AUTOBIOGRAPHICAL
Born in Taichung, Taiwan, Wei-Chieh Lin’s music has been performed at venues including the Gaudeamus Muziekweek, Centre Pompidou in Paris, Avery Fisher Hall and Alice Tully Hall, Peter Jay Sharp Theater at Lincoln Center, Weill Recital Hall at Carnegie Hall, Jordan Hall in Boston, Yallow Barn, Nasher Sculpture Center, and the National Concert Halls in Taiwan. Among the ensembles that have performed or commissioned his works are the, Ensemble Intercontemporain, Orchestre Philharmonique de Radio France, National Taiwan Symphony Orchestra, Taipei Philharmonic Orchestra, Le Nouvel Ensemble Moderne, Insomnio Ensemble, Alarm Will Sound, Cadillac moon Ensemble, Formosa Quartet, members of Klangforum Wien, Xasax Ensemble, Makrokosmos Ensemble, The New Juilliard Ensemble, the Juilliard Orchestra, members of eighth blackbird ensemble, DZ4 Wind Quartet, the Formosa Performing Arts Association, the Hudson Symphony Orchetra, the New York Asian Symphony Orchestra, the New Asia Chamber Music Society, and the New York Classical Players Ensemble. Mr. Lin also has an upcoming performance with the Asko/Schoenberg Ensemble.
Mr. Lin’s compositions have received awards including the Honorable Mention of the Gaudeamus Muziek Prize of 2011, selection for the 2012 International Composer Pyramid Competition, two ASCAP Morton Gould Young Composer Awards, the 2009 and 2010 National Symphony Orchestra of Taiwan Composition Competitions, the 2010, 2011, and 2012 National Taiwan Symphony Commissioning Award, and the Palmer Dixon Award. Mr. Lin has participated in music festivals including the Aspen Music Festival, The Wellesley Composers Conference and Chamber Music Center, MusicX Festival, Académie musicale de Villecroze, Domain Forget Asian Composers League Music Festival (Taiwan), active participant in the Manifeste/Acanthes@Ircam, Voix Nouvelles Royaumont, and the 2013 Mizzou International Festival.
Mr. Lin completed his BM, MM, and DMA with scholarship at The Juilliard School under the tutelage of Milton Babbitt.
ACKNOWLEDGEMENT
I would like to thank the Paul Sacher Foundation in Basel, Switzerland for allowing me to access and reproduce the sketches and drafts of Dérive 2, plus all the relevant research materials in the Pierre Boulez Collection. I also would like to thank the staff of the Foundation for their support, especially to Dr. Robert Piencikowski for his generosity and assistance in understanding Boulez’s sketches, as well as his invaluable knowledge on Boulez’s music in general.
I also would like to thank the Universal Edition for granting me permission to use passages from Dérive 2 in my examples, as well as providing information regarding the publications and the performances of Dérive 2. A special gratitude also goes to Yu-Ting Hung for assisting the preparation of all the musical examples and her encouragement throughout the whole process of completing this document.
I must thank the Doctoral Committee and the faculty members at Juilliard for their guidance over the years. I particularly like to thank and acknowledge my advisor, Jonathan Dawe, for his invaluable advice and countless hours of support not only through the process of this document, but also for the years I have known him.
A special tribute must be paid to my teacher, Milton Babbitt, from whom I have learned so much over the years, and there is no word for me to express my deepest gratitude for everything he had given me.
Finally, to my parents, whose support, love, and all they have done for me is beyond anything I could have asked for. I owe an enormous debt to them.
CHAPTER I.
1.1.
1.2.
1.3.
1.4.
CHAPTER II. FORMAL STRUCTURE
2.1.
CHAPTER III.
3.1.
LIST OF FIGURES AND MUSIC EXAMPLES
Ex. 1.4.15. Ligeti Piano Concerto – String pizzicatos
Ex. 1.4.17. The polyrhythmic ratio between the two periodicities
Ex. 1.4.18. 56:45 polyrhythm in A Celebration of Some 100x150 Notes
Ex. 1.4.19. A reduction of the opening measures of sur Incises 66
Chapter 2.1
Fig. 2.1.1. Formal and instrumental outline of Le Marteau san maître
Chapter 3.1
Ex. 3.1.1. The opening viola line up to the first double barline
Ex. 3.1.2. The opening viola line partitioned into 24 trichords, labeled with set-classes
70
74
75
Ex. 3.1.3. Trichords in the woodwinds and strings in the opening measures up to the first double barline (boxed numbers refer to trichords in ex. 3.3.2) 78-80
Ex. 3.1.4. Opening horn part, along with cello, cor anglais, and bassoon
Ex. 3.1.5. Trichords are combined to form 6-element collection
Ex. 3.1.6. Trichords are combined to form 9-element collections
Ex. 3.1.7. Trichords are combined to form 12-element collections
Ex. 3.1.8. Ascending order for the combined 6, 9, and 12-element collections
81
82
83
83
84
Ex. 3.1.9. Horn part starting from R5 to R13 87
Ex. 3.1.10. A realization of the 6-element collections from R5 to R6 -3 89-90
Ex. 3.1.11. A realization of the 6-element collections from R6 -3 to R8 93-94
Ex. 3.1.12. A realization of the 6-element collections from R8 to R9 -3 96-97
Ex. 3.1.13. A realization of the 6-element collections from R9 -3 to R9-4 98
Ex. 3.1.14. A realization of the 6-element collections from 2 -R11 to R13 99-103
Ex. 3.1.15. A realization of the 9-element collections from R14 to R16 106-109
Ex. 3.1.16. The opening all-trichordal hexachord 111
Ex. 3.1.17. A reduction of the simultaneities in the opening measures 111-117
Chapter 3.2
Ex. 3.1.1. The opening viola line up to the first double barline 74
Ex. 3.1.2. The opening viola line partitioned into 24 trichords, labeled with set-classes 75
Ex. 3.1.3. Trichords in the woodwinds and strings in the opening measures up t o the first double barline (boxed numbers refer to trichords in ex. 3.3.2) 78-80
Ex. 3.1.4. Opening horn part, along with cello, cor anglais, and bassoon 81
Ex. 3.1.5. Trichords are combined to form 6-element collection 82
Ex. 3.1.6. Trichords are combined to form 9-element collections 83
Ex. 3.1.7. Trichords are combined to form 12-element collections 83
Ex. 3.1.8. Ascending order for the combined 6, 9, and 12-element collections 84
Ex. 3.1.9. Horn part starting from R5 to R13 87
Ex. 3.1.10. A realization of the 6-element collections from R5 to R6 -3 89-90
Ex. 3.1.11. A realization of the 6-element collections from R6 -3 to R8 93-94
Ex. 3.1.12. A realization of the 6-element collections from R8 to R9 -3 96-97
Ex. 3.1.13. A realization of the 6-element collections from R9-3 to R9-4 98
Ex. 3.1.14. A realization of the 6-element collections from 2 -R11 to R13 99-103
Ex. 3.1.15. A realization of the 9-element collections from R14 to R16 106-109
Ex. 3.1.16. The opening all-trichordal hexachord 111
Ex. 3.1.17. A reduction of the simultaneities in the opening measures 111-117
Chapter 3.2
Ex. 3.2.1. Rhythmic pattern of 2-1-3-1-1-2-1 122
Ex. 3.2.2. The opening viola line re-barred under the pattern of 2-1-3-1-1-2-1 122-123
Ex. 3.2.3. The opening instrumental parts re-barred under the rhythmic pattern of 2-1-3-1-1-2-1 123-126
Ex. 3.2.4. Rhythmic cycle of 2-1-3-1-1-2-1 articulated by horn and other instruments 127-128
Ex. 3.2.5. Partitioning the rhythmic pattern of 2-1-3-1-1-2-1 with E-n-n-n-E-E-n-E-E-n-n 129
Fig. 3.2.6. Instrumental assignments according to the E -n-n-n-E-E-n-E-E-n-n partitioning 129
Ex. 3.2.7. Opening measures re-barred according to the instrumental partitioning of E -n-n-n-E-E -n-E-E-n-n 131-133
Ex. 3.2.8. Periodicities of the resonant instruments in alignment with the rhythmic pattern of 2-1-3-1-1-2-1 and the pattern of E-n-n-n-E-E-n-E-E-n-n 135-138
Fig. 3.2.9. Periodicities of Section A 140
Fig. 3.2.10. Periodicities of Section B 143
Fig. 3.2.11. Instrumental and Periodicity assignment in Section B 143
Ex. 3.2.12. The first 3 cycles of EN with annotated rhythmic patterns in Section B 144-145
Ex. 3.2.13. The next 2.5 cycles of EN with annotated rhythmic patterns in Section B 146-147
Ex. 3.2.14. The next 2 cycles of EN with annotated rhythmic patterns in Section B 148-149
Ex. 3.2.15. The next 1.5 cycles of EN with annotated rhythmic patterns in Section B 150
Fig. 3.2.16. Dynamic scheme of Section B 151-152
Fig. 3.2.17. Periodicities of Section C 153
Ex. 3.2.18. Rhythmic transformation in Section C 153
Ex. 3.2.19. Horn part with annotated periodicities in Section C 154
Ex. 3.2.20. Annotated periodicities in Section C 155-159
Ex. 3.2.21. Periodicities of Section L 161
Fig. 3.2.22. Instrumental assignment in Section L 161
Ex. 3.2.23. Annotated periodicities in Section L 162-165
Chapter 3.3
Fig. 3.3.1. Formal Structure of Dérive 2 168-171
Fig. 3.3.2. The periodicity cycle of 3 x 4 x 7 172
Fig. 3.3.3. The periodicity cycle of 3 x 4 x 7 173
Ex. 3.3.4. The form of Dérive 2, with the 3 x 4 x 7 periodicity and the interruptions 174-175
Ex. 3.3.5. Instrumental assignment in Coda I 179
Fig. 3.3.6. Dynamic Scheme in the first half of Coda I from R225 to R231 179
Fig. 3.3.7. Dynamic Scheme in the second half of Coda I from R231 to R234 179
Fig. 3.3.8. Duration of phrases in Coda II 180
Ex. 3.3.9. The concluding measures of Dérive 2. 182-183
Ex. 3.3.10. Opening horn solo 185
Ex. 3.3.11. The first interruption 186
Ex. 3.3.12. The second interruption 187
Ex. 3.3.13. The fourth interruption 188
Ex. 3.3.14 SACHER pitch sequence 190
Ex. 3.3.15. Symmetrical pitch structure in the interrupting sections 191-195
Chapter 3.4
Ex. 3.4.1. Ending for the 1993 version 204-205
Ex. 3.4.2. Ending for the 2001 version 206-207
Ex. 3.4.3. Ending for the second 2001 version 208-209
Ex. 3.4.4. Ending for the 2002 version 210-213
Ex. 3.4.5. Ending for the 2004 and 2005 version 214-218
Ex. 3.4.6. Concluding measures in an earlier version of 2006 and 2007 (UE31940) 219-224
Ex. 3.4.7. Ending for the most current version 225-230
Ex. 3.4.8. Earlier version at R129 231
Ex. 3.4.9. Chronological history of Dérive 2 232-3
Excerpts from Dérive 2, reprinted by permission from Universal Edition.
Pierre Boulez „Dérive 2|für 11 Instrumente“
© Copyright 2006 by Universal Edition A.G., Wien/UE 32528
PROLOGUE
Dérive 2 (1988-2009) for 11 instruments by Pierre Boulez (1925-) is one of his longest works, second only to Pli selon pli: Portrait de Mallarmé (1957-62/83/89/2000).1
The current version of Dérive 2 lasts approximately 45-50 minutes, while Pli selon pli lasts about 65 minutes.2 Dérive 2 is written for the second largest chamber ensemble that Boulez has ever scored, rivaled only by Éclat (1965). 3 Dérive 2 marks an important departure from Boulez’s later works which are categorized into three genres. The first is works involving electronics (Dialogue de l’ombre double (1982/84/85) for clarinet and tape, Répons for 6 soloists, ensemble, computer sounds and live electronics, …explosantefixe…(1991/…), …explosante-fixe…Transitoire V (1991/1993), …explosantefixe…Transitoire VII (1991-93) for flute, various ensembles, and live electronics, and Anthèmes 2 (1997) for violin and live electronics). The second group consists of works for large orchestral forces (Répons, Notations I-IV, Notations VII for orchestra, revisions of Pli selon Pli for soprano and orchestra, and Boulez’s orchestration of Ravel’s Frontispice for orchestra). The third comprises solo instrumental works (Anthèmes (1991) for solo violin, Incises (1993-94/2001) for solo piano, and Une page d’éphéméride (2005) for solo piano).
Boulez’s return to a purely instrumental medium of mixed chamber ensemble in his late
1 This does not include the “unfinished” or “work -in-progress” pieces such as the Third Piano Sonata (1955-
2 Like most of Boulez’s works, it is uncertain whether Boulez plans to revise Dérive 2 in the future. The other two major late works, Répons and sur Incises (1996/98), last about 43 minutes and 38 minutes, respectively, in their latest versions.
3 Éclat is scored for 15 instruments: piano, celesta, harp, glockenspiel, vibraphone, mandolin, guitar, cimbalom, tubular bells, alto flute, cor anglais, trumpet, trombone, viola, and violoncello; though in the subtitle Boulez regards Éclat as “pour orchestra.”
years,4 a genre that had interested him throughout much of his earlier career, is significant, if not refreshing.5
Dérive 2 is scored for 11 instruments: cor anglais, clarinet in A, bassoon, violin, viola, violoncello, horn in F, vibraphone, marimba, harp, and piano.6 Its mixed instrumentation is quite rare in the chamber ensemble genre; however, it is typical of Boulez to employ a dichotomy in contrasting resonances between natural and artificial resonant instruments, exemplified in works such as Pli selon pli, Éclat, sur Incises, Répons, or even Le Marteau sans maître. 7 Moreover, the combination of and the fascination for the sound of piano, harp, vibraphone, and marimba can be found in many works throughout his œuvre.8 A characteristic in this scoring is that the four woodwind instruments are the only monophonic instruments in the whole ensemble (Boulez does not employ any
4 The only other mixed chamber ensemble work in recent years is sur Incises, scored for three pianos, three harps, and three percussionists. This instrumentation should not be considered as a mixed ensemble since Boulez typically groups these instruments together as a single unified force. There are also two lesser-known relatively recent chamber works, Initiale (1987/92) for brass ensemble and Petite Dérive – en echo (1998) for alto flute, clarinet, vibraphone, marimba, violin, and viola; though both works are quite short and have not been widely performed.
5 Some of the major mixed chamber ensemble works before 1988 are Le Marteau san maître (1953/57), Éclat, Pour le Dr. Kalmus (1969), … explosante-fixe… (1972-74), Dérive 1 (1984/86) for 6 instruments, and Mémoriale (… explosante-fixe…Originel) (1985) for 9 instruments.
6 This is the first time where Boulez prominently used cor anglais and bassoon in his chamber works two instruments that are less common in the chamber music repertoire, similar to his use of alto flute in Marteau. As for the other instruments in the ensemble, Boulez has either written solo works or works that prominently feature them. For example, clarinet in Domain (1961/68) and Dialogues de l’ombre double, violin in Anthèmes 1 & 2, viola in Marteau, violoncello in Messagesquisse (1976), and horn in Tombeau (1959/62/83) are works that all feature these instruments prominently. The scoring of Dérive 2 would normally be considered a large chamber ensemble, though it could arguably be categorized as a small chamber orchestra or a sinfonietta force, since the subtitle is particularly vague, as Boulez simply writes as “for 11 instruments.”
7 For Boulez, the natural resonant instruments are instruments where the resonance after the initial attack is not manufactured by the performer instruments such as piano, harp, guitar, vibraphone, marimba, and various percussion instruments. The artificial resonant instruments are ones where the performer needs to maintain the sustained sound after the initial attack such as all the string, woodwind, and brass instruments. Boulez will utilize this contrast in timbre, resonance, and sound production effectively in Dérive 2.
8 Works such as Pli selon pli (especially in Improvisation sur Mallarmé no. 1, 2, and 3), Éclat, Éclat/Multiples (1966-70), Répons, and especially sur Incises where these instruments are frequently grouped as a unified ensemble, and are featured prominently in these works as well.
multiphonics). This is comparable to his approach to the three string instruments, despite the fact that the strings are not limited to monody.9 Thus, the whole group is divided into seven melodic instruments (woodwinds and strings) against four harmonic and resonant instruments (piano, harp, and percussion). This is an important characteristic that Boulez utilizes in Dérive 2.
In comparison to Boulez’s other works, or even to most contemporary music, Dérive 2 is quite traditional in its approach to instrumental timbre: it does not employ any indeterminate-pitch percussion instruments, nor does Boulez explore indeterminatepitches from these traditional instruments. In addition, the three string instruments draw solely on conventional extended techniques (such as pizzicatos, snap pizzicatos, harmonics, jéte/thrown bow, con sordino, and a few instances of col legno and sul ponticello). In comparison to the rest of the ensemble, the string instruments produce the widest range of timbre differences; while the instrumental writing for the others is straightforward, as the rest of the ensemble does not employ extended techniques such as slap tongue, flutter-tongue, multiphonics, quarter-tones (as used in the earlier versions of Le Visage Nuptial (1947/52/89), or the quarter-toned harps in Improvisation III sur Mallarmé), harmonics in the piano (compare to the opening of Dérive 1 and sur Incises where the piano uses the sostenuto pedal with pressed keys in the lower register to create sympathetic resonances and overtones)10 , or any nonconventional modes of playing.
The instrumentation of Dérive 2 naturally suggests several possible pairings based on timbre: a trio of strings is paired with a trio of woodwinds, a duet of piano and harp is
9 Excepting the Coda (rehearsal number 225) and a few other instances, the strings rarely play double-stops.
10 This of course is not the case for the use of the piano resonance (pedal effects) seen in the very opening measures of Dérive 2, where the pedal “catches” the resonances after the attack of the keys.
coupled with a duet of vibraphone and marimba, while the horn acts as a mediator that blends all the timbres together.11 An alternative arrangement based on range offers another possible combination, with bassoon, violoncello, viola, and horn covering the lower register; clarinet, cor anglais, violin, and vibraphone covering the upper register; and piano, harp, and marimba covering the whole range from low to high. This registral distribution is significant since the range of these instruments (especially the woodwind section) tends to have a richer sonority in the mid-low register, specifically with the use of clarinet in A and cor anglais instead of oboe; while piano, violin and harp are relatively speaking the only instruments that can cover the upper end of the registral spectrum. Thus with these registral and timbral constraints, the majority of the work is fixed within the mid-low register. As the work unfolds and approaches the midpoint, the register of the full ensemble expands to its fullest range, reaching the highest possible register at rehearsal numbers 114 and 129, and the lowest possible register at the end of rehearsal number 166 (where the midpoint section also concludes.) As the work retraces its steps and moves toward the Coda at rehearsal number 226, the registral span likewise slowly retracts back to the mid-low register.12 With this set of instruments, Dérive 2 offers a unique sonority of colors and timbres, and the intentional mixture of instrumental forces will serve Boulez to create a wide variety of textural variations, sonic explorations, as well as unconventional instrumental mixtures all of which become vital aspects of Dérive 2.
11 This is obviously Boulez’s intension, since his sketches, drafts, and the engraved score all list the instruments in these particular combinations (woodwinds, strings, horn, percussion, harp, and piano) instead of the customary orchestral ordering.
12 This registral expansion and retraction reinforces the symmetrical structure of the work, an essential feature which will be discussed in chapter 3. The Coda (starting with rehearsal number 225) does not fall into this registral outline.
Dérive 2 is dedicated to Elliott Carter for his 80th birthday anniversary in 1988.13 It was premièred on June 21, 1990 at the Grande Salle, Conservatorio di musica Giuseppe Verdi di Milano, conducted by the composer with the Ensemble Intercontemporain.14
Dérive 2, similarly to most of Boulez’s works, has gone through numerous revisions and extensions throughout the intervening years.15 Boulez began the work in 1988, and the latest primary version was completed in 2006, published by Universal Edition (UE 32528), while Boulez continued to make minor adjustments and revisions to that edition until 2011.16 The two available commercial recordings of the piece, one is of an earlier edition and was made by Boulez conducting the Ensemble Intercontemporain, released in 2005, while the other was recorded in 2011, and released in 2012.17 The former recording runs about twenty-four and half minutes, while the latter runs about fifty-one minutes.
One of the more recent performances, also given by the composer and the Ensemble
13 The majority of Boulez’s works have dedicatees: Le Visage Nuptial was originally dedicated to Messiaen, the First Piano Sonata (1946) was originally dedicated to René Leibowitz; Le Marteau sans maître is dedicated to Hans Rosbaud; Tombeau (the last movement of Pli selon pli) was a tribute to Prince Max Egon zu Fürstenberg; the initial version of …explosante-fixe… (1971) was written as a memorial to Stravinsky; Mémoriale (… explosante-fixe… Originel) was dedicated to flautist Lawrence Beauregard; Rituel in memoriam Bruno Maderna (1975) is dedicated to Bruno Maderna; Messagesquisse (1976) and sur Incises are dedicated to Paul Sacher; Dérive 1 (1984) is dedicated to Sir William Glock; Dialogues de l’ombre double was written for Luciano Berio’s 60th birthday; Répons and Anthèmes are dedicated to Alfred Schlee; Fanfare (1992) was written for Sir Georg Solti’s 80th birthday; Derive 3 is dedicated to Michael Gielen, and Petit Dérive – en echo was dedicated to Elliott Carter’s 90th birthday. Consequently, Carter has also dedicated works to Boulez: Esprit Rude/Esprit Doux (1985) was written for Boulez’s 60 th birthday, Esprit Rude/Esprit Doux II (1995) was written for Boulez’s 70th birthday, Retrouvailles (2000) was written for Boulez’s 75 th birthday, and Réflexions (2005) was written for Boulez’s 80 th birthday.
14 On the same program, Boulez also conducted Octandre by Edgard Varèse, Boulez’s own Mémoriale (…explosante-fix e…originel) and Dérive 1, Tema by Franco Donatoni, Jalons by Iannis Xenakis, and Oiseaux exotiques by Olivier Messiaen. See Susanne Galaise, “Les écrits et la carrière de Pierre Boulez: catalogue et chronologie” (PhD diss., Université de Montréal, 2001).
15 The history of revisions and extensions of Dérive 2 will be documented in chapter 3.
16 Pierre Boulez, Dérive 2 pour 11 instruments 1988/2006 (Vienna: Universal Edition (UE 32528), 2006).
17 Pierre Boulez, Le Marteau sans maître, Dérive 1 & 2, Ensemble InterContemporain dir. Pierre Boulez, Deutsche Grammophon CD DDD 0289 477 5327 8 GH (20/21 Series), 2005. This recording was recorded at Ircam in Paris in September of 2002, but was not published until February of 2005. This recording used the 2002 edition of Dérive 2. A more recent recording by the Ensemble Orchestral Contemporain, conducted by Daniel Kawka, was released by Naïve Records in March of 2012.
Intercontemporain in 2010, is about 45 minutes, almost double the length of the first commercially available recording.18 Curiously, both performances that took place in 1998 and 2001 only lasted about 7 minutes.19 Between 1988 and 2011 not only has Boulez drastically expanded the work, he has written and revised several other pieces as well.20 In this regard, Dérive 2 represents a significant work, a magnum opus in Boulez’s catalogue as he continuously expanded it for more than 20 years, longer than any of his previous revisions of works.21
Dérive 2 bears little or no relation to Dérive 1. 22 The only connection between the two is that both works derived materials from Répons. 23 Yet, unlike Dérive 1 where the
18 This performance was given by Pierre Boulez with the Ensemble Intercontemporain at the Cité de la musique in Paris on December 3rd, 2010.
19 Both performances were given by Pierre Boulez with the Ensemble Intercontemporain at the Cité de la musique in Paris on October 28th, 1998 and March 17th, 2001 respectively.
20 Between 1988 and 2010, Boulez had written and revised several works: in 1988, revisions were made to Livre pour cordes and Figures, Doubles, Prismses; in 1989, a third version was made to Don (from Pli selon pli); from 1991 to 1992, Anthèmes was composed; in 1992, Fanfare was composed; from 1993 and 1994, …explosante-fixe… was composed and revised in various versions and extensions, and the first version of Incises was written; in 1995, Dialogue di l’ombre double for bassoon and electronics was transcribed; in 1996, the first version of sur Incises was composed; in 1997, Anthèmes 2 and Notation VII were composed; in 1998, revision was made to sur Incises; in 2001, revision was made to Incises and Messagesquisse was transcribed for violas; and in 2005, Une page d’éphéméride was composed This list does not include the continuous revisions he has made on Dérive 2 during this time span. Th is chronology is important since these works share a close connection to Dérive 2, and many ideas that were formed in the later stages of Dérive 2 are indirectly informed by and seeded within these works. Moreover, what makes Dérive 2 unique among the late works is that it is the only work where the pitch and temporal material is constructed anew individually instead of reusing materials from an earlier work. The later works are predominately based on either the 7-note series taken from …explosante-fixe… , or based on the SACHER series. See Galaise for a detailed chronology of Boulez’s works during this time span. Galaise, “Les écrits et la carrière de Pierre Boulez: catalogue et chronologie.”
21 One can argue that the intervening number of years Boulez has worked on Notations is far greater, since he wrote the piano version of Notations in 1945, and the orchestra version starting in 1978 up to the present day. Another case can be argued for Pli selon pli, since all the movements were written or revised sporadically from 1957 to 2000.
22 Dérive 1 (1984) was written for the occasion of Sir William Glock’s retirement, and was premiered on January 31st, 1985, conducted by Oliver Knussen with the London Sinfonietta.
23 “It’s a tree which gives another tree which is another tree. Therefore, the title Dérive. Derive 1, for instance, is from Répons. Part of the material for Répons I did not use, actually, and that became the material for Dérive 1. And Dérive 2 is from studies I did for the part of Répons which is still not written.” Andrew Carvin and Joshua Cody, “Pierre Boulez: An Interview,” Paris New Music Review (November 1993) http://www.paristranstlantic.com/magazine/interviews/boulez.html (accessed October 18, 2011).
principal pitch material (the SACHER series based on name of its dedicatee: Eb, A, C, B, E, D) is shared with Répons (Dérive 1 is built exclusively on the SACHER chord and its transposed rotational array), Dérive 2 is constructed on completely new and independent material, a rarity for Boulez.24 The two works also do not share any rhythmic or temporal scheme. Moreover, the two works are not considered or performed as a cycle, unlike several other works that share the same title in Boulez's catalogue.25 The instrumentation between the two works is also entirely different: Dérive 1 is scored only for a Pierrot ensemble of six instruments (flute, clarinet in A, violin, violoncello, vibraphone and piano), lasting about 8 minutes. On the other hand, another sibling to these two works, Dérive 3, is an incomplete piece that originated as Initiale (1987) for brass ensemble.26 It was then expanded with an added percussion section to become Fanfare in 199227, which was then expanded again and retitled as Dérive 3 in 1997.28 Dérive 3 offers very little resemblance to
24 Boulez has a history of reusing materials from work to work, or using the same series or collection in a number of works. A good example is the 7 -note series that first appeared in …explosante-fixe… (1971), which is used again in Rituel, …explosante-fixe for MIDI flute, ensemble and live electronics (1991/…), Mémoriale (… explosante-fixe…Originel), Anthèmes 1, and Anthèmes 2. The already mentioned SACHER series is employed not only in Répons and Dérive 1, but in fact began in Messagesquisse (1976) where the series is derived from the last name of the dedicatee (Paul Sacher), and subsequently, used again in Incises and sur Incises, the latter piece also dedicated to Paul Sacher. Though there are instances of the SACHER chord in Dérive 2, it is not as importance and visible as in the other works, and the underlying pitch construction in Dérive 2 has very little to do with the SACHER series. From this perspective, Boulez is radically different from Schoenberg, Webern, and Stravinsky who use a new series or collection for each piece. Boulez’s method of w orking, especially reusing the same series or collection in a number of works, is much more similar to the methods of Carter and Babbitt. Carter typically uses the two all-interval tetrachords and the all-trichordal hexachord in almost all of his works, while Babbitt tends to use the same all-partitioned array in a number of his works.
25 The cycle of pieces refers to works that share the same title, and are closely related with one work inspiring the other: Éclat/Multiples is the expanded version of Éclat, Anthèmes 2 is the expansion of Anthèmes 1; sur Incises is based on Incises; Notations I-IV, VII for orchestra are based on the short piano pieces with the same title; and the … explosante-fixe… series all came from the same source. Dérive 1, Dérive 2, and Dérive 3 do not share such a connection; however, earlier performances of Dérive 2 were often paired with Dérive 1, though such pairing is no longer in practice in the recent years of performances.
26 Initiale was premiered on June 4th, 1987 in Houston, Texas.
27 Fanfare was premiered as a birthday present for Georg Solti’s 80th birthday in Chicago.
28 Boulez, however, claims that Dérive 3 is derived from Le Visage Nuptial. See Carvin and Cody, “Pierre Boulez: An Interview.”
Dérive 2 in terms of pitch material, rhythmic structure, and instrumentation. In contrast with the other two works, Dérive 2 has a relatively individual and distinct compositional history, since it does not relate or rely on any previous work, but its history after the premiere makes it difficult to decipher the exact creative path due to the voluminous revisions Boulez has made. Despite these trivial differences, the three Dérives nonetheless share many similar approaches to harmony, harmonic rhythm, texture, rhythm, meter/pulsation, and musical time in general.
The program note to Dérive 2 provided by the publisher states, “Dérive 2, dedicated to Elliott Carter on his 80th birthday, was the result of ‘research into periodicity’. ‘When I reflected on some of Ligeti’s compositions,’ wrote Boulez, ‘I felt the desire to dedicate myself to some almost theoretical research into periodicity in order to systematically examine its overlays, its shifts and its exchange.’ “29 In a more in-depth program note, Boulez wrote:
The sustained contact with certain works from Ligeti brought me to think about the rhythmic life of a musical composition. Starting from a narrowly focused perspective, Dérive 2 has evolved in compositional time well beyond my initial point, for meanwhile it has endured interferences from other completed works. In short, the word Derive evokes the meandering that this work has progressed through in its realization. Thus it became a kind of journal that reflects not only the evolution of the musical ideas themselves, but also the ways of organizing them in a kind of narrative.30
29 Universal Edition, “Pierre Boulez, Dérive 2 for 11 instruments – Work Introduction,” Universal Edition, http://www.universaledition.com/Pierre-Boulez/composers-and works/composer/88/work/9777/ work_introduction (accessed October 18, 2011).
30 “Le contact suivi avec certaines oeuvres de Ligeti m’a amené à réfléchir sur la vie rythmique de l’oeuvre musicale. Partant d’un point de vue étroitement ciblé, Dérive 2 s’est développée dans un temps de composition bien au-delà du point de départ, subissant les interférences d’autres oeuvres achevée s entretemps. Le mot dérive peut, en somme, s’appliquer aux nombreux méandres que cette oeuvre a décrits le long de sa réalisation. Elle est devenue ainsi une sorte de journal reflétant l’évolution des idées musicales proprement dites, mais également la façon de les organiser dans une sorte de mosaïque narrative.” Pierre Boulez, “Program note to Dérive 2,” November 7th, 2006 at the Cité de la musique in Paris. Translation provided by the author.
Furthermore, during a BBC interview that took place at the Barbican in 2004, Boulez clarified his thoughts:
Dérive means derived from, but in the same time when a boat as you know [with] no motor, and no sail, and just lets the currents push him, that’s also derive … it drifts, … there are these two meanings and I like these two meanings, … I like these types of pun. … When I write a piece generally I have a lot of sketches which are not always used. You know that’s like pages of a diary which I take and then amplify, and expand. Dérive 2 is not derived from a work specifically. But I was interested by the periodicity in the works in the recent works by Ligeti, in the works by Carter, the notion of time in Carter, and also Carter gave me a clue to that, to the works of Nancarrow, the American who was living in Mexico. What I think [of] my periodicity that’s when you have you know phenomena which come[s] back at a regular pace, or according to certain developments, and when you have something which is periodic and something which is not periodic you find that the fights between the two is interesting. And therefore, I gave a series of lectures31 on the periodicity in these three composers, with not only examples from these composers but examples from myself, just sketches you know, [to] articulate examples let’s say. And it gave me the incentive to write a piece according to these datas.32 And the secondary reason in this direction: what I did in this piece that is to try to have a tempo quick, and tempo rather slow but with full of activity. By tempo I mean the change of harmony, but I don’t take that from Nancarrow, or from Carter, or from Ligeti, I take that from Beethoven. Simply the system of variations of Beethoven, the slower it is, the more notes you have; you have even 64th and 128th-notes in some variations by Beethoven, but the harmony is very slow, but the number of events is very big. And then I tried you know to have this kind of dialectic with quick tempo with few events, relatively, and slow tempo with lots of it. … To simplify; quick, many, slow, few.33
31 Boulez is referring to a series of lectures he gave at the Collège de France between 1976 to 1995 on various musical topics. These have been subsequently published as Points de repére III: Leçons de musique: Deux décennies d’enseignement au Collège de France, ed. Jean-Jacques Nattiez (Paris: Christian Bourgois Éditeur, 2005).
32 According to Wolfgang Fink, these periodicities and examples “were initially worked out on a computer so that they could be handled more easily, but in the process they developed a life of their own.” See Wolfgang Fink, linear notes for Le marteau sans maître, Dérive 1 & 2 by Pierre Boulez, Deutsche Grammophon CD DDD 0289 477 5327 8 GH (20/21 Series), 2005.
33 This interview along with a performance of Dérive 2 took place on October 13th, 2004 at the Barbican in London, with Boulez conducting members of the London Symphony Orchestra. This performance lasts approximately 25 and half minutes and it is already different from the commercial recording of 2002 and the 2003 edition of the score. The final horn solo (which imitates the opening) was h eard here for the first time. This Boulez interview is transcribed by the author.
This document, then, will focus on two important aspects in Dérive 2: Musical Time and Formal Structure. The first chapter presents Boulez’s conception of musical time in general, and more specifically traces some of the conceptual developments and practices with regard to rhythmic construction (chapter 1.1), smooth and striated time (chapter 1.2), meter, grace-note, tempo (chapter 1.3), and periodicity (chapter 1.4) from the earlier works up to and including Dérive 2. The second chapter addresses Boulez’s conception of form and the idea of trajectory of large-scale organization in the previous works in relation to Dérive 2. The third and last chapter examines Dérive 2 in detail, and the process of realizing these concepts of musical time and formal structure that were discussed in the previous two chapters, in addition to their transformations and manipulations by Boulez in the discourse of Dérive 2.
CHAPTER 1. MUSICAL TIME
Chapter 1.1. Rhythmic and Temporal Conception in Boulez’s Early Works
Influenced by the rhythmic innovations of Bartok, Stravinsky, and Messiaen1, Boulez set out to develop his own approach to rhythm.2 From Messiaen, he learned the importance of the independence of rhythm. Rhythm should no longer be considered as a secondary parameter to pitch; rather, rhythmic construction can and should have its own internal structure.3 Unlike Messiaen, Bartok, and Stravinsky, Boulez was not interested in transporting another culture’s rhythmic constructions to his own music, nor was he interested in imitating another culture’s rhythmic devices.4 In fact, Boulez strongly criticized Messiaen’s use of Greek or Indian rhythms in his music.5 Instead, one sees in early Boulez the use of automatism in rhythmic construction through mathematical or
1 From Messiaen, Boulez not only had gained an interest in rhythm, but also in harmonic thinking, voicing, and a keen sensitivity to color and timbre, not to mention Messiaen’s interest in the music of Debussy, and in non-Western music. All these ideas continued to influence Boulez for many years to come. See Peter O’Hagen, “Pierre Boulez and the Foundation of Ircam,” in French Music since Berlioz, eds. Richard Langham Smith and Caroline Potter (Aldershot: Ashgate, 2006), 303-307.
2 See Pierre Boulez, “Proposals,” in Relevés d’apprenti, ed. Pale Thévenin, trans. Stephen Walsh as Stocktakings from an Apprenticeship (New York: Oxford University Press), 47-54.
3 “… I already considered that rhythmic writing ought to be something worked on for its own sake, and I think this is the lesson I learnt from Messiaen, particularly from his classes on music from Stravinsky onwards. After having analyzed The Rite of Spring with him, or even his own works, I was convinced for the necessity of working at purely rhythmic invention.” Pierre Boulez, Par volonté et par hasard: entretiens avc Célestin Deliége, trans. Robert Wangermé as Pierre Boulez: Conversations with Célestin Deliége (London: Eulenburg Books, 1976), 13-14.
4 “You could say I was very influenced when I was young by cultures of Asia and Africa. But I saw these cultures from a very different point of view than that of the original cultures. I could not pretend that I understood them. I understood them not from their point of view; I understood them from my point of view, which is completely different. And that I called a misunderstanding a misunderstanding because, fundamentally, what you pick up is the kind of impression you have of the music you hear.” Rocco Di Pietro, Dialogues with Boulez (Lanham: Scarecrow Press, 2001), 47-48.
5 “As a matter of fact, that side of Messiaen has never much interested me. As you know, he very often makes use of rhythms drawn from either Greek or Indian music, and to my way of thinking this poses a problem. It is very difficult to introduce fragments of another civilization into a work. This is what I believe now, but I also believed it then: we have to invent our own rhythmic vocabulary in accordance with our own norms. In this sense, even in my earliest works, there is what one might call a contrast between free forms (sometimes there are, for instance, extremely free rhythms – almost improvised, or written down as they are thought up) and on the other hand extremely strict sections. This is something I still practice; it is one of my main ideas.” Boulez, Par volonté et par hasard: entretiens avc Célestin Deliége, 13.
serial formulas, and any sense of traditional rhythm and meter in addition to any cultural references or connotations is completely abandoned if not destroyed.6 In the Sonatine for Flute and Piano (1946/49), for example, Boulez had constructed a rhythmic scheme based on two principle motives that are then extended to become the rhythmic basis for the whole piece.7 Besides the serial technique and its realization of the 12-tone row in the pitch domain, what is innovative in the Sonatine is that the rhythmic device is constructed entirely in isolation from pitch.8 The rhythmic complexity (the abandonment of meter, the use of polyrhythm, and the layering of superimposed rhythms) is unmatched by any piece Boulez had written up to this point.
A few years later, in Polyphonie X (1949/51) for ensemble, Structures I (1951-52) for two pianos, and Le Marteau san Maître for voice and ensemble, Boulez conceived of an analogy of the serial method in the pitch domain applied to the temporal domain with the durational series9 a technique that provides Boulez complete control of the rhythmic
6 Boulez had gotten to know the principal s of the 12-tone technique (and the music of Schoenberg and Webern as well) from René Leibowitz, who was a student of Schoenberg. The 12-tone system, for Boulez, posits a completely new solution to musical coherence. For Schoenberg and Berg, the 12-tone system was a renewed grammar and syntax to re-create the tonal system and language, and it is quite evident in their use of form, meter/rhythm, and the thematic treatment of the series in their serial works (for example, Schoenberg’s works after op. 25 show a great detail of imitation of the classical forms, which are drastically different from his innovative use of form and rhythm in the post -tonal works such as Pierrot Lunair, Erwartung, and the piano pieces of op. 11 and op. 19. Similarly, the use of classical forms in Berg’s Wozzeck also poses a problem for Boulez). See Boulez, Par volonté et par hasard: entretiens avc Célestin Deliége, 17-18. Boulez was not interested in renewing the past, instead he uses the 12-tone system to create a new path.
7 By this time Boulez had already been studying with Messiaen for more than a year at the Conservatoire, while studying counterpoint privately with Andreé Vaurabourg (the w ife of Honegger) since April 1944, and also privately with René Leibowitz starting in 1945. Though most people usually associate Boulez’s musical influences from Webern, however, at this point Boulez hardly knew any late Webern works (with the exception of Symphony Op. 21), he was still under the influence of Messiaen and Honegger. See Gerald Bennett, “The early works,” in Pierre Boulez: a Symposium, edited by William Glock (London: Eulenburg, 1986), 41-84; and O’Hagan, “Pierre Boulez and the Foundation of IRCAM,” 303-330.
8 See Bennett, “The early works,” and Boulez’s own analysis of the use of the “rational” and “irrational” rhythmic cells in the Sonatine. Boulez, “Proposals,” in Relevés d’apprenti, 47-54.
9 Boulez is not the only one who had experimented with the durational series, Messiaen, Babbitt, Berio, Nono, Stockhausen, Wuroinen, Ferneyhough, and even Grisey had come up with similar processes in their
domain and insures its independence.10 A durational series subsequently allowed him to apply the same kind of transformation and manipulation that takes place in the pitch domain to rhythmic construction.11 The rhythmic structure is thus freed from meter, pulse, or temporal hierarchies, and it breaks away from any tradition or cultural implications, in addition to eliminating any personal freedom and choice to a certain extent. Rhythms, along with pitch, dynamics, and articulations (modes of attack) thus have a parallel and equal weight in the structure of the music, and these four parameters are completely independent of each other. Most important, all four parameters are governed and generated from a single 12-tone series (hence Total-Serialism), thus unifying all aspects of music to and from the same structure.12
music with varying approaches. Babbitt also developed a “time-point” system in which a measure or a meter is analogous to the octave in the pitch domain, and a measure divided into 12 equal time-points, with each point corresponding to a number in the series. See Milton Babbitt, “Twelve-Tone Rhythmic Structures and the Electronic Medium.” Perspectives of New Music 1, no. 1 (1962): 42-79. On the contrary, Stockhausen experimented with the Fibonacci and the overtone series to determine rhythmic structure and construction.
10 “Looking at Schoenberg’s method, which was preoccupied only with pitches, I thought (especially given the influence of Messiaen and his rhythmic procedures) “Why not try to make everything under the same control and order?” At this moment, it was called pointillistic, because we were dealing with point after point, and the reunion of point. After a while, I was bored, because you can’t only work with separated notes, you can’t always only work with number one. It wasn’t enough for me, and once I had taken the consequences of serialism as far as that, I was aware that anarchy produced practically the same results. It proved the absurdity of the extreme logic, which is equivalent to the absurdity of no logic at all.” Paul Steenhuisen, “Interview with Pierre Boulez,” in Sonic Mosaics: Conversations with Composers (Edmonton: University of Alberta Press, 2009), 66.
11 With the durational series, Boulez permutes the series instead of transposing it as in the case of the pitch domain.
12 “The series is in very general terms the germ of a developing hierarchy based on certain psychophysiological acoustical properties, and endowed with a greater or lesser selectivity, with a view to organizing a FINITE ensemble of creative possibilities connected by predominant affinities in relation to a given character; this ensemble of possibilities is deduced from an initial series by a FUNCTIONAL generative process (not simply the consecutive exposition of a certain number of objects, permutated according to restrictive numerical data). Consequently, all that is needed to set up this hierarchy is a necessary and sufficient premise which will ensure the total cohesion of the whole and the relationships between its successive parts.” Pierre Boulez, Penser la musique aujourd’hui, trans, Susan Bradshaw and Richard Rodney Bennett as Boulez on Music Today (London: Faber and Faber, 1971), 35-36.
The serial method in the temporal domain (mainly the durational series) provided a short experiment for Boulez, and he immediately knew the limits of pure Total-
Serialism:
It is very easy to see how the situation has developed in just this way. When the serial principle was first applied to all the components of sound, we were thrown bodily, or rather headlong, into a cauldron of figures, recklessly mixing mathematics and elementary arithmetic; the theory of permutations used in serial music is not a very complex scientific concept … rhythmic organization [of the serial method] disregarded realizable metric relationships, structures of timbres scorned the registers and dynamics of instruments, dynamic principles paid no heed to balance, groups of pitches were unrelated to harmonic considerations or to the limits of tessitura. Each system, carefully worked out in its own terms, could only cohabit with the others through a miraculous coincidence. The works of this period also show an extreme inflexibility in all their aspects.13
From another perspective, Boulez’s total-serial works led to surprising comparisons to Cage’s chance or aleatoric works, since arguably, both methods could inevitably lead to similar results:
If you are only obsessed with organization, then practically you arrive at chaos, because an excess of organization in physics bring chaos. Chaos alone does not bring any order. Therefore, I have to accept the stream, which is an order, and within this stream I must accept the unforeseeable elements, which you can not control. But I have to make the best use of them that is possible. I think that in life that’s exactly the same. You have opportunities which come which will never come back, for instance, and you have to see-to judge, even-if this opportunity will serve your purpose or not. If you see that it is of no value for you, or it takes away more than it contributes to your purpose, then you have to let the accident go.14
Boulez quickly moved away from the rigidity and automatism of Structures Ia, and starting with Marteau and Pli selon pli, Boulez allowed personal freedom, creativity, spontaneity, and “accidents” into the process of music making, while greatly extending the
13 Boulez, Penser la musique aujourd’hui, 25.
14 Di Pietro, Dialogues with Boulez, 98.
possibilities of the series through many layers of manipulation and transformation in all parameters.15 Even though Marteau is still composed with the durational series, its surface rhythmic construction and the temporal organization are much more varied and are manipulated on a detailed level. The works that followed Marteau, Pli selon pli and Troisième Sonate, showed even greater freedom and inventiveness on the realization of the rhythmic construction in relation to the multiplication technique.16 One no longer perceives the “point” based rhythmic values, but instead, a fluidity of rhythms and a smoother surface. However, after Marteau, Boulez knew he had to reconstruct once again a new syntax for his rhythmic construction and conception.
15 “A progressive loosening of the vice-like grip of strict writing will finally lead to complete freedom –freedom, of course, within general structural principles. … The play of structures implicitly suggests a scale of relationships going from the chance of automatism to the chance of choice.” Boulez, Penser la musique aujourd’hui, 106.
16 See also Catherine Losada, “Isography and structure in the music of Boulez,” Journal of Mathematics and Music 2, no. 3 (November 2008): 135-155.
Chapter 1.2. Smooth Time and Striated Time
French philosopher Gilles Deleuze (1925-1995) proposed two readings of time: Chronos time and Aion time, where “each one of which is complete and excludes the other: on one hand, the always limited present, which measures the action of bodies as causes and the state of their mixtures in depth (Chronos); on the other, the essentially unlimited past and future, which gather incorporeal events, at the surface, as effects (Aion).”17 Deleuze further defines Chronos time as:
… only the present exists in time. Past, present, and future are not three dimensions of time; only the present fills time, whereas past and future are two dimensions relative to the present in time. In another words, whatever is future or past in relation to a certain present (a certain extension or duration) belongs to a more vast present which has a greater extension or duration. Thus, the relativity of past and future with respect to the present entails a relativity of presents themselves, in relation to each other.18
On the contrary, Aion is defined as:
… only the past and future inhere or subsist in time. Instead of a present which absorbs the past and future, a future and past divide the present at every instant and subdivide it ad infinitum into past and future, in both directions at once. Or rather, it is the instant without thickness and without extension, which subdivides each present into past and future, rather than vast and thick present which comprehend both future and past in relation to one another.19
Aion is, then, “infinitely subdivisible”20 and it is “no longer the future and past which subvert the existing present; it is the instant which perverts the present into inhering future and past.”21 For Deleuze, the duality between Chronos and Aion time is:
17 Gilles Deleuze, The Logic of Sense, eds. Constantin V. Boundas, trans. Mark Lester and Charles Stivalep (NY: Columbia University Press, 1990), 61.
18 Ibid., 162.
19 Ibid., 164.
20 Ibid., 61.
21 Ibid., 165.
[Chronos is] limited and infinite, Aion is unlimited, the way that future and past are unlimited, and finite like the instant. Whereas Chronos was inseparable from circularity and its accidents such as blockages or precipitations, explosions, disconnections, and indurations Aion stretches out in a straight line, limitless in either direction. Always already passed and eternally yet to come, Aion is the eternal truth of time: pure empty from of time which has freed itself of its present corporal content and has thereby unwound its own circle, stretching itself out in a straight line.22
Deleuze then relates his concept of Aion time and Chronos time to Boulez’s concept of
Smooth time temps lisse and Striated time temps strié, respectively,23 where smooth time refers to music that is non-pulsed, while striated time refers to music that is pulsed.
According to Boulez,
In Pulsed time, the structures of duration will be related to chronometric time as landmarks, or, one might say, systematically placed regular or irregular beacones: these constitute a pulsation, either of the smallest unit … or of a simple multiple of this unit (the smallest common multiple of all the values used), or of a simple multiple of this unit (two or three times its value). … Amorphous [non-pulsed] time is only related to chronometric time in a global sense; duration, whether with defined proportions (not values) or having no indication of proportion, appear in a field of time. Only pulsed time is susceptible to speed, acceleration or deceleration: the regular or irregular referential system on which it is based is a function of a chronometric time of greater or lesser delimitation, breadth or variability. The relationship of chronometric time to the number of pulsations will be the index of speed. Amorphous time can vary only in density according to the statistical number of events which take place during a chronometric global timespan; the relationship of this density or an amorphous timespan will be the index of content. … Beneath a line of reference, place a completely smooth surface and a striated surface … I will call these two categories smooth time and striated time.24
22 Ibid., 165.
23 “Aeon [Aion]: the indefinite time of the event, the floating line that knows only speed and continually divides that which transpires into an already -there that is at the same time not-yet-here, a simultaneous toolate and too-early, a something that is both going to happen and has just happened. Chronos: the time of measure that situates things and persons, develops a form, and determines a subject. Boulez distinguishes tempo and nontempo in music: the “pulsed time” of a formal and functional music based on values versus the “nonpulsed time” of a floating music, both floating and machinic, which has nothing but speeds or differences in dynamic.” Gilles Deleuze and Félix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia, trans. Brian Massumi (Minneapolis: University of Minnesota Press, 1988), 262; see also in the same book, “The Smooth and the Striated,” 474-500, for detailed explanations.
24 Boulez, Penser la musique aujourd’hui, 88-89.
Deleuze proposes that smooth and non-pulsed time is a “kind of floating time that more or less corresponds to what Proust called ‘a bit of pure time’,” and that is duration “freed from measure, be it a regular or irregular, simple or complex measure.”25 Additionally, nonpulsed time “puts us first and foremost in the presence of a multiplicity of heterochronous, qualitative, non-coincident, non-communicating duration,”26 and that the “non-pulsed space-time detaches itself in turn from the striated one. It only refers to chronometry in a global way: the cuts are indeterminate of an irrational type, and the measures are replaced by distances and proximities that cannot be broken down and that express the density or rareness of what appears there (statistical distribution of events).”27 In comparing the two, as Deleuze puts it most vividly, that smooth time and non-pulsed time “occupies [time] without counting instead of [striated time and pulsed time] counting to occupy.”28
Boulez has scrutinized extensively his concept of smooth and striated time as first defined in Penser la musique aujourd’hui in various forms throughout his own writing, and it is clear that such concept is important to him and to his own music.29 Boulez even goes as far as to state that “I regard the two categories – smooth and striated time – as capable of reciprocal interaction, since time cannot be only smooth or only striated. But I can say that
25 Gilles Deleuze, “Making Inaudible Forces Audible”, in Two Regimes of Madness: Text and Interviews 19751995, rev. ed., ed. David Lapoujade, trans. Ames Hodges and Mike Taormina (New York: Semiotet(e), 2006), 157.
26 Ibid.
27 Deleuze, “Occupy Without Counting: Boulez, Proust and Time”, in Two Regimes of Madness, 294. In this article Deleuze corresponds Boulez’s conception of time to Proust’s tempor al qualities in À la recherché du temps perdu.
28 Ibid.
29 Gérard Grisey dismissed these two temporal concepts by Boulez, since “the notion of smooth (unmeasured) and striated (measured) time … is merely the invention of a conductor bereft of any phenomenological awareness. Who perceives the differences between time divided up periodically by a meter … [or] by a virtual pulse maintained by the composer/musicians, and smooth time, without a pulse, if the rhythms which overlay it are there precisely to destroy all feeling of periodicity?” Gérard Grisey, “Tempus ex Machina: A Composer’s Reflections on Musical T ime,” Contemporary Music Review 2 (1987): 240.
whole formal time system is based on these two categories and on them alone.”30 Boulez’s concept of smooth and striated time is not new; in fact, it can be traced to a number of sources. The most obvious similarity to smooth time is static time–time that is nondirectional, immobile, and is a “temporal continuum determined by progression toward unpredictable goals.”31 Static time can be found in the music of Stravinsky and Messiaen, or even earlier in the music of Wagner (The Ring cycle and Parsifal) and Debussy (Pelléas et Mélisande). Boulez, however, also associates static time with the gagaku Japanese court music:
If I hear the gagaku Japanese court music (as I will remember hearing it in 1945 or ’46), the first thing which is very impressive is the expansion of time, because the sustained pace of this music is very slow for a long time. And that’s completely different from our conceptions of time. A related phenomenon is the use of small intervals in gagaku-intervals which do not seem to move. This is kind of destruction of the intervals. And that, for me, was very important because I speak in my own terms when I speak of the category of time. That’s comparing my perception of gagku time with that we are doing here, generally, in Western civilization-namely, to go from a point to another point, which is moving and developing. On the contrary, here in gagaku, I had the impression that the music is completely static.32
These two seemingly opposed temporal conception “cannot be separated in watertight compartments, as antithetical but must be regarded as two poles of a continuum.”33 They can in fact co-exist simultaneously, or juxtaposed intermittently and in succession in time. The distinction between the two concepts is a matter of perception
30 Pierre Boulez, Orientations: Collected Writings by Pierre Boulez, ed. Jean-Jacques Nattiez, trans. Martin Cooper (London: Faber and Faber, 1986), 87.
31 Jonathan D, Kramer, The Time of Music; New Meanings, New Temporalities, New Listening Strategies (New York: Schirmer, 1988), 452
32 Di Pietro, Dialogues with Boulez, 48-49.
33 Jean-Jacques Nattiez, “On Reading Boulez,” in Orientations, 22.
and perspective, as each can be easily infused with the other.34 While giving a lecture at IRCAM in February 1978,35 Deleuze discussed the mixture of pulsed time and nonpulsed time, where the two concepts are closely related:
We saw a kind of non-pulsed time emerging from a pulsed time, even though this non-pulsed could become a new form of pulsation. The first work (Ligeti) [Ligeti’s Kammerkonzert] showed how a non-pulsed time rose from a certain pulsation; the second [Messiaen’s Mode de valeurs et d’intensités], third [Boulez’s Êclat] and fourth [Stockhausen’s Zeitmasse] works developed or showed different aspects of this non-pulsed time; the fifth and last work by Carter [Carter’s A Mirror on which to Dwell] showed how a non-pulsed time could lead to a new form of original pulsation, a very particular, very new pulsation.36
As early as Pli selon pli, Boulez was already composing music in non-pulsed and pulsed time (for example, the senza tempo sections). This is a significant departure from the earlier serial works Structures, Polyphonie X, and Marteau where the rhythmic and temporal conceptions are completely detached from the idea of pulsation. However, it is not until Éclat that Boulez had refined these ideas of smooth and striated time in the most practical and audible way. In Éclat, the resonances of the ensemble (piano in particular) and their acoustics are composed into the score, and the duration of these resonances is left to be determined by the conductor. These sections correspond to the smooth time conception, since it is not possible to sense any internal pulsation or rhythmic pattern
34 “[Deleuze] is surely correct in suggesting that Boulez’s distinction of the smooth and the striated is of less value as a division than as a continuum, since they can be alternated or superposed, a phenomenon we will meet, for example, in sections of Répons.” Edward Campbell, Boulez, Music and Philosophy (New York: Cambridge University Press, 2010), 132.
35 Boulez organized and gave a series of lectures at Ircam, titled “Le Temps Musical,” between 17th to 21th of February in 1978. Boulez presented and analyzed the following five works: Kammerkonzert by György Ligeti; Mode de valeurs et d’intensités by Olivier Messiaen; Éclat by Boulez, Zetimasse by Karlheinz Stockhausen; and A Mirror on which to Dwell by Elliott Carter. Deleuze lectured on the last day of these lectures.
36 Deleuze, “Making Inaudible Forces Audible,” in Two Regimes of Madness: Text and Interviews 1975-1995, 157.
from these undetermined resonances and their unpredictable acoustics (for example, rehearsal numbers from 3 to 7 and 14 to 21). Rhythms in these sections are usually grouped as gestures without any metric clarity. This is emphasized through long passages of static harmony of stretched durations. The middle “Vif” section (rehearsal numbers 8 to 13) and the last section (rehearsal 27 to the end) of Éclat corresponds to the striated time concept, despite the fact that these rhythms do not form any clear pattern or meter, the underlying constant 16th-note pulsation is clearly audible, and the entire rhythmic construction is based completely on the 16th-note and its multiples. In Rituel, the two contrasting sections – static harmonic long held chords by the full ensemble and the multilayered texture of heterophony of various instrumental groups, with each group accompanied separately by a steady pulsation played by the percussion, are perhaps the clearest demonstration of the contrast between pulsed and non-pulsed time in Boulez’s music.37 Similarly, in Messagesquisse, the running 16th-note and 8th-note sections (rehearsal numbers 4 to 7, and 10 to 12, respectively) are pulsed by a permutation of a rhythmic pattern, and every single beat is filled in with at least one event. On the other hand, the solo sections (rehearsal numbers 1 to 3, 8 to 9) are semi-improvisatory in nature, the music purposely avoids any clear sense of pulsation or meter, and the discrete rhythmic patterns in the accompaniment are Morse codes derived from the dedicatee’s last name, with permutations in each cello part (ex. 1.2.1).38 These striated sections are also characteristically filled with long pauses, rests, and unpredictable durations.
37 See Jonathan Goldman, The Musical Language of Pierre Boulez: Writings and Compositions (New York: Cambridge University Press, 2011), 100-115.
38 Antoine Bonnet, “Ecriture and perception: on Messagesquisse by Pierre Boulez,” Contemporary Music Review 2 (1987): 174.
Ex. 1.2.1. Morse Code of the name SACHER translated into rhythmic patterns
Boulez’s next large work, Répons, takes these two temporal conceptions to the next level in the latter half of the work, where these two opposing ideas are juxtaposed simultaneously – the notated rhythmic and pulsed orchestra parts against the ornamented unmetered music played by the resonant instruments (rehearsal numbers 42 to 47).
Boulez continues to use this opposition in temporal conception in his more recent works such as Dérive 1, Incises, sur Incises, and Dérive 2. 39
The unpredictable resonances of the instruments become an important method for Boulez to have musical time that is flexible, a time that is not restricted by pulsation.
Time in these works is therefore guided by sound, not by arbitrary serialized durations or integer based pulsed rhythms. The striated and metered sections that involve complex subdivisions or the constantly varied pulsations and rhythms, still confine musical time into subdivided compartments. Dérive 2 will utilize these two concepts to challenge our perception of musical time.
39 On the employment of Smooth and Striated time in Incises, see Goldman, The Musical Language of Pierre Boulez, 174-185.
Chapter 1.3. Tempo
As an experienced conductor, Boulez knows intimately the effect and the capability of tempo manipulation on both local and structural levels. Tempo, more precisely, the fluctuation of tempi becomes another method for Boulez to engage in more levels of temporal manipulation beyond the typical operations of rhythm and meter.40 Tempo, for both Carter and Boulez,41 is different from rhythm and meter:
If I distinguish between tempo and rhythm as such, it is because I regard these two aspects of musical time as essentially different. The latter is a function of the unit of duration, a unit which can, for the purpose of analysis, be abstracted from the speed at which it happens. The former is ultimately a rate of unfolding of musical text, and by its nature pragmatic.
… The crucial factor in the choice of different tempos … [is] a hierarchy of tempo relationships, which comes back to a relation between speeds of musical unfolding.42
Boulez’s interest in utilizing tempo as another temporal manipulation is much more evident in the more recent works. These works employ tempo in various ways. In some works, tempo manipulations are used to fluctuate the surface level of speed. These
40 Boulez’s interest in the manipulation of tempi, much more prevalent in the later works, might be due to the fact that Boulez was becoming an experienced conductor. Not only has he conducted music which requires constant tempo fluctuations, both interpretatively and specifically notated in metronomic markings, such as in the music of Wagner, Mahler, Schoenberg, Bartok, Berg, Debussy, Stravinsky, and Carter; Boulez has also conducted almost all the premieres and the subsequent performances of his own music. Such experience allows him to manipulate tempo in a practical manner, as well as be confident that these tempo manipulations and interpretations can be altered and decided when he conducts his own music. Furthermore, Boulez often leaves these temporal decisions open in the score, so that the interpretative quality of tempi and the specific temporal modifications directed by the conductor would allow him freedom to determine these features during the performances.
41 See Elliott Carter, Collected Essays and Lectures, 1937-1995, ed. Jonathan W. Bernard (Rochester, New York: University of Rochester Press, 1997), 224-228; and 262-280. One typically associates “metric modulation” with Carter’s music. However, it is a misleading term since Carter generally works with tempi, not meter in his music. Meter implies a hierarchy of downbeats and upbeats, a pattern within pulsations. Carter’s pulsations do not imply a hierarchy of order or pattern. When Carter “modulates” from one tempo to the other, or changes from one meter to the other, the underlying pulsation changes its speed while keeping its internal rhythmic subdivisions the same (but certainly the notation will obviously be different). Therefore, it is the change of tempo that interests Carter, not the change of meter. It is much more appropriate to use the term “tempo modulation” or “temporal modulation” to refer to Carter’s technique of temporal transformation. However, in 90+, the long-range pulse remains fixed while the surface tempo changes.
42 Boulez, Relevés d’apprenti, 132.
manipulations are placed between important structural points or tempi, but their speeds and internal organizations do not form part of an overall scheme (for example, see in the 1986 version of Cummings ist der dichter or in Mémoriale (…explosante-fixe) where almost every single measure has surface tempo manipulation). In some other works, tempo serves as a structural device to differentiate the various sections or their internal divisions.
In Dérive 1, for example, the whole work can be divided by its temporal design into two halves.43 In the first half, measures 1 to 27, the tempo marking “Très lent, immutable (q = maximum 40)” is maintained throughout without a single fluctuation (with the exception of the last measure). The meter is also fixed in 4/4 throughout, with only 16thnote rhythmic value and its multiples, though the meter is obscured by the use of varying length of grace-notes in all the instruments. The second half, measures 27 to 46, goes through multiple tempo changes. As the larger pulse/speed becomes slower, the subdivisions become larger and more complex for the first part; and after the midpoint, as the larger pulse/speed becomes faster, the rhythmic subdivisions become less complicated for the second part. This whole second half starts with “Très lent (q = maximum 40)” tempo, with only quarter-notes, 8th-notes, and 8th-note triplets (measure 27). Then the tempo changes to “Elargir le tempo (e = 72)” in measure 36, and the rhythmic value grow to include 16th-note triplets and 16th-note quintuplets. Then the tempo changes to “Elagir le tempo encore plus (e = 63)” in measure 38, and the rhythmic values adds 32nd-notes. In measure 41, the tempo changes to “Elargir le tempo toujours davantage (e = 60)”, while the rhythmic values further include 32nd-sextuplet notes as the music reaches its slowest
43 Jonathan Goldman also makes a similar point with regard to Dérive 1’s symmetrical structure based on its temporal organization of striated time. See Jonathan Goldman, The Musical Language of Pierre Boulez, 116127.
speed and the highest degree of subdivision. Starting from measure 42, the tempo markings are reversed. At first the tempo marking changes to “Resserrer le tempo vers le tempo initial (e = 66)”, while the rhythmic value again add 16th-note septuplets. In measure 44, the tempo changes to “Resserrer encore plus vers le tempo initial (e = 69)”, while rhythmic values are limited to 16th-notes, 8th-notes, 16th-note triplets, and 8th-note triplets. In measure 45, the tempo changes to “Resserrer advantage (e = 75)”, while rhythmic values are limited to only 16th-notes, 8th-notes, and 8th-note triplets. At the end of measure 45, the tempo changes back to the initial tempo of (e = 80), and rhythmic values are only left with 8th-notes and 8th-note triplets. In the second half of the piece, grace-notes are used sporadically, and each time with only a few notes. In comparison, the first half is rhythmically simple, but metrically ambiguous with the use of many gracenotes while keeping the underlying speed/pulse the same. The second half is rhythmically complex, but metrically simple while varying the underlying speed/pulse. The whole musical time in the entirety of Dérive 1 relies fundamentally based on these tempo changes and their rhythmic subdivisions to create temporal fluctuations.44
44 Goldman analyses these oppositions in musical time in terms of Boulez’s concept of smooth and striated time. Ibid., 116.
In Dérive 2, tempo or metronomic speed has two principal purposes: one functions at the local level and does not have an overall organization, and the basic pulse or speed remains undisturbed; the other functions at the structural level and manifests on a larger time scale, and at times, alters the underlying pulse and speed. The first function of local fluctuation (accelerando and ritardando) often bridges adjacent sub-sections or phrases that are in different tempi. These manipulations of tempi stretch or compress the duration of events; and more specifically, slow down or speed up the rate of unfolding of musical materials while keeping the internal activities (rhythm, meter, or pulsation) unaltered. Boulez’s constant fluctuation of tempi is directly influenced by Mahler and Debussy, whose music constantly require suspension of time and temporal modifications on the local level.45 In a way, these local tempo fluctuations are similar to rubatos in Chopin’s music, whose moments of tempo fluctuation suspend meter and the flow of time.
In Dérive 2, the various local accelerations and retardations tend to happen in the interruption sections – sections that are outside of the overall periodicity structure that governs the whole piece.46 These surface level tempo modifications usually help to bridge sections that are in different tempi. Between R6647 and R83, one of the longest interruptions in the piece, the tempo goes through numerous subtle and drastic changes (fig. 1.3.1). Within this section, Boulez has maintained an equal subdivision of 32nd-notes throughout (with the exception of from rehearsal numbers 81 to 83 where the subdivision goes to a sextuplet within an 8th-note), and all the rhythmic values are limited to 32nd-notes
45 Boulez has conducted and recorded almost all the orchestral works of Mahler and Debussy. In works such as Mahler’s symphonies, and Debussy’s La Mer and Jeux, one sees frequent changes of tempo.
46 The interrupting sections and their function in relation to periodicity will be discussed in chapter 3.
47 Throughout this document, Ry will denote rehearsal number y, x-Ry will denote x measures before rehearsal y, while Ry-x will denote x measures after rehearsal y.
and their multiples. With the constant 32nd-notes and 8th-notes as the constant pulsation in the background, the tempo changes are immediately audible. Nevertheless, these changes do not alter the basic pulsation - an overall idea that Boulez was very much influenced by Carter:
I was immediately fascinated by his rhythmic writing. I think the principle of rhythmic modulations is particularly interesting. The shifts in rhythmic values are perfectly clear where they occur in the writing; the rhythmic relationships reach their fullest expression, as it were, when they can be heard. In some cases, however, you have to rely on the metronomic relationships. You realize this when conducting, because if you’re not in control of what you hear, the rhythmic modulations are executed more loosely. This idea is found in a simpler form in Stravinsky’s work. More often than not, he used relationships of 3 to 2 or 4 to 3, as in the Symphonies for Wind Instruments, a work which is entirely based on rhythmic relationships of 2, 3, and 4.48
R66 Assez vif (e = 120)
R76-4 poco rall.
2-R67 en reserrant le tempo R76-5 Plus calme (e = 88)
R67 Plus vif (e = 132) 1-R77 poco rall.
R67-2 revenir au R77 Encore plus calme, mais san trainer (e = 84)
3-R68 Assez vif (e = 120)
2-R68 Plus vif (e = 132/138)
R77-4 accélérer
R77-5 Plus vif
R68 revenir au R77-6 ravenir rapidement à
R68-2 Assez vif (e = 120) R78 Très calme, hesitant (e = 78)
R68-3 acelérer brusquement
R68-4 Plus vif (e = 132/138)
R78-5 accélérer progressivement à
R78-7 Animé (e = 98), poco rall.
R79 Sub. piécipité (e = 132)
R72 Sub. Tempo (e = 104) revenir à
R72-4 Sub. Tempo (e = 96) Assez vif (e = 120)
R73 Sub. Tempo (e = 90)
R79-3 ralentir rapidement à
R74 Sub. Assez vif (e = 120) R80 Très modéré (e = 98), ralentir
R74-2 Plus vif
R80-1 Plus calme (e = 90),
1-R75 ralentir à R80-2 ralentir
R75 Modéré (e = 84)
R80-3 Encore plus calme, presque lent (e = 82)
R75-3 poco accel. R81 accélérer brusquement et beaucoup
R75-4 À peine plus animé (e = 88) R81-2 Assez vif (e = 120)
1-R76 poco accel.
R81-4 aussi rapide que possible sans changer le tempo
R76 Un peu plus animé (e = 92) R83 Plus modéré (e = 98)
Fig. 1.3.1. Tempo manipulation and fluctuation from R66 to R83
48 Philippe Albéra, and Pierre Boulez, “Pierre Boulez in Interview (2): On Elliott Carter, ‘A Composer Who Spurs Me On’,” Tempo 217 (July 2001): 2.
Example 1.3.2 demonstrates an instance where the acceleration is not only written in the note values, but also indicated with a tempo modifier (the accel. marking). Writtenin acceleration and retardation are often found in the music of Carter, whose practice Boulez admires.49 In this example, the alternation of chords between monophonic instruments and resonant instruments occur from two per measure, to three per measure, and finally to seven per measure, as the harmonic rhythm speeds up (ex. 1.3.2).
49 “[My] point of interest in Carter’s music was the principle of the written-out accelerandi and ritardandi which are often found in his music and which are extremely effective. One might say that these are primarily gestures; but, in Carter’s work, they form part of the structures along with various intricately overlaid values.” Philippe Albéra, and Pierre Boulez, “Pierre Boulez in Interview (2): On Elliott Carter, ‘A Composer Who Spurs Me On’,” Tempo 217 (July 2001): 2-3.
Ex. 1.3.2. Written-in accelerando from rehearsal 3-R26 to 1-R26
Structural tempo, a second approach, distinguishes sections by employing two different tempi or speeds, or uses the same tempo to draw a connection between two or
more non-adjacent sections, even if the subdivision within each section is different.
Tempo, for both Carter and Boulez, is not limited to surface level modifications of speed, but it is capable of serving a structural role in a large-scale composition, as it can have an organization of its own. Structural tempo in Dérive 2 essentially functions as an important divider for all the sections throughout the entire work. For example, the metronome marking at R5 is q = 138, and the smallest subdivision is the 16th-note, which divides the quarter-note into 4 equal parts. At R10, the metronome marking slows down to q = 92.
Yet because the change of tempo, it is immediately clear that the basic pulsation has shifted to a slower rate, and signaling the beginning of a different section (ex. 1.3.3). Four measures later, the tempo goes back to q = 138 (2 measures before R11) and with the same 16th-notes as in R5. There is no doubt that one immediately draws a connection to the previous section just right before the tempo change at R10. In retrospect, it is evident that the music between R10 to two measures before R11 (a total of 4 measures) is an interruption or an “insertion” of some sort, since it interrupts the quarter-note pulse of q = 138. By the virtue of disrupting the pulse, this interruption section sounds “out of time.” Additionally, Boulez emphasized the change of time in these 4 measures by eliminating all the 16th-notes in the first two measures of R10, so that the shift of pulse is clearly articulated (ex. 1.3.4).
Ex. 1.3.3. Two measures before R10 to 5 measures after R10
Ex. 1.3.3. (cont’d)
From another perspective, the metronome marking (q = 92) at R10 is actually a tempo modulation from the previous metronome marking (q = 138), where the relationship between the two tempi is 2 to 3. A dotted half-note in q = 138 is equivalent to
a quarter pulse in q = 46, while a half-note in q = 92 is also equivalent to a quarter pulse in q = 46. This modulation is emphasized through the use of grace-notes. One measure before R10 the rhythmic grouping articulates a duration of a dotted half-note (starting with the grace-notes in cor anglais, bassoon, horn, and marimba), while at R10 all the grace-notes articulate an equal subdivision of the half-note in the new tempo. The larger pulse that takes place in both parts, the dotted half-note in the old tempo, and the halfnote is the new tempo, is actually the same; but their subdivisions are different. The effect is that as if a constant pulse is being divided different from one division to the other.
Ex. 1.3.4. Tempo modulation at R10
Consequently, if the fastest speed at R5 and 2 measures before R11 is the 16th-
note MM = 582 (where q = 138, 4 x 138 = 582), Boulez maintains the same relative speed of the smallest subdivision in the subsequent sections, despite the change of the metronomic tempo. For instance, at R14, the smallest subdivision is the sextuplet within a quarter-note, which makes the speed of a single sextuplet MM = 540 (where q = 90, 90 x 6 = 540). At R26, the smallest subdivision within a quarter-note is the 32nd-notes, which makes the speed of a single 32nd-note MM = 568/608 (where e = 142/152, 142/152 x 4
= 568/608). At R83, the smallest subdivision is the sextuplet within an eighth-note, which makes the speed of a single sextuple MM = 588 (where e = 98, 98 x 6 = 588). The speed of the fastest note in each of these sections, MM = 582, 540, 568/608, and 588, respectively, are relatively similar within a very small margin, which makes the association among these discrete sections clearly audible. The effect is that all the fast notes will sound fairly equal in speed, while the larger pulse shifts to a faster or a slower rate.50
Structural tempo has another role that spans through a longer duration. Starting at R167, the subsequent tempo markings clearly distinguish two contrasting and alternating sections. One section is marked “Rythmique, énergique” while the other is marked “Très calme” (fig. 1.3.5). These two opposing characters, one clearly rhythmic and polyphonic, the other less metrically orientated and homophonic, are juxtaposed in alternation. The tempi in the beginning for both sections are relatively close, q = 74 and q = 60, respectively. As both sections unfold, the “Rythmique énergique” tempo gradually increases from q = 74 to q = 156, while the “Très calme” tempo gradually decreases from q = 60 to e = 96 (q = 48). Furthermore, the durations of each section are systematically shortened towards the end of this large section. At R220 the two contrasting tempi are juxtaposed down to measure to measure with the greatest difference in tempo, further highlighting the “opposite” characters between the two.
50 Curiously, this method is opposite from Carter, whose tempo changes typically maintains the same basic pulse intact while varying the surface rhythm and the subdivisions within this overall pulsation.
Rehearsal Numbers Tempo Marking
R167
R175
R176
R180
R181
R185
R188
R189
R190
R193
R194
R196
R197
R199
R200
R202
R203
R205
R206
R208
R209
R210
R211
1-R213
R213
R213-4
R214
R214-5
R215
R215-4
Rythmique, énergique (q = 74, e = 148)
Très calme, suspend, régulier (q = 60)
Rythmique, énergique (e = 150)
Très calme, suspend, régulier (q = 60)
Rythmique, énergique (e = 156)
Sub. Très calme, suspend, régulier (q = 60)
Rythmique, énergique (e = 160)
Très calme, suspend, régulier (q = 60)
Rythmique, énergique (e = 166)
Très calme, suspend, régulier (q = 58)
Rythmique, énergique (e = 180)
Très calme, suspend, régulier (q = 58)
Rythmique, énergique (e = 180)
Très calme, suspend, régulier (q = 56)
Rythmique, énergique (e = 184)
Très calme, suspend, régulier (q = 56)
Rythmique, énergique (e = 184)
Très calme, suspend, régulier (q = 56)
Rythmique, énergique (tempo rigide) (e = 188)
Très calme, suspend, régulier (q = 54)
Rythmique, énergique (e = 188)
Très calme, suspend, régulier (q = 54)
Rythmique, énergique (e = 192)
Très calme, suspend, régulier mais tendu (q = 52)
Rythmique, énergique (e = 192)
Très calme, suspend, régulier mais tendu (q = 52)
Rythmique, énergique (e = 192)
Très calme, suspend, régulier mais tendu (q = 52)
Rythmique, énergique (e = 196)
Très calme, suspend, régulier (étirer le tempo) ( q = 52)
R216 Rythmique, énergique (q = 108, e = 216)
R216-3
R217
R217-3
Très calme, suspend, régulier mais tendu (q = 52)
Rythmique, énergique (q = 114)
Sub. Très calme, plus étiré (q = 52)
R217-4 Rythmique, énergique (q = 120)
R217-5
Sub. Très calme, toujours plus étiré (q = 52)
R218 Rythmique, vif (q = 126)
R218-2
Sub. Très calme, tendu (q = 50)
R218-5 Rythmique, vif (q = 132)
R218-6
Très calme, tendu (q = 50, e = 100)
R219 Rythmique, vif (q = 138)
R219-3
R219-4
Très calme, tendu (e = 100)
Rythmique, vif (q = 144)
R219-5
Très calme, tendu (e = 100)
R220 Rythmique, vif (q = 150)
R220-3
Très calme, tendu (e = 96)
R220-5 Rythmique, vif (q = 156)
R220-6
Très calme, tendu (e = 96)
R221 Très rapide (q = 164)
Fig.
1.3.5.
Tempo markings from R167 to R221
Between R26 to R66, the music goes through several interruptions and tempo changes. It is not immediately clear what relationships there are between these sections, or their underlying organization. Boulez, however, maintains the same tempo marking for some of these sections while varying the tempi for the others, prominently highlighting the alternation of these contrasting sections. In the “Vif” sections, Boulez also rhythmically preserves the same subdivision of 32nd-notes and sextuplet throughout, so that these sections are perceived as a unified whole, with intermittently interruptions that use different rhythmic subdivisions (fig. 1.3.6). Similarly, the next section from R83 to R129 goes through the same process of maintaining the same tempo marking for one group of sections while varying the other, further highlighting these alternations and interruptions.
Rehearsal numbers Tempo Markings
R26 Vif (e = 142/152)
R35 (e = 108)
R37 Vif, comme précédemment (e = 142/152)
R45 (e = 96 – 108 – 102 – 96 – 92 - 108)
R49 Vif, comme précédemment (e = 142/152)
R56 (e = 108 – 138 – 118 – 114 – 110 – 106 – 102)
R63 To Vif (e = 142/152)
R66 Assez vif (e = 120 – 132 –
R83 Plus modéré (e = 98)
R85 Plus calme (e = 76)
R87 Plus modéré (e = 98)
R89 Plus calme (e = 74)
R91 Plus modéré (e = 98)
R94 (e = 84 – 92/88)
R102 Plus modéré (e = 98)
R105 Tempo détendu (e = 74), très régulier
R111 Plus modéré (e = 98)
R114 Large (e = 62), très régulier
R126 Plus modéré (e = 98)
R129 Assez modéré (e = 76 – 74 – 72 – 70 – 68 - 66)
Fig. 1.3.6. Tempo markings from R26 to R129
