude the movement. The flute, oboe, and horn materials differ from their counterparts in bars 43-49. Specifically, the flute and oboe play three short bursts of material derived from Ts(P): the flute in bars 51, and the oboe in bars 50 and 52. The horn plays the pitch classes B, Bb, and Eb, which do not form a segmental trichord of any row form derived from P. All three of these instruments finish before the final two bars and play much more sporadically than in the previous subsection, bars 43-49 (Figure 3.11). Bars 41-56 are a continuous section, unified by the repeated clarinet and bassoon material, the repeated notes in the horn heard in bars 45 and 54, and a growth and dispersion of density over the course of the passage. The texture is thinned to finish the movement; this thinning acts as both a final cadence and a transition to the next movement (the third movement begins with solo clarinet). 106 FI. O b . Cl. Hn Bsn The use of smooth transitions and of cohesive thematic materials, achieved through gradual changes in row forms and textures, figures prominently in the second movement. This allows the listener to hear the movement as much more unified than the previous movement, which employed more abrupt changes of texture and pitch material. It is interesting that the second movement should be much more aurally unified since it is 107 a link between the outer two movements. Will the third movement be as unified in form and texture? Let us now examine this movement. 108 Chapter 4: The Third Movement and its Rhythmic Motives We have examined thus far the use of contrasting textures in the first movement of the Woodwind Quintet and the use of contrasting segmentation within subsections of the second movement. The repetition of rhythmic motives is a significant attribute of the third movement of the Woodwind Quintet, and as such the analysis of these rhythmic motives and their context will be the focus for the discussion of this movement. A table provided at the end of the discussion of this movement lists the sectional divisions with their instrumental components, row forms, segmentations, and a brief description of their content, including the source of rhythmic motives. The recurring rhythms in this movement are often built from repeated cells or variants of previously-heard rhythms; this is true of the first and second movements as well, but is especially emphasized in the third movement. The present discussion will examine several families of rhythms, providing a general description of each family, its usual context, and how its variants are related (providing only a superficial overview of the relations between rhythmic motives in this movement). After this, selected passages from the movement will be discussed in detail, with excerpts provided from the score, to show how the motives are varied through instrumentation, rhythmic variation, and pitch content (this latter section will provide the analysis of the movement). The first two passages in the movement present distinct but related rhythms. The first passage, heard in bars 1-8, presents a clarinet solo characterized by the rhythm ^ ^ * ^ (henceforth labeled "RC1") as a repeated cell. The passage includes an alternation between 2/4 and 3/8; in the latter the rhythmic cell is truncated to J J to fit 109 into the last eighth-note beat of the 3/8 bar (the 2/4 and 3/8 bars both begin with a pair of slurred sixteenth notes, a rest, then a staccato sixteenth note). This pattern is repeated, and then followed by a cadential rhythmic variant. The rhythms for the entire phrase (bars 1-8) are as follows: Rhythmic Motive 1 J J 9 J . H V J J ? J n J J ? J n IJ J J J J J J J J ^ We shall henceforth refer to the rhythm identified by the brace on bars 1 -2 as "Rhythmic Motive 1" (RM1). Bars 1-8 are essentially an ostinato on RM1. The second passage occurs in bars 9-24, and presents a compound rhythm built from two characteristic rhythmic cells: 7 / 3 and 7 J> (henceforth referred to as "RC2" and "RC3," respectively), played as an isorhythmic duet by two instruments in combination with a beat-marking counterrhythm in a third instrument (usually bassoon but occasionally horn). This ensemble usually occurs as the accompaniment to yet another melodic part. The two-part rhythm described above occurs in bars 10-11 as follows, and is henceforth labeled "Rhythmic Motive 2" (RM2):22 Various means for describing melodic motivic relationships are used in this chapter; they are similar to those found in Lora L. Gingerich, "A Technique for Melodic Motivic Analysis in the Music of Charles Ives," Music Theory Spectrum 8 (1986): 75-93. 110 Rhythmic Motive 2 9 n i J > 7 7 * Another rhythm, also heard in bars 9-24 and henceforth identified as "Rhythmic Motive 3" (RM3), is built from the same two rhythmic cells but occurs in solo melodies. This rhythm is played first by the flute (in bar 12), then imitated - with different pitches -three quarter notes later by the oboe. In this particular passage, the melodies are played over RM2 as accompaniment, which continues unabated in bars 9-17. The following example is taken from the flute, bars 12-13: Rhythmic Motive 3 Although the four eighth notes could be interpreted as a variant of the four sixteenth-note motive in bar 7, the underlying eighth-note pulse will not be treated here as derived from previous material (nor will it be treated as a separate motive). A similar rhythm will be examined shortly as RC4. The other important rhythmic motives of this movement can all be derived from RM1, RM2, and RM3 either as variations, as combinations, or as composite rhythms. 9 f~l J J J 3 J 3 / v ; v ; RC2 RC3 eighth-note pulse I l l The process by which this occurs will now be examined for the major rhythmic motives of the movement. The component cells of RM1, RM2, and RM3 create several composite rhythms that occur in the third movement of the Woodwind Quintet. The first is given in the diagram below; the new rhythmic cell will henceforth be labeled "RC4": RCl combined with RC2 produces j^£2- f f ] attacks on every sixteenth note. This results in RC4. (RC4 is also reminiscent of the RC4: J^^^^^T^^ four eighth-note motive derived in RM3) This composite rhythm occurs in two rhythmic motives in the Woodwind Quintefs third movement. The first of these is heard in bars 25-30, in which repeated sixteenth notes generate an isorhythmic accompaniment. An example of this rhythmic motive, henceforth labeled "Rhythmic Motive 4" (RM4) is given below (this particular example shows the rhythm of the accompaniment in bars 26-27): Rhythmic Motive 4 4 J J J 0 RC4 (modified) J V_ n J J J J RC4 RC4 (modified) J V_ RC4 112 The first quarter beat presents a modified version of RC4 in which only half of the sixteenth notes are presented (with a rest substituting for the two missing notes); this cell is also similar to RC3 because both employ a rest on the downbeat. The second quarter beat presents RC4 without modification. The combination of these two forms of RC4 is repeated to form RM4. Bars 51-54 present another rhythmic motive based on RC4. A melody and countermelody occur in this passage with isorhythmic accompaniment (the melody returns in several locations in this movement and will be discussed in detail later in this chapter). The rhythmic motive begins in the melody, and is soon reinforced by a shorter version of the same rhythm, beginning five eighth-durations later, in the countermelody. It occurs as follows in bars 51-54 (and will henceforth be labeled "Rhythmic Motive 5" or RM5): Rhythmic Motive 5 RC6 RC5 RC5 r \ r m J 2 4 ^ r n m j. } J } y J } i Brackets are included on RM5 to show how the upper part of this rhythmic motive has been derived. The same rhythmic cell (labeled "RC5") occurs twice and is indicated by the first two brackets. This is derived from bars 7-8, seen in RM1: in bars 7-8 four sixteenth notes are tied to a quarter note, which is in turn tied to the first of a set of four sixteenth notes. In the first bracketed statement above, the rhythm has been 113 modified by merging the quarter note and final four sixteenth notes of the original motive into a single duration; the second bracketed statement is similar, but its longer duration is a dotted-quarter note. The third bracket surrounds a statement in which a series of attacks occurs at every dotted-quarter interval, henceforth labeled "RC6." This rhythmic motive is often heard with a specific ordering of pitches, to be discussed later in this chapter. Another composite rhythm is created through the two parts of RM2. This is illustrated in the diagram below: The first rhythm combined with the second rhythm produces the pattern of attacks given in the third rhythm. The rhythmic cell J J ^ is repeated three times in the example given above. This cell, henceforth labeled "RC7," is used to form another rhythmic motive in the Woodwind Quintet •& third movement. One example of this occurs in bars 131-134, where two isorhythmic duets present similar rhythms in counterpoint. The rhythms of these two duets are presented below, a motive that will be labeled "Rhythmic Motive 6" (RM6): 114 Rhythmic Motive 6 m m 2 4 j r n * m J HI j~n J This motive could also be derived from RM5, as shown below: r m J J J. u h mt—\ m m JT] / T 3 J JTJ J JT] J r m (Rhythmic Motive 5), upper line (Rhythmic Motive 6), upper line In this interpretation the two groups of four sixteenth notes seen in RM5 are truncated to two groups of two sixteenth notes in RM6, indicated by the first and third brackets on each rhythmic motive. Along the same line, the durations of the two quarter notes tied together are halved to produce two tied eighth notes, indicated by the second bracket on each rhythmic motive; the material shown by the fourth bracket on each rhythmic motive is similar, with a dotted quarter shortened to a quarter duration. This motive is also used earlier in the work; in bars 36-41 two of the three instruments present a repeating pattern of J J J-—J . As can be seen in RM6, a similar process occurs in bars 131-134, the only difference being that the eighth note of this cell in bars 131-134 is tied to varying durations. In the upper line of RM6, RC4 is tied to an eighth note in bar 131, to a quarter note in bar 133, and to a quarter-note-plus-sixteenth in 115 bar 134; in the lower line RC4 is tied to an eighth note in bar 133 and a sixteenth note in bar 134. In bars 131-134 RM6 is used in isorhythm to create a transition; bars 36-41 (given in Figure 4.1), on the other hand, use this motive to create counterpoint. Figure 4.1: Bars 36-41, third movement In this passage, all three instruments play melodies derived from Tjo(P). In bars 37-40 the flute presents a melody based on RM6; this is echoed by the clarinet beginning on the last eighth note of bar 37. From bars 40-41 the flute and clarinet play interval classes 3 and 4 in rhythmic unison. The oboe's material in bars 36-41 is loosely based on the melodic motive to be associated with RM5 in a later passage (to be discussed); RC5, associated with RM5, is seen in bars 39-40. For these reasons this passage anticipates the main statement of RM5 in bars 42-59. This will be discussed in more detail later in this chapter. Another motive is inspired by the use of changing metre. The clarinet in bars 1-8 presented an alternation between 2/4 and 3/8 metre. This alternation recurs elsewhere in the movement, and generates another rhythmic motive based on the triple metre. Bars 116 60-62 present an alternation between 2/4 and 3/8 metre: the 3/8 bar presents solo oboe material in which three eighth notes (four, including the eighth at the end of bar 61) are heard without accompaniment. This can be seen in Figure 4.2. Bar 63 (not shown) returns to a 2/4 metre; the interjection of a single 3/8 bar continues intermittently to the end of this section (bar 95). An overview of the subdivisions within this section is given on Table 4.1 at the end of this chapter. Figure 4.2: Bars 60-62, third movement Triple groupings are used within notated 2/4 passages as well. Instead of changing the time signature, however, the composer writes triplet quarter notes or a rhythm with a similar attack pattern, as seen in bars 106-116 (given in Figure 4.3). This has a different rhythm than the 3/8 metre; it is reminiscent of the 3/8 metre because of the triplet groupings, but the effect is different since the 2/4 metre (without triplets) continues in the accompaniment. 117 Figure 4.3: Bars 106-116, third movement I7(P): Another significant rhythm occurs in bars 117-130, given in Figure 4.4. This rhythm occurs as a combination of two cells: one consisting of a single eighth note, the other consisting of varying durations of rests. The material heard in this passage is characterized more by its texture than the other motives presented in this movement: 118 instead of employing a repeating rhythmic pattern, this motive uses simultaneous eighth-notes in between two or more instruments that act as an accompaniment. These eighth notes are separated by varying numbers of rests, and their articulation is usually accented. In bars 117-130 of Figure 4.4, 8 out of 11 cases present a half-note interval between attack points: the exceptions occur in bars 117-118, with an interval of a dotted-half note between attack points, bar 124, with an interval of a quarter note between attack points, and bars 125-127, with intervals of five eighth notes and then three eighth notes between attack points. The overall effect is one of shifting metres (mostly involving 3/4 and 2/4), which are generally syncopated against the notated metre. This energizes the dialogue between the accompaniment and the solo flute. One could also interpret the accompaniment in this passage as being repeated, marked with brackets underneath the staff on Figure 4.4. This repeated motive is varied by compression, truncation, and syncopation. This is stylistically similar to bars 16-23 of the second movement; both passages present a repeated accompaniment with solo flute in an improvisational style. Bars 117-130 of the third movement, however, present variation in the accompaniment, whereas bars 16-23 of the second movement simply restated the accompaniment material. 119 Figure 4.4: Bars 117-130, third movement Clarinet X X (continued from bar 1231 I (variant - second chord syncopatei I [(variant -first two attacks the same, but ends | | differently) This analysis will continue by discussing selected examples of these rhythmic motives and how they are developed within the movement. Bars 1-8 are significant in rhythmic and serial derivation of other passages; they are given in Figure 4.5. In this 120 passage, the clarinet begins the movement with a solo in which the first trichord of Tio(P) is repeated. As previously discussed, this material is the basis for RM1. Bars 9-24 introduce RM2 and RM3, and continue the trichordal segmentation of Tio(P). Bars 9-24 in particular are interesting for their segmental properties: the instruments involved in presenting RM2 play trichords 2 and 3 of Tio(P) as simultaneous trichords in alternation, while the instruments presenting RM3 play trichords 1 and 4 melodically. This is shown on Figure 4.6 through the use of coloured boxes: purple represents trichord 1, blue trichord 2, green trichord 3, and red trichord 4. Figure 4.5: Bars 1-8, third movement J - 116 121 TZ1 MU L 3 116 6 IT; | 3 « 6 l|3 The rhythmic motives presented in this passage are developed in two sections. In bars 9-18 of the flute and oboe the rhythm is that given as RM3; the two instruments alternate RM3 "out of phase" (the flute starts during beat 1, the oboe starts during beat 122 2), so that they overlap. In bars 19-24 the rhythm is varied. Specifically, the 9 I 3 cell is retained, but is tied to a longer duration (in the flute this is tied to a quarter note in bars 18, 19, and 21, an eighth note in bar 22, a dotted-eighth note in bar 23, and another quarter note in bar 24; in the oboe this is tied to an eighth note or its equivalent in bars 18-19, and breaks with this pattern in the remainder of the passage) instead of to the first of a group of six eighth notes. The development of RM2 has a similar fragmentation: the motive occurs in bars 9-18 as given for RM2, but in bars 19-24 varying durations of rests are inserted between the constituent cells of this motive. Bars 42-59 develop RM5 and the melody associated with it; this passage is anticipated by material in bars 36-41, discussed previously with Figure 4.1. The melodic motive soon to be associated with RM5 first occurs in the oboe in this section: <F#, A, F, E, Eb> = T,0(P) <6, 7, 8, 9, t>. This serial motive is adopted by the horn at the first literal statements of RM5, bars 42-45 and 46-50 (which can be seen in Figure 4.7). The horn is accompanied by a countermelody in the bassoon beginning with the same rhythm but on the second eighth beat in the bar instead of the first (similar to the flute/oboe displacement in the preceding example). The horn pitch-class sequence is similar to the oboe's statement of bars 36-41 except the pitch class {G} has been substituted for the oboe's original {A}. This substitution changes the pitch class and intervallic content, but the contour of the two motives remains the same. In this passage a variety of row forms and fragments emerge: a modified Tio(P) fragment occurs in the horn, as just examined; the first hexachord of TpCP) occurs in the bassoon; and accompanimental material occurs in the flute and oboe 2 3 As in previous row-form discrepancies, this may be an error on the part of the composer. It is, however, repeated four times (in bars 42, 43,46, and 47) in the same form, which implies that the G is an intentional substitution by Weinzweig. 123 derived from the first hexachord of Tn(P). This material states three row forms, each a semitone transposition from one of the others. Figure 4.7: Bars 42-50, t h i r d movement Clarinet The next statements of RM5 occur in bars 51-54 and 55-59, seen in Figure 4.8. Here the flute plays the oboe's former melody, now derived from To(P), and the clarinet has the bassoon's former countermelody, now derived from Tn(P). Aside from the changes in transposition level, this passage is similar to bars 42-50: the rhythm is the same in both passages as well as the interaction of parts (a melody stating RM5, a countermelody in the same rhythm, and an accompanimental isorhythmic duet). In fact, the horn and bassoon in bars 57-59 are retrogrades of the flute and oboe, respectively, in bars 44-46. Bars 51-59 present RM5 in its original form, with an ic3 as its first interval (the horn statement in bars 42-50 has an ic2 as its second interval). Without the difference caused by this one particular interval, the melody and countermelody in bars 124 51-59 would be T2 transformations of bars 42-50, presenting fragments from To(P) and Tn(P) in bars 51-59 instead of Ti0(P) and T9(P). Figure 4.8: Bars 51-59, third movement [Town 51 6 7 1 9 1 6 7 8, 9 t e t 6 7 8 9 t 8('p| , l ?|'p rT>—ft 6 7 8 9 t 3 . e 3 e |TllC a, 0 1 2 3 4^ |Tn(P»: -jr-y—i-RM2 reappears in bars 63-66 (flute and clarinet duet with horn), 68-70 and 74-76 (clarinet and horn duet with bassoon), and so on, up through bar 85, with varied instrumentation throughout the passage. As in bars 9-24, the rhythm occurs in two parts: two instruments isorhythmically play the rhythm based on RC2 and RC3 and 7 J 1 ) of RM2 while either the bassoon or horn plays the complementary part ( J 1 7 7 , and so forth, with the eighth notes on the beat). Between bars 68-85, short sections based on RM2 alternate with short sections in which the bassoon plays a solo melody based on other material. Figure 4.9 shows a representative excerpt, bars 68-80. 125 74 I I 8 ( P ) : 1 f 0 9 ' 2 0 1 1 1 \ | I 8 ( P 0 1 e 0 0 0 | T < P ) : | 2 2 |I8(P ) : | o i o 2 —a—1* 1 0 2 1 0 S>j» —m— 2 3 , 4 5 6 • M 1 6 7 8 This material culminates in bars 81-85, where the two instrumentations listed above alternate with one another. The intensification caused by the accelerated alternation (the statements of RM2 are shorter in duration) creates a climax. This passage is given in Figure 4.10. The remaining bars of the larger section (bars 68-95, given on Table 4.1 later in this chapter) vary this material and dissipate the tension created by the climax. 126 Figure 4.10: Bars 81-85, third movement Flute Oboe Clarinet Horn Bassoon The rhythmic properties of bars 117-130 have already been discussed in conjunction with Figure 4.4; however, the serial properties also merit discussion. Bars 117-130 present Is(P) as a flute melody with accompaniment chords derived from T6(P). These row forms are given in Row Diagram 4.1. Row Diagram 4.1 I8(P): G# F E B Bb G C A C# D Eb F# T6(P): F# A Bb Eb E G D F C# C B G# The shortest common segment between these two row forms is the 10-pitch-class segment from {l...t}; both rows start and end with {F#} or {G#}. This is the first passage examined in this thesis involving two rows, used simultaneously, that do not have any segmental dyads, trichords, tetrachords, or hexachords in common; the only similarity between these two row forms is that {G} and {C#} occur as order positions 127 {6} and {9}, respectively, in both row forms (which is not that unusual since a similar effect will happen between any row forms related by an even inversion). This passage occurs near the centre of the work in two ways: bars 100-101 are the centre of the movement (which has 201 bars in total), and according to this division this section would occur near the beginning of the second half. However, another division according to the metric and serial content occurs in bar 135: metric instability occurs in bars 135-149. Perhaps the dissimilarity of row forms in bars 117-130, in a sense an "instability" of row-form relations, anticipates this metric instability. Admittedly, there is little other evidence to substantiate this, especially since the serial processes within the passage are quite consistent: the flute presents a melody from Ig(P) while the remaining four instruments play segmental isorhythmic tetrachords of T/6(P). Bars 154-174, given in Figure 4.11, present an alternation between two groups of repeating materials, leading towards the end of the movement. The first group consists of oboe and clarinet, which play short mostly-isorhythmic duets (the first bars of each of these passages presents solo clarinet), each instrument presenting a trichord of Ts(P) in repetition. They use a rhythm which could be derived in two ways: firstly, from RC6 (J J J ), characteristic of RM6; secondly, as a modification of the clarinet's opening motive (in fact, the same order positions, {0, 1,2}, occur in the clarinet in both passages). The following diagram illustrates this derivation: 128 ' ^ 0 1 2 1 2 1 0 1 2 1 2 iUAO JJ'jl'UJ. JJJ , * N 154 0 1 2 1 2 I „ r ttr r r TT= (motive is transposed and rest removed) Clarinet plays both passages (bars 1-2 and 154-156) 0 1 2 0 1 2 cJr r 1» cir r The short oboe/clarinet duets occur in bars 154-156, 160-164, 167-169, and 170-172. The second component in the texture consists of flute, bassoon, and horn, which play a three-bar passage that also uses R C 6 (among others); this material is heard in bars 157-159, 164-166, and 172-174, with one instrument added each time. The flute, bassoon, and horn material acts like cadential material due to its repetition and the unison F# on the last eighth-beat of each segment. 129 Figure 4.11: Bars 154-174, third movement 0 1 0 2 1 0 3 1 0 T5(P):j 4 mi? 1 0 3 1 0 3 4 5 3 4 1 — i l l 7 "FT 5 3 4 5 0 1 2 J? .. r¥T -J b J ^ 7 0 1 2 0 1 rirT- rr ?«* 1 * 2 r .. > 0 1 2 1 2 rftrrfr-0 1 2 > rfrr r™"1 1 7 r 1 1 i f a g S B ' 7 J i l l | T n ( P ) : | 6 7 8 6 7 9 t e 1 3 —1 6 7 t e 8 0 1 0 2 1 0 3 1 0 Bars 175-181 continue the flute, bassoon, and horn material, with variations in length (cadencing on a unison F# in each statement, as in bars 154-174), but the oboe and clarinet now present new material. The clarinet plays material based on the flute variant 130 of RM3 in bars 12-16 (in counterpoint with the oboe) with only slight modifications in bars 175-179 (again in counterpoint with the oboe). Figure 4.12 shows bars 175-181 for comparison with the flute in Figure 4.6. The oboe states a melody that derives from two different sources: in bar 175 it is derived from bar 13 (similar to the flute, whose material is from bars 12-16), whereas in bars 176 and the second statement in bars 178-179 the serial derivation is like earlier statements of RM5. The main difference between RM5 and this statement is the rhythmic compression: the half-note durations of previous statements become eighth-note durations here. The oboe's material in bars 178-179 states the same pitch classes as the flute statement in bars 51-52, although in a different rhythm. This statement is introduced in bar 176 by the same motive beginning two semitones higher. Figure 4.12: Bars 175-181, third movement 131 Figure 4.13 presents bars 182-191. RM1 returns in bars 182-189; like its first statement, it is heard in the clarinet. The clarinet plays segments of To(P) in bars 182-189 (bars 182-191 present all but the final pitch class of To(P); {e} occurs in the bassoon in bar 191), while in bars 1-8 it played the first trichord of Tio(P). This is an appropriate change of row form since the movement (and thus the entire work) is nearing its conclusion: To(P) appeared at the beginning of the entire work, and having it appear at the end would help to round out the three movements. In bars 182-189 the clarinet is accompanied by isorhythmic oboe, horn, and bassoon gestures repeating the RC5 rhythm in two different metric alignments: 3 ' J J I -1. Bars 190-191 continue the clarinet solo with material whose rhythm and serial derivation correspond to earlier statements of RM5; it once more states the same pitch classes as the flute in bars 51-52 (and consequently bars 178-179 as well). These short statements beginning on G# (or Ab) present the second segmental hexachord of To(P), the prime form row, and like the material of bars 182-189 help to bring the work back to its initial pitch collection. Lastly, the way in which the trichords are used in bars 182-187 is tidy: the first trichord of To(P) occurs in the melody, with trichord 2 in the horn, trichord 3 in the oboe, and trichord 4 in the bassoon (the last three instruments in isorhythm). Bars 188-191 do not, however, continue the use of trichords: the clarinet plays hexachords while the accompaniment presents simultaneous trichords in bars 188-189 and a melodic trichord (played by the horn) in bar 189. 132 Figure 4.13: Bars 182-191, third movement 182 Bars 192-200 (given in Figure 4.14) present material derived from RM2. Here the accompaniment plays a variation of RM2 alternating between 2/4 and 3/8 metre: the rhythm is modified from RM2 in the 3/8 bars, which present § ? J J J 7 instead of I ? F 3 r $ . The former is derived from the latter as follows: 133 (1) i* r~} •/ ;> (2) | ^ / J v (the final eighth note is removed and the metre changed) (3) i ? J J J i (the eighth note is subdivided) Like the statement of bars 9-24, this is a two-part rhythm, with the bassoon in alternating rhythm. The horn in this passage is mostly isorhythmic with the flute, oboe, and clarinet, but also presents independent material during their rests, functioning as accompaniment and melody simultaneously. This is the only time in the movement that all instruments present material derived from RM2, and the resulting energy leads into the conclusion in bar 201. 134 Figure 4.14: Bars 192-200, third movement Clarinet 196 7-f f f f f r r r T f 7 „ 5 f f f f f r r r - T r c-r ., T r r 68 The final bar of the work, given in Figure 4.15, presents a few surprises: the 5/8 metre rarely appears in this movement (although it is not necessarily heard as such because of the rests on the first two eighth notes - the only other instance of 5/8 occurs in bar 143), and the row form used for the accompaniment is at first difficult to determine. 135 Bar 201 has been composed in a similar style to bars 1-14 of the first movement (previously discussed with Figure 1.1 and Figure 1.17): a melody is played by one instrument, against tetrachords (composed of melodic and simultaneous dyads) playing an isorhythmic accompaniment in the remaining instruments. In bar 201, the clarinet plays the melody (derived from the first hexachord of T2(P)) in consecutive sixteenth notes. The remaining four instruments make up the accompaniment: the flute and oboe play the first hexachord of Ti(P) as three simultaneous dyads, in consecutive eighths; the horn and bassoon play the second hexachord of Ti(P) in a similar way, as simultaneous dyads on three consecutive eighth notes. Weinzweig effectively creates unity within the Woodwind Quintet by returning to the same compositional technique used at the beginning of the work. As well, he uses common order-position set classes, another technique used earlier in the work (previously discussed in Chapter 1); the flute and oboe each present OPSC (014) and SC (013), while the horn and bassoon each present SC (026) but different order-position set classes. 136 This chapter will conclude with a table giving a brief overview of the third movement, and a discussion on the overall form of the movement. Table 4.1 is given below. 137 0> > o E o 'E © s H o fl o 2 S, c co 6 'I cx co co cx 3 eft oo e '•5 co CO 43 o o 00 .3 t: o cx cx 3 c n L H CO o •5 o ca cx co M T 3 C ca II C O oa 3 4= 43 o "S o O •2 b Q IS) I s -s; 7S> CU t o s u a -~ -2 <; o, o 5 K ^> a C o « J 5 -a £ -a co 4= 00 .3 S -a CO ca CO cx CO C|-i o o •= O 4= 4= >-O - w - — c n H «2 co •*-» co PH O ^ 3 c o o 3 T3 O s— fl-« e •*-» 2- < ca o •e 45 2 .S o o ^ c n > .2 ca •n co -2 & co T3 CO +n O CO O C -a -S C U ca CO 43 ri= ^ 6 2 1 § •fi ° fe c n O c n c n eg co - ° 4= 2 c 2 fl I £"§ S 73 a 3 CO '3 > c" C3 2 T3 cx 8> 4= O g o o o is ca P H o C/3 X u Q pa CO C3 c n CX fi o CO H * 0 O ca c c n c n C3 43 P H O ^ 3 H fe O u co CO .3 c fe o ca o -S 8 -3 • s "2 C e co fe c n O co c n fl 3 2 > J* CO 4J cx c n * ^ C ca J3 S * 2 U « o ^ o c n ca P3 4= T3 i4 co 3 3 00 M . _ J c n j2» ca .23 3 -S3 t3 ca ^ co .23 T fc ^ o ^ o u c n fl CO ^ 3 o 'S ^ 2 3 O co cn rfi "3 CO o ^ - v O P H fe fl ^ Q 138 -»~» K K •2 •B-b 3 05 s Ik p i 1 ^ i l l -s cj j k ca 2 o 0 •3 1 s -a I-2S ,1 ON >/-> 1 O H cu oo s a CU 1) O cu .> o 6 o 2 £ i f IM cu ^3 cS C H cu •a CO t n r ; 5 -2 o B 0 -s cn g O XJ B § cu X) O H . 2 fi e cd . S cx ^ £ cu 8 3 3 . 2 cu -tn _cu "a. . S cu «J CX g . ^ »M , B ^ B PH, O [ T O OH O 2 g ^ c • _ cj s o C H CN ^ CU S2 6 cd O X> cn 0 -a 1 s S-2 Cd CU 'C g cu 5 SI CU ° ^ HM J H X i cn !> CU - f i „ <u O *H cn cu < -S ^ S3 5^ cj T3 a, § 3 « ~2 .2 53 *H x i cd H-» g <*H fi O • f i . cn f S cx cu .22 cn M3 O O CX O cn „ . 2 o 4= « 3 ex •a o X i cj cd X cu X) c cu 6 00 S <« cn OT cu . C d f I r X l o S . 2 'cn ^ C 43 o x o cu cx cx a O O PH O PH O C H O ' O ^— ' O C - C - C u 55 CQ cu o 3 T3 o .5 CU OX) cd cn cn cd CX . O 1 X ! r o cn vo cn m XJ H xi I i S cu cn ucn cu C J o 1H CX cn cn 0 cu 0 cn O CX ^ . S cn cu 5 / 3 •-• o . .. .22 O O £ * ^ H < rs CHT 3 e S B | 1 1 .5 IM *^ st-s o cu C o — 3 U TM c « o .2 » fc 4 3 cu 'cn " s 2 S3 cx o .53 cu X I 5 8 6 0 3 « t/1 a 3 . . X> ctl •a « ^ x i <D 1 ° - ix> . ^ <U o 0 o 3 ^ 8 ^ CU 2 S 2 « to c l O cn •rt cu cn cn cn O cd cx 73 <u XJ T3 a M, .13 O CX cu o x; -cu CU > cn O N cu O CU CU op XJ (/) : • O 3 o CX B „ o t 0 cd cu C X X fj x. « >M _3 o H T fc S cu cx°o B K = 8 vo-U s ~ 12 X I <HH •fi _g"2 cj M cd ' C fi B fi o tS r^'43 c "-1 3 — > 3 M r r \ X ) cn co cd 2 M - cx •S g « E ? . 2 £ —H *H cu •^J S fi S ' cj 0 fi 2 •T3 cd O % >» ~ cd _ . +-» 3 cu e . f i cn 00" n » . Cd CJ orC 73 « eg vo •S fi cn « S3 c o o o ^ ;c +3 ' in C J cu O cu cn Q . fc <u o £ S3 Jn « "2 •fi s +H O • • X M • t > X3 cu § I ° S B <o fe § 8 ^ 8 ^ 139 St <D K , O 1^  s: . g •S-b to cu l l 5 5 7 3 ^ .— o C C8 O 05 ca ca t3 1^  , 1) t o - O ca s o a ^ 5, o •3 K cu S §1 ST o U •3.1 5 -a «5 w " ° c -2 H <u M 6 § I! r v C U 6"" >-O cC O t 3 ca ca C D M c o C N CX "ca fe •C X £ o ca 2 .§ X3-S p DS 2 Cw 'I °M "ex ~ a fe ° o CO 1 ) CX c j '3 -S c O > co • S 5 c H U E CU «Z3 £T fj i n I w 3 O a £ ° 8 .a fi CO , c ca p r-x ca B 1 ) CO g J 2 CX X g o .5 " _ o b o .2 x S u C J •a P H 3 .3 Cw O C X i fe g > o < o .s s p "o CO Cu) X p c a cx 3 o u xi -S <u "HJ o fe 8 u - B i s ' CL) CU cx is •C J> H 6 cx 6 ^ o CL, O O cu '3 X X «H X 1 3 o n CN S 3 f CO g>j2 co 3^ *CO w C C 0 C D C J <o 0 1 LH CX CX 3 O ca X O co £ .2 H cx cx 3 O tab n i w o n co ca 3 M -w CO ca CL) CX X * -H X cu 6b 5 .3 "« "2 C 3 c P fe S L ^ . S CO PQ X o Q x o c w O cu OJ) ca cx p o -a cu 3 o 1 4 0 R K O i t b 5? ta l l 1^  l l "5.15 s s -a v. ^ I<§ 3 o CX 3 <* £ o £ - « c o a » . 2 o S t ; u a Cd r~, > <u B-I Si § <u 0) ^ crj cn Q , C L . "§ s - s 1 1 1 an cu cu •tl -3 ° § c ° s cn . 2 c" " j _ Cd a x> > cu < £ o P M P M 3 O u 3 C. cu a s cu "3 -s g tw CX o 6 3 o CU o a cd TJ O 43 O 6 JB cu "3! >-cn X! i . § _9 cu cu X! £ H </5 £5 s s e •2 3 5 x i u e £ •« cx -3 'fi" cu ^  X> « H M T3 3 O J2 S cn X) 3 cu s is 2 CQ CM g o CM -3 TJ 23 -S x l .9 TJ o > g * CU cu .S TJ DO o_ fi £ cd cd <2 cn Z CU £ . CM cu cu "cx "CX s _ e Cu cu ti, o M-° W H W o o P M o <Z> M M P M 3 o "S > £ . > g £ . § en B 1 8 cfc 0 • i l l a § P M O TJ c o o cu CO cu -"-> - f i co -M* «-§ :§ i * > .5 TJ > 3 O e l l £ 6 6b 8 I P CJ fi 43 cd i n cu cu cu *" X5 X3 • S .3 .9 3 T J T J (M IM 8 o o o -fi -fi u o u -r^ cd cd O H X X M ? x i ^ 2 1 CM 3 C*H C J ° 8 M M M 2 ^ P M S cu cd CU 3 O •fi H M 2j cu o cu .23 -~ TJ cu 1 — 1 9- § C U 60 cd CM o CQ X P H ^ cn 0 cd O-cu 1 c el l CU o .§ 8 1 cn CX -2 £ O O -fi 8 'o. cu X 3 cu cd cd cu cn 3^ >>-fi JS *cu ca 5> so tt cu S feb fi-00 J3 X) cu _ M -3 ~ 3 X M. c2 s >,X3 - . cu _3 -fi ° t -fi 2 cj X3 * J +M •S cu CX 60 =3 ° cd H TJ cd 3 o T J CU 00 TJ cd cu cu XI 00. cu <u cn B l l _ c fi-td 3 fi 3 fa 3 ^ > T J & T ? ^ £d xi O O o -t2 Cu 3 +-» cn cu o -2 g H & " MM « CO Q T 1 «H '—' (-H Q . C C t3 T3 «S *-* 25 *-* — t r t ^ CD 1 3 g s l 00.23 ''5 T J r-• S 6 cd S fi fi S cu cd cn ^ cu X/ ~ 1 3 TJ 2 o u in £ U 1) *" TM S 1 ' ! SL & I t ^ f i B cu cn fi c3 <u CU H M CU x) S } H H TJ rg 3 cu O O TJ 3 cd cu a> M - & cn b 3 in 3 cu o « « 00 o CX ft cd o (7) 4M CX cd —"H CQ U O o 141 cu K O o .2 o fi 43 lH "S 2 o o .23 8 o i l '•s J .5 'fe | 1 5 ° 3 43 6 o P3 ^ i 3 c o CH O 3 C D • w 73 fe Ci3 t 3 is <L> 6 »-fe "P 1 \ I S 43 O H CL) c o & ^ TO C D c o 4 J 2 C D C H 53 H-H -g 4 H co r. £3 — .3 •2 8 CO 0 9 •§ 43 i i O I C cj 53 ° -3 73 .23 *3 3 '2 ^ > I a p ^ fe P o c o c3 43 CL) ^3 £3 S fi 43 c o O £3 ca X 43 C D C J CO ^—^ , a - o C+-* CD 2 ta 43 * i 43 o .3 T 3 C D Cw X O C D T3 C D >- 43 43 on ca C 2 8 43 w +H O , S2 .« CD 43 2 c o C D CO <2 •-H § J2 S fe I -9 3 fe p > U C D 43 H fi * 3 * 43 P H e •*> P 3 43 - ~ P o . CO _ca 73 >. 4-* O p C O T3 3 C O _P ca o 'C C O ca C O a 43 7a fi > 3 s. 43 o p C O fro T H bas T3 fi bas ive C D C D 43 ive C D C D M - H H T3 •3 d cn O play SSOO] c sol C D O ba 73 o X > T3 o fi C D T3 a 3 fi ca C D fi ort CD 3* fe 43 C O 73 C O >. C D C D j ? 5 11 73 < C J 73 <U CD CO 3 £ C H ° - a 43 4 J 3 .3 P 72 CO 3 T3 O 2 S s 3 CD 3 T3 C D _ > 'C C D X ) CD fe CD T 3 fi CD ca ca T3 ca fi 3 c o «n c o T3 > > C D ca c3 * 6 co P 22 c fe It 43 CO - - a '—v L H O H P ^ t n 43 o -b .3 CfH P •ca C D 4 i ca 43 CO -ji. ^ e C3 C D "3. 3 £ 2 q=l . f i C D ^ _ 43 -3 C D 00 ca CO CO -w ca fi 23 3 r* c o .3 c ca C D c o o CO CO ca 4 3 3-g : ca o <« ,P _r P 43 * . o fi ca 43 C D 3 w " ^ 3 43 C D c C D 43 T3 C 3 CO C C D ca S "2 « C D ta c i 3 fi CD T3 ca t o 1^  T 3 P u • 73, 'fi CD 43 'fe § S > as -a 5 1^ P H ^ H a H a £ a X a £ 8 £ 8 ~ ^ t o II a 5 -a ,1 °5 OQ C D a ^ ° 0-.3 71 a ° C HH" WT ^T-' H-H" C U ^ — , t5 PH, 71,^ 2 a m„ p ^ C J p , .3 ' • C O C D C O PH, H PH O P , OH P , &J PH O ^ O t f e c j f e u O P H m u CQ pa u o o O O Q 142 CU S t , o K K O l l r- © O •2 „ O 3 £ > •§ I O T3 '43 CU o > <" CU g -o O "cu > .s cu i_ cd 2 T3 >- S co cd B ° CZ) o 3 cu cu s S "S ao_2 2 ° c C cu cu X i -»-» 60 .£5 is ft cu 5. j2 -5 P-H S « cn • — cu X J ft * O c/f Q 6 CU e g O O H C w O T3 » H O X3 a H cu cn fi ,3 cu *+- X J cu , cu X I H s £ ft X i e M O O P - C cn cfa 3 h g s •c 2 £ o ft o 6 « * _ c _ O O P B 1 cu c2 - > a o J S S P cn »M cn .23 cu ~ 5 5 0 O O u 1) T ] 1 s i ^ cn X3 t> 23 2 •S & £ !a « *-» BI a c j ,3 ,3 cu ^ ^ x i cu cu $££ cn" 2P 2 cd ° S o _e cu cd cd 3 OOS i cn cd o ON X> •a •$ cn 13 o £- in cd cu x i X> e .3 o X ! HH J U o CU cn IS o •s X ) o o os" o o he trich H trich cu -.S E c3 c « g, cu o O ' 3 x i S o 3 , H-» CU 3 •£ 153 T3 .a -2 C H c d 3 CU 3 CL. ^ e fj Cd O +J cn 3 — i cu B s H C H cd B s e x i 5 T3 X J cu o a 43 cu i n '2 cu s ^ S2 <u . § ! .B c^  cn cd cu cn 3 cu cu cd < - ^ O cd <o 2 a g -t» CU 3 m cu C H S o I & S O o o CH a •§ * cu o ft •tS 3 ft o fi s43 cn X S cu X l a - 2 •S ^ <u x> ;3 -a 3 o - 2 „ 6 T3 SH 00 Cd . o cu >A CfH cn CU cn l l cu .S -B - H cd a £ * s c .5 o ^ b ^ > CU 3 cd I o u a > a • o < as 1^ cu CU ft ^ O CH Cu cu V . S cJT cu _cu ft s o cu j - ^ CU H H -"ft H ft o cu -t-» cu f HH -^oovse^SiSs P H o H Cu o l a s 1^ "5. o K cu C J V III s S o, r o CQ •—-on O —' C O 5 -a -• ,1 P I on" CQ CZ) CQ 143 Overall, as can be seen on Table 4.1, the third movement seems to be divided into three sections: bars 1-30 (with bars 31-35 acting as a transition), bars 36-130 (with bars 131-134 establishing a rhythmic motive and acting as a transition), and bars 135-201. Each has a distinct quality: the pitch-class materials of bars 1-30 are all derived from Tio(P); the first four rhythmic motives are presented in this passage. Bars 36-130 present larger sections featuring solo instruments and a more extended development and variation of some rhythmic motives; bars 36-59 feature alternating solos by each instrument, bars 68-95 feature solo bassoon, and bars 95-130 feature solo flute. Bars 135-201 consists of subsections that often present row fragments instead of complete row forms; these fragments are often taken from different row forms, creating passages in which up to five row forms occur simultaneously. Another form is alluded to throughout the movement. There is an alternation between several families of material within all three sections; the form of this movement corresponds more closely to rondo form than either of the other two movements of the Woodwind Quintet (although the three-part form discussed in the previous paragraph, in my view, is the principal form). In the "formal division" column of Table 4.1, there are seven different section types (labeled A through G): the A and B families of material return later in the movement, alternating with statements of new material. Specifically, A2 returns in bars 182-191 to return to the original clarinet motive and help to conclude the work. B material occurs more often, with variants in bars 63-67, 68-79, 81-85, 135-147, and 192-200. Several other families of material are developed and varied, but usually within a single section instead of throughout the work; the D family is a typical example, with all three statements occurring between bars 36-59. 144 We have seen in the third movement that a variety of related rhythmic motives recur and structure the movement in a way that alludes to rondo form. The end of this movement also alludes to material from the first movement, creating closure. The conclusion will discuss this and other aspects of unity (such as common developmental techniques and structural forms) found within the Woodwind Quintet. 145 Conclusion Now that the analysis of the Woodwind Quintet is complete, a few concluding comments will be made. The analysis in this thesis has revealed how Weinzweig focuses not just on serial materials but on other aspects, especially those that affect tone colour. The composer manipulates these aspects to create contrast from one section to the next, and thereby to differentiate sectional divisions. In this work, contrast is achieved through serial techniques, instrumentation and texture, segmentation and motivic development, and the interplay of melody and accompaniment. Many serial techniques occur throughout the work: segmentation (of a particular row form into 26, 34, and so forth) is a common example, with different types of segmentation placed in adjoining sections (such as a passage with trichordal segmentation leading into a passage with tetrachordal segmentation) to emphasize the contrast of smaller segments with larger ones. The same process also accentuates segmentation by developing motives created from segmentations of the row, a melodic contrast instead of a textural contrast (consider the 014 trichord, which occurs in many ways throughout the work). Other common techniques of serial development used throughout the Woodwind Quintet include rotation and the preservation of common segments under specific operations. One way in which differentiation of texture occurs is by contrasting homophonic components and independent melodic components, a process especially prominent in the first movement - this was, in fact, the focus of the analytical commentary on the first movement - but which also occurs in the other two movements. The textural differentiation caused by the interplay of melody with accompaniment, for instance, is 146 discussed explicitly in conjunction with the first movement, but also occurs in the third movement, where the melody often states linear materials while the accompaniment repeats and varies the rhythm of a particular motive. Weinzweig uses various developmental techniques other than contrast throughout the work. His use of rhythmic development was discussed in conjunction with the third movement; the "tight motivic organization" based on serialism, as mentioned in the introduction, is present in all movements (especially the second and third) and helps to unify the work by reprising previously-heard material. The use of segmentation is also a unifying feature of the Quintet (to be discussed shortly). Instrumentation and texture help the listener to identify returning themes and sectional divisions. Unifying material occurs throughout; Weinzweig seems to deliberately strive for unity in several aspects of the work. In the most basic sense, the work is unified by the use of a single twelve-tone row and its transformations; the work is based on the same larger store of motivic relationships. In addition, a limited number of P-related row forms are used: the row forms T0(P), T2(P), T4(P), T]0(P), I0(P), I5(P), and I7(P) are prominent in the three movements; although other row forms occur, they are not as prominent as these. The manner in which the prime form row has been constructed also helps to create unity: the hexachordal properties (of retrograde inversion and symmetry) and trichordal properties (the recurrence of SC (014)), as discussed in Chapter 1, create "families" of row forms related by shared segments. Specific thematic links occur between sections in each movement and between movements as a whole. The example discussed at the end of Chapter 4 briefly examined the return of the material from the beginning of the first movement at the very end of the 147 work, a process that rounds out the work. "Rounding" also occurs at a smaller scale in the Woodwind Quintet; in the use of rotated row forms and the symmetrical construction of the first hexachord of P. Both techniques demonstrate the idea that material from the beginning returns at the end. The three movements are unified through a shared attitude toward the presentation and elaboration of material. Each is constructed in the same general form, namely with motivic material presented in the first section, varied and developed in the second section, and restated (often with slight development or disintegration) in the final section. Although the formal relationships at times allude to traditional forms such as sonata and rondo, the form of each movement of the Woodwind Quintet does not strongly conform to any one of these. There are elements reminiscent of traditional materials and tonalities (for example, the octatonic sonorities discussed in Chapter 1), while at the same time the pitch elements are based on serial methods. The approach to the material of the work is also somewhat traditional: Weinzweig plays with melodies and motives, varying and developing them, and then winding down to a conclusion; he could have written a more abstract work that did not introduce and vary motives in the traditional way, as had many other serial composers by the early 1960s, but he did not do so. Richard Henninger and John Beckwith discuss a similar idea in their article on Weinzweig in the Encyclopedia of Music in Canada. They state: "Weinzweig was called a 'radical romantic' by a magazine interviewer in 1981 ... alongside his unrepentant modernism and concentrated fervour one finds 148 humour - especially in the late works, inspired partly by his interest in Satie and the Dadaists - and a recognizable streak of the North American vernacular." The writers go on to suggest that the Quintet emphasizes the "romantic" style because of the relationship of P to blues materials: the prime-form row is based on the segmental trichord 014, which contains "a minor third and a semitone (the intervals of a familiar blues formula)." I think the dichotomy between "radical" and "romantic" could apply to the Woodwind Quintet in a different sense - specifically, the radical/romantic view espoused by Henninger and Beckwith is manifested in the form and construction of the Woodwind Quintet. The serial materials and an approach to form that appears more concerned with different instrumental combinations and textures than with traditional notions of thematic material represent the "radical" aspect, and the allusions to traditional forms (within each movement and the three-movement work as a whole) and means of motivic development represent the "romantic" aspect. The misleading and jargonistic moniker "radical romantic" is only partly clarified by Henninger and Beckwith's comments in the quoted passage. It is unclear, for instance, how humour, an interest in Satie and the Dadaists, and the use of North American vernacular could jointly, or even in some cases individually, exist under the banner of the term "romantic." Here we shall simply take the expression "radical romantic" as identifying two tendencies in Weinzweig's work: his "unrepentant modernism" (as Henninger and Beckwith put it), and his commitment to fairly traditional notions of musical form and rhetoric. Unfortunately, the term "radical romantic" has Henninger and Beckwith, "Weinzweig, John," 1392-1393. 149 been perpetuated by several Weinzweig researchers: it appears in the titles of both Rhombus Media's documentary on and Elaine Keillor's biography of Weinzweig. A few other points are worth noting in this discussion of compositional unity. All three movements have aspects of classical form, especially prominent in the three-part structure of each movement, but do not adhere to any particular type of classical form (such as sonata, rondo, or sonatina). Other aspects of the work discussed in this thesis also show traditional means of development in a modern context: segmentation, texture, and (rhythmic and melodic) motivic development (discussed in Chapter 2, Chapter 3, and Chapter 4) are developmental techniques common to classical works, but the use of twelve-tone materials as the source of this development produces a style more suitable to the twentieth-century. The use of solo material, prominent in each movement, is evident from the very beginning of the quintet (where the oboe is featured as the solo instrument). This implies another classical form: Baroque Concerto Grosso. The solo-versus-ensemble approach customary to concerto form continues through all three movements (although sometimes multiple solo instruments are featured): the first movement highlights solo oboe; the second movement accentuates solo flute in the first section, and horn in the later part of the work, with a shorter section of solo clarinet in the middle; and the third section emphasizes solo clarinet at the beginning and end, with less important solos by the flute, horn, and bassoon in between. Interestingly, many of Weinzweig's other works feature solo instruments: his divertimenti - the orchestral form he uses most often - each feature a particular instrument. John Weinzweig taught dozens of Canadian composers, and was the first in Canada to use and teach serial methods. Examining his work can provide great insight 150 into the work of later Canadian composers; for me it offers an important stepping stone into further analysis and discussion of Canadian music. Weinzweig incorporates traditional and non-traditional ideas into his compositional style, creating works that are nonetheless effectively unified by these traits. His early works are more strictly serial; his later works involve music and theatrical performance, but almost all of his works, regardless of when they were composed, employ the methods of development discussed in this document. 151 Bibliography Works Cited Babbitt, Milton. "Set Structure as a Compositional Determinant." Journal of Music Theory 5.1 (1961): 72-94. Reprinted in Perspectives on Contemporary Music Theory, ed. Benjamin Boretz and Edward T. Cone, 129-147. New York: W. W. Norton & Company, Inc., 1972. Babbitt, Milton. "Twelve-Tone Invariants as Compositional Determinants." Musical Quarterly 46, no.2 (April 1960): 246-259. "Dr. John Weinzweig." Canadian Music Centre's Directory of Associate Composers [on-line]. Canadian Music Centre; available from; Internet; last accessed 10 July 2002. Gingerich, Lora L. "A Technique for Melodic Motivic Analysis in the Music of Charles Ives." Music Theory Spectrum 8 (1986): 75-93. Henninger, Richard, ed. "Writings of John Weinzweig." Les Cahiers canadiens de musique / The Canada Music Book 6 (1973). Henninger, Richard, and John Beckwith. "Weinzweig, John." In the Encyclopedia of Music in Canada, 2nd ed, ed. Helmut Kallmann, Gilles Potvin, and Kenneth Winters (Toronto: University of Toronto Press, 1992), 1391-1394. Keillor, Elaine. John Weinzweig and his Music: The Radical Romantic of Canada. Metuchen, NJ: Scarecrow Press, Inc., 1994. Kurth, Richard B. "Mosaic Isomorphism and Mosaic Polyphony: Balance and Imbalance in Schoenberg's Twelve-Tone Rhetoric." Ph. D. diss., Harvard University, 1993. Lewin, David. "A Theory of Segmental Association in Twelve-Tone Music." Perspectives of New Music 1.1 (1962): 89-116. Reprinted in Perspectives on Contemporary Music Theory, ed. Benjamin Boretz and Edward T. Cone, 180-207. New York: W. W. Norton & Company, Inc., 1972. Martino, Donald. "The Source Set and its Aggregate Formations." Journal of Music Theory 5.2 (1961): 224-273. Mead, Andrew. "Some Implications of the Pitch Class/Order Number Isomorphism Inherent in the Twelve-Tone System: Part One." Perspectives of New Music 26.2 (1988): 96-163. 152 Morris, Robert D. Class Notes for Atonal Music Theory. Lebanon, NH: Frog Peak Music, 1991. Weinzweig, John. "Interview!" Interview by Jane Champagne. The Canadian Composer, no. 100 (April 1975): 24-33. Weinzweig, John. Anthology of Canadian Music: John Weinzweig. Radio Canada International ACM 09, 1978. LP. Weinzweig, John. Woodwind Quintet (1963-1964). Toronto: John Weinzweig, 1972. Works Consulted " 'Canadian Music in Wartime' Programme." Canadian Review of Music and Art 3 (1944): 34.35. "Music on Radio." CBC Times, 21-27 September 1968, 16. "Weinzweig Works Featured by CBC in Premiere of Anthology Series." The Canadian Composer 139 (March 1979): 8-10. Bartolozzi, Bruno. New Sounds for Woodwind. London: Oxford University Press, 1967. Bradley, Ian. Twentieth Century Canadian Composers, vol. I. Agincourt, ON: GLC Publishers, 1977. Carey, Pauline. "On John Weinzweig." Onion 2/1 (July 1976): 1-2. Carlson, Effie B. Twelve Tone and Serial Composers. Metuchen, NJ: Scarecrow Press, 1970. Chamberlain, F. "Canadian Press and Radio Make a Deal." Saturday Night, 26 July 1941,22. Champagne, Jane. "Interview of John Weinzweig: What One Man's Done to Help Us Understand the Composer's Role as Part of Our Life." The Canadian Composer 100 (April 1975): 24-33,43. Claghorn, Charles Eugene. Biographical Dictionary of American Music. West Nyack, NY: Parker Publishing Co., 1973. Cogan, Robert. New Images of Musical Sound. Cambridge, MA: Harvard University Press, 1984. 153 Eatock, Colin. "An Interview with Four of Canada's Senior Composers: Murray Adaskin, Violet Archer, Jean Papineau-Couture, and John Weinzweig." SoundNotes 1 (Fall/Winter 1991): 4-11. Gefen, Pearl Sheffy. "Calm and Composed." Music Magazine 13/2 (1990): 18-24. Green, J. Paul and Nancy F. Vogan. Music Education in Canada: A Historical Account. Toronto: University of Toronto Press, 1991. International Service, Canadian Broadcasting Corporation. 34 Biographies of Canadian Composers. St. Clair Shores, MI: Scholarly Press, Inc., 1964. Kallmann, Helmut, Gilles Potvin, and Kenneth Winters. Encyclopedia of Music in Canada, 2nd ed. Toronto: University of Toronto Press, 1992. Kallmann, Helmut. "The Canadian League of Composers in the 1950s - The Heroic Years." Studies in Music 9 (1984): 37-54. . "Weinzweig, John." Die Musik in Geschichte und Gegenwart, vol. XIV. Kassel: Barenreiter, 1968. . Catalogue of Canadian Composers, rev. ed. Toronto: Canadian Broadcasting Co., 1952. Kasemets, Udo. "John Weinzweig." Canadian Music Journal 4/4 (1960): 4-18. Kolodin, Irving. "Voices from Canada." Saturday Review 8 (October 1981): 55. Krehm, William. "Music." The Critic (July 1951): 3. . "Our Composers' New Attack." Saturday Night, 22 March 1952, 19. Krenek, Ernst. Studies in Counterpoint Based on the Twelve-tone Technique. New York: G. Schirmer, 1940. Kroker, Arthur. Technology and the Canadian Mind: Innis/McLuhan/Grant. Montreal: New World Perspectives, 1984. MacMillan, Keith, and John Beckwith. Contemporary Canadian Composers. Toronto: Oxford University Press, 1975. Markow, Robert. "Good Neighbors to the North." High Fidelity Magazine, April 1983, 61-63. Pentland, Barbara. "Canadian Music, 1950." Northern Review 3 (1950): 43-46. 154 Proctor, George A. "Canadian Music from 1920 to 1945: The End of the Beginning." Studies in Music 9 (1984): 2-26. Sadie, Stanley, and John Tyrell, eds. The New Grove Dictionary of Music and Musicians, 2nd ed. London: MacMillan, 2000. Schulman, Michael. "Profiling Canadian Composers on Film Demystifies the Creative Process." The Canadian Composer 232 (July-August 1988): 12-16, 44. Schwartz, Elliott, and Barney Childs. Contemporary Composers on Contemporary Music. New York: Holt, Rinehart, and Winston, 1967. Slonimsky, Nicolas. Baker's Biographical Dictionary of Musicians, 8th ed. New York: G. Schirmer, 1992. Stewart, Sandy. From Coast to Coast: A Personal History of Radio in Canada. Toronto: CBC Enterprises, 1985. Stone, Kurt. "Reviews of Records: Music and Musicians of Canada." The Musical Quarterly 53 (1967): 440-452. Such, Peter. Soundprints: Contemporary Composers. Toronto: Clarke, Irwin & Co., 1972. . "One Score and Five Years Later." The Canadian Forum 56/667 (December/January 1976-77): 6-10. Vinton, John, ed. Dictionary of Contemporary Music. New York: E. P. Dutton & Co., Inc., 1974. Weinzweig, John. "A Note on Program Notes." The Canadian Composer 223 (Sept. 1987): 24-25. . "Notes on a Visit to Britain, Part I." The Canadian Composer 20 (Sept. 1967): 16-17,42-43. . "Notes on a Visit to Britain, Part II." The Canadian Composer 21 (Oct. 1967): 8-9,38-41. . "The Making of a Composer." The Canadian Composer 211 (May 1986): 34. . "The New Music." Canadian Review of Music and Art 5/5 (June 1942): 5-6, 16. 155 . John Weinzweig: His Words and His Music. Grimsby: Poole Hall Press, 1986. . Sounds and Reflections. Grimsby: Poole Hall Press, 1990. Wilson, Milton. "Music Review." The Canadian Forum 31 (July 1951): 88. . "Music Review." The Canadian Forum 32 (August 1953): 232-233. Winters, Kenneth. "Eight Canadian Composers Talk About Their Works for the Future." The Canadian Composer 56 (January 1971): 32-37, 46. Other Works on John Weinzweig and his music Beckwith, John. John Weinzweig at Seventy. Toronto: New Music Concerts, 1983. Beckwith, John, and Udo Kasemets. The Modern Composer and His World. Toronto: University of Toronto Press, 1961. "John Weinzweig, a Portrait." Musicanada 9 (March 1968): 8-9. Weinzweig, Helen. "Field Guide to the Care and Feeding of Composers." The Canadian Composer 17 (April 1967): 8-9, 44-45. 


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items