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Swallow, egg, chrysanthemum : music composition with document Pritchard, Robert Blake 1992

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SWALLOW, EGG, CHRYSANTHEMUMMUSIC COMPOSITION WITH DOCUMENTbyROBERT BLAKE PRITCHARDB.Mus., The University of British Columbia, 1974Mus.M., The University of Toronto, 1982A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF MUSICAL ARTS(Composition)inTHE FACULTY OF GRADUATE STUDIES(School of Music)We accept this thesis as conformingto the rçquirecl stncIard 7)THE JNIVESITY OF BIR1FtH COLUMBIAApril 1992© Robert Blake Pritchard 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Dedmentof_____The University of British ColumbiaVancouver, CanadaDate• 1’29/DE-6 (2/88)IIAbstractSwallow, Egg, Chrysanthemum is a sixteen minute work for piano andorchestra. The title refers to symbols from Greek, Western and Asian cultures, with all ofthe symbols being associated with life, death, or resurrection. Over the course of thepiece the interaction of the piano with the orchestra creates a metaphor for the journey ofthe human soul through the three states of existence. Each of the three contiguousmovements carries the name of one of the symbols, whose physical aspects influence theinternal form of the movement. In recognition of the conflict between an acceptance oflife and death, and a belief in life, death and resurrection, the work contains coexistingtwo- and three- part forms. At the temporal level, “Swallow” is balanced by “Egg” and“Chrysanthemum”, and this balance is aided by a blurring of the boundary between thelast two movements.The musical language of the work is based in part on the use of cyclical,diminishing permutations of pitch collections, which are themselves derived from amaster pitch group. The permutations reduce the number of pitches in each collection,creating an apparent “zeroing in” on a single pitch or “tonic goal”. As a result, movingbackwards or forwards through the reductive process can increase or decrease the musicaltension of a particular passage, by altering the number of pitches present. Twelveharmonic areas are created using this technique, and over the course of the work each ofthem is touched upon, with certain ones being of greater importance.Foreshadowing has been used in the form of the work as a unifying device and ispresent at the micro and macro levels. The form of the Introduction can be mapped ontothe first two movements, and onto the piece as a whole. In the last movement a processof postshadowing occurs, whereby earlier material is reinterpreted and transformed in asummation of the work.IIITABLE OF CONTENTSI. ABSTRACT iiII. TABLE OF CONTENTS iiiIII. LIST OF FIGURES ivIV. INTRODUCTION 1V. THE USE OF SYMBOL AND METAPHOR 2VI. THE LANGUAGE 5Procedure of permutation 5Harmonic area 9Harmonic form 11Rhythmic concerns 14Direction and gesture of sections 15The role of the piano 15Orchestration 16VII. THE INTRODUCTION 17Goals of the Introduction 17Mapping 17VIII. SWALLOW 19Goals of the movement 19The integration of two- and three-part forms 20The conflict between harmonic areas 21The transition into the second movement 22IX EGG 27Goals of the movement 27The area of escape 28The piano solo 28X. CHRYSANTHEMUM 30Goals of the movement 30The final transition 33XI. SWALLOW, EGG, CHRYSANTHEMUM (Score) 34ivLIST OF FIGURESFigure 1 Symmetrical permutation applied to a five element set,using 4,1,2,5,3 as the pattern of repeating permutation. 6Figure 2 The master pitch group. 6Figure 3 The extracted pitches.- 7Figure 4 Result of cyclical, reductional permutation on theextracted pitches. 8Figure 5 The derivations of the twelve harmonic areas. 10Figure 6 Structural divisions in Swallow, Egg, Chrysanthemum. 13Figure 7 Normal form of the five-pitch collections. 23Figure 8 The ordered five-pitch collections. 24Figure 9 Expansion of the interval collections. 251INTRODUCTIONSwallow, Egg, Chrysanthemum is a sixteen minute work for piano and orchestra,in which the musical roles of the soloist and the ensemble combine to create a metaphorfor the soul’s progression through life, death and resurrection. The conflict between anacknowledgement of life and death, and a belief in life, death and an afterlife is reflectedin the coexistence of a two-part and a three-part form, creating a structural tension. Thetwo-part form is the weaker structure, and is created, in part, through a temporal balancebetween the length of the first movement, and the combined lengths of the second andthird movements. This formal interpretatiàn is assisted by a blurring of the divisionbetween the second and third movements. The three-part form occurs throughdifferences in such areas as tempo, texture, dynamics, harmonic structures, melodic lines,and orchestration, with these differences helping to defme the musical character of eachof the movements.In both the two- and three-part forms the piano represents the human soul, and theorchestra assumes the role of the continuum of time from the point of the individual’sconception. Each of the movements can represent a different stage within the continuum,but the relation of movements to states of being is not necessarily direct, due to thecoexistent forms in the work.The musical language of the work is based on a process of cyclical permutation ofprimary pitch material, but the process used in this work has the added refinement ofgradually reducing the number of elements in the pitch collections. The completepermutation of each initial pitch group results in one remaining pitch, which is arbitrarilylabeled as the “tonic-goal”. By using this technique, progressions of pitches are2established, and these progressions are used to help define harmonic areas and melodicpatterns.Throughout the work, these harmonic areas and melodic patterns assist in thestructural delineation of the music. In general, different musical ideas are associated withdifferent harmonic areas, and these ideas may be supported or opposed with rhythmic,dynamic, timbral or temporal devices.THE USE OF SYMBOL AND METAPHORThe title of the work refers to symbols representative of life, death andresurrection by Greek, Western and Asian cultures respectively. In Greek folklore, theswallow is the harbinger of spring, and is considered to be good luck. A classical Greekfable tells of swallows dying in their nests in clay cliffs during autumn, and links theirspringtime reappearance with resurrection. In Western secular culture, the egg has longbeen held as symbolic of the cyclical nature of life, and as representative of fertility andnew growth. Within the Christian Church it is associated with the season of Easter, thetime of celebration of Christ’s resurrection. In Japanese culture, washing with dew fromthe chrysanthemum is believed to produce longevity, and the flower and chrysanthemumwine are associated with the autumn rice harvest festival. It is also a very commonflower in funeral ceremonies of Shinto beliefs, and during the last century it came tosymbolize the god-Emperor.Thus, the chosen symbols are associated with spring’s arrival, resurrection,fertility, cyclical life, longevity, the autumn harvest, death, and the god-head. The use of3symbols from different cultures is in recognition of the universal nature of our attempts tounderstand our lives, and to attach purpose to our existence. The belief in an afterlife isreflected in the title by the “Chrysanthemum” interrupting the cycle of “Swallow” and“Egg”. However, the title may also be viewed as symbolizing only life and death, withthe swallow and egg being representative of the former, and the chrysanthemum beingsymbolic of the latter. From this point of view, the title itself could be viewed assupportive of both two- and three-part forms.The large-scale integration of the two-part form into this work of threemovements occurs through a temporal balance, in which the length of the first movementis balanced by the combined lengths of the second and third. The clearly defined divisionbetween the first two movements, and the ambiguous junction between the second andthird movements assist in supporting a binary interpretation of the form..Within the piece there are different levels of specific musical reference to each ofthe symbols. In the first movement — “Swallow”— the ternary form is a result ofcontrasting the opening motoric figurations with introspective, more rhythmicallycomplex writing, prior to the reappearance of active lines. The active-passive-activecharacter of the form’s sections relates to the above-mentioned classical Greek fable, withthe introspective section representing the swallows’ apparent deaths. A second relationbetween form and symbol is found in the parallel between active-passive-active, andwing-body-wing. These two relations contain differences, for the first promotes the ideaof stasis during the middle section (death), which is then followed by a reawakening. Incontrast, the second relation promotes the sense of life at all times, with the outer sectionsrepresenting physical movement, and the inner section hiding complex biological andmental processes.4In the second movement, the symbol of the egg is used in the creation of ametaphor for death and resurrection. Only the piano and strings are present in thismovement, with the absence of the winds and percussion being symbolic of the lack ofbreath and internal rhythms during death. In the strings, each voice of an eight-part canonforms a layer of “shell” around the piano. Eventually the piano finds the weak point inthe shell, escapes the harmonic constraints of the canon, and begins a solo passage.The symbol of the egg in association with the conifict between life and death isparticularly apt, since the unbroken egg is both a womb and a prison. Failure to escapefrom the prison will result in death, as will too early an emergence. In this movement,the piano’s successful emergence from the “egg” (the canon), and the subsequentharmonic and melodic exploration introduces a symbolical problem: any recapitulationby the piano may be construed as a re-entry into the egg or a reversal in time, yet thecyclic nature of the form and function of an egg seems to demand some form ofrecapitulation. To accommodate these conflicting ideas a more complex formal structureis necessary; the strings recapitulate the opening material in diminished retrograde at theoriginal tempo, closing the shell of the egg, while the piano continues in a different tempoto develop new material with the winds, brass and percussion. As a result, while thestrings are completing the second movement in ternary form, the piano is completing abinary form before joining with the remainder of the orchestra to start the thirdmovement.The third movement contains four sections, and each of these “flowers” in somemanner, by increasing one or more of the rhythmic, dynamic, timbral or harmonicactivities. The first three sections make use of previously appearing gestures ortechniques, but do not quote earlier material in a recapitulatory sense. Rather, these5sections may be likened to memories from life, which are discrete rather than continuous,and which are not necessarily of events of major importance. The final section is amodified retrograde of the transition from “Swallow” to “Egg”, a transition which in itsearlier context carries the soul from life to death. Here, the reversal of the transition’sharmonic progressions and dynamic changes, coupled with the absorption of the pianopart into the overall orchestration, creates a metaphor for the soul’s assumption.THE LANGUAGEProcedure of permutationThe harmonic language of the work is created using a system of permutationwhich is modeled on that used by Messaien in Chronochromie. In Messaien’s system,thirty-two rhythmic patterns were created by symmetrically reordering the elements of arhythmic set. Figure 1 shows how the process would work on a set with five elements,using a pattern of 4,1,2,5,3. (The pattern refers to the fourth element, the first, thesecond, and so on.)Using this pattern, the fourth element of the initial set becomes the first element inthe new set, and the first element of the initial set becomes the second element in the newset. This continues through the entire pattern until all five elements have been reorderedto create the new set. The new set then becomes the source for the creation of the nextset.6Figure 1.Symmetrical permutation applied to a five element set, using4,1,2,5,3 as the pattern of repeating permutation.original order3.5.(4 1 2 $ 3)4J:’ J .(4 1 2 5 3)2.(4 1 2 5 3)4.J(4 1 2 5 3)6.original orderIn Swallow, Egg, Chrysanthemum the system of permutation is similar toMessaien’s, but the permutations are applied to pitch, and the process is not strict. Theinitial material — the master pitch group — is shown in Figure 2.Figure 2. The master pitch grouppl,p •t,. 1 — —1.1 2 3 4 5 6 7 8 9 10 11 12From these twelve pitches, eight were extracted and permuted, with the eightpitches selected being those numbered 2,3,5,8,1,4,6, and 7 in the master pitch group.7Figure 3. The extracted pitches23581467This ordering was created by using two Fibonacci series in which the differencesbetween successive numbers in the second series are the retrograde of the differences ofthe first series. Thus, the first four numbers creates differences of 1,2 and 3, while thelast four have differences of 3,2 and 1, creating a symmetrical form in the order ofpermutation.After each permutation of a collection, the highest order number is dropped fromthe system of permutation, resulting in a reduction in the subsequent collection size byone, a process which I refer to as “cyclical, reductional permutation”. For instance, afterreordering the first eight pitches using 2,3,5,8,1,4,6 and 7, the number 8 is dropped fromthe system of permutation, and only seven notes are selected on the next pass through thecollection (2,3,5,1,4,6,7). Figure 4 shows the application of this process to the originalpitch material.8C0IC0CtIII02i9This recursive application of the technique continues down to the last twopermutations. At this point the pattern is changed, and the lowest numbered pitch isdropped, so that in the first harmonic area, the tome goal is Ab, instead of F#.The effect of playing through the resulting note orderings is one of “zeroing in”on tonic goal of the original collection of eight pitches. Moving forwards through thepermutations creates a lessening of harmonic tension as the number of “non-tonic”pitches is reduced, while moving backwards through the permutations can create anincrease in harmonic tension.To generate the next series of permutations, the original master row is rotated byone element, with the first pitch being moved to the last position. Eight pitches are thenextracted using the Fibonacci-based selection process, and cyclical, reductionalpermutation is applied to them. In this way, twelve “harmonic areas” are created throughthe processes of rotation and cyclical, reductional permutation. (See Figure 5.)Harmonic areaThe term “harmonic area” is used rather than “key centre” because the piece is notwritten within the traditional tonal framework. Also, the process of pitch selection doesnot attempt to establish an acoustically-based pitch and interval hierarchy using the eightextracted pitches. (Attempts to create vertical sonorities which would be consistent inhierarchy through all twelve harmonic areas proved to be fruitless.) The hierarchy whichdoes exist is the result of simple, mathematical processes which arbitrarily result in theeighth pitch of any twelve-pitch collection being the tonic goal.10I1%.LI= =— S • ••.: :;111’!iI.H44I4II44ui’ILic’ C) QI‘I.4IIIII‘I.IL2 I41.SIU I11When using the permutations, one cannot refer to a dominant, mediant orsubdominant harmony in relation to the tonic goal. However, as one moves closer to orfarther from a progression’s tonic goal, one is aware of increasing or decreasing harmonictension by the changing rate of the tonic note’s occurrence and by the introduction orremoval of pitches from the progression. Thus, as one moves further back in theprogression (leftward on the graph), the sense of tonic is weakened, facilitatingmodulations into other harmonic areas. Such modulations are especially effective if thereis considerable overlap in the pitches present in the two harmonic areas. For example, theharmonic areas of Bb and A have six notes in common, making a smooth transition alongthe path from the tonic goal of Bb, back through the Bb permutations, into the Apermutations and down to the A tonic goal. Conversely, the harmonic areas of C# and Dhave only four pitches in common, resulting in a more abrupt change from one harmonicarea to the other. (As in tonal harmony, the greater the number of common tones betweenharmonic areas, the stronger the relation.)Harmonic formThe piece uses each of the twelve harmonic areas, but certain areas are of greaterimportance than others. In discussing the use of harmonic areas, changes from one areato another aze referred to as progressions or modulations. These terms are not meant toimply a hierarchy of harmonic strata, but are used as a convenient and familiarnomenclature.The selection and ordering of the harmonic areas for each of the movements wasthe result of a desire to use descent and ascent archetypes at the harmonic level, as well asan awareness of symmetries within the graph of harmonic areas (Figure 5). The twelve12harmonic areas were divided into two groups, based on their positions in the graph,resulting in the groups Ab, Eb, D, E, F, F# and G, C#, B, Bb, C, A. The first harmonicarea of each (Ab and G) became the first two areas to be used. E became the final area ofthe first movement, since it continued the harmonic descent of Ab and G, and on thegraph it is positioned midway between the first harmonic areas of the two groups. Figure6 shows the harmonic areas and formal divisions of the piece.Since the first two harmonIc areas are six steps apart on the graph, it was decidedthat the area for the second movement would also be six steps away from the last area ofthe first movement. This decision was supported (or rationalized) by the resulting Bbharmonic area being a tritone away from the previous E material, an appropriate tonalrelation between the life and death sections of the piece, since the tritone is oftenconsidered to be the most dissonant interval in tonal music.While the strings remain in the Bb area throughout the second movement, theirinfluence on the piano is not absolute, and other harmonic areas are explored by thesoloist. The areas of A, B, C and C# were chosen because they form an ascendingprogression, and because they are distributed symmetrically around the Bb harmonic areaon the graph. The rising harmonic progression is especially important, for it negates thedescending harmonic motion of the first movement, and initiates an upward motionwhich continues on through the third movement.The third movement explores the harmonic areas of D, Eb, F and F#. Although Eis not a factor in the large-scale harmonic direction of this movement, the harmonic areasused are symmetrical about the E on the graph of harmonic derivations (Figure 5). E wasthe last harmonic area of the first movement — the movement associated with life— so138C ri0 CI-UiIIo —LJCDCD—‘li CoCD CDU13w—‘UUCD EEU134.. CD4 ømE —1.)44.. -CDCI,00CI)CC.0 4:.uI-,DCDL. DIIEIS0—iiiiicd— 9I.D wo jea,it14it is appropriate that the harmonic areas of the resurrection movement can be derived bytransferring the symmetry of the “death” harmonic areas onto the life harmonic area E.Two interruptions occur within the harmonic form of the piece, and both aretransitional. The first occurs from measures 133 to 156, and the second at the end of thepiece from measures 243 to 266. In both instances, all twelve harmonic areas arepresented through the use of chords built from the five-pitch collections created in theprocess of reductional permutation. While the second transition is a retrograde of thefirst, the roles of the two are different. The first transition creates a smooth flow betweenmovements, joining two harmonic areas, and fulfilling the traditional role of a transition.The second transition is the last large gesture of the piece, and as such, it becomes thefinal goal of the musical structure. However, because it is a transition, it must carry usforward, and in this sense it fulfils the role of a transition into the unknown.Rhythmic concernsWhile large-scale, metrical rhythmic concerns were not of primary importance inthe formal conception of the work, a few observations may be made as to the manner inwhich such rhythm assists the formal structure. The overall rhythmic sense of the piece isone of increasing complexity through the first two movements, followed by a reductionof rhythmic tension through the last movement. At its simplest interpretation, therhythmic structure can be attached directly to the symbolic aspects of the work, with themotoric drive of the first movement representing the forward motion of life in time, andthe tension of the interwoven voices in the second movement representing the grip ofdeath. The easing and eventual elimination of rhythmic tension through the thirdmovement supports the concepts of resurrection and assumption.15Direction and gesture of sectionsAt various times in the piece there is an exponential increase in rhythmic activity,culminating in a complex rhythmic gesture announcing the next section. This gestureappears twice in the Introduction, the first time in measures I to 4, where it precedes the“ametric” section of bars 5 and 6, and the second time as a very active transition into thefirst movement. Other examples include parts of the first movement (mm. 12 - 45, 62 -82 ), the solo piano section of the second movement, and the first three divisions of thelast movement.This pattern of “simple-to-complex” is reinforced by certain aspects of the music,while other aspects may work against the pattern. Reinforcement can include increasingthe dynamics, bandwidth, texture, or tempo, and in some cases there is a concurrentincrease in all attributes. Examples of opposition to this pattern are found in the strings inthe second movement (especially after their re-entry at measure 200), and in the firsttransition, which is discussed below.The role of the pianoWhile the symbolic role of the piano is that of the soul, its musical role is that of aprotagonist who attempts to influence the harmonic and rhythmic direction of eachmovement. This influence is quite strong at the beginning of the piece, but during“Chrysanthemum” it is eliminated, and the piano is absorbed into the orchestra during thefinal transition.16OrchestrationThe instrumentation of the work consists of doubled winds, four horns, twotrumpets, three trombones, two percussion (no timpani), piano and, in the strings, aminimum of six each of first and second violins, four violas, four ‘cellos, and threebasses. There is an emphasis on colour in the outer movements, created in part by thescoring of the winds, by the choice of percussion, and by the use of mutes and stopping inthe brass.In the first movement, the motoric sections are all derived from the piano’sactivity, and the orchestra supports or comments on this activity through doubling theline, or by providing brief episodes of contrasting or complementary material. In theabsence of the piano, the entire orchestra is involved in a sectioft of widely contrastingcolour (mm. 83 -104), which is enhanced by the large range of dynamics, rhythmicmaterials, registers and articulations.In the second movement, only the strings and piano are used, with the absence ofwinds and percussion being symbolic of the lack of breath and biological rhythms duringdeath. In this movement the reduction of the orchestration to solo piano is countered bythe subsequent expansion of the range used by the piano.In the fmal movement, the orchestra is used in a manner similar to the firstmovement. However, the waning of the piano’s influence on the harmonic and rhythmicdirections eliminates the piano’s importance as a soloist, and it assumes the role of amember of the orchestra.Although orchestrational techniques are important throughout the work, the17previously mentioned transitions are particularly dependent upon orchestration for muchof their effectiveness. They are discussed in detail below.THE INTRODUCTIONGoals of the IntroductionSymbolically, the Introduction begins at the point of human conception, andopens with a “conception motif’ in the piano and percussion. This motif recurs indifferent forms at strategic points in the first movement, and also announces the finaltransition of the piece. The goals of the Introduction include the presentation of thismotif, the foreshadowing of the conflict between the harmonic areas of Ab and G, and theestablishment of a micro-structure which operates throughout the piece in local sections,entire movements, and in the work as a whole. The foreshadowing of harmonic conflictis achieved through the presentation of Ab pitches in the strings in the first half of theIntroduction, and both Ab and G in the second half. A descending glissando(portamento) by the trombones, beginning on both notes, foreshadows the harmonicconflict of the first movement and its eventual resolution to a lower harmonic area, andserves to join the two halves.MappingThe act of applying a formal structure from one dimension onto anotherdimension is referred to as “mapping”. This activity is not uncommon within serial18music, where it is possible to assign numeric values to music parameters, and then maporderings from one set of parameters onto another.This piece is not a serial work, but it does make use of mapping in conjunctionwith the formal organization of rhythm, timbre, register, dynamics and texture. While notconsistently used, the technique is applied at both micro to macro levels. For instance,ternary divisions can be seen in the Introduction, the first movement, and the work as awhole. The overall growth of the Introduction from passive to active, or from simple tocomplex, is paralleled throughout the piece, from the local musical level to the abstractsymbolic level. Even the dualist interpretation of the overall form of this work can beheard in the Introduction, where the two presentations of the conception motif can beinterpreted as announcing the beginnings of two similar sections.“Counter relations” are ones which operate against the predominant direction ofchange. Such relations occur in the large transitions, where parameters (e.g. timbre ordynamics) may change from complex to simple. Other counter-relations may be heard inthe middle section of the first movement, where the rigid, notated materials of the windsand brass give way to sections using aleatonc methods.19SWALLOWGoals of the movementThere are various compositional goals in the first movement, but of primaryimportance is the establishment of the piano’s independence from the orchestra during thefirst two sections. In the first section (mm. 12 - 82) this is achieved through the nearlyconstant presence of the piano (as opposed to the intermittent appearances by theinstruments of the orchestra as they double the piano’s material), by the piano’sintroduction of compound rhythmic figures against the omnipresent motoric sixteenths,and by the piano’s use of pitch material from outside of the Ab harmonic area (i.e., theuse of the pitches D, Eb, E or F).In the second section (mm. 83 - 104), the independence of the piano isdemonstrated by its almost complete disappearance from the section, except for itspresentations of conception motif variations, which act as announcements of compoundrhythmic figures in other parts of the orchestra. With the disappearance of the piano, theorchestra loses its forward momentum, and the section becomes introspective.In the third section, (mm. 105 - 132), the piano reappears as a motonc force,generating a series of orchestral entries. The first of these orchestral entries is by thepercussion, where rhythmic cells are exchanged over the piano’s developing line. Withthe entry of the cellos in measure 113 (announced by compound rhythms in the piano),the rhythms and harmonic explorations of the piano’s material spread to all of the stringlines, and the music drives forward to the transition. During this third section, theindependent melodic line of the piano becomes merged with similar lines in the strings,foreshadowing the eventual assimilation of the piano in the third movement.20The integration of two- and three-part formsThe integration of two- and three-part forms in the first movement is achieved atvarious levels, and in various ways. The most obvious reference is to the three-partstructure of the first movement, delineated by the three sections previously referred to asactive-passive-active. Moreover, the first section is itself a ternary structure containing acontrasting middle section, with the segments occurring in measures 12 - 45,45- 63, and63 - 82.In the middle section of the first movement (mm. 82 - 104), the three part form isdelineated by timbre rather than by rhythm. In the first segment, the strings provide thetirnbral underlay for measures 83 to 91. In measure 91 the woodwinds enter to mix theirtimbres with the strings, creating a second timbral division, and in measure 101 the thirddivision is created when the brass replace the winds.The two-part forms are not as easy to perceive as the three-part, but the mostobvious example of a binary delineation occurs at the changes of rhythm, texture andtempo in measure 83. (These changes define the beginning of a second section for bothtwo- and three-part interpretations of the movement.) The boundary between the secondand third sections is blurred; the second section ends at measure 115, while the thirdsection starts at measure 105. Due to this, a strong parallel exists between this movementand the two-part interpretation of the entire piece, which also involves an overlapping ofthe second and third divisions.21The conflict between harmonic areasOne of the important goals of the first movement is the establishment of the twoharmonic areas foreshadowed by the Introduction, and the resolution of the subsequentharmonic tension. The establishment of harmonic areas occurs through the tracing out ofthe permutations, the emphasizing of certain pitches and pitch groupings by accentuation,dynamics, durations, or orchestration, and through the contrasting of h.armonic area pitchmaterial with non-area pitches. In establishing a harmonic area, trills with the notesAb/G# or G as one of the components are common, and provide a locally constantreiteration of the tonic-goal of a harmonic area. Chords created from the last four or fivepitches of a permutation (although not always with the tonic-goal present), providereinforcement of the harmonic area, and examples of this occur in measure 16 in thestrings and piano, and in measure 28 in the piano, strings and winds. As the movementdevelops, there are a growing number of instances of simultaneous presentations of bothAb and G, and their respective harmonic areas, thereby increasing the harmonic tension.In the second section, the harmonic conflict continues as the violins presentpitches from both areas. The conifict is further accentuated by the horns’ pulsing figurewhich uses only Ab and G. However, the actual change in harmonic balance from Ab toG occurs with the entry of the brass, where the shift of harmonic area is signalled by thepitches E and F, which are foreign to the harmonic area of Ab.The resolution of the Ab - G conflict to the harmonic area of E occurs through theintervention of the piano, which begins directing the harmonic flow towards E at measure105. Here, the piano enters in a G orientation, picking up from the brass. Following acompound rhythm statement in measures 112 - 113, the piano presents G material in the22left hand, and Ab material in the right. This dual harmonic orientation influences thesubsequent entries by the sthngs, for both Ab and G permutations are introduced andfollowed, some more strictly than others. Finally, in measure 132, the entire stringfamily is oriented towards E, in preparation for the beginning of the transition into themiddle movement. However, having set the harmonic changes in motion, the piano nowremains defiantly in G, and it is only after the beginning of the transition that it resolvesits own harmonic tension by moving into the E harmonic area, although it attempts tomaintain its independence from the transitional process through rhythmic, dynamic andarticulative methods.The transition into the second movementThe transition into the second movement symbolizes the crossover from life todeath, and is effected through harmonic, dynamic, durational and timbral changes. Themodifications are designed to create the illusion of gradually moving from two- to three-dimensional timbral space, and take place amid shifting harmonies as all twelve harmonicareas are touched upon.In determining the order of presentation for the harmonic material, an initialdecision was made to use chords constructed from the fourth permutation of eachharmonic area, so that only five pitches were present in each chord. This decision wasbased on acoustic and perceptive restrictions. The acoustic restriction was that if morethan five pitches were used, the results of later interval manipulations might cover toolarge a bandwidth to be effectively scored in the orchestra. The perceptive restriction wasthat the creation of chords with more than five pitches would result in fewer differencesbetween some chords during progressions, while any fewer than five notes would resultoo0000000000‘I’.)Ca)-‘-‘10-aa.a.a1’)C.)1%).C.)C.)C.)101%310C.flLJ(21010)0)=0)0)0)-j.J0)CDCD0)01CD—.T1CDSDC -‘CDC)_mCD0 ‘.‘—.ELz-e0oCD•03Cl)I--+Cl)0i- CDCD3 a —o00g-(IQ0CD0-‘I0C)—C—.=,Cl) 0o 2..0-C) oCD.Cl)0‘.s:.Cl)-e0CD—C Cl)CDCD0CDCDCl)Cl)C) 0Cl)=CD Cl)CDC) 0 ‘•l 0 Cl) 0 — CD Cd) Cl) Cl)>C.)a2Ci,11ma)eItIIp z 0-024The interval lists were then placed in reverse dictionary order according to the“left-packing” of the intervals. (“Left-packing” refers to smaller intervals being closer tothe beginning of the list.) The resultant tonic-goal ordering , beginning with B, was usedas the harmonic order of the progression.Figure 8. The ordered five-pitch collections.Interval Distance Above Tonic Goal-Lowest Pitch03457 B02368 F#02358 Bb02348 E01456 C01456 G01368 F01248 Eb01247 C#01247 Ab01246 A01245 DPart of the transition’s role was to emphasize a change in timbral space, and toachieve this, the interval sets were inverted when scored, with the first note of each setbeing placed highest, and the following notes placed sequentially underneath. Figure 9shows the results of this._0‘•CD0CD =:o• p-CD-C)CDCDo -.I1EfICDE.C)CD00CD-c’OC)-,••4—.Cf)0CD I.-.I-I-I-CDCDCDp-’.= C)I—00--*-‘Wino—0CDCD—QQ00 CD0-—.—c—.-(D0D.-CD0-riCD0 CDC)CD0-_CDDC)CDCDCD0-C)CDI— — CD —0•-0-nCD C -I CD CD m x•0 Cl) 0 z 0 -‘I CD CD -‘ C, 0 CD C) p. 0 00 0 B 9 0- II’ ‘IFbw-l-I‘--I-0z •I9.++++0.3.J.32 >IIaIaIaIa26The scoring of the transition begins with the “pure” timbres of the differentfamilies and ends with the sound of the full orchestra. While the homogeneity of timbreis good for the strings, the concept of timbral purity is weakened in the case of the brass,and is quite questionable for the woodwind family. However, given the timbres of thevarious instruments, the application of the idea of timbral progression does create agradual change of timbral depth.As an important aid to the timbral shift, the dynamics of the transition begin atdouble forte, and end at double piano. The effect of this is a gradual reduction in theovertone content of each timbre, creating a progressively better blended sound. This lossof timbral detail is a parallel to the visual world where, as an object recedes from theviewer, there is a reduction in the perceived detail.Although the total number of instruments which play simultaneously increases, atthe local level the dynamics decrease, and in an ideal performance the volume wouldremain constant while the timbre shifted. Since it was recognized that this is quiteunlikely in practise, the ideal performance was used as a model and not as a goal.However, this does not deny the fact that overall dynamic compensation will occurduring the process of timbral shift.The result of the transition is an arrival on the final harmonic area of D, but theinfluence of the independent piano, which has explored the E harmonic area during thetransition, is felt as the strings reiterate the E chord, providing a harmonic resolution ofthe first movement at the end of the transition into the second.27EGGGoals of the movementLike the first movement, the second movement creates a situation of conifictbetween the piano and the orchestra, but the resolution of the conifict is somewhatunusual. The harmonic centre of this movement is Bb, a tritone away from the finalharmonic area of the previous movement, and this area was chosen for symbolic reasons(the tritone and death) and graphic reasons (the harmonic centre is six places removedfrom E on the chart of permutations, the same separation as between Ab and G. SeeFigure 5). Throughout the movement the strings remain in Bb, while the piano exploresother harmonic areas.The physical characteristics of the egg influence the form and techniques used inthis movement. An eight-voice canon in the strings creates a “shell”, surrounding thepiano and restricting its melodic and harmonic movement. Encased by these layers, thepiano is forced to play all parts of the canon, while exploring other harmonic areas in anattempt to discover the weak point of its prison. Diminution is applied to each of thecanon’s voices, with later entering voices having smaller rhythmic values.The piano announces each string entry with a quintuplet figure, and tries to escapethe Bb orientation by investigating other harmonic areas. The first example of thisinvestigation occurs in measures 166 - 168, where the left hand of the piano is doublingthe canon, and the right hand is working through a D harmonic area permutation, in anunsuccessful attempt to break out. Between measures 171 and 180 the pianounsuccessfully explores the harmonic areas of D, C#, C and B. Finally, in measure 181,28it settles back into the Bb area. This chromatic descent of the harmonic areas from D toBb represents the realization that escape from the egg must come from the application ofinner forces; the piano is incapable of breaking the egg from outside of the harmonic area.The area of escapeThe piano’s escape occurs at a structurally significant point. Ui measure 192 thesecond group of first violins overtakes the first group of second violins, who enteredearlier in the canon. This is the weak point in the “shell”, since this is the only point atwhich such an event occurs. Here, in effect, an inner layer of shell is pushed through anouter layer, and the piano takes advantage of this occurrence to escape the harmonicconstraints imposed by the canon. As the piano begins its subsequent explorations, thestrings drop out, symbolic of the abandonment of the shell, and of the soul’s escape fromdeath.The piano soloThe piano solo begins in the harmonic area of A, and rises through B and C toarrive in the C# area in measure 200. Through this section the piano occasionally makesuse of non-harmonic area pitches for added colour, but it remains closely aligned with theharmonic material of the area of exploration. The shift from A material to B materialoccurs at rehearsal letter 3, where there is a vertical presentation of B material. Duringthe next two systems, the B and C material is mixed, and the tonic-goal pitches arejuxtaposed in trills. The successful shift to C during the tnlls is immediately followed bythe combination of C and C# material, until a descending retrograde of the C permutationleads into measure 200 and the definite arrival in the C# harmonic area. At this point the29piano continues its solo in C# until the end of the movement at measure 203a.Over the course of the piano solo a number of motifs are introduced. Thesemotifs include the accelerating repetitions of a pitch or pitches, the block chordspresented alone or in simple and compound rhythms, tremolos and trills, the shortmelodic figure announced by an upward leap, and the accelerating, descending, chromaticlines. Each of these motifs plays a role in maintaining the forward moçion of the solo.For instance, as the number, density and rate of change of trills and tremolos increases,there is a thickening of texture and an increase in the energy. Linear figures, whichoperate at both foreground and background levels, provide direction, and contrast thechords of punctuation and the block chords. As the solo unfolds, these block chordsincrease in number, assuming an aspect of linearity and developing the local harmonicactivity, to become the eventual culminating gesture of the solo.The arrival of the piano solo in C# at measure 200 is the cue for the re-entry of thestrings. As mentioned previously, certain aspects of the egg’s symbolism demand someform of recapitulation while other aspects require an on-going development. The solutionto this formal problem lies in the use of coexisting forms. The strings work through theretrograde of the Bb permutation using the original tempo while reducing the dynamiclevel to triple piano, thereby completing the cycle and symbolically making the shellwhole. The piano ignores the strings and begins the third movement in conjunction withthe winds, brass and percussion, at a tempo nearly double that of the strings. Thedifferent tempi assist in delineating the independence of the two instrumental groups.The result is a ternary form in the strings, and a binary form in the piano, with an overlapof several bars.30CHRYSANTHEMUMGoals of the movementThe compositional goals of this movement include the creation of a process ofsummation through postshadowing, the continuation of the rising harmonic patterninitiated by the piano in the second movement, the elimination of the piano’sindependence, and the development of an open-ended transition. Also, since this lastmovement symbolizes, in part, the final stage in the transition from death to after-life, itis based on the life-to-death transition between the first and second movements. It wasimportant, though, that the harmonic progression continue through the areas of D, Eb Fand F#. In order to do this, it was necessaiy to modify the transition. This is discussedbelow.The movement contains four sections, each of which bears some relation to earlierparts of the piece. These relations are like memories, which may or may not be of eventsof major importance, and which may or may not be accurate. Each section of“Chrysanthemum” flowers in some manner, symbolic of the physical aspects of theplant. This flowering is accomplished through modifications to rhythmic, dynamic,timbral or harmonic material.In order to create the sense of postshadowing without direct recapitulation, eachof the four sections makes use of material from the first movement, but the relativeimportance of the material is modified in each case. Mapping is at work here, for thelarge-scale order of the material remains the same, and the character is maintained at thelocal level. It is important to realize that due to the process of mapping, a restatement of31a gesture from the Introduction or first movement can be interpreted as a restatement of aparallel section from the second or third movements, or even as a restatement of an entiremovement. Throughout this movement the review of earlier material maintains theoriginal ordering, and thus symbolizes a review of the entire piece.The solution to the problem of maintaining the rising harmonic line, whilemodelling the movement on earlier transition, lay in a symbolic modification. Since thistransition is from death to after-life, it was appropriate to reverse the harmonic order ofthe life-to-death transition, resulting in P. A, Ab, C#, Eb, F, G, C, E, Bb, F#, B. Withthis done, D, Eb, F and F# occur in the required order in the list of harmonic areas. Thisnew ordering allows for the use of all twelve harmonic areas, as long as the fourharmonic areas of importance are signified in some manner. To this end, the arrival ofeach of these harmonic areas is marked by the appearance of an arpeggiated gesturesimilar to the piano’s conception motif. For ease of discussion, such figures in the thirdmovement are also referred to as conception motifs.The first section of the third movement occurs between measures 203 and 212,overlapping the strings’ completion of the second movement. Like the first section ofSwallow, and the first movement as a whole, this section contains motoric and compoundrhythms, and there is a contrasting section of lesser energy in the middle. A conceptionmotif is presented by brass and winds in measure 205, generating the first transitionalchord and marking the start of the D harmonic area. Overall, the growth of this section ismarked by an increase in dynamics, bandwidth and texture.The second section ( measures 212 - 225) reinterprets specific gestures found inthe middle section of the first movement, and by its character and harmonic stasis it is32related to the middle movement. The gestures consist of a triplet figure, long, highpitches, harmonic glissandi, and repeating, randomized material of limited pitch content.Unlike the first movement, here the gestures combine to create a gradual increase inactivity and density. Again, it is the horns which perform the pulsing, triplet figure withtimbre changes created by using stopped and open technique, but the high pitches arenow taken by the solo flute, oboe and clarinet, creating a keening, ascending gesturewhich mixes with the ethereal harmonic glissandi of the violas. Midway through thissection the upper strings introduce rapid pizzicati at triple piano, thickening the texture.Except in the viola glissandi, the number of pitches used increases, resulting in anincrease in the local harmonic complexity. In measure 221 the trombones enter with areference from the middle section of the Introduction, playing descending glissandi in thesame register as the horn figures, thereby adding to the local density. A rhythmicallycomplex figure is presented by the orchestra to close this section, and announces themove to the Ab harmonic area.The third section (mm. 226 - 241) opens with a forte Ab transition chord, and thenmoves to scattered rhythmic presentations of the D, A and Ab transition chords. Theseirregular rhythms parallel those beginning in measure 105, and this section gathersmomentum in a similar manner. In measure 231 there is a shift to the harmonic area ofEb, which is an important structural point, and therefore is marked by the appearance of aconception motif.This third section includes a canon, which begins at measure 236 in the stringsand flutes. The canon continues through to the end of the section, while the winds andbrasses mix pitch material from Eb and F harmonic areas, and drive forward to the finaltransition which begins in measure 241.33The final transitionWith the arrival of the structurally important F harmonic area in measure 241, theconception motif is presented by piano and percussion. It is at this point that thepostshadowing process encounters material from the third movement itself. This resultsin the movement “remembering” itself, restarting the harmonic progressions of thetransition upon which the third movement is based. This occurs in measures 245 - 246,where the brasses’ muted D chord, underneath the G material of the winds andpercussion, restarts the progression. As in that first transition, there there is an attempt tosuggest a move from a two-dimensional to a three-dimensional timbral space through thegradual mixing of timbres. This time, though, the dynamics begin at piano and increaseto triple forte, increasing the timbral detail. There is also a concurrent diminishing of thetime between entries of the transitional chords, and an increase in their durations,resulting in an overlapping and clouding of the boundaries between the chords.There is one last twist in the completion of the harmonic organization. The finalharmonic centre of the transitional progression is B, but the fmal harmonic centre of theoverall scheme is F#. The solution is to treat the B material as an “overshoot”, andresolve back to the F#.Throughout the final transition the piano loses energy and identity, and in a movesymbolic of absorption or assumption, the piano’s compound rhythms — reminiscent of aheart beat — are replaced by quieter tremolos which blend with the rest of the orchestra.However, due to the timbral, registral and dynamic levels, this is not an introspectiveending, but one which is triumphant and extroverted.34SWALLOW, EGG, CHRYSANTHEMUMInstrumentation2 Flutes2 Oboes2 Bb Clarinets2 Bassoons4 Horns2 Trumpets3 Trombones2 Percussion Vibraphone, Xylophone, Marimba, Glockenspiel,Roto Toms, Woodblock, Temple Blocks,Tam Tam, Tambourine, Jawbone, Bass DrumPianoStrings: Minimum of 6,6,4,4,335In MemoriamG.AR.B.M.P.G.&F.S.LCj’2 CLO<<p-nF.:=_p—=—BpC.E=—pfrpF°‘9 A00t-a’.‘jp•l0U.pa aVQCpNa2nStdp•<p.pw aa “IwUa 00Na ‘ap90InI.tJIp< p‘I II IOil.a1IOi(a aUI’Oippp90tJIPFip-p0 0RI 121IJII 0’ IU)ciPCIjP-PPpP—00LII1Ill1Eld->,t—>—>.,—>p—p.nC-9-p 0•w pp—,IjIdp.F-q>pp C.ElF‘HIIIIIIIIIL1.1IYHyyI—Cl>a’ —I9 Sp<<p.ppFI0 ‘aNpdpe<•<-nW()C———Fl I1F-UI”JII 1H0frntaPN SRS‘I0•1N.-4I a.0(‘I ‘40.L0“C’I-J 001•4%)I. 0t S I— 0 IIIII S“C0w I00 CwFacp000—•0’HfrppF1 I00 f-fl.EpH0000-I00 0000p•<<pVp<<p.jpVI)pH HIIHpM‘CScp<<pp’HHx-12]I(,I>145—L0UIl‘FeI00I1 F51 Igj t’J C’ i?ia’4-40u

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