PLACE WHERE RUSHES GROW: Analysis of the first sixty-five bars from Iannis Xenakis’ Jonchaies Xenakis’ Jonchaies
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Iannis Xenakis (1922-2001) was a Greek-French architect who was as much a composer as he was an engineer and designer. Born in Brăila, Romania, he moved to Greece in 1938 to study civil engineering in the National Techni cal University of Athens (also known as Athens Polytechnic), graduating in 1946 despite the ongoing violent conflicts in the country. Xenakis personally participated in the fight, first as part of the National Liberation Front in resistance against the Axis occupation during World War II, then as part of the Greek People’s Liberation Army against the British occupation. It was during a street fight against British tanks that Xenakis was wounded and disfigured by a tank shrapnel that left his face he avily scarred and blind in his left eye. In 1947, when the Greek government started to track down resistance members as criminals, Xenakis fled Greece to Paris, France. Th ere he found employment in the studio of the architect Le Corbusier, one o f the major pioneers of modern architecture, quickl y working up from an assistant to managing major p rojects independently. This architectural experience heavily influenced his compositional approach, leading to the critical acclaim of his first major work Metastaseis (1953-54) that premiered in the Donaueschingen Festival. Xenakis would quickly rise to be considered one of the most original composers po st-World War II, specializing in graphic and computer-assisted compositions, notably the UPIC.1 The piece Jonchaies was composed in the middle of Xenakis’ compositional career (the first major work being Metastaseis in 1955, and final work being O-Mega in 1997). It was written in 1977, commissioned by Radio-France for the finale of Cycle Xenakis, a month-long festival dedicated to his music. Premiered by the Orchestre National de France on December 21st, this piece was a major orchestral work for 109 musicians. This piece, especially the opening
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Benoît Gibson, The Instrumental Music of Iannis Xenakis: Theory, Practice, Self-Borrowing (Hillsdale NY: Pendragon Press, 2011), xvii.
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section, showcases his period of interest in the ide a of pitch sieves. Sieves are devices to separate wanted material from unwanted material; Xenakis develops the term into the sieve theory, a musical tool that emphasizes the concept of symmetry through a series of points either constructed intuitively, given by observation, or fabricated completely from moduli of repetition.2 These sieves have no pitch predominates that can be considered a tonic. Comprised of five major sections, Jonchaies explores the relationship between individual and collective motions in the fractal phenomenon proposed in 1975 by mathematician Benoit Mandelbrot (1924-2010), and the relation of the fractal concept to the title of the piece. This paper will focus on analyzing the first section: the first sixty-five measures. The first thing evident when looking at this section is the instrumentation: only strings are playing with touches of percussion. The strings begin notated in the traditional order, but mix together by measure 10 into a string formation composed of six separate parts with three subgroups, each instrument specified down to the seat number.3 This unusual choice reflects the nature of the title; Jonchaies is French word that roughly translates to “place where the rushes grow”. Rushes, scientifically known as Juncaceae, are a grass-like plant that grows in clusters; when blown by the wind, each strand of rush would respond, but from the observer’s point of view the cluster would also be considered an entity in of itself responding to the wind. This reflects the idea of fractals. Fractals are figures where each part of the figure would be a smaller replica of the figure itself, creating a never-ending pattern. The fractal phenomenon can be found in nature as well, but as approximate models with finite repetitions like the crystallization of snowflakes. Though each instrument has its own response to the parts it is given, from the
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Iannis Xenakis and John Rahn, “Sieves,” Perspectives of New Music 28, no.1 (1990): 66. Arturo Tamayo, “Notes on the Interpretation of Iannis Xenakis’ Jonchaies,” in Performing Xenakis, ed. Sharon Kanach (Hillsdale NY: Pendragon Press, 2010), 353. 3
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listener’s point of view the instruments and parts would be co nsidered collectively as a single entity of sound. In this section, three layers of fractals can be seen in the instrumentation: first layer being the fractal of each section to the collective melody, second layer being each subgroup of glissando, arco, and pizzicato to their corresponding sections, and the third layer being each individual instrument to their corresponding subgroups. The imperfection of natural fractals will be a crucial theme in this section, referencing back to the inspiration that formed the title of this piece. Another element that is evident right away are the pitches and intervals used in this section: after the dramatic opening glissando and sustained B6, Xenakis sets up context for the main motif cycle in measures 10 and 11 by a small modal melody made up of minor second and major third intervals.4 This modal melody paves a structure of intervallic seconds and thirds by which the section’s pitch sieve builds upon; a mode of seconds structured around two major thirds and one minor third.5 These two measures and the resulting pitch sieve hints at the sonorities of the pelog scale of Indonesian gamelan music, something Xenakis admits to being influential to his music.6 To further this relationship between the pitch sieve to the pelog scale, interlocking fourths were constructed by a major third surrounded abov e and below by a semitone. This is a device Xenakis personally found to be a “a powerful melodic structure” within the pelog scale.7 It can also be found in the sieve, outlined in measures 10 and 11 in stepwise motion to evoke the atmosphere and sonority of gamelan music.8 Interestingly, the sieve pattern does not repeat at the octave, but rather at intervals of seventeen semitones, or an
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Appendix Figure 1. Appendix Figure 2. 6 Bálint A. Varga, Conversations with Iannis Xenakis (London: Faber and Faber, 1996), 144. 7 Ibid., 145. 8 James Harley, Xenakis: His life in Music (New York: Routledge, 2004), 109. 5
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octave and a fourth. However, unlike the pelog scale which traditionally consists of seven pitches, the pitch sieve consists of nine pitches before restarting the pattern. Structurally, measures 10 and 11 are a continuation of the sustained B6 from the introduction, being an elaborate embellishment that functions to introduce the sonorities to be evoked by the first major section’s pitch sieve. This view is merited due to the sustained monophonic texture until measure 12 and the changes that occur in that bar. In measure 12, the sustained B6 breaks into a small transitional segment by repeating the B6 as an embellishment tone; this repeated B6 is important to note as this is the only time that a repeated note occurs within the entire section outside of the introduction. The unique occurrence of this repetition suggests that this is an deliberate compositional choice; a nd with Db7 as the focal point of measure 12, the repeated B6 becomes the point of separation between the previous sustained note and the new transitional material. The repeated B6 also establishes the breakawa y from monophony as String 2 separates from the t exture with a condensed transition, leading to the first but hidden entry of the pitch cycle by the end of measure 12.9 This first easily unnoticed entry of the pitch cycle relates back to the idea of the movement of rushes in the wind, how typically the first rushes that sway would be undiscerned until the collective cluster begins swaying as well. Visually and aurally, measure 12 represents a departure and transitional point into the first major section of Jonchaies. The first major section (bars 14-63) builds itself entirely on a pitch cycle. T he pitch cycle is officially introduced in measure 14 by Strings 1, 4, 5, and 6, beginning with pitches D6-F#6G6-D6.10 The entire cycle can be found in String 2, beginning from the D6 on the last eighth beat
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Appendix Figure 3 Appendix Figure 4.
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of measure 12 to the triplet eighth C6 ending on the second beat of measure 49, repeated in every other part in different rhythms.11 Lasting approximately two hundred eighty-six pitches before restarting, it is interesting to note that Xenakis introduces the cycle prematurely in String 2 at the last eighth beat of measure 12, and in String 3 at the third beat of measure 13 before strongly stating the cycle in the remaining four string parts in measure 14. This relates again to the image of rushes reacting to the wind; there will be strands of rushes that begin to sway before the cluster follows, yet the observer still realizes that the actions stem from the same origin. One would also quickly notice that even though the form of a pitch cycle exists, there are many liberties in handling pitch and embellishments amongst the different parts. These liberties can be found as early as measure 14 in String 3 before the supposed fourth pitch of the pitch cycle (D6), where the D6 is delayed by embellishment pitches C-D-F#-G functioning to prolong the G6. Differences can be seen even in the transitional material. Though String 1 and 2 follow the same pitch material beginning in measure 12, String 1 encompasses an extra G6 absent in String 2 that acts as a passing tone between B6 and F#6. Despite the differences in parts, this section should not be considered an texture of imitative polyphony, but rather heterophon y, as the parts still stem and follow the same material in a linear fashion. Just as the rushes all sway in the same direction, the parts all follow the same material even if there are discrepancies in the details. These liberties from the cycle do not deprive the parts from the sense of conforming texture in this piece, but create an “organic” texture emphasizing the special relationship between individual and collective motions within a natural fractal phenomenon. The discrepancies between parts ultimately differentiates the progress of each part along the pitch cycle; each part ends at a different area along the pitch cycle when they arrive at
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Appendix Figure 5.
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measure 63. This is the order of the parts starting from the part that ends the earliest in the cycle with the least number of pitches: String 1, S tring 5, String 4, String 6, String 3, and finally String 2 being the part with the most number of pitches. The endings of parts with less pitches can be found in the parts that have more pitches. The ending for String 2 appears the earliest even though it has the most number of pitches because it extends past the first cycle to repeat the pitch cycle a second time. The ending of String 2 is also the only ending marked in all the parts with a ( ) cresc poco a poco; this dynamic marking, as well as pizzicato changes in group C are f structural checkpoints along the pitch c ycle. Though the markings itself are subject to the variations as well, they generally fall within these areas: the first violin pizzicato occurs on the D6 four pitches in, contrabass pizzicato on the sixty-fifth pitch on E3, ( ) cresc poco a poco on f the lowest pitch of the cycle of A2, return of violin pizzicato on G#3 symmetrically reversing the 4 pitch figure from the contrabass pizzicato checkpoint (C#4-A3-G#3-E3), and violin arco returning sixty-five pitches away from the end of the cycle on F#6. These markings can be found in position in appendix figure 5 except for the second violin pizzicato, where String 2 shifts the marking to A#3 two pitches after G#3.12 The pizzicato changes assist the parts in understanding their current position on the contour that the cycle forms amidst their individual variations. Though the “base” cycle is not one of the parts itself, it is evident the parts are all mo ulded from this cycle; just as observers can identify rushes for what it is even if there are no single exemplar rush, the pitch cycle can be observed in the parts. These general checkpoints act as distinguishing features for their coherence. These checkpoints function structurally as well, signifying changes in the cycle contour: the D6 violin pizzicato signals the beginning o f the contour’s descent in pitch and the entry of
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Appendix Figure 5.
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cellos, the E3 contrabass pizzicato signals the disappearance of the violins, the A2 ( ) cresc poco f a poco sounds the lowest pitch and signals the pitch to begin their ascent, the G#3 violin pizzicato marks the return of the violins, and the F#6 violin arco signals the top registers of pitches along with the departure of cellos. If graphed, the contour of the cycle based on just the checkpoints would form the shape of a “V”; it starts and ends in a similar position, with the middle dipping down to the lowest position. Arguably then, the motif D6-F#6-G6-D6 that introduces the listeners to the cycle does not actually start at the beginning of the cycle, but rather an entry into the loop. This reflects the nature of fractals as a never-ending pattern, and entry to this phenomenon does not equate to realizing the beginnings and ends of the fractal but rather just a point of reference to begin exploration. It would be more appropriate then to refer to the contour of this section as part of a continuous sine wave, rather than the shape of a “V”.13 If seen as a sine contour then, it can again be a reference to the infinite nature both the sine wave and fractal, as well the finite nature in the natural occurrences of both phenomenon, attaching to not only the title but also the medium of sound the piece is conveyed through. It is also interesting to note the pitches of these structural checkpoints: D6, E3, A2, G#3, F#6. Not only is the idea of symmetry seen in their registers (6-3-2-3-6), the pitches between the identical registers form ascending major third intervals leading to the singular A2. This is an interesting detail and potential reference to Xenakis’ value on symmetry and structure. In conclusion, Xenakis’ Jonchaies incorporates multiple levels of musical structures such as sonority and form to the imagery of natural “jonchaies”; even from just the first sixty-five measures, the elegant display in interweaving com plex idea of natural fractals into the music on
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Appendix Figure 6.
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multiple levels is worthy of discussion and analysis. As James Harley words the imagery, “from the global perspective, there is an identity to the behaviour of the rushes, but from a more microscopic perspective, there is much variation and complexity in the relationship between the stalks.”14 Xenakis accomplishes exactly this musically in the first sixty-five measures of Jonchaies; even without approaching the mathematical side of the music, a serious attempt to analyze his music will open the observers’ minds to a dif ferent approach to the use of music and structure. Even though this music may be difficult to approach both visually and aurally for most people in the beginning, an attempt is highly recommended due to the results it yields after overcoming these hurdles.
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James Harley, “Graphic conception of musical structure and sonority in Jonchaies by Iannis Xenakis” in Xenakis Matters, ed. Sharon Kanach (Hillsdale NY: Pendragon Press, 2012), 209.
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Appendix
Figure 1. Melodic line that transitions the opening into the main cycle; at first glance it may suggest the key of G major, but the line functions more likely as an embellishment for the prolonged B6 while introducing gamelan-like sonorities. Xenakis’ preference towards the distinct sound of interlocking fourths inside the Indonesian pelog scale can be seen here, using the minor second intervals as neighbour tone pivots (red boxes). The red arrow suggests an intentional intervallic retrograde inversion (pivoting on an imagined A6), beginning on the first beat of measure 10 and ending at the red line.
Figure 2. Sieve used for the first section of Jonchaies; it is a 17-semitone pattern accentuating 2 major third intervals (4 semitones) and 1 minor third interval (3 semitones). There are 2 interlocking fourths built within pattern (5 semitones). These elements resemble the sonorities of gamelans playing in the pelog scale.
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Figure 3. The transition from introduction into the pitch cycle. The aural center breaks away from the sustained B6 to D b7 in measure 12 before descending onto D6, beginning the pitch cycle (red arrow). The B6 is repeated in measure 12 as an embellishing passing tone towards the D b7 (green box); this is the only time a note is repeated in the entire section since the staves split from traditional notation into specific string parts. The transition also introduces heterophonic texture and foreshadow the liberty the parts have away from the pitch cycle. Rhythm aside, String 1 deviates from String 2 by the measure 13 with the inclusion of G6 functioning as passing tone (blue circle). The G6 can also be a reference to the interlocking fourths between pitches B6-F #6 and pitches G6-D6, reminiscent of the pelog scale. However, it can also be argued that it is String 2 that deviates from the transitional material by excluding the pitch G6 on its descent to allow for the inconspicuous first entry of the pitch cycle on the last eighth beat of measure 12. Since there are no “correct” part to compare to, this is up to speculation; creating variations that run on the smaller scales while maintaining unity on the larger scales sums up the intention behind this section.
Figure 4. The beginning of the approximately 286-note pitch cycle that is the base material of measures 14 to 63. Though these pitches introduce the cycle, the first checkpoint occurs four pitches away (D6 end of first bar) with the violin pizzicato marking in group C. Upon looking at the contour and checkpoints of the cycle, these pitches can be reassessed as simply an entry point into a continuous cycle rather than a definite beginning. This idea ties into the concept of fractal in its continuous patterns, and how analysis must begin with the awareness the entry point for said analysis may occur at any point along the pattern.
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Figure 5. Pitch cycle, based on the String 2 part. As each part has its own slight variations it is impossible to define the base pitch cycle that the parts are based off. This relates back to the title Jonchaies, where there are no “epitome” rush that defines the rest, but rather a cluster of highly similar rushes that the observer would then conclude as derived from the same origin. It is noted that unlike the other markings, the locations for markings sempre cresc and ff sempre cresc are independent of the pitch cycle; sempre cresc occurs on beat 1 of measure 34 and ff sempre cresc on beat 1 of measure 46 on all parts. All other markings occur as checkpoints for the pitches, with slight variations:
The first V.pizz is usually 4 pitches from the beginning of the pitch cycle, near D6 (String 3: C6, second String 6 entry: F#5) CB pizz is usually 65 pitches from the first V.pizz, near E3 (String 3: A3) ( f ) cresc poco a poco is usually 19 pitches from CB pizz, and foreshadows the ending pitches of string 2’s cycle, on A215 Second V.pizz is usually 27 pitches from ( f ) cresc poco a poco, near G#3 (String 2: C#4) V.arco is approximately 107 pitches from the second V.pizz, on on F #6; this is the only marking that has no distinct amount other than being above 100 pitches Pitch cycle makes a full circle and restarts exactly 65 pitches away from V.arco, on D6 These observations are adapted from the 1977 Salabert edition score. -
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String 1 and String 5 of the Salabert edition placed marking “( f ) cresc poco a poco” on the first beat of measure 30, physically located on the first bar of a new page after a page flip, on the B b2 twenty pitches from CB pizz for String 1, and on the third tied A2 pitch for String 5. Due to the ongoing presence of errors in the edition, a decision was made after lo ng deliberations to shift the marking in these two parts to the beginning of A2 nineteen pitches from CB pizz consistent with the other parts.
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Figure 6. Graphic representation of the pitch movement from each string part in Jonchaies, from measure 10 to measure 63. The “V” contour can be seen based on the pitch cycle (red arrow and circle at t he beginning and end of pitch cycle on String 2). However, when using string 2’s contour as a reference for how contour will continue, a sine wave contour would be a more appropriate categorization.
Figure 7. Comparison chart between the pitches from the first violin pizzicato in group C of each instrument until contrabass pizzicato. There are consistent patterns in the differences between parts; the first cycle of String 2 lacked a pitch “c” but contained an extra pitch between pitches “ea” that no other parts, even in the second run of the c ycle in String 2. Each part contains similar discoveries though it will not be shown here; there are no individual parts that can be considered the “base” pitch cycle, even if it is evident they all stem from the same cycle by their similarities.
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Bibliography
Varga, Bálint András. Conversations with Iannis Xenakis. London: Faber and Faber,1996.
Gibson, Benoît. The Instrumental Music of Iannis Xenakis:Theory, Practice, Self-Borrowing . Hillsdale NY: Pendragon Press, 2011.
Harley, James. Xenakis: His Life in Music. New York: Routledge, 2004.
–––. “Formal Analysis of the music of Iannis Xenakis by means of sonic events: Recent orchestral works.” In Presences of Iannis Xenakis, edited by Makis Solomos, 37-52. Paris: Cdmc, 2001. ––– . “Graphic conception of musical structure and sonority in Jonchaies by Iannis Xenakis.” In Xenakis Matters: Contexts, Processes, Applications, edited by Sharon Kanach, 205-217. Hillsdale NY: Pendragon Press, 2012.
Tamayo, Arturo. “Notes on the Interpretation of Iannis Xenakis’ Jonchaies.” In Performing Xenakis, edited by Sharon Kanach, 353-366. Hillsdale NY: Pendragon Press, 2010.
Xenakis, Iannis. Jonchaies pour grand orchestre. Paris: Editions Salabert, 1977.
––– . Formalized Music: Thought and Mathematics in Composition. Edited by Sharon Kanach. Stuyvesant NY: Pendragon Press, 1992.
––– , and John Rahn. "Sieves." Perspectives of New Music 28, no. 1 (1990): 58-78. doi:10.2307/833343.
