The Philosopher's Stone Matrix
Site of Composer and Artist Elodie Lauten

Composing with Universal Hierarchies
an article by Elodie Lauten

[Note: illustrations not included, available upon request]

Is there any point in composing in a world of chaos, facing the absurdity of wars, conflicts of ideologies and religion, economic inequities, mass starvation, epidemics? Everything has become a mixed signal. Everything has been done before. At what level should a composer be involved? The world of classical music is disappearing due to the audiences' lack of education and/or interest - or is it becoming something that only the elders appreciate?
"There is no longer an avant-garde, political, sexual or artistic, embodying a capacity for anticipation; hence the possibility of any radical critique - whether in the name of desire, of revolution, or of the liberation of forms - no longer exists. The days of that revolutionary movement are gone. The glorious march of modernity has not led to the transformation of all values, as we once dreamed it would, but instead to a dispersal and involution of values whose upshot for us is total confusion - the impossibility of apprehending any determining principle, whether of an aesthetic, a sexual or a political kind.. (...) Communication 'occurs' by means of a sole instantaneous circuit, and for it to be 'good' communication it must take place fast - there is no time for silence. Silence is banished from our screens; it has no place in communication. Media images (and media texts resemble media images in every way) never fall silent: images and messages must follow one upon the other without interruption. But silence is exactly that - a blip in the circuitry, that minor catastrophe, that slip which, on television for instance, becomes highly meaningful - a break laden now with anxiety, now with jubilation, which confirms the fact all this communication is basically nothing but a rigid script, an uninterrupted fiction designed to free us not only from the void of the television screen but equally from the void of our own mental screen, whose images we wait on with the same fascination. (...) Art has disappeared as a symbolic pact, as something thus clearly distinct from that pure and simple production of aesthetic values, that proliferation of signs ad infinitum, that recycling of past and present forms, which we call 'culture'. There are no more fundamental rules, no more criteria of judgment or of pleasure. In the aesthetic realm of today there is no longer any God to recognize his own. Or, to use a different metaphor, there is no gold standard of aesthetic judgment or pleasure. That situation resembles that of a currency which may not be exchanged: it can only float, its only reference itself, impossible to convert into real value or wealth."
Jean Baudrillard, The transparency of Evil, translated by James Benedict. pp 10, 12, 14.

The sense of loss of aesthetic values expressed by Baudrillard is the underlying factor which any contemporary artist has to deal with - whereas it is experienced as a void or as an overload of information.
Any meaningful composition entails the redefinition of musical values, in relation to fundamental principles, musical structures and new technologies, at macro and micro levels, and the awareness that music transmits states of consciousness. Beyond musical notes, the representation of music should reflect the sound space, the pleroma of sound of the entire aural spectrum.
In this process of reevaluation and search for truth, certain fundamental principles emerge as the foundations of a new music:
  1. The scale as a path of correspondence to universal hierarchies
  2. The predominance of the tone
  3. Tuning as tuning in
  4. Macro composition: the use of a matrix
  5. The need for new instruments
  6. Micro composition styles
  7. A new approach to notation
  8. The composer's role


What is universal about the scale? C,D,E,F,G,A,B. What is mysterious about that? It seems so simple and obvious. The scale is formed by a series of intervals. Robert Fludd, whose work revolved around the monochord, a single vibrating string, established a universal correspondence between two octaves and three 'spheres', consisting respectively of elements (air, fire, water, earth), planets, and angels. If his interpretation is highly poetic, his work takes after Pythagoras in the search for a universal scale connection.
In the order obtained on the monochord, the intervals are the octave, fifth, fourth, third and second. The sixth and seventh are derived from the third and second by mirroring or inversion. These basic proportions form a hierarchy:
RatioInterval Name
1/1 (0 cents)unison
2/1 (1200 cents)octave,diapason
3/2 (701.955 cents)fifth,diapente
4/3 (498.045 cents)fourth, diatessaron
5/4 (386.314 cents)third
9/8 (203.910 cents)second
5/3 (884.359 cents)sixth
15/8 (1088.269 cents) seventh

These intervals are considered as abstractions rather than precisely quantifiable values and independently from any particular tuning. The values in brackets, from the smallest to the largest value of the interval in any tuning, are expressed in cents. Once represented visually, this hierarchy applies to other realms besides music - architecture and science are the most obvious. The diapente ratio of 0.668 is very close to the golden section ratio of 0.618.
A=220 to A=440.
in Hz
A3 1/220 0.00454
B31/246.9 0.00405
C41/261.6 0.00382
D41/293.7 0.00340
E41/329.6 0.00303
F41/349.2 0.00286
G41/392 0.00255
A41/440 0.00227
In order to explore the hypothesis of the scale as universal hierarchy, I worked with architect Carl Karas on the design of a harmonic proportion matrix or 'Scale Matrix' expressing the geometric relationships of this particular series of intervals. This one is based on the wavelengths of an equal-tempered scale, which are the most direct expression of the 1/2 octave ratio: (See diagram at left)
The diagrams (Examples X1, X2, X3) shows the formation of the intervals from the fold to the octave, the harmonic rectangles, mirroring and the rotation which reflects the relation between ascending and descending scale. The diagram elicits a spiral progression, derived from stacking the intervals. These intervals forming the scale also correspond to the harmonic series: octave (interval between 1st and second harmonics), fifth (between 2nd and 3rd harmonics), fourth (between third and fourth harmonics), third (between 4th and 5th harmonics), second (between 8th and 9th harmonics). The 7th harmonic - the one that is considered 'out of tune' with the fundamental, is actually the dynamic point of the spiral.
The scale and harmonic series are in a relation of horizontal/vertical correspondence or bi-axial symmetry, which is one of the guiding principles in my music. This leads to the second fundamental principle: the supremacy of the tone.


"There is a fundamental difference between a tone (in the dynamic, vital, magical, and/or sacred sense of the word) and a musical note as part of a scale (thus in relation to other notes). (...) Sound, tone and note each have a specific meaning, even though they may refer to the same auditory phenomenon. Each represents a different response to a musical event - a different way of feeling and thinking about what has been heard. Sound (in the non-metaphysical sense) simply refers to the transmission of vibratory motion and its perception by the auditory center in the brain after the various parts of the ears have resonated to it. A tone is a sound that has conveyed (or can convey) significant information to the consciousness of the hearer because it is charged with and transmits (or can transmit) the special nature and character of the source of the sound. Thus a tone is a meaning - carrying sound. A tone has meaning in itself, as a single phenomenon experienceable by a living being endowed with some degree of consciousness."
Dane Rudhyar, The Magic of Tone and the Art of Music, p.13.

"The common ground on which the postwar avant-garde met, transcending all their ideological differences, was tone. Call it also timbre, tone-quality, pure sound: it was that dimension of music which had been comparatively neglected during several centuries of harmonic, melodic and rhythmic exploration. (...) When Wagner first analyzed a tone in the Prelude to Rheingold, showing over eight minutes how it is made from the series of overtones in increasing density and rapidity of vibration, the first step had been takentowards a penetration by the listener of the single tone, as a microcosm to be explored in its own right."
Joscelyn Godwin, Harmonies of Heaven and Earth, 120.

I usually work from a drone as a harmonic structure - one tone with its harmonics - which opens a door to dissonance, atonality, chromaticity, rather than stacking tones together as chords. Once you determine the chord everything is closed in. The tone is the basic unit, not the chord. The difference between working with a matrix and working with a chord is that you simply have more choices. The improvisation stems from a base-tone and its harmonics instead of a series of chords as in jazz, or a key signature in classical music. It is tone-music, not tonal music. The fact that I use key signatures is a smoke-screen. My tonalities do not always correspond to the ones indicated by the key signature, even if they have the same amount of sharps and flats. Working with the tone, I am also dealing with a broader range of frequencies than the range of traditional instruments - ideally, the entire range of human hearing (20 to 20,000 hertz).
"A music intending to communicate the psychic energy of actual tones could be called 'syntonic' music. It would be based on an experience of tone, unconstrained by the intellectual concepts of the classical tonality system or made difficult by the habits and memories of conditioning or academic training. (...) Tonal relationships are included in the space relationships of syntonic music, but the rules, patterns and cadences obligatory in a tonality-controlled music hinder the development of a syntonic consciousness. The restrictive patterns and formalism of a music controlled by the tonality-system undoubtedly have served as a valid purpose for the European culture and its American and global extension. Today, however, as all cultural traditions disintegrate, the use of precisely tuned scales and essentially separate notes having an abstract, intellectual existence on the background of empty space hides a psycho-musical inability to respond to the possibility allowing the full vibrancy of the whole musical space to inspire (or inspirit) a new consciousness of Tone. In syntonic music, because the fullness of the entire humanly experienceable musical space is the fundamental reality, any sound can be used as part of a sequence (melody) or simultaneity (chord) of sounds. But this does not mean the absence of selection in the composition of a particular work of music intended to communicate a particular state or fulfill a particular personal or collective function and purpose. What is selected is from the whole musical space, and that wholeness remains potentially involved in the resonance of the total work. The process of selection is an open process."
Dane Rudhyar, 'Dissonant Harmony', Pleromas of Sound', Music Physician for Times to Come, an anthology by Don Campbell, p. 281.


When thinking in terms of frequencies, tuning becomes very important. Pioneers like LaMonte Young and James Tenney showed us the power of just intonation. Beyond finding the correct tuning for an instrument, one must find the correct reference pitch. There is something basically wrong in presenting the commonly used reference pitch as an absolute. When people are said to have perfect pitch it is actually an illusion: it is only that they are extremely trained in recognizing pitch in relation to a particular reference pitch which is currently at A=440 Hz and which some people are trying to raised up to A=442 Hz. I am very concerned with this tendency to go for higher speeds of performing and higher pitch. The higher the pitch, the less in tune we are with our natural environment. After all, Mozart's reference pitch was 421.6 Hz (close to the Moon tone, 420.8 Hz), and Bach's tuning fork vibrated even lower at 415.5 Hz. A lot of my work in the more recent years has focused on trying to find a correct reference pitch and this is what has led me to look into an earth connection. Tuning into the Earth tone seems a viable alternative. We are getting further and further away from the essential elements which make our lives possible. Music should be not only tuned up, but tuned into the elements: water, air fire, earth and akasha - the source of everything, the unknown element, the void. This kind of tuning can be therapeutic. The effect of the fast beats and high pitches is to create a stressful music, whether it is the translation of a strained environment or an unfulfilled society. Performers, emulating the world of sports, appear to be striving to break a record in speed and brightness. I think this tendency has to be corrected in order to preserve the integrity and the power of music as a source of harmony between the human being and the universe.
There are some limitations of using alternative tunings with acoustic keyboard instruments. With a piano tuned in just intonation you are limited to one key in that particular tuning - which causes practical problems when you want to change to a different piece. In mean tone, you have access to a series of keys that have either flats or sharps. But again, it is either or. Vallotti- Young and Werckmeister tunings offer a better solution: the intervals are more natural than equal temperament but allows you to play all in all keys and go into chromaticity. The qualities of these tunings have led me to work with harpsichords and Baroque instruments, in the Deus Ex Machina Cycle.
A revolution has occureed with the new synthesizers which flexible tunings capabilities. However, the use of digital increments in the tuning process can be complex, due to the fact that cents are decimal and digital increments work from 1 to 128 or from 0 to 127.
Also, in electronic music, harmonics are somewhat larger than life. They can be expanded by filtering, independently of any 'natural' resonance. They can be simulated, manipulated and enhanced, but the technology still has to reach that break-through when truly 'natural' harmonics can be completely synthesized.
As to the limitations of conventional tuning I have pragmatic attitude - when it is sometimes necessary to work in equal temperament - but I think it is more essential that the reference pitch be changed. As much as possible I use the Earth Tone (low C# at 136.1 Hz)instead of A = 440.
Tuning in is even more important than tuning. When tuning an instrument, what are we tuning into? It is not so much how the instrument is tuned to itself, but the tuning relates to the environment. Should we tune into the fast pace industrial society with a very high reference pitch and faster cycles, or should we tune into the universal sound, the Logos?
I envision music as an open axis to infinity. The abscissa represents the layers or the instruments and the ordinate is the time structure. My scores depict spatial relationships as well as notes. The way that I first conceived a piece that was not a mere series of unrelated parts (like a commercial album for instance) but a whole entity, was in the form of a grid matrix: on the vertical axis, the different patterns and on the horizontal axis the duration of each sequence. I use the matrix as a macro-structure to define a general framework and I use a number of micro-structures within it. What I refer to as macro-composition and micro-composition relates to Boetius' concept of 'music mundana' (music of the universe) and 'musica humana' (music of the human being). Our time is comparable to the Renaissance, an era of new discoveries and technological revolutions. It is somewhat natural to turn to the Renaissance for a better understanding of modernity and for an answer to the over-specialization which pervades our society. The composer may follow the example of the Renaissance humanist, versed in different disciplines, music being more closely connected with the arts and sciences.
What led me to compose with a matrix is an interest dating back from the early 70's for what I might refer to as "Harmonia Mundi" (to borrow the term from Kepler) expressed in the various universal correspondence systems of the European esoteric tradition (Robert Fludd, McGregor Mathers), alchemy - and more recently in the work of cosmologists and quantum physicians (Hawking, Schroedinger). What these different schools of thought have in common is the search for an understanding of the universe not as chaos but as an organized hierarchy. The new concept of fractals organizes even randomness itself. I am especially interested in correspondence systems, which parallel different levels of consciousness and different aspects of reality such as colors, body parts, signs of the zodiac, spirits, animals, metals, brain functions, ad infinitum. The idea of connecting otherwise disparate elements into a universal order appeals to me. I have always thought this form or organization would be a valid framework for a composer, preferably to a form of organization that had been thought out by another composer or was the result of a folk tradition. This is the key to the creation of some kind of 'musica mundana'.
On the 'musica humana' level, I am very concerned with expressing the stream of consciousness - as for instance in the writing of Marcel Proust. In his work, there is a sense of direct communication of a mental process, which relates to everyone. This is the consciousness I want to reflect in my music, to emulate flow of a meditative state when observing one's thoughts - as if each thought were a theme and each thought development an improvisation. This is how my music works. Within the current of improvisation, I follow a loose structure that doesn't have too many artificial limitations.
My musical orientation also relates to the fact that I started to compose on tape with multitracking: I recorded one track and listened to it until I knew what the next track was going to be. It was a cumulative process, a modern process, using electronic technology. Composition and studio production were inseparable. My first challenge as a composer was the issue of using technology in my own way. I am more interested in breaking new grounds than keeping up with traditions - therefore, concerned with new technology and how to make use of it, in line with the principle of eternal transformation.
Obviously, at this point, composing means staying away from standard formats whether classical, pop or jazz, like the song, the sonata with its typical thematic developments, anything that is pre-conceived. Composing a work means creating a piece that has an existence of its own. Whenever I refer to existing formats, they are re-interpreted in a different way. I always try to stretch from whatever structure, if and when I use a given structure, I adapt it. For instance, the Sonate Ordinaire can be perceived as a piano sonata although it is a long continuous movement containing a succession of varied improvisational structures. The Concerto for Piano and Orchestral Memory has separate movements but the orchestral background is modified electronically. It is meant to be amplified when performed, or played on tape. Whereas the orchestral parts are written, the piano movements do not contain themes and developments but open improvisational structures none of which are frozen.
Sometimes, working with an existing form means playing with the form itself. In terms of form, I see opera as an open field. There is a repertoire which can be an inspiration but it does not have to be a limitation. The idea of 'total work of art' brought forth by Wagner can be applied to the inclusion of new media and technologies. New opera is media opera. Because they are part of our daily experience, it seems important to include moving images in a contemporary complete work of art; to use new technologies and new ways to present texts not just as lyrics but as narratives, as simultaneous layers, sometimes in different languages, through interactive screens. Above all, the human voice as a performing instrument remains mysterious and surprising. I am always amazed at how a melody sounds when a singer performs it - it always comes out so different than anything I had imagined because the sound of a voice is unique. The range of expression cannot be replaced by electronic instruments - it makes a good match for technology, retaining the human element, bridging the gap between the human and the mechanical. An opera is basically and simply a work for voice. It does not have to have a linear plot or describe an emotional vortex. It also touches upon the issue of universal language - a solfege made of phonemes common to different languages - which I used in Existence. Opera already exists in several languages. African languages, American Indian dialects have even found their way into the world of popular music. In new opera one can be playful with languages. One aria in The Death of Don Juan uses English, French, Italian and German simultaneously. I see 'new opera' as a universal, flexible form of expression, more appealing to the imagination than any other type of music.
Musically, I belong to a generation who, fed up with rock music, experienced both free jazz and minimalism as fresh, exciting reference points. Minimalism was my springboard. What I liked about minimalist music is that it induces a kind of a trance. This is close to what I wanted to do but it wasn't quite it: eventually the trance state induced by the repetition makes you forget the music. I wanted to stay with the flow and not go beyond it, so there had to be more stimuli in the music, variations of rhythm, of accents, of notes. This is what I did in the Piano Works: working out texture out of a minimalist pattern and stretching it. This improvisation style developed over the years into what I now call UMI - Universal Mode Improvisation - a method that gives me the freedom to move from a basic modal scale into polytonality or atonality.
What I retained from minimalism is the hypnotic power of repetition. What I gathered from free jazz is the power of breaking the rules - including one's own. In the heritage of free jazz, I claim the absolute breaking down of musical structures and the atonality they achieved in a different way than the 12-tone school: spontaneous, carefree instead of stiff, belabored. Between these two inspirations: minimalism with its trance-like quality and free jazz with its explosive quality, my music eventually developed in its own direction. I use semi-repetitive patterns which are constantly modified. The mind is semi-repetitive, it goes around in circles for a while, then there is randomness, unexpected leaps. A thought wanders away and connects with something unrelated - my music mirrors this kind of activity. In free jazz, what comes out of the unbridled collective improvisation is often frustration, anger, sometimes joy. Everything comes out without any censorship - that's the beauty of it - but that's not what I want to do. I do not want to transmit raw emotional states to the audience unless they lead to something else, a tranquillity of mind, a peaceful state, a heightened consciousness, a way of connecting with the universal, the 'Devachan' described by Rudolph Steiner as a plane of inspiration where "tone becomes akin to words ". Rudolph Steiner, The Inner Nature of Music and the Experience of Tone, p. 16.
"Music is not usually Zen practice, but it can be, If the player just plays and becomes one with the playing it can be called Zen. But most of the time the direction is not clear in music. Usually there is some emotional control, some direction given by the emotions. And the musician may be trying to control the emotions of the audience. In fact, we speak of 'good music' as having this sort of effect on other people's emotions. Emotional music means opposites-mind: wanting or not wanting, good feeling, bad feeling. But true Zen music is different. It has been compared with the jumping of a fish up and own in the river."
Seung Shan, Perceiving Universal Sound. Music Physician for Times to Come, an anthology by Don Campbell, p. 303.


In my work a matrix is an organizational structure that reflects universal forces and functions as a general ordering device. I have used matrices consistently from 1981 through the present. Examples will illustrate this process. The Scale of Number Seven was the first matrix, designed in 1981. It was derived from a correspondence table in the form of a 7x7 grid. (See Example 1a,b,c,d) I used the structure to order different patterns together. The Scale of Number Seven matrix is designed in such a way that the patterns match whether you read them from left to right or from top to bottom. I worked on The Scale of Number Seven on and off between 1981 and 1984. In 1984, I had access to a computer at NYU, the Fairlight CMI, and I started using The Scale of Number Seven matrix to program patterns into it. It worked wonderfully with the logic of the instrument. I used MCL, the computer language accepted by the Fairlight CMI, to input the notation. Once in the computer, the matrix generated many individual pieces, including The Death of Don Juan. In 1984, I started The Soundless Sound matrix. I was working on a harmony of tones I heard during silent meditation. Silence is filled with subtle sound vibrations. A deep concentration on silence unfolds its polyphonic structure. This phenomenon has been identified and documented in both Eastern and Western cultures: the 'anahata' of the Indian spiritual masters, the Zen koan about 'the sound of one hand clapping', an image often misunderstood, which actually expresses the fact that there is no beginning and no end to the sound - it is not uttered - but it is there (not subject to time) and exists outside of the hand producing it (not subject to space); Robert Schuman's diary refers to 'the voice of the angels', a sound that came from within. Others refer to a 'logos', a universal sound from which language is created. For scientists, the hypothesis is that this sound is produced by the simultaneous, multiple vibrations of the human nervous system as perceived by the ear. But why, then, does the sound seem to surround the listener as if coming not from within the body, but from outside?
"The Logos of Creative Voice is personified as the goddess Vâch, the female aspect of Brahma, the God of Creation. Esoterically, she is the subjective creative force, which, emanating from the Creative Deity, becomes the manifested world of speech, i.e., the concrete expression of ideation, hence the Word or Logos. (...) The conception of Vâch plays a prominent part, not only in the Brahmanical system, but in the cosmogonies of most religions. It is the 'word made flesh' of the Bible; the 'nada' or soundless sound of the Upanishads; the 'nam' or 'gurbani' of the Sikh Adi Granth; the 'kalma-i-ilahi' or inner sound of the Koran; and the 'saute Surmadi' or 'hu' of Sufism. It is also synonymous with Platos' logos, with Madame Blavatsky's 'voice of the silence', with Patanjali's 'om', with the Pythagorean music of the spheres and with the lost word of masonry. (...) Buddhism knows it as 'fohat' - the light of the Logos. In Tibetan Buddhism it is related to the Bardo Thodol, while Chinese mysticism recognizes it as the 'kwan-yin-tien' or the 'melodious heaven of sound'."
Gordon Limbrick, 'The Hidden Significance of Sound'. Music Physician for Times to Come, an anthology by Don Campbell. p. 308.

When analyzing the structure of the silence-sound, one hears the resonance of the Seven Fundamentals (seven tones of a diatonic/Pythagorean scale) sounding simultaneously, while harmonics rise and form oscillating rhythmic patterns, developing in time, both harmonically and melodically. According to the Indian theory, each fundamental tone corresponds to a nervous center of the body or 'chakra': lower spine (C), genitals (D), navel (E), solar plexus (F), throat, (G), forehead (A), crown of the head (B). Although this resembles an ordinary scale, the difference is that the actual frequencies of these tones range from the very low to the very high. As the nervous centers are directly affected by the resonance of the seven fundamentals, the overall effect of the perception of 'the soundless sound' is an intense experience, both peaceful and exhilarating. In order to transmit it so other people could hear it the way I did, this work had to be realized through electronic synthesis because the tones cover the entire spectrum of the human ear, including limit tones - one as high and one as low as we could possibly hear and synthesize. I worked on it and off for several years until I recorded it digitally at the Center for Electronic music during a residency in 1989. The score for this piece is an 8x8 grid expressed in hertz. (Example 2a,b,c,d) In the Soundless Sound matrix, the stacking of fundamental tones works horizontally and vertically: they form a scale and a harmony - an unlikely one, a CDEFGAB cluster - but the harmony works because each tone is in a different frequency range. So we have a set of continuous tones that is an absolute vertical/horizontal match and creates an atmosphere of patterns within the tones. It is a scale that also works as a harmonic cluster - the grid can be read either way. This idea seems to be like an opening, a connecting point, the beginning of an understanding of the universe. If you can get the music to work that way it is an expression of a point of connectivity between time and space. What interests me is to find different ways of achieving it. It is basically the same idea to create a piece based on a tone and its harmonics while using the same set of tones as a scale to develop the melody. The next matrix I worked on starting in 1989 was the Solar System matrix. I was moving from a static grid to a a circular or cycle matrix. It is based on the idea of the planet-scale, connecting the different planets with certain scales - taking the musical scale as an direct expression of the universal order. At the root of this idea is the work of Pythagoras, which established a parallel between the spatial relationships and the intervals contained in the scale.
"The Pythagorean scale is not a mode, for a mode is the product of special conditions belonging to the realm of culture and myth. The Pythagorean scale is an unconditioned, archetypal manifestation of cosmic principles. Number and proportions, as Pythagoras understood them, belong to the realm of archetype. In order to effectively operate in that realm man needs to develop a mind that has basically freed itself from bondage to biological energies and mythic-cultural specialization and exclusivism. When conceived by the archetypal mind, music can become, at least potentially, a universal, supercultural language."
Gordon Limbrick, 'The Hidden Significance of Sound'. Music Physician for Times to Come, an anthology by Don Campbell. p. 308.

There are a number of different planet-scale schemes. One common element I found between them is the desire to find a true relation between music and our perception of outer space, whether the schemes seemed arbitrary, intuitive or actually scientific. For the purpose of ordering a piece with this type of hierarchy, I came up with a scheme. I used the pitches of a minor scale to start (G minor natural) for respectively Earth (G), Moon (A), Venus (Bb), Mars (C), Mercury (D), Jupiter (Eb), Saturn (F). For the the more remote planets, Uranus, Neptune and Pluto, I used a series of pitches that were not included in the original G minor natural scale - therefore opening a door to chromaticity and dissonance. The initial inclusive scale ("Basic Scale" on the example) was transposed in all the keys contained in the scale to establish a continuity - there is a progression in the succession of pieces, the first in the key of G, the second in the key of A, etc. That is how the internal logic was devised. To that original scale, I superimposed a "harmonic scale" a minor third above. At that point, I had enough of a structure to work with and enough freedom to develop material uninhibited. This is how Existence was developed. (See examples 3a,b,c,d) Since 1991, I have been working with the Earth Tone in both of its aspects: the correspondence with the 24-hour cycle and the correspondence with the yearly cycle. According to the method devised by the Swiss Scholar Hans Cousto, planetary frequencies can be made audible by octave transposition.
Planetary frequencies are based on orbiting times: 24 hours for the Earth, 224 days for Venus, 4,332 days for Jupiter, etc. Rotations entail vibrations. In order to move from the planetary vibrations to those of our earthly music one must 'octavise' between 26 and 50 times - depending on the planet's distance from the sun. Our solar system thus covers a range of exactly ten octaves, exactly paralleling - in another of those miraculous suprises - our ear. (...) The ratio between time (still with reference to the Cousto method) and frequency is:
                   Frequency =       1/Time
The frequency produced by the Earth's orbit around the sun (365 1/4 days) is thus calculated by dividing 1 by 365 1/4. To make that frequency audible I must double it - i.e. octavise it - until I reach the sphere of tonal vibrations perceptible to our ears. (...) This is the most precise and most plausible of the many procedures discovered since Pythagoras for making audible the sounds made by the planets - the 'harmony of the spheres'."
The Third Ear, by Joachim-Ernst Berendt, Element Books, 1988, p. 88.

Two works emerged from this hypothetical connection. The first one is Variations on the Orange Cycle and the second one is the Gaia Cycle matrix, from which I created Tronik Involutions. (See example 4) Created in1993, The Gaia Cycle Matrix is a mandala which parallels a succession of twelve I Ching hexagrams, a twelve zodiac signs sequence and a twelve key signature sequence. This is how the connection between I Ching hexagrams and the key signatures works: the first piece, Earth, corresponds to the 11th month and to the I Ching hexagram which contains six Yin lines. The key used, based on the Earth Tone (C# = 136) is a modified C# minor (with the addition of an occasional A#). C# minor has four sharps (F, C, G, D). In the next piece, Return, the hexagram contains one Yang line under six Yin lines. In this Yin/Yang logic, evolution is created by the replacement of a Yin by a Yang. One more Yang, one less sharp: only three sharps now, (F,C,G) and have F# minor. Next piece - can you guess - is represented by an I Ching hexagram with two Yangs under four Yins - and one less sharp again (F, C) - B minor. Heaven, which is all Yang, is the only major key used (B flat). From here on the process reverses to one less Yang/one more flat. The subsequent hexagram, Encounter, proceeds with one Yin under six Yang lines. So there is a dynamic between each part, a certain logic is established.
These various matrices represent the macro-structure of a work which could be one to two hours long. Within this framework, each section is usually 5 to 10 minutes long. This is all I want determined before hand. Once the basic structure of the entire piece is set up it functions as a guideline, a grounding, an orientation. Within the macro framework I use a number of microstructures, and I allow myself the freedom to sometimes break out of them. Whereas all my macros are somewhat similar in their style the micros are varied and inclusive. At the micro level, freedom of form is my main concern. I draw upon a number of methods including instrument design, universal mode improvisation, aleatory series, and texturing, and using texts.


INSTRUMENT DESIGN: THE TRINE One answer to tuning relativity was in my case to design an instrument that could be easily retuned: the trine, a 21-string, triangular, electro-acoustic lyre, amplified via contact microphone. I chose a string instrument because of my experience playing piano and guitar. The trine can be played by plucking or strumming with the hand, a rubber mallet or a glass rod. It offers a wide range of tuning and sound processing options. The tuning of the trine is half of the composition: once it is tuned the rest is improvised in layers within that particular tuning. The creation of the trine was the point of coincidence of two conceptions: one, that sound has become such an integral part of the compositional process that one may want to actually create a new sound, as it is done with electronic synthesis; the second, that the physical presence of the object/musical instrument should reflect the channeling phenomenon between universal forces, the composer/performer and the listener. The shape and name of the trine were inspired by astrology. My birth chart displays the equilateral triangle called a "trine" which symbolically represents a harmony between three planets; the shape established a mystic correspondence between the instrument and astral influences. A physical correspondence was realized by proportioning the instrument to the length of my forearm and hand according to the golden section. The way the trine influenced my composition is the fact that a piece could be based on 21 fixed pitches. It focused on the creation of 'rasas' - a rasa in classical Indian music represents a combination of a Thath (raga scale) and a particular mood. My custom rasas are more environmental, less emotional that the Indian rasas which express epic moods like desperate love or conquest. It is again a horizontal-vertical scheme: the tuning provides the harmonic framework and the basic scales for patterns and melodies. (See example 5 - Music for the Trine).


A basic tone and its harmonics define the scale for a piece and around that scale an improvisation is developed. There is a difference between a scale and a mode. A mode is a scale plus a myth. It contains cultural references. In universal mode, there is modulation not into another key but into atonality or polytonality. When using a tone and its harmonics as a basis for a mode, there is access to dissonance but it is compatible dissonance - a note that is included in the harmonics of the original tone. Some dissonance is unsuitable. This can be determined by ear or by a reflected choice. UMI, which I have developed over the years, is a non-constricting form of improvisation which stems from a tone and a mode-scale or a combination of scales. Usually they are modified existing modes from all different traditions. Besides major and minor, I reclaim Gregorian modes, raga Thaths, Oriental pentatonals, Ethiopian modes, Arabic modes. But they are not used as such. The important consideration is how one particular accidental can change the entire 'rasa'. For instance: you are in F# minor but you add a B# instead of a B natural. It is an interesting mode that keeps you between the major and the minor, it's a rich combination, it yields an occasional compatible dissonance. This is what happens in music when you have these alterations within a mode - certain alterations that are permitted, particularly one that would be a flat normally but occasionally could be natural. This is a type of modification that I use to create my mode-scales. This relates to the variations between the 'arohi' (ascending scale) and the 'avrohi' (descending scale) in ragas. The arohi may have one less note than the avrohi, the avrohi may have a different accidental. An example shows the 10 raga Thaths and their correspondence with Western modes, and the 12 modes used in Tronik Involutions. (example 6a, b)
The other micro-method that I have occasionally used is the aleatory series method. It seems that I am dealing with an oxymoron here: chance composition and total organization. What I mean by aleatory series is combining a certain serial method with a chance process, thereby correcting the mathematical stiffness of the series by randomness. For instance, I come up with a series of chords and their succession is determined by chance. Example: the last part of The Four Stages of Manifestation was done this way - it is difficult to memorize, as they are no recognizable progressions. The effect is not unlike that of a serial method. I have occasionally used a serial method. I used this method in the composition of the Concerto for Piano and Orchestral Memory for the arrangements for the acoustic quartet (violin, viola, trombone and cello). I started from a series of intervals which I used to create instrumental parts - but the way I used the series was not a systematic but a selective process. In other words, I used the series as a matrix of possibilities to choose from. (See example 7). This is in agreement with my macro methods - to follow some kind of structure: design a series, use it to create a consistency of mood, while keeping an element of randomness, creating an order only to break free of it.
Also, in the Concerto, the way the quartet arrangements were matched with the piano was determined by the atonal framework, but anything beyond that was chance. There was a general harmonic background. The details were not pre-determined, they were free, open - which is unusual in orchestration where most of the time everything is so determined, to tightly matched. It worked because it was actually in universal mode - I had the concept but not yet the term. I was surprized at how the structure fit with the piano and how it worked. So that's an example of universal mode used in writing a chord series and combining a written arrangement and an improvisation. Here, the harmonic structure is pre-determined but because it is in universal mode, it does not restrict the improvisation to following chord changes strictly. Usually, in my music, the harmonic structure is present as a seed in the base-tone so I do not have to relate to as a superimposed structure.
Another micro composition method I share with the totalists is the layering of different meters. However there are usually in the same tempo. I like the complexity of 2 against 3 against 4, but beyond that what is exciting to me it is to have a web of rhythmic patterns that are atypical, but still form a cohesive part, even though any standard beats are avoided. I see rhythms as a series of cycles which are already contained in the tone resonance, so their arrangement is an enhancement of the original cycle. Also, I am extremely conscious of the pitch of rhythm tracks. Especially when playing on a multitimbral percussion keyboard there is more awareness of pitch relationships between certain drum sounds so those are like 'musical' patterns, not like drum rhythms. (See example 8 - rhythmic texturing)
At first my compositions did not have percussion or drums. The basic rhythm cycle was established by an analog sequence, which leaves the music more open rhythmically - unlike playing to a stiff beat or click track. When I started working with the Fairlight computer, the Scale of Number Seven matrix generated a series of percussion sequences of an amazing complexity and oddity. They were obtained by programming a series of patterns that were pitched and orchestrating them with different arrangements of percussion and drum sounds. Of course they sounded automated, somewhat stiff. The rhythm textures in The Death of Don Juan are computer rhythms derived from the same program. The monotony of the electronic pulse was modified by the addition of live improvised tracks. I never used this program by itself, it was always combined with live, human playing. I stayed away from 'real' drums until Existence. In the recorded version, I used programmed electronic patterns enhanced by improvised live percussion. The important element to retain from these different examples is that in terms of rhythm the truth is in the middle. There is a truth to the stiff beat, the steady electronic pulse which is so typical of our time. It is obvious people in the past were into tempos that were not only slower - their entire life was a slower pace - but changing (rubato). This is why conductors were necessary: the beat was determined by a human being and of course it had a unique flexible quality. Some people like the idea of a conductor who could actually control the computer beat. This will probably be achieved in the future. But I don't think that given the technology we are using, there is much need to escape from the stiff beat. I did say that I want to break away from any limitations, but I do not find a beat to be a constriction at all. It is a facilitating device for the layering of different rhythms. The art consists in how to disguise it.
In Tronik Involutions the technique I used to generate the drum tracks it to play the drum parts on a multitimbral percussion keyboard while listening to an automated sequence which I did not record. The sequence ensured a steady beat and tempo so the drum tracks are tight but not stiff. I was uninhibited about the kinds of beat patterns that I came up with. There are no standard beats, which would have been impossible to achieve by working with a drummer.
My sound textures are inclusive. They can combine sounds of any sort, whether musical or noise-related. At one time I was very concerned with including ordinary life sounds because they were part of the consciousness that I experienced. One piece I performed at Dance Theatre Workshop had these 'sound intruders' that would actually disrupt the performance. At the time, I was living in a neighborhood in the Lower East Side where often in the middle of the night a loud Tarzan call, a ghetto blaster or a scream of fear would tear the silence - and stop just as unexpectedly. Other sounds like water running, traffic sounds, pinball machines, cars in the rain, typewriters, bits of TV soundtracks, found their way into my music - those New York subway rides, that ever-present rumble, fragments of muzak in fast-food restaurants. Since these sounds were already in my consciousness while I was composing, the whole picture required that they be represented. Later on, as I started to work on the Soundless Sound, and with the creation of the trine, I began to understand the nature of the universal sound and to recognize its presence within the environment, and I no longer felt the need to include the extraneous noise. The turning point happened in the piece called Seabird Transmission where I played the sound of the seabird on a fiddle instead of using a bird recording. This is part of the texturing process I went through in recreating my consciousness of the sound.
An example of the new texturing technique, excluding environments, is Action Music, an installation-performance I did at the Whitney in 1985. Powered speakers in the space representing of five elements (earth, water, air, fire, other) were each playing a different electronic drone. To this harmonic background I performed piano, trine and vocal improvisations. At that point, there was a kind of coming together of my musical world. The texturing included electronic, electro-acoustic and acoustic sounds. Tronik Involutions is an all-electronic texturing. Example 9 illustrates the different layers: bass drones and bass lines, percussion/drums, mid-range textures with double keyboard improvisations, high pads.
Working with texts defines a piece in terms of rhythms and melodies - there is an inherent melody in the language, and I like to use a variety of languages for that reason. Sometimes the text comes after the music - I write lyrics in certain cases, or have a writer write lyrics to a piece but more often I start with a text - I have worked with a lot of public domain texts, the poetry of Rilke, Verlaine, Apollinaire, Trakl, Ezra Pound, e.e. cummings, Gertrude Stein, and with contemporary writers including Allen Ginsberg, Melody Sumner Carnahan, Steven Hall. Whether there is a meter or not in the text has never posed a problem for me. If I like the text, there is always a way to find the music "inside of it".


I am extremely concerned with notation, that is, with a notation that actually be an inspiration beyond just reading, a notation that can be an art form in itself. That's why I have developed various types of visual scores. It seems I have tried every possibility in notation. I use traditional notation quite often, but I find it both cumbersome and incomplete. There is a need to account for other processes besides notes and for different frequencies besides those of traditional instruments. It is awkward to notate very high or very low frequencies in traditional notation, there are so many little lines under or above the staff; especially when working with electronic instruments it much easier to refer to a frequency expressed in hertz. In a work programmed on computer and performed by a computer, the notation is in computer language. Why use any other? This is something that machines accept but that humans may or may not accept, which makes it all the more difficult for modern music to find its way to the public because institutions still require scores in traditional notation, even if the work involves electronics or concrète.
I have no problem with the notation of macro-scores. The matrices are from my point of view the ideal notation. On the micro level, however, when more detail is required, since improvisation is an essential part of the micro-structure, I have to deal with the issue of scoring improvisations. Micro-structures are usually scored 'after the fact', that is transcribed from tape. I compose on the piano or electronic keyboard and with my voice, and when I come up with something new, I just turn on the tape-recorder. Should anything come out of it, I transcribe the basic keyboard/vocal parts on the computer. From then on I orchestrate it either harmonically or by layering. On the micro level, I will take the time to write something down only if I have it performed by others or only to the extent I need to keep track of it for myself.
There is a general problem with notating improvisation. If you read a transcription of a Thelonius Monk solo, you can play it, but that's not it. Something is reproduced but the source is missing. I am sure that if Thelonius had notated it, it would have been very succinct. In order to get to the truth of the music you cannot just copy his solo - you have to somehow rework it from the source. That's a very challenging notation problem which I have to deal with when I have someone else perform my keyboard work. It takes several different transcriptions of the same work to get closer to reflecting the spirit of the piece. I like some of John Cage's experiments in notation where he uses a combination of geometric drawings and traditional notation. Not everything has to be notated, only the source of the inspiration. On the other hand, if a piece becomes too improvisational there is no more control over the material. It could become self-indulgent and shallow, relying entirely on the performers' creativity. The challenge is to come up with a notation which functions as a strict guideline, sufficient to keep the spirit of the piece, without making it frozen.
There is also the issue of keeping the freedom to change, update a score. If I am performing the Variations on the Orange Cycle, the version I do now is quite different from the one I recorded in 91. My compositions are always in progress. In a way, I hate to notate them because at that point it's over. I would like to continue to change them until I am gone. Music is like the stream of life, it often seems like a routine or a repeat but it is always changing.
These considerations, including the concern for presenting an uncompromised version of my music, have led me to compose work that I can perform alone - like Tronik Involutions, for instance. It involves a lot of layers on tape or computer and something I play live. In such cases, because I have a functional musical memory, I do not need to write a micro-score of the piece. If I prepare a performance for 3 singers and 2 percussionists I write down all the vocal arrangements very carefully, but I coach the percussionists and give them nothing written. Occasionally I have had to teach opera singers how to improvise beyond their written parts. I don't like to notate my own keyboard parts because reading them blocks me.
There is a certain incompleteness that I feel is required in notation. This is why I refrain from using dynamic markings in my scores because the dynamics have to be worked out at the moment the piece is rehearsed. It depends on the performers' ability to an extent, there are practical concerns. On the other hand, a part does not necessarily sound better if always played with the same feel. The same applies to phrasing: the phrasing is already engraved in the underlying logic of music. Those elements should be left open. A lot of baroque pieces were originally meant to include improvisations. Later on they were notated and published and a tradition was established of how the piece has been performed so far, and the fun of it is gone - most classical performers have stopped doing the cadenzas and ornamentations that were left open by the composer. I think a lot of music is too fixed. Of course, it has to has to be accurate to a certain extent but there has to be some kind of opening, a sense of freedom of expression for the performer which should be reflected in some way in the notation - or the lack of it.


A composer has the ability to make music and this carries a responsibility to share it with others. It is not a self-serving activity. There is no point in composing and not having the work be heard. Music is for people, it is to be experienced. The composer is like a transmitter. But what is the experience a composer is transmitting? The neurotic pangs of an egomaniac? Or is it the 'Great Mystery' as the American Indians call it. Making music to draw attention one's self would ruin the transmission. There is a certain role to play, nothing glamorous - to put together a certain sort of music that will connect with universal forces. That is a lifetime goal. At the same time, one has to have a kind of detachment from it. What does success really mean? Success means being to reach more people in the appropriate way. If composers can't reach anybody, they fail. If they reach masses of people, but with an incomplete or incorrect transmission, they fail. But if they manage to reach people in the right way, when the music approaches a perfect expression of the great mystery, when the experience is transmitted, the goal is achieved.

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