Unless otherwise indicated, program notes are written by the artists.
Phases (detail) (2020)
Across the surface of the elevated glass box in KINDL, Mareike Lee spatializes enlarged elements from James Tenney’s score Phases and creates a room that glows from within with coloured light. This is in response to and an elaboration of Tenney’s sense of form being the result of structure and their relation in space (also on the page). A hybrid installation, the graphic “postal pieces’ scores will be projected via overhead projector onto a window of the glass box.
Aggregates and Processes (2020)
Aggregates and Processes is a series of 13 posters: a tribute to James Tenney’s inclusive, vibrant and inspirational artistic community. This is a pluralistic collection to honour Tenney’s keen visual sense, and his diverse and curious appreciation of and collaboration with a vast array of composers, visual artists, and friends. The poster images (drawings, photos, scores, words), both archival and newly created, are contributed by Tenney’s colleagues and close inspirations. Lee has worked closely with Lauren Pratt (Tenney’s partner) to source these. Lee enlarged, adapted, and reproduced the material as needed. Images, work, writings, etc., are heterogenous, and include contributions from Phil Corner, Alison Knowles, Malcolm Goldstein, Catherine Lamb, Carolee Schneemann, Chiyoko Szlavnics, Marc Sabat, Nathan Tenney, Justin Tenney, Michael Winter, Walter Zimmerman, et al. The posters are hung spatially in a wavy line echoing forms in Tenney’s scores.
Harmonium #7 (2000) »
Harmonium #7 is one of a set of pieces for various instrumental combinations, all of which are based on variations of the same harmonic progression – moving, by way of a series of gradual transformations, along the “series of fifths”. A companion to Harmonium #1, in which the chords are also microtonally tuned according to JI frequency ratios, this piece explores a symmetric tuning restricted to a space generated by partials 2, 3, 5, 7 and their intervallic combinations, rather than building spectral structures with higher partials as in the earlier piece. It also lies one fifth lower in register. In both scores, the music consists of a sequence of bars containing available pitches, from which the musicians freely choose, playing single notes cresc.–dim. followed by pauses, favouring notes that might not be sounding and thereby creating a shifting kaleidoscope of timbre.
Postal Pieces (IV, VIII, X) »
Koan, August Harp, and Having Never Written A Note For Percussion are three of a set of ten Postal Pieces for various instruments and ensembles, mostly composed in 1970–71. Besides the fact that their scores are notated in such an abbreviated way that each can fit onto a postcard, many of them share another feature: they have the character of a sonic “koan” – a difficult, often paradoxical question given to the Zen student as a means of achieving “enlightenment”. While I am certainly no Zen master — nor have I even had any direct involvement with the discipline – I was intrigued by the idea of an unpredictable experience, for both the performer and the listener, arising out of an apparently predictable, mechanical, yet finally “impossible” musical task. Koan was written for Malcolm Goldstein, August Harp was written for Susan Allen, and Having Never Written a Note for Percussion was written for John Bergamo.
Addendum to Tenney's notes:
The Postal Pieces were written between 1965 and 1971 and produced at the California Institute of the Arts in 1971 with the help of Alison Knowles and Marie McRoy. Continuing a tradition of compact graphic and text scores emerging out of the dada and Fluxus art movements, these works echo La Monte Young’s 1963 Anthology of Chance Operations, including his aphoristic Compositions 1960, as well as numerous other text performance pieces by George Brecht, Yoko Ono and others. Growing out of Tenney’s collaboration with Carolee Schneemann and his work in the 1960s New York performance art scene, as well as his experiences with computer music, the series marks an encapsulation of his interest in static, ergodic textures, clear formal processes or divisions, and increasingly, in musical experiences rooted in fundamental psychoacoustic phenomena and realised on acoustic instruments.
The compositions include three glissando string pieces (#1 Beast, for double bass, #4 Koan, for violin, and #9 Cellogram), which highlight beatings and the subtleties of gradually varying microtonally tuned intervals. The violin work later was adapted and harmonised as the seminal extended JI work Koan for String Quartet (1984) in which enharmonically shifting microtonal intervals to the violin’s open strings generate a remarkable progression of harmonic changes driven by combination tones. #2 A Rose Is... is a visual mandala, a round, minimalistic endless canon on Gertude Stein’s poetic text, reminiscent of the small counterpoints from Bach’s Musikalisches Opfer and the shaped notations of ars nova. #3 (night) is an open text score suggesting a textural possibility and a visual correlation (“very soft, very long, nearly white”). #5 MAXIMUSIC asks the performer(s) to create a three part form in which each part is shorter than the preceding one and in which a soft, resonant cymbal roll (parts 1 and 3) is interrupted by a physically exhaustive, loud complex of freely improvised actions. #6, #7a, and #7b are a set of three Swell Pieces in which instruments fade in and out on individual tones, establishing a style of playing which Tenney often used in later works like the Harmonium series, Critical Band, ‘Scend for Scelsi, and others. #8 August Harp rigorously exhausts the 81 possible pedal positions (flat, natural, sharp) of four notes (A, B, C, D) in four different octaves, always played in a tempo that follows the player’s breath. Finally, #10 Having Never Written a Note for Percussion, perhaps the most simple and remarkable of the entire set, is an extended gradual crescendo from silence to fff and back again played on a large tam-tam.
addendum by Marc Sabat
‘Scend for Scelsi (1996) »
scend...To heave upward on a wave or swell...
[Perhaps from earlier ‘scend, short for DESCEND or ASCEND.]
The American Heritage Dictionary
‘Scend for Scelsi involves a mixture of notations and performance procedures: metrical notation and conventional procedures at the beginning, at a mid-point, and at the end, and – in between – a non-metrical, “available pitch” notation, involving certain decisions and choices on the part of the performers. The procedure to be followed by the players in interpreting this “available pitch” notation is as follows: each player chooses one of the available pitches given by the notation for that segment of the piece, favoring pitches not already being played by someone else in the ensemble, and plays it for approximately 10 to 30 seconds, with the dynamic shape: ppp < p > ppp. After a few seconds pause, the player chooses another of the available pitches and repeats the process described above. During these sections, the conductor does not conduct metrically, but rather – following a stop-watch — simply indicates the times when a new pitch is to be added to the set.
The saxophone begins like just another woodwind instrument, going through the available pitch selection process in the same way as the flute, oboe, and clarinet. But gradually the saxophone separates itself from those other instruments, becoming more active, rhythmically, and more involved in the creation of melodic phrases.
My intention in the piece has been simply to explore new harmonic processes made possible by non-standard or non-tempered tuning systems. In this case, the tuning is based on segments of the harmonic series over three different fundamental frequencies, which together comprise an extended “I-V-I” harmonic progression. This work was commissioned by Westdeutscher Rundfunk Köln for Klangforum Wien on the occasion of the Giacinto Scelsi Festival, December 1996.
Plainsound Study 1 (2015) »
The Two Diatonic Divisions of the Major Third Presented in the Dorian Mode, for violin and double bass, op. 61a
The Plainsound Studies are dedicated to Helge Slaatto and Frank Reinecke, as well as to all violinists and bassists with an interest in the sound and the special performance techniques of non-tempered just intonation. I conceived these etudes in the hope to provide some adequate musical material for the study of intonation. It is about working on the harmonic intonation (the endeavour to research, memorize and optimize the specific timbre of the many different interval sonorities) and in particular about refining the melodic intonation. The latter also involves memory: for the pitches occurring and recurring within the musical context, and for the size and the character or melodic feeling of the interval steps between them.
If we want to further sensitize and train the ear’s melodic feeling, I was thinking, then we could perhaps begin with some systematic rehearsals aimed at producing a conscious distinction between the Major Whole Tone and the Minor Whole Tone. The Major whole-tone step is defined as the difference between a perfect fifth and a perfect fourth (the frequency ratio 9:8 or circa 204 cents), whereas the Minor whole-tone step is established by the difference between a perfect fourth and a pure minor third (10:9 or circa 182 cents). These two intervals constitute the basis for the practice of non-tempered just intonation, and they sound as distinct from each other as the sun and the moon, even though their difference in size is but a Syntonic Comma.
During the preparations for the composition of the etude I found, to my surprise, an extremely effective rehearsal method which makes it possible to acquire a feeling for this distinction between the two whole-tone steps within a very short amount of time: the comparison of the two diatonic divisions of the major third. This is as it were the subject of the piece. The melodic progression G–A–B, for example, can be sung or played on the violin in two different ways, simply and solely by following the natural instincts: first according to the frequency ratio 8:9:10 as in the G major sequence G–D–A–G–A–B, and then in the related key of E minor as in the sequence G–E–A–G–A–B, where the note A is understood as the perfect fourth above E and thus tuned a comma lower, so that this time the order of the two consecutive whole-tone steps is reversed.
The melody that comes in at the beginning of the piece almost imperceptibly in the double bass part and is later continued by the violin (all the way up into the highest register at the end of the fingerboard) is in the old syntonon-diatonic Dorian mode, based on the tonic note E, which is tuned to the G string and a comma lower than the pitch of the E string. This mode features both diatonic divisions of the major third between its 3rd scale degree (G) and 5th scale degree (B), as it employs both a major sixth (C#), the so-called Dorian sixth, as well as a minor sixth (C) on its 6th scale degree. It is quite astonishing that these minute comma distinctions can indeed be heard and performed on the violin with great precision and pleasure even in the very highest register, thanks to the drones played by the double bass.
Ryoanji (1983–5) »
John Cage’s Ryoanji was inspired by the famous Japanese rock garden, or kare-sansui, at the Zen temple of the same name located in Kyoto, which contains 15 stones of different sizes surrounded by raked white sand. Ryoanji is actually a series of works – pieces exist for solo oboe, voice, flute, double bass, and trombone, each accompanied by a percussion or 20-member orchestra part. Any combination of the solo pieces may be played simultaneously.
Cage developed the solo parts by tracing the contours of 15 stones. These curving lines are to be played as smooth glissandi within specified pitch ranges, according to the performance notes, “as much as is possible like sound events in nature rather than sounds in music.” At times the curves overlap with each other; in such cases the soloist may prerecord the overlapping parts and perform live along with the recorded playback.
The piece for trombone, composed for James Fulkerson, is notable for its extremely low tessitura. This presents a perceptual challenge for the listener: to detect often slight differences of pitch in the near-infrasonic range.
text by M.O. Abbott
Part Song (2017) »
for violin and contrabass
Part Song was composed as part of an ongoing series of pieces exploring extended just intonation on acoustic instruments in small chamber ensemble settings. In this case, the symmetrical tuning of violin and contrabass suggested an unfolding fanning outward from unison, featuring along the way the absolute consonances between open strings (2/1, 4/1, 8/1, 16/1) and various other simple, wide tuneable intervals of the form n/1, n/2, n/3, n/4, n/5, met in a simple melodic counterpoint of two parts.
Quintext : Five Textures for String Quartet and Bass (1972) »
The five textures alternate three perspectives on the harmonic series (I, III, V) with two stochastically pitched textures. Each is dedicated and titled with respect to a colleague composer of experimental music, and is offered as a kind of homage-distillation of some element inspired by their respective practices.
The first texture, Recent THOUGHTS for Morton Feldman, consists of tones, entering always at the beginning of a bar, fading up to pp during one quarter-note, and sustaining through some number of bars before fading down for one additionally tied quarter-note beat. The first 13 odd harmonics of F are treated as pitch-classes, presented without hierarchy in all registers, defying the normal disposition of an harmonic series while exploring various resulting microtonal chords. As the movement concludes, in its last four measures, the fundamental is doubled in both bottom and top voices, combined with partials 3°, 5° and 7° in the inner voices to produce a kind of “tonal” cadence. The title acknowledges the soft dynamics and especially harmonic character in Feldman’s music, notably offering a microtonal shading that Feldman himself was to take up five years later with his own use of enharmonic spellings in “Spring of Chosroes” and many of the subsequent chamber works he is now so renowned for.
II. CLOUDS for Iannis Xenakis alternates blocks of approximately placed and tuned pizzicati in all five instruments with blocks of collective silence. The sound-silence units are reduced in length by one second on each iteration, while the balance of the two components gradually shifts to favour sound rather than silence. Halfway through, the pattern reverses. By attending precisely to the less immediately perceptible parameter of slow formal time and delineating it as figure and ground, the construction of temporal gestalt units as Tenney describes in his “Meta+Hodos” is highlighted.
III. A choir of ANGELS for Carl Ruggles honours Tenney's friend and mentor, recalling the muted brass of Ruggles’ well-known chamber work Angels by the use of extreme ponticello and maintaining a similarly narrow register. Returning to the harmonic series of texture I, here the consistent use of the middle register allows more complex, dissonant intervallic relationships to shine as extended JI since their implied fundamental remains, though still low, more stable and salient.
IV. PARABOLAS and HYPERBOLAS for Edgard Varèse, with its continuous band of glissandi, fff and full-toned throughout, echoes both Varèse’s poetic notion of a complete and continuous sound-space offering a new world of musical possibilities and also reminds us of his use of sirens to sculpt pitch in an almost visual manner.
Finally, V. SPECTRA for Harry Partch, employs scordatura strings to establish a branching network of harmonics of harmonics (a technique revisited in one of Tenney’s final works, Arbor Vitae for string quartet), providing effortless access to the more microtonal high primes 7°, 11°, 13° and their partials. With the unchanging low F in the contrabass, these harmonics explore the contrast between identities as actual pitches, and their capacity to double spectral components of the fundamental, making this composition one of the early examples of the uniquely North American approach to the spectral technique of composition. As in the later work BRIDGE, Tenney responds to Partch by focussing on his harmonic theories, countering the rhythmic patterning of Partch’s music with a softer, Cagean world of pitches played in time-space notation against a time-clock.
text by Marc Sabat
View (2019) »
View is a piece for cello in 13-limit just intonation and was written for cellist Émilie Girard-Charest in 2019. The performer of the piece uses a curved bow (Bach-bogen) to produce dyads and triads, melody and counterpoint. The top string of the cello is tuned down to create a neutral third – 11/9 with the lower adjacent string, and this neutral third is a recurring pivot point from which the music bifurcates into denser harmonic fields. The piece was composed using a guitar that could resemble the specific cello set up – namely a 4-string fretless acoustic guitar played with a violin bow. View can be actualized on such an instrument, and in this way it is a part of an ongoing project of extending the prospect of the guitar as an instrument apt for tuning issues and sustained sound.
Partite Requiem (2019, German premiere) »
commissioned by Jay Campbell and the Los Angeles Philharmonic
Partite Requiem was written in remembrance of the life and work of one of America’s most remarkable 20th century composers, just intonation pioneer Ben Johnston (1926–2019). I had the opportunity to meet Ben in 2008, when we worked together to realise a performance of his long unheard orchestra work at the Donaueschinger Musiktage in Germany. His gentleness, warmth and insight has had a profound influence on my own work. He suggested that choices we make in artistic creation might come from sensing the interconnectedness of things: of thought, matter and vibration. As makers we share a responsibility to reveal such experiences in all their complexity and simplicity: direct, true, untempered, unadorned. The perception of harmonic sound senses proportional relationships of frequencies as interactions of tone, opening a subtle continuum of relative consonance and dissonance, becoming melody, counterpoint, music.
Prisma Interius VIII (2018) »
“The intention is to narrow (our own) filters and to approach a kind of thread that could have a feeling of an infinite space. From one inner point of listening, being very individual and personal – from that point one could listen with the others into the outer atmosphere and see the connectivity of everything. That’s ideal. That’s what i am trying to find, that space. What is the limit of connectivity from one point to the absolute, outside...”
from an interview with Rebecca Lane (2019)
From a series of nine pieces, Prisma Interius VIII has three layers of duo parts. The first being the melodic duo, whose role is to guide the momentum forward—melodicism initiates harmonicity. The second duo is referred to as harmonic smearing, creating residues or augmentations to the initial duo’s unfolding. The third layer are two secondary rainbow synthesizers gathering the outer environmental atmosphere with live microphones, and through a kind of Aeolian harp processing via resonant band pass filters, they highlight/follow the harmonic space of the piece. Beginning within an 81/80 pivot, the piece continues to shift/blur between low prime-limit relations, searching for the edges of their complexity while allowing for patterned aggregates to blossom.
WENN (2020, premiere) »
In its original form, WENN is a song based on a poem by Luisa Rüster titled Wenn wir es wiedersehen.
Wenn wir es wiedersehen.
Wenn wir uns wiedersehen.
Wenn wir es anders wiedersehen.
Wenn wir uns anders wiedersehen...
Verabschieden wir uns neu.
Verabschieden wir es neu.
Verabschieden wir uns anders neu.
Verabschieden wir es anders neu.
Und sehen erneut mit anderen Augen.
What draws me most into this small text is how Rüster employs a simple, linear process of transformation as a structural framework on which to explore – briefly, directly – a complex interplay between some of the perhaps most characteristic sounds in the German language: w, v, s, sch, etc. For me, the process of composing in just intonation often forms a rather direct analogue: simple, even non-rhetorical temporal forms and processes form an ideal basis to investigate characteristic interactions of tone deeply linked to auditory perception. In this performance with the Harmonic Space Orchestra, we strip away the surface-most layer of WENN's sound by substituting voice with alto flute. In a sense, what remains is what might have been the voice's tonal resonance, and – as if with magnifying glasses – Rebecca Lane, Sarah Saviet, Sam Dunscombe, and Michiko Ogawa carry out a particular examination of the piece's harmonic and melodic substance.
Partial Response (2000) »
Partial Response was the precursor of the compositional method that came to me in 2003: producing beautiful line drawings as the basis of my work. This was my first (and only!) purely graphic score (from which musicians perform), and I created it using a now-obsolete graphic notation program, called "Notewriter", which enabled me to work with extended lines, and place visual elements however I pleased. This piece was my second exploration of ratio-related intervals. But it was my first scoring of extended sustains, slow glissandi, and intentional beating. It opened up the path for the many compositions that followed, for over a decade, from 2003–2014, all of which first appeared as line drawings.
For this solo acoustic guitar performance, so sensitively and carefully prepared by Fredrik Rasten, the original score for three musicians has been adjusted to accommodate the single timbre of the guitar, and in response to some of the physical challenges the material presents, like playing simultaneous glissandi, or using multiple ebows. The resulting magical music is very close to the heart of my musical aesthetic – i.e., sinewaves – but the interpretation and physicality of Fredrik playing his guitar makes some of my favourite sounds truly alive.
Quick Figure (first steps in harmonic space)(2010) »
Quick Figure is one of a series of works I created for a concert of violin duos in 2010 at Berlin's exceptionally resonant Haus19. Its first performers were Daniella Strasfogel and Biliana Voutchkova. The piece began as a very reduced drawing. I decided to interpret the lines in a new manner (new for me, at least), and that was to create some simpler intervals around the difficult-to-tune 13-limit of the harmonic series. Although some of these "simple intervals" are easily recognizable as a pure ninth (9:4), a large major second (8:7), or a pure fifth (3:2), they are extremely difficult to perform, as is playing a glissando while sustaining another string!
The subtitle, first steps in harmonic space, referred to my first conscious use of creating simple intervals around a prime greater than 3, as inspired by Tenney's notion of a "harmonic lattice". I am grateful to Sarah Saviet and Johnny Chang for also being brave enough to take these first steps with me.
Freehand Poitras (2008) »
Originally composed for a dance project by Canadian choreographer and dance artist, Robin Poitras, the string trio, Freehand Poitras, explores the space within certain bounding intervals of the D and C harmonic series through a single glissando, and through (often subtle) chordal shifts. Each measure is followed by a breath-like rest, and some measures are repeated several, or many times. I am excited to hear this version performed by HSO members Johnny Chang, Sarah Saviet, and Judith Hamann!
BRIDGE (1984) »
Plainsound Glissando Modulation (2006–7) »
Raga in just intonation, for violin and double bass, op. 49
Some basic questions for the composition of this piece
How can a viable completely microtonal music be made – and function in a graceful way – in which as many different pitches of the glissando continuum as possible are distinguished and tuned harmonically to each other?
How can this microtonal pitch repertoire be successfully accessed and refined by a rigorous application of non-tempered just intonation, so that a wealth of complex harmonic sounds will emerge: surprising new consonances and new dissonances that will immediately make sense to the ear, even if they may have never been heard before?
How can the ancient performance practice of just intonation be revitalized now through a concerted effort of composers and performers to thoroughly explore and demonstrate its wonderful brilliance and sonority (like it happened in the choral music of the Renaissance, or continually in the classical Indian music), so that it may perhaps find new friends within the realm of western music as well?
How can the instrumental and ensemble playing techniques be developed and practiced that will enable musicians to familiarize themselves with the specific timbres (“periodic signatures”) of the various microtonal just intervals, so that these sounds may indeed become readily retrievable with an astounding degree of precision?
Which aesthetic and structural concepts can be derived directly from these new virtuoso tuning and performance techniques? How can the counterpoint and its instrumentation be optimized in their function to support the intonation in each instance, and how can a continuous musical flow be generated by a polyphonic harmony incorporating natural sevenths, tuned quartertones, and just intervals based on higher partials (13, 17, 19, and 23) in its microtonally modulating sound progressions? – The piece is dedicated to Helge Slaatto and Frank Reinecke.
V1 (2020, premiere) »
V1 was composed for the Harmonic Space Orchestra in spring 2020, intended as the first in a series of works focused on trichords wherein two pitches are easily tuneable to a third pitch, but not to each other. In V1, these trichords are made larger by adding tuneable first-order sum and/or difference tones, resulting in chords with 4–7 total pitches. The net effect is that each larger chord has two subsets (which share one common tone) that are relatively easy to tune in isolation, but difficult to tune when all pitches are sounding. Entrances are staggered in each large chord in an effort to more easily facilitate the possibility of precise tuning. The chords are linked together by a series of common tone modulations, on a stochastic journey through James Tenney's model of harmonic space. Variations in orchestration and register over the course of the piece provide further dimensions for contemplation.
Mirror (2006/7) »
Mirror (2006/7) came out of a period of early development exploring string harmonics, timbre, and subtle coloration through various alterations of sympathetic resonances. This was my way of “unlearning” western harmonic theory. It is one of the first pieces where, through the use of scordatura, I became interested in the differing resonating capabilities of the body of the instrument, where particular nodes are highlighted simply by those alterations. The sounding body transforms and breathes differently, due to particular harmonic alignments as well as the materiality of various nodes being activated which otherwise might be sleeping.
The piece emerged out of a quartet for bass flute, viola, contrabass, and contrabass clarinet entitled Alchemy/Bloom, the last piece I was able to share with James Tenney before his passing in 2006. Alchemy/Bloom has a strictly notated structure, where methodically, slowly, over time, the musical material opens into the tuning cavity of the contrabass. In comparison, Mirror begins, immediately, purely in sound, in that resonating cavity Alchemy/Bloom opened into. The structure is looser and more open to a being activating the sound, as well as the sound itself directing the musician. Pathways unfold and linger into various areas of the cavity, crystal, or wave – directing the attention to various portions of it, moving from one angle to its inverse.
The harmonic material is instigated by the partial relationships of the four fundamentals of the contrabass. The simple reduction of the material, perhaps, is the relationship of 50:49 and it’s inversion 49:25, two saturated tones multiplied, in relation to one another and together instigating a concentrated timbre containing the vibrating whole.
Around 2008 in Los Angeles, Frank Reinecke and Helge Slaatto were working with and performing Wolfgang von Schweinitz’s Plainsound Glissando Modulation. I was so taken with Wolfgang’s piece and their beautiful interpretation that I, without thinking, lost my shyness for a moment and gave Mirror to Frank. Around 2013 I got a call from him to say that he had been working on it every now and then and would like to record it! It was revealing for me to listen to a musician tuning their harmonics with such subtle care, simply because the relations he was shaping with his bow were so familiar to him!
Divide (2019, premiere) »
a lullaby for Murielle
The simplest divisions of a perfect fifth are made by groups of neighbouring harmonics. Division into two parts produces the major triad 4:5:6, highlighting the 5° partial; into three parts, the septimal tetrad 6:7:8:9, highlighting 7°. By extension to four and five parts the aggregates 8:9:10:11:12 and 10:11:12:13:14:15 derive. Each such combination, when sounded as a chord, increasingly manifests a sensation of psychoacoustic consonance known as spectral fusion. Individual pitches become subsumed within a collective sonority called the periodic signature.
The characteristic intervallic flavour of each odd partial is most striking, however, when combined with mainly Pythagorean notes (3,9,27,...). This highlights perceived consonance whilst retaining the qualities of an independent note. Thus, the simplest chords featuring 11° and 13° are 8:9:11:12 and 10:12:13:15. Both introduce harmonic series gaps forming symmetric difference-tone chords (1:2:1 and 2:1:2 respectively). Notice that the traditional minor triad of partial 5°, 10:12:15, which inverts the order of constituent intervals 4:5 and 5:6, is contained within the chord of 13°.
I imagine these sounds, embedded within a stable 2:3, as root position basic chords of extended rational intonation, providing a sonic bridge balancing the intense periodicity of fusion, and the microtonality of the constituent notes. Divide is a flowing poem ebbing between the three higher-prime tetrads modulating through all their combinations as chords, melodies.
Glissade (1982) »
Within the total "sound-space of musical perception" (a term coined by John Cage) there is a more limited region that I call harmonic space. This region is bounded by various thresholds of harmonic perception, which lie somewhere between the polar extremes of tone vs. noise, stable vs. unstable pitches, rational vs. irrational pitch-relations, etc. Near these thresholds, specifically harmonic relations between sounds may suddenly seem to emerge from chaos – and then just as suddenly sink back into it – like some "elementary catastrophe" of René Thom. Glissade explores these thresholds, while at the same time manifesting some of the same formal concerns which have characterized my work for many years: stochastic processes (as in movement V), canon (I, II, and V), and simple forms delimited by boundaries which are somehow intrinsic to a given medium (II and IV). This work was commissioned by the Ontario Arts Council for the Array Ensemble.