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Musica para dos megainstrumentos y grupo de camara Vasquez, Hebert Andres 1998

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MUSICA PARA DOS MEGAINSTRUMENTOS Y GRUPO DE CAMARA by HEBERT ANDRES VAZQUEZ B.Mus., Conservatorio Nacional de Musica, 1989 M.F.A., Carnegie-Mellon University, 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF MUSICAL ARTS in THE FACULTY OF GRADUATE STUDIES (School of Music) We a c c e p t this t h e s i s as conforming t Q t h e required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1998 ©Hebert Andres Vazquez, 1998 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 written permission. Department of M \J S \' c The University of British Columbia Vancouver, Canada Date 7 DE-6 (2/88) Abstract Musica para dos megainstrumentos y grupo de camara (Music for two Mega-instruments and Chamber Ensemble) is a six-section piece written for two violins (treated as a megaviolin), two flutes (treated as a megaflute) and chamber ensemble. Both the form and the different tempi of the piece are determined by the interaction of the two mega-instruments and the ensemble. The piece is an original contribution in its concept and use of the mega-instruments. A mega-instrument is composed by two single instruments of the same kind. The main function of the mega-instrument is that of expanding the technical possibilities of the individual instruments that constitute it, as well as creating new possibilities, while keeping, at the same time, the specific characteristics or "personality" of the original instruments. In the Primer ensamble and Segundo ensamble sections the two mega-instruments are incorporated into the ensemble and treated as four individual instruments. The basic pitch structure of the piece is represented by SC [014], which is further organized in a six-note scale that is a member of SC [014589]. The six-note scale (used in the piece as an unordered set) and its three available transpositions create a universe of four pitch regions with two different modulation levels to connect them. Pitch Regions are also used simultaneously in the piece. This procedure (that I have called a multi region) includes harmonic and/or melodic intervals that are not available within single pitch regions. The piece could be defined as atonal or without pitch centers. It is characterized by an interaction of the tempered system and the pitch continuum (microtones and glissandi). Table of Contents Abstract ii Table of Contents iii r List of Figures iv Notas sobre la partitura v Notes on the Score viii StrumenW Instrumentation xi Part One: Score Preludio/ Prelude 1 Primer ensamble/ First Ensemble 5 Primerinterludio/ First Interlude 20 Segundo ensamble/ Second Ensemble 27 Segundo interludio/ Second Interlude 53 Postludio/ Postlude 66 Part Two: Analysis and Commentary a) Formal Principles (number of sections, relationships, length) 91 b) Pitch Structure 93 c) Influences 106 d) Orchestration 107 e) Rhythmic Organization and Tempi 111 f) Style 112 g) Sense in which the Work is an Original Contribution 113 Notes 115 Bibliography 116 iv List of Figures Figure 1 Duration of the Piece 92 Figure 2 Members of SC [014] embedded in SC [014589] 93 Figure 3 SC [014589] and its Four Representatives 94 Figure 4 Close Modulation 96 Figure 5 Distant Modulation 98 Figure 6 SC [048] Common tones 100 Figure 7 Multi-Regions 101 Figure 8 Climactic Chord of Primer ensamble 102 Figure 9 Multi-Regions used in Chord Expansion 103 Figure 10 Use of Pitch Continuum 104-105 Figure 11 Sacher's Series 106 Figure 12 Chord System in Derive 106 Figure 13 A Passage for Mega-Instruments 108-109 Figure 14 Table of Tempi 111 Notas sobre la partitura: 1.- Los instrumentos solistas (dos flautas y dos violines) cumplen una doble funcion en la obra; a veces se integran en pares para formar instrumentos ampliados o aumentados (las dos flautas se convierten en una megaflauta y los dos violines en un megaviolin), mientras que en otras ocasiones se incorporan al grupo de camara como cuatro instrumentos individuales mas, abandonando el papel protagonico. Para enfatizar este doble papel los solistas tocaran de pie en los movimientos para megainstrumentos y sentados cuando formen parte del conjunto, de acuerdo al siguiente esquema. 1. Preludio: violinistas de pie. II. Primer ensamble: todos sentados. III. Primer interludio: flautistas de pie. IV. Segundo ensamble: todos sentados. V. Segundo interludio: flautistas y violinistas de pie. VI. Postludio: flautistas y violinistas de pie. Los ajustes necesarios para la ejecucion deberan llevarse a cabo en forma rapida, sin interrumpir la continuidad de la obra. 2. - Las notas de adorno (o grupos de notas de adorno) deberan ser atacadas siempre sobre el tiempo. Esto hace que las notas reales a las que estan conectadas sean ligeramente desplazadas y pierdan una porcion de su valor real, como podemos ver en los siguientes ejemplos. vi En el ejemplo a) el ataque del fa sostenido (cuarto con puntillo) y el la natural es desplazado (retrasado) ligeramente por el grupo de notas de adorno que le preceden, por lo que ambas notas pierden una fraccion de su duracion real. a) En el ejemplo b) el grupo de notas de adorno y el do sostenido (indice 6) tendran que invadir una porcion de los silencios que les siguen, lo cual es perfectamente valido. b) Los unicos casos en los que las notas de adorno son interpretadas en forma tradicional, esto es antes del tiempo, se encuentran en la parte del piano, en los compases 166, 168 y 177 (cabe senalar que en todos estos casos el adorno es un anticipo). Simbologfa: Los sfmbolos \ y t representan un cuarto de tono ascendente y descendente, respectivamente. Ambos sfmbolos (como sucede normalmente con el sostenido y el bemol) se mantienen vigentes durante todo el compas, a menos que sean invalidados por un becuadro (o cualquier otra alteracion). VII frullato (alientos) pizz. de labios (flautas) tongue-ram (flautas) nota superior: digitacion. nota inferior: sonido resultante. sonidos cantados (flautas) a e con vocales 1 >r armonicos (flautas) o o O nota superior: armonico. nota inferior: generador. aire afinado (eolico) (flautas) pizz. alia Bartok (violines) ? ^ f - > — « P rasgueo (violines) pizz. h — ^ • • i las flechas indican la direccion del rasgueo pizz. con ligadura (violines) pizz. la segunda nota de la ligadura es accionada unicamente por la mano izquierda VIII Notes on the Score: 1.- The four soloists (two flutes and two violins) have been assigned a double role in this piece; sometimes they play by pairs creating magnified instruments (both flutes are treated as a megaflute and both violins as a megaviolin), while on other occasions they form part of the chamber ensemble as four individual instruments, thus abandoning their leadership role. To emphasize this double role, the soloists will play standing in the megainstrument movements, and seated when forming part of the ensemble, according to the following chart. 1. Preludio: violinists standing. II. Primer ensamble: everybody seated. III. Primer interludio: flutists standing. IV. Segundo ensamble: everybody seated. V. Segundo interludio: flutists and violinists standing. VI. Postludio: flutists and violinists standing. The necessary adjustments for performance should be made quickly, without interfering with the continuity of the piece. 2. - Grace notes (or grace-note groups) are always to be played on the beat. This alters to some degree both the position of the attack point and the duration of the note to which the grace notes are attached, as shown in the following examples. ix In example a) both the attack points of the F sharp (dotted quarter note) and the A natural are shifted by the grace-note groups that precede them, causing them to lose a fraction of their total duration. a) i T3n -v. k J In example b) the grace-note group and the C sharp will continue to sound over (a portion of) the rests that follow them. This is perfectly valid. b) [-£ • i The only cases where a grace note is to be played before the beat occur in the piano part, measures 166, 168 and 177. In these cases they are all apoggiaturas. Notation: The sign j denotes the raising of the note by a quarter-tone. The sign t denotes the lowering of a quarter-tone. Both signs (as in the case of ordinary sharp and flat signs) are valid for a whole measure, unless they are invalidated by the use of a natural sign or the appearance of a new accidental. X Flatterzunge (winds) Hp pizz. (flutes) tongue-ram (flutes) upper tone: fingering, lower tone: actual sound. sung (flutes) harmonics (flutes) aeolian (flutes) CO -< using different vowels 0 O upper tone: harmonic, lower tone: fundamental. <-pizz. alia Bartok (violins) 3± strumming (violins) pizz. TIT arrows indicate strumming direction pizz. slur (violins) pizz. second note in the slur is to be played only by the left hand xi StrumenVi/lnstrumentation 2 flauti (megaflauto) 2 violini (megaviolino) 2 oboi 2 clarinetti in sib 2 fagotti 2 corni in fa 2 trombe in sib 2 tromboni timpani (anche campane) xilofono pianoforte Gli strumenti scritti in do (tutti ali strumenti sono scritti in note reali tranne il xilofonoh The score is in C (all instruments appear at the actual pitch except for the xylophone). Durata: circa 19 minuti. Duration: circa 19 minutes. Miisica para dos Megainstrumentos y Grupo de Camara (1997-1998) Violino 1 Megaviolino < Violino 2 VI. 1 Mg.vl. V). 2 m pp non cresc. J? sul pont. m. o. sul pont. Jf sul pont. Mg.vl. VI. 1 Mg.vl. VI. 2 8 © 1998, Hebert Vazquez Mg.vl. •' VI. I Mg.vl . • gliss. continuo ,' VI. i Mg.vl . i VI. 2 sulla tastiera poco ppsubito sulla tastiera poco gliss. continuo poco ppsubito poco poco f VI. 1 ' VI. 2 poco poco sul pont. m. o. Mg.v l . VI. 2 subito VI. 1 Mg.v l . . VI. 2 31 k L sul pont h ^ - ^ - M ^ J W art. „^ ^—J^u JU^J sul 7 ^ 7 7 ?fl " r p — r - = ° pont. m. o. f J •• J • . 7 ±AAA—7 i i S f 7 ^ fljj. W ^ 1 - ^ r " ' — / VI. 1 Mg.v l . l, VI. 2 /VI. I Mg.vl . W l . 2 ,fj • - — ^ J J" 3 y —^  >-T r — 1 / ^ ^ 1 • VI. I Mg.vl . VI. 1 Mg.vl . ' VI. 2 -A s/iz sempre P sempre sul pont. attacca II. Primer ensamble Oboe 1 Clarinetto 1 Clarinetto 2 Fagolto 1 Fagotto 2 pleggero VI. 2 Ob. 2 CI. 1 CI. 2 Fg. 1 Fg .2 poco 6 P ° c o p subito 7 10 A - 'i i ib i | 1 5 | H M i l l — 1 ^pp subito it—- • f b>)- - frJ iLJ J J J B-H 1 1 I ! 1 Mill =^ t *r f r 1 T *T f f f 1 3 1 1 3 1 ^ = t e 9 — = Cor. 2 f Tr. 1 ( Tr.2[ Trb. 21 11 12 64 chiuso 13 . ^ 1 Cor. 2 Trb. 1 Trb. 2 Fl. 1 ( < v i . 11 19 Ob. 1 ci. I ( a. 2 ( Fg. 1 Fg-2 Jp"p % * -^-+ • pp — H *0J =4 $* i 1 PP r~i 1 -0 -ffr-^? U J ' p attacca 58 poco a poco cresc-attacca 78 87 4161 3 I I 3—) | 3 igg ^ vibrato rapido pf. \ pppfappeiia udibile) -jjL—— -. . , ~ gliss. ppp\ ppp{appena udibile) ppptappend udibile) pppiappena udibile} 91 Analysis and Commentary a) Formal Principles (number of sections, relationships, length) The form of the piece is determined by the interaction of the two "mega-instruments" (see Orchestration section) and the chamber ensemble. There are six sections in the piece: -Preludio (megaviolfn) -Primer ensamble (grupo de camara) -Primer interludio (megaflauta) -Segundo ensamble (grupo de camara) -Segundo interludio (megaviolfn y megaflauta) -Postludio (megaviolfn y megaflauta mas grupo de camara) -Prelude (megaviolin) -First ensemble (chamber ensemble) -First interlude (megaflute) -Second ensemble (chamber ensemble) -Second interlude (megaviolin and megaflute) -Postlude (megaviolin and megaflute with chamber ensemble) The mega-instrument sections (Prelude and First and Second interludes) alternate with the chamber ensemble sections (First and Second ensemble). In the mega-instrument sections the ensemble is silent, and, conversely, mega-92 instruments do not participate in ensemble sections, in which they are treated as traditional instruments (see Orchestration section). The only exception to this procedure occurs at the beginning of the First interlude (mm. 80-88), in which the megaflute is heard over a sustained chord from the previous section, played by the ensemble as a background sonority. The passage, however, is merely transitional, without any interaction between the mega-instrument and the ensemble. The Postlude, which is the only section that incorporates the two mega-instruments and the chamber ensemble, represents the climatic section of the piece. In general the mega-instrument sections are more virtuosic than the ensemble sections, and they also incorporate non-traditional timbral techniques that are not used in the ensemble sections (see Orchestration section). Figure 1 shows a list of the individual durations of the different sections of the piece, as well as its total duration. Figure 1. Duration of the Piece -Prelude (Preludio) 1'40 -First ensemble (Primer ensamble) -First interlude (Primer interludio) -Second ensemble (Segundo ensamble) -Second interlude (Segundo interludio)— -Postlude (Postludio) 4'54 4'20 3'31 2'40 V48 Total duration= 18'53 (With the inclusion of fermatas, the total duration of the piece is 19 minutes). 93 The formal design of the piece comprises an additive process directed towards a structural climax. On the one hand, the mega-instrument participation becomes increasingly complex. Thus, only one mega-instrument participates in both the Prelude (megaviolin) and the First interlude (megaflute), while the two mega-instruments join forces in the Second interlude, and finally they play with the ensemble in the last section of the piece (Postlude). On the other hand, each section of the piece is longer than the preceding one; the final section (Postlude), in fact, is almost three times as long as the first section (Prelude). b) Pitch Structure In this piece, the pitch structure is dominated by SC [014]. Members of SC [014] are further organized as subsets within members of SC [014589]. Figure 2 a) shows a representative of SC [014589] and Figure 2 b) shows the six trichordal subsets that are members of SC [014]. The compositional process focussed to a large degree on SC [014], although this trichordal SC was set in the context of SC [014589] hexachords. Figure 2. Members of SC [014] embedded in SC [014589] a) b) SC 6-20[014589] (E) (I) 014 (D#) 014 (Ab) (I) 014 (G) 014 (C) (I) 014 (B) 014 94 Other trichordal subsets are prominent in this hexachord, like SC [015], and SC [037], which occur six times within the collection, and SC [048], which occurs twice. Although these trichords do occur in the piece, they did not play the same self-consciously prominent role during composition as did SC [014]. Among these other subsets, however, SC [048] does have special importance, as will be seen shortly. The interval-class vector (V) for SC [014589] is V=[303630]. The inversion invariance vector for (VV) SC [014589] is VV=[303630363036]. (1) This tells us that any set within this SC has (total) invariance under 3 Tn and 3 Tnl operations. Therefore SC [014589] has a degree of symmetry of 6 and contains only 4 (24/6) distinct pcsets. These 4 representatives, labelled H0, H-,, H2, and H3, are shown in Figure 3. Figure 3. SC [014589] and its Four Representatives Hr v ' —: Whm # H, H1 -no common tones-I—I -/ i v^ V a # *"*— -0 »_K 1 H5 b o 95 The vertical line in Figure 3 indicates that there are no common tones between Ho and H2, while the dotted line indicates that there are no common tones between Hi and H3. Each hexachord shares common tones with two other hexachords. The common tone relation between different hexachords is expressed in Figure 3 by the use of black and white noteheads. In the case of H-i, for example, its three black noteheads (E, G-sharp and C) are common tones with Ho, while its three white noteheads (C-sharp, F and A) are common tones with H2. When a pair of hexachords intersect, their intersection is a representative of SC [048]. Note that in this piece the six-note collection is used as an unordered rather than as an ordered set. The four hexachords of Figure 3 create a pitch-class universe of four pitch-class regions: Ho = Rgn.o (Regiono); Hi = Rgn.-i; H2 = Rgn.2; and H3 = Rgn.3; with two different modulation levels to connect them. Regions are conceived differently from hexachords, in the sense that more than one case of a specific pc may occur within a single region and that regions may be represented by SCs with cardinalities smaller than 6 (in fact any [01] dyad within a region will uniquely determine that specific region). Although the concept of modulation has strong tonal connotations, it has to be understood here as the process of moving from one (non tonal) pitch-class region to another. The first level of modulation, or close modulation, is the result of moving within regions that share three common tones, (for instance, from Rgn.o to Rgn.3 (or vice versa), or from Rgn.1 to Rgn.2 (or vice versa), and so forth) (see Figure 3). Each region can move by close modulation to two other regions. An example of close modulation in the actual music is shown in Figure 4, the passage is presented in a six-part reduction. 96 Figure 4. Close Modulation (J = 7C) m.60 r I 3- ??5 61 fr. VI. 1 fespressivo tr. VI Staff 3 Staff 4 Staff 5 Staff 6 fespressivo ppsub. ppsub. ppsub. H J. sub. Si Rgn. c 1 3 1 IC.T. 45.T. («) IC.T. C.T. Rgn. I 5 -r ~ 3 i R g n . 0 VI. 1 VI. 2 I A 6 2 1 63 I 3' Staff 3 Staff 4 Staff 5 tr - r t . Sit C.T. c.-ri ^ C . T . W Staff 6 C.TJI Rgn.1 Rgn. Rgn. 97 In the passage shown in Figure 4, the three common pes between Rgn.o and Rgn.3 (that is pes 3, 7 and B) are sustained in staves 3, 5 and 6 during the first modulation of the passage. Common tones sustained across the boundary between regions are labelled as C.T. (common tone) in Figure 4. Although non-sustained pitch classes shared by adjacent regions are not labelled in Figure 4, they also play an important modulatory role. Since all common tones between regions form members of SC [048], this SC becomes an important sonority during close modulation. Common tones sustained by individual parts are not a requirement for close modulations; if they are stressed in Figure 4, it is only to illustrate the closeness (in terms of not moving too far away) of this kind of modulation. Since each pitch-class region has only 6 different tones and 3 of them will always be kept invariant during close modulation (even if they do not appear in the same voice), it will also be common to find, within one or more voices, two or more tones that belong to both regions acting as a bridge during the modulation (see for example the last pes of the quintuplet in the second violin in m.60, that is pes B and 3, followed by pes 7 and 3 in the first beat of m. 61). Distant modulation is the result of moving within regions that do not share any common tone (thus forming an aggregate), that is either from Rgn.o to Rgn.2 (or vice versa), or from Rgn.i to Rgn.3 (or vice versa) (see Figure 3). An example of distant modulation is shown in Figure 5 in a six-part reduction from the actual passage (in this case modulation is achieved through canonic imitation). 98 Figure 5. Distant Modulation Staff 1 Staff 2 Staff 3 Staff 4 Staff 5 Staff 6 Rgn. 56 -4i Staff 1 Staff 2 pp Rgn. Staff 3 P P Staff 4 Staff 5 Staff 6 Rgn.2 99 Two or more pitch regions are frequently used simultaneously. This procedure (which I call a multi-region) includes harmonic and/or melodic intervals that are not available within single pitch-class regions. Since the interval-class vector (V) for SC [014589] (the SC of the four pitch-class regions) is V=[303630], each region contains 3 different minor seconds or major sevenths (ic 1); 3 different minor thirds or major sixths (ic 3); 6 different major thirds or minor sixths (ic 4); 3 different perfect fourths or perfect fifths (ic 5); but no major seconds or minor sevenths (ic 2) and no augmented fourths or diminished fifths (ic 6). Multi-region technique is not the only available means of accessing melodic or harmonic ics 2 and 6; a simple modulation between single pitch-class regions might be sufficient, as in Figure 4, mm.60-61, in which pc 0 in the first violin (the last note of m. 60) moves to pc 2 (that is by means of ic 2), while pc 0 on staff 4 (the last note of m. 60) moves to pc 6 (that is by means of ic 6). A staged modulation between single regions, like the one illustrated in Figure 5, represents a short multi-region passage in which even harmonic ics 2 and 6 are available. For example, pc 4 in staff 2, mm. 55 and 56, forms a harmonic ic 6 with pc A—the first sustained note in the individual Rgn.3 canonic entrances— in the other staves, while at the same time pc 0 in staff 3 forms a harmonic ic 2 with the same multi-voiced appearance of pc A. Figure 6 shows the different SC [048] common-tone relations between the four pitch-class regions. 100 Figure 6. SC [048] Common tones R2: Ri: |E G# C| C# F A C# F A | D Gb Bb| R0: I E G# d R3: D# G B D# G B 1 D Gb Bb1 We can see in Figure 6 that regions 0 and 1 share a E-G#-C trichord; regions 1 and 2 are connected by means of C#-F-A; regions 2 and 3 are connected by means of D-Gb-Bb; and regions 0 and 3 share D#-G-B. These relationships are exploited at the beginning of a 16-measure multi-region passage shown in Figure 7. In mm. 153-154, a Rgn.0-Rgn.3 multi-region is shared between the piano and the xylophone. Some of the notes of the Rgn.0-Rgn.3 multi-region are doubled in staves 1 through 3 (Bb, Gb, D) and staves 4 through 6 (C, E, G#), and these representatives of SC [048] form a Gb-Ab-Bb-C-D-E whole-tone collection. In m. 155 a minor-second melodic movement in the individual parts of staves 1 through 6 incorporates pes C#-F-A to create Rgn^ (staves 4-6), Rgn.2 (staves1-3), and a Rgn.2-Rgn.i multi-region (pes C#-F-A represent the common tones between regions 1 and 2—see Figure 6). These three pes complete the aggregate and potentially provide access to all available harmonic and melodic ics in the passage. 101 (J = 7g) 153 | F Figure 7. Multi-Regions Staff 1 Staff 2 Staff 3 Staff 4 Staff 5 Staff 6 PP 7 I I 7 " Rgn.2 ft Rgn.i » Rgn.0l Pf. + Xyl. Rgn.3| Staff 1 Staff 2 Staff 3 Staff 4 Staff 5 Staff 6 Pf. + Xyl. l mfsubito mfsubito mfsubito mfsubito Rgn. Rgn.! Rgn.0 Rgn.3 102 Another important use of multi-regions is that of prolonging a specific pitch-region sonority, in the case of Figure 8, a single chord. Figure 8. Climactic Chord of Primer Ensamble The chord of Figure 8 represents the climactic point of the second section of the piece (Primer ensamble). It is a very tense chord, formed by the 6 tones of Rgn.-i, that spreads harmonically through 4 octaves by means of an inner major seventh-perfect fourth symmetric structure. Figure 9 shows how the multi-regions appear in the form of grace notes that propel the expansion of the Rgn.rchord for another eleven measures (only the first measures are shown in the orchestrally reduced version of Figure 9). 103 104 The pitch continuum is also used in the piece in conjunction with the four-region pitch-class system, as shown in Figure 10. In Figure 10 a) the two violins, integrated as a mega-instrument (see the Formal Principles and Orchestration sections) make use of the pitch continuum by means of their glissandi and microtones. In Figure 10 b) both the two violins (megaviolin) and the two flutes (megaflute) make use of the pitch continuum. It is important, however, to note that the pitch continuum in this piece is always used within the boundaries of the four-region system. The passage in Figure 10 a) projects pes from Rgn.i; the endpoints of glissandi, A, C, and Db uniquely determine that region, and cannot all belong to any other single region. Figure 10. Use of Pitch Continuum Mg.vl gliss. continuo Mg.vl. VI. VI. 2 *5= 25 ^ ^ ^ gliss. continuo gliss. continuo gliss. continuo gliss. continuo Mg.vl. vi.: 27 poco pocopp subito P o c o sulla tastiera poco ppsubito poco poco 105 On Figure 10 b) boxes enclose glissandi and quarter-tone shifts that project Rgn.3 unambiguously. Other regions are similarly represented (often only partially) by glissandi and quarter-tone shifts elsewhere on the Figure, b) (J = *w) m. 295 296 poco 297 298 Mega-FI. Fl. 1 Fl. 2 VI. 1 tr<* Mega-VI. m.o. , VI. 2 f V f p gliss. continuo gliss. continuo Rgn.3 106 c) Influences Boulez's methods of pitch organization, especially those used in Derive (1984), for flute, clarinet, violin, cello, vibraphone and piano, are an important model for this piece. In Derive (as in Repons and Messagesquisse), the pitch material is organized in a six-tone series derived from Paul Sacher's last name, as shown in Figure 11. (2) Incidentally, the pitch material used in Musica para dos megainstrumentos y grupo de camara is also hexachordal (see Figure 2). Figure 11. Sacher's Series Unordered pitch intervals: 6 3 1 5 2 S A C H E R The series in Derive is then rotated and transposed to begin on Eb to create a system of six different chords (see Figure 12) that are used in the piece as regions, in a way similar to that described in the Pitch Structure section. (3) Figure 12. Chord System in Derive Chord 1 Chord 2 Chord 3 Chord 4 Chord 5 Chord 6 107 There are important differences, however, in the way pitch material is manipulated in the two works. In Boulez's piece the regions are "fixed in pitch-space." That is, the individual pitches of each chord have a fixed register. Whereas in Musica... regions are pitch-class oriented, and individual pitches are not assigned to a specific register. Unlike the pitch-class material used in Musica..., which emphasizes the use of SC [014] (see Figure 2), the Sacher series in Derive is very diverse; each one of its adjacent intervals is different, as shown in Figure 11. The six-region chordal system of Derive controls all other musical parameters (especially in the second part of the piece, mm. 27-54) such as form, instrumentation, tempi, dynamic markings, pulse and rhythm. Although the four pitch regions have an important impact over the other parameters, no such post-serial techniques are used in Musica... . Another influence of Derive is the use of grace-note groups that are to be played on the beat. These grace-note groups have a defined attack point, whereas their release point remains undefined (see the Rhythmic Organization section). The use of grace-note groups in Musica... is exemplified in Figures 4, 5, and 9. Musica... , as most of the works I have composed in the last five years, has been also influenced by Donatoni's virtuosic style, and his use of musical "gestures". di Orchestration There are two basic orchestrational ideas in the piece: 1) the two mega-instruments and 2) the chamber ensemble. A mega-instrument is composed by two single instruments of the same kind. An important function of the mega-instrument is that of expanding the technical 108 possibilities of the individual instruments that constitute it. This can be seen in Figure 13, in which the continuous shifts of timbre (natural sound, tongue-ram, lip pizz., frullato, and aeolian sound in the megaflute and arco, pizz., pizz. alia Bartok, strumming and harmonics in the megaviolin) could not be achieved by a single flute or violin at the speed required in the passage (note also the megaviolin chord in m. 264 that could not be played by a single violin). Figure 13. A Passage for Mega-instruments Rgn.2 Rgn-o R9 n -o 109 Note: Pitch-class regions on Figure 13 are defined by specific modes of sound production, (see p. 110) therefore regions can be represented by only one pitch class in the Figure. Even the limited contrapuntal capabilities of the violin are developed in the megaviolin (see Figure 10). The mega-instrument, in fact, does not only enhance the technical possibilities of the individual instruments that constitute it, but also creates new possibilities. Thus a monophonic instrument like the flute can become a polyphonic mega-instrument. There is a potential risk in the expansion of the technical possibilities of a mega-instrument, since its specific characteristics (based as much in its capabilities as in its limitations) could be nullified, and at a certain point the mega-instrument could be transformed in a two-instrument texture (especially when two monophonic instruments become a polyphonic mega-instrument). In order to prevent this from happening, the mega-instruments have been assigned, in difficult 110 passages, a strictly codified range of action that imposes on them a controlled behaviour (and an instrumental personality). In the second interlude (see the Formal Principles section), for example, the two mega-instruments move within the following range: Megaviolin: normal sound (with bow), spiccato and trills are used with Rgn.3; harmonics, pizz. alia Bartok and tremolo =Rgn.n; pizz. , strumming pizz. and glissando = Rgn.2. Megaflute: normal sound = Rgn.,; tongue-ram and lip pizz. = Rgn.2; frullato and aeolian sound = Rgn.n. This leaves both mega-instruments with a pitch region of their own when playing with ordinary sound (Rgn. 3 is used only by the megaviolin and Rgn^ is used only by the megaflute), while keeping Rgn.n and Rgn.2 as a common zone when using different timbral techniques (see Figures 10b and 13). Dialogue passages between individual instruments that form part of the same mega-instrument are also rejected, since they enhance the traditional two-instrument relationship. When the two flutes and two violins appear in the First and Second chamber ensemble sections, they behave like individual instruments that form part of the larger ensemble, whereas in the Postlude they are treated as mega-instruments opposing the ensemble. A passage of the First ensemble section is shown in Figure 4. In this passage, the two violins are engaged in a free imitative dialogue. 111 e) Rhythmic Organization and Tempi There is not a specific rhythmic system in the piece. There is a distinction, however, between strictly controlled durational values, and partially controlled durational values. Controlled durational values correspond to traditional fixed rhythmic values like those found in Figures 7, 10a and 13 (i.e. eighth notes, triplets, quintuplets, etc.). Partially controlled durational values are created by attaching grace note groups to fixed rhythmic values (see Figures 4, 5 and 9). Since grace notes in this piece are to be played on the beat, the attack point of the grace note groups is always controlled, whereas both the attack point and total duration of the notes to which they are attached is determined by the number of its grace notes and the speed of performance on the instrument. In Figure 9, measure 71, for example, the first C# in staff 6 is a half note. However, the exact attack point and total duration of this half note are determined by its five-note grace note group. The interaction of controlled rhythmic values and partially controlled rhythmic values creates a complex rhythmic texture whose individual parts are not necessarily demanding for the performers. Figure 14. Table of Tempi -Prelude (megaviolin) quarter note=108 -First ensemble (chamber ensemble) quarter note=76 -First interlude (megaflute) quarter note=108 -Second ensemble (chamber ensemble) quarter note=76 -Second interlude (megaviolin and megaflute) quarter note=108 -Postlude (megaviolin and megaflute with chamber ensemble) quarter note=92 112 We can see in Figure 14 that tempi are arranged according to specific instrumental relationships, that is the mega-instrument sections are always assigned the tempo of a quarter note=108, while the ensemble sections have been assigned the tempo of a quarter note=76 (as mentioned In the Formal Principles section, the mega-instrument sections are more virtuosic than the ensemble sections). Since the Postlude is the only section to use both the mega-instruments and the chamber ensemble, its tempo is set halfway between quarter note=76 and quarter note=108, that is quarter note=92 (although the Postlude contains a fifteen-second passage marked // Piu presto possibile in m. 379). f) Style The piece could be defined as atonal or without pitch centers. It is characterized by an interaction of the tempered system and the pitch continuum (microtones and glissandi). Another stylistic aspect of the piece is its use of extended instrumental techniques for the mega-instruments, in addition to traditional instrumental techniques in the ensemble. I would also like to point out that the appearance of passages in which the pitch structure has been reduced to the use of a single note, such as those found in mm. 1-9, 305-322, and 399-431 (see score), are common in the music I have written during the last 10 years or so. The purpose of these passages is to emphasize color (timbre), density, instrumentation (use of double stops in the violins and extended instrumental techniques in general), and/or volume, by confining the pitch parameter to the background. The piece, in fact, begins and ends with a unison section, suggesting a circular form as well as the metaphor of the unison as 113 nothingness, or representing the original and final void. From an aesthetical perspective, Musica... could be defined as a progressive work, in its search for new means of expression and avoidance of nostalgic reminiscences of the past (including the avant-garde past). I strongly believe that music should undergo a process of constant renewal, in order to remain healthy. In this sense, the most innovative aspect of the piece is perhaps its proposition of a new aural approach to instrumentation, through the use of the mega-instruments. In my view, the problem with some avant-garde composers (and sometimes even "schools") of this century is that their precise and refined intellectual approach to music is not always translated to the field of perception with effectiveness (in terms of being aurally perceived), causing their music to be generally perceived as mere "chaos". My main aesthetic concern is that music should always be aurally intelligible (and not just intellectually). In order to achieve that, without resorting to techniques such as tonality, triadic chord organization, etc., which I consider historically obsolete, musical processes and goals must be clearly established; contrasts must be carefully wrought; symmetry (i.e. points of reference) must be provided through the interaction of musical gestures; and the pitch universe of the piece must be restricted, so its presence and manipulation are clearly perceived. These issues represented my main aesthetical concern during the composition of the piece. a) Sense in which the Work is an Original Contribution The piece is an original contribution in its concept and use of the mega-instruments. Although two instruments are commonly used as one in traditional chamber and orchestral works, both the term mega-instrument, as defined in this 114 document, and the formal structure of the piece, based on the alternation and interaction of the two mega-instruments and the ensemble, are original features. Musica... is the result of a personal search for expression and structural coherence that is characteristic of the works that I have been composing during the last five years or so. In Musica... the carefully designed pitch structure, saturated by SC [014], interacts with the use of the pitch continuum and with the unison as a source of instrumental color and textural exploration, creating a universe of its own. Musica... represents my first attempt in adapting all these features coherently to the structural requirements of a large multi-movement work. In this sense it was a challenging project that offered an invaluable opportunity for language expansion and personal growth. 115 Notes (1) Regarding the inversion invariance vector, see Morris, Robert D. Class Notes for Atonal Music Theory (Lebanon, New Hampshire: Frog Peak Music, 1991), pp. 27-29. (2) Paul Sacher (b. Basle, 1906) is a Swiss conductor, founder of the Basle Chamber Orchestra, who has commissioned works from distinguished composers, including Bartok, Henze, Hindemith, Honegger, Ibert, Krenek, Lutoslawski, Strauss, and Stravinsky. On the compositional techniques used by Boulez in Derive, see Bradshaw, Susan, "The Instrumental and Vocal Music," Pierre Boulez, a Symposium, ed. William Glock (London: Eulenburg Books, 1986), pp. 221-222, and p. 226. (3) Bradshaw, Susan, "The Instrumental and Vocal Music," Pierre Boulez, a Symposium, ed. William Glock (London: Eulenburg Books, 1986), pp. 222-223. 116 Bibliography Babbitt, Milton. "Some Aspects of Twelve-Tone Composition," The Score and I.M.A. Magazine 12 (1955): 53-61. Babbitt, Milton. "Twelve-Tone Invariants as Compositional Determinants," Musical Quarterly 46 (1960): 246-59. Babbitt, Milton. "Since Schoenberg," Perspectives of New Music 12/1 and 12/2 (double issue, 1973-74): 3-28. Forte, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973. Gamer, Carlton. "Some Combinatorial Resources of Equal-Tempered Systems," Journal of Music Theory 11/1 (1967): 32-59. Gilbert, Steven. "An Introduction to Trichordal Analysis," Journal of Music Theory 18/2 (1974): 338-62. Glock, William, ed. Pierre Boulez, a Symposium. London: Eulenburg Books, 1986. Griffiths, Paul. Boulez. London: Oxford University Press, 1978. Howe, Hubert S. "Some Combinational Properties of Pitch Structures," Perspectives of New Music 4/1 (1965): 45-61. Lewin, David. "The Intervallic Content of a Collection of Notes," Journal of Music Theory, 4/1 (1960): 98-101. Ligeti, Gyorgy. "Pierre Boulez," Die Reihe 4 (1960): 36-62. Jameux, Dominique. Pierre Boulez. Trans. Susan Bradshaw. London: Faber and Faber, 1991. Martino, Donald. "The Source Set and its Aggregate Formations," Journal of Music Theory 5/2 (1961): 224-73. 117 Morris, Robert D. "Generalizing Rotational Arrays," Journal of Music Theory 32/1 (1988): 75-132. Morris, Robert D. Class Notes for Atonal Music Theory. Lebanon, New Hampshire: Frog Peak Music, 1991. Rahn, John. Basic Atonal Theory. New York: Longman, 1980. Starr, Daniel and Morris, Robert. "A General Theory of Combinatoriality and the Aggregate," Perspectives of New Music 16/1 (1977): 3-35 and 16/2 (1977): 50-84. Straus, Joseph N. Introduction to Post-Tonal Theory. Englewood Cliffs, N.J.: Prentice Hall, 1990. 

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