Philosopher Stones: Dinergy in musical composition

Here are some of the more unusual aspects of my compositional devices, as opposed to conventional methods of composition. These are my philosopher's stones - once found, they transformed all things not into gold but into music, which to me is more precious than gold.

Introduction

In the beginning of the eighties I was influenced by minimalism. But for myself, instead of the monotony of the repetition, I heard another layer of improvisation on top of the minimalism repetitive patterns. I also heard more varied rhythms. How to balance the order of minimalism and the freedom of improvisation? My answer to that was to create a double underlying structure, consisting of a macro structure ordering the succession of parts, key signatures and temporal development of the piece, and a micro structure on top of it, consisting of melodies and rhythms with a degree of improvisation. The macros I designed, what I call my philosopher's stones - because they yielded gold for me, are inspired by the theory of universal proportion or dinergy and correspondence systems found in ancient cultures both in the East and the West.

One book in particular was a major inspiration. It is The Magus, or Celestial Intelligencer, a Complete System of Occult Philosophy, by Francis Barrett (London, 1801). This book explained the correspondences associated with the planets, organized in correspondence tables connecting different realms: planets, angels, animals, the human body, elements (air, fire, water, earth, metals, stones), plants, as well as the dark forces of death and suffering. Barrett presented these correspondences in the form of tables, grids, and that was the inspiration for my first composition matrix. I envisioned that musical elements could be connected with these infinite correspondences. In Sri Chinmoy, I found references to similar correspondences between the tones of the musical scale, the chakras (energy centers corresponding to certain body parts), colors, deities, and seed mantras (sacred syllables).

The idea that planetary bodies could be connected with music is not a new one. The famous but misunderstood music of the spheres can be traced to Pythagoras.

The mythical lyre of Orpheus with its 7 strings, represents the 7 astral bodies seen from the Earth: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, corresponding to the diatonic scale, C,D,E,F,G,A,B. A string, plucked a midpoint, yields the higher octave or first harmonic. As in many other hierarchies discussed here, the planets are limited to the seven visible planets. Early cosmologies did not account for Uranus, Neptune and Pluto, as they had not yet been discovered. These ancient cosmologies however need not be dismissed, as Pluto, Neptune and Uranus are considered as higher octaves of respectively Mars, Venus and Mercury.

According to Plato, it is Pythagoras of Samos (6th-5th century B.C.) who established the scale from identifying consonant intervals - the legend says that he lived next to a blacksmith's shop, and while listening to the sound of the hammering identified its pitches. Pythagoras devised a simple musical instrument with one string, the Monochord, and he used it to organize the pitches forming the diatonic scale.

Robert Fludd, a lesser known contemporary of Johannes Kepler, expanded upon the Monochord of Pythagoras, devising a 3-octave Monochord, showing correspondences with planets and elements earth, water, air and fire. Kepler, in his master treaty Harmonia Mundi, shows the mathematical relationships (ratios) common to the celestial bodies and certain tones and intervals.

In the 20th century, these ratios were clearly established by mathematician Hans Cousto, whose book, The Cosmic Octave, shows calculations of the pitch corresponding to each planet. Pythagoras established the scale based on a set of proportional relationships, the main ones being double (octave), two-thirds or fifth, and three quarters or fourth. These harmonic proportions found in music are echoed in multiple realms of our reality.

"The Pythagorean scale is an unconditioned, archetypal manifestation of cosmic principles. Number and proportions, as Pythagoras understood them, belong to the realm of archetype(…) When conceived by the archetypal mind, music can become, at least potentially, a universal, supercultural language." Dane Rudhyar, The Magic of Tone and the Art of Music.

The riddle: what do the diatonic scale, the maple leaf, the human body, the Empire State Building and the butterfly have in common? The answer: a set of universal proportions, the 2/1 ratio, or the octave; the 3/4 or the fifth; and the 3/4 ratio or the fourth.

I became fascinated with this concept of universal proportion or dinergy. There are certain constant mathematical ratios that appear to rule form. The most important is the golden proportion or golden section, a:b = b: (a+b), the numerical expression of which is Phi = 1.618. The musical fifth, 0.6, is the inversion of this ratio. The golden proportion is present in many aspects of nature, whether natural or man-made, in the human body n animals, in architecture and art.

"If we look closely at a flower, and likewise at other natural and man-made creations, we find a unity and an order common to all of them. This order can be seen in certain proportions which appear again and again, and also in the similarly dynamic way all things grow or are made - by a union of complementary opposites. (...) Since there is no adequate single word for this universal pattern-creating process, a new word, dinergy, is proposed. Dinergy is made up of two Greek words: dia (across, through, opposite) and energy". Gyorgy Doczi, The Power of Limits.

These beautiful symmetries however only describe what is harmonious. Not everything in nature follows an organized pattern. What about things not harmonious but ragged, random, unpredictable? I was thrilled when I found that Benoit Mandelbrot discovered new universal number relationships that applied to randomness.

In The Fractal Geometry of Nature, Mandelbrot says: 'Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity.' Computers can now iterate these equations to infinity - which allows patterning of chaos, showing us a key to apparently random phenomena such as the curves of a sea shore, the erosion of a rock, even the fluctuations of the stock market. The Mandelbrot fractal formula is as simple as the Fibonacci series. It starts with z, which is multiplied by itself, plus constant, a non-linear equation: z x z+constant (1 for isntance) = 1,1x1+1=2, 2x2+1=5, 5x5+1=26, 26x26+1=677, 677x677+1=458330. It is a wild progression in which the numbers become huge, very, very quickly. It is a pattern for organic growth.

From my point of view, as a composer, music lies between the two extremes of complete order and complete indeterminacy. If everything is left completely free and up to the performer, there is no longer a composition. On the other hand, if the piece is completely mathematical and non-intuitive, produced by formula, it is no longer a composition but a set of cleverly interacting parameters. Neither of these extremes allow the kind of freedom I am looking for, but I believe that music will be enhanced by a connecting to the proportional laws that rule the infinitely large and the infinitely small, the macrocosm and the microcosm, in their own patterns of order and chaos, whatever the case may be.

I envision music as an open axis to infinity. The abscissa represents the layers or the instruments and the ordinate is the time structure. In my mind, 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 sections (like a commercial album of songs, for instance) but a gestalt where the parts and the whole are interrelated, was in the form of a grid matrix: on the vertical axis, the different patterns and on the horizontal axis the durations of each sequence. I use the matrix as a macrostructure to define a general framework, and I use a variety of possible microstructures within that framework, which may or may not rely on improvisation, and can be stacked in many layers or tracks.

A system lining up a simple set of pitches with corresponding elements of the cosmos is my subtext, organizing the general structure. It is all there, underneath, like an alpha wave in the brain of the quiet meditative state, while the beta wave carries on the conversation or stream of consciousness, and that level is improvised or semi-improvised. There is a balance between the macrostructure of the piece, organizing the key signatures and sections, while the microstructure, the actual texture of the music is loose. At this micro level, I am concerned with letting the stream of consciousness flow as if each thought were a theme and each mental association a development an improvisation. This is how my music works: within the current of improvisation, while following a basic structure that doesn't have too many limitations, I maintain a degree of indeterminacy, of openness. I am speaking from an entirely creative perspective, trying to communicate some of what inspired me and some of the more unusual aspects of my compositional devices, as opposed to conventional methods of composition. These are my philosopher's stones - once found, they transformed all things not into gold but into music, which to me is more precious than gold. They are:

1.The Scale of Number Seven
2.The Soundless Sound

3.The Solarsys

4.The Earth Tone and the Gaia Cycle
5.The Rainbow Cycle

The Scale of Number Seven was the first matrix I designed in 1981. It was derived from a correspondence table in the form of a 7x7 grid. I used this structure to order different musical patterns together. The patterns go together 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 Computer Musical Instrument, and I started using The Scale of Number Seven matrix to program patterns into it. It worked wonderfully within the logic of the instrument. Once in the computer, the matrix generated a lot of the material for my first opera The Death of Don Juan.

This correspondence grid associates parts of the human body, planetary bodies, metals, natural elements, animals, concepts, and the seven tones of the diatonic scale.

This matrix is a musical score, the first one of seven similar grids. Each square indicates a repetitive pattern with pitch and duration. The length of the pattern is left to be defined later in the process. There is a C drone at the bottom and the harmony is based on the diatonic scale. The scale is used both horizontally for melody and rhythmic development and vertically for harmony. This way of working off of the same scale or mode melodically and harmonically has always given me an immense satisfaction, like a good shoe that fits and keeps you walking.


The Soundless Sound is an expansion upon The Scale of Number Seven. It started out as a 7x7 correspondence grid, but it evolved into an 8x8 grid. First of all, the subtext is not completely abstract. The creative springboard is to find/recreate this secret silence-sound of the boundless time-space-mind. In my research, I encountered many references to sound as a medium of universal connectivity.

"In the beginning was the word..." The Gospel of St John contains the metaphor of a constant, universal quantity, otherwise referred to as the Logos, or principle governing the cosmos, which is also expressed as unuttered, universal sound, existing since the beginning of time.

The Vedic tradition from India echoes this metaphor with the Om mantra, a 'bija' or seed-sound.

In Zen Buddhism, the famous 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 Schumann's diary refers to 'the voice of the angels', a sound that came from within. 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? That could be what drove Schumann to insanity.

A diatonic tone cluster over a wide frequency range I found The Soundless Sound through the practice of a Yogananda meditation technique; closing the ear lobes, one listens to the inner sound.

This sound unfolded for me as a diatonic tone cluster, the resonance of the Seven Fundamentals (seven tones of a diatonic Pythagorean scale i.e., C,D,E,F,G,A,B) sounding simultaneously, while harmonics rise and form oscillating patterns developing over time.

In relation to an ordinary scale, the difference is that the actual frequencies of these tones range from the very low to the very high, over the entire span of human hearing (20-20,000 Hz).

In the electronic piece, I added a 'limit tone' that is so high it is at the edge of hearing perception (maybe cats or dogs could hear it better than humans). The piece is in Pythagorean tuning.

This is how the 7x7 grid transformed into an 8x8 grid, which allowed a correspondence with the powerful 8x8 hierarchy of the I Ching, which opens up to the time and space correspondence with geographical locations and times of the day. In Vedic hierarchies, correspondence tables match the diatonic set of pitches with the chakras, or energy centers girating in the astral body (a few inches around the physical body) and corresponding to the crown of the head, the brow (between the eyes), the throat, the heart, the navel, the spleen and the genitals. Besides the chakras, the Vedic template shows corresponding elements and mantras (sacred sounds), and I used this as a departure for composing the piece electronically. For the time/space relationship I used the I Ching primary trigram family and its correspondences with geographic locations (North, South, East, West) and times of the day. I worked on this idea 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 of continual frequencies expressed in hertz. There are 8 versions of the score each with a different fundamental. Each section is 8 minutes totaling 64 minutes. Similarly to The Scale of Number Seven, In the Soundless Sound matrix, the stacking of fundamental tones works both 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. 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 boundless space-time. 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.

Note that the main difference between this matrix and the previous Scale of Number Seven matrix is that the order of pitches is reversed: the higher pitch here, B, corresponds to the lower charka and the C root is matched to the crown of the head chakra The Soundless Sound, the actual piece, bearing the same name as the matrix, (composed 1984-89) is an electronic ambiance based on the harmonic vibration of silence - and the piece is an invitation to share the experience. Silence is both impossible to attain and ever-present. The noisier the lifestyle, the more important it becomes to find one's silent voice, one silent space. This is a perception of the time-space continuum which is neither subjective nor objective - the 'soundless sound' simply exists, and one can tune into it.

This score matrix is for the first section of the piece. Each of the eight sections has a different fundamental. The order of the sections is determined by the time cycle from early morning to midnight. Originally this piece was planned as a sound installation with a 64 minute loop. The placement of the speakers is planned to follow a octagonal pattern corresponding to the eight orientations east, west, north south, north east, north west, south east, south west. This sound installation actually has not yet been presented as it was planned. It was performed at different stages of development in 1984 as purely electronic playback with slides, (Experimental Intermedia), 1991 (LaMama) with the Trine and video animation, and in 1998 at the Knitting Factory with seven live performers under the title Initiation to the Soundless Sound, as an installation/performance. It was also presented with tape, vocals and slides within the group exhibition Degrees of Embodiment - Art and Mind Physics at Federal Reserve Gallery, Boston, and revisited again in October 03 at Music Under Construction in New York, with a new choreography by Nancy Zendora. The piece is usually performed as a performance/installation, combining a tape playback and a variable live performance. I plan to continue to work on this piece over my lifetime.


The next matrix I worked on starting in 1989 was the Solar System matrix or Solarsys. I was moving from a square grid to 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 a direct expression of the universal order. There are a number of different planet-scale schemes (see examples below).

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 used a minor scale to start (G minor natural) for Earth, Moon, Venus, Mars, Mercury, Jupiter, Saturn. For 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 to chromaticism 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.

Solarsys Matrix

 

The Solarsys is what gave birth to Existence, an opera of consciousness, a meditation on the dialectic between man and the universe. Even though scientific theories are getting closer to explaining the dynamics of the universe, there still is a zone of mystery that metaphysicians and philosophers of all times have tried to explore. Quantum physics show the amazing range of realities from the infinitely small scale of the atom to the infinitely large scale of the expanding universe. Looking back at Pascal's Pensées on the two infinities, it is remarkable how similar the analysis of the 17th century philosopher and the new scientific theories are. There is actually no way of establishing the existence of anything outside the presence of the observer. Man is the creator of the so-called outside world, both subject and object of a simultaneous, multidimensional reality. This is reflected in the process of mental activity, constantly weaving patterns from different levels of thoughts and harmonizing them as they proceed in time, as would a musical score. This transparency of consciousness, and its evolution since the beginning of time is the theme of the piece. I created the libretto out of excerpts/adaptations from Pascal, Agrippa Von Nettlesheim, and some of my own lyrics and custom universal phonetic solfege. The different scenes focus on key moments or key thoughts: the big bang, the planting of the first seed, the awareness of spatial relationships, contemplative mind, the alteration of reality, the empowerment of women.


Tuning to the earth: the Earth Tone and The Gaia Cycle

In my search for a holistic musical framework, I discovered Cousto. There are three cycles for the earth rotation: the daily cycle (the earth revolving itself), the yearly cycle (the earth revolving around the sun) and the inner rotation of the axis of the earth. Hans Cousto found the corresponding pitch for each of those. The idea that one could tune into the earth tone fascinated me.

This is how Cousto explains his theory. Planetary frequencies are based on orbiting times, i.e. 24 hours for the Earth. Rotations entail vibrations. In order to translate the planetary vibrations to music we can hear, 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 our ear.

The ratio between time and frequency is: Frequency = 1 /Time. The frequency produced by the Earth's orbit around the sun (365.25 days) is thus calculated by dividing 1 by 365.25. 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'.

Two works emerged from this 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.

Variations on the Orange Cycle relies entirely on a G tonal center. G is the tone of an earth day. Ideally, the G should be at 194 hz and the entire piano tuned to it, i.e. if in equal temperament, establish the A reference pitch at 438 hz instead of 440 hz. In standard tuning at A 440, the same G is 196 Hz. I am not sure that this 2 Hz difference is audible to most ears; in order to make this slight flatting perceivable, I added a the seventh, F, to make the G sound flatter. This way, the tuning is built into the piece regardless of tuning.

Variations on the Orange Cycle is about the experience of time. It translates brain activity into music in real time, music inherent to the unfolding of time, mirroring a conscious experience of space-time. The starting point is the 24 hour cycle (the rotation of the earth) with its succession of phases of activity, leisure, transport, rest. The succession of moments, both similar and different, is comparable to variations on a theme. In the Orange Cycle, the traditional parameters of theme and variations are altered.

The theme and variation are in a subjective to objective partnership. The four variations or phases refer to subjective modes of experience that occur at any point. The theme - objective - exists not as a melody but as unchangeable fact, a reality to be accepted just as the rotation of the earth. It is the most basic musical utterance, a fundamental tone.

In terms of melodic development, the Variations are an example Universal Mode Improvisation.

The four phases are different treatments of the G fundamental: modal (phases 1 and 4), chromatic (phase 2) and polytonal (phase 3). In the chromatic mode, dynamic textures are superimposed to the fundamental in a bitonal framework. The polytonal mode explodes the textures into free form while holding the fundamental. This piece was composed in 1991 in New York, subsequently recorded in one take at Cedar Sound and later revised in 1995 to prepare for the New York premiere at Merkin Hall by pianist Lois Svard.

In order to score the piece, I recorded my improvisation on computer via midi for automatic transcription. The advantage of this method is to retain the freshness and spontaneity of the original impulse. Because of the poly rhythmic combinations and the fast tempo of the input (there was no way I could play the piece slowly without changing its feel), the first draft was incredibly complicated and I had to experiment with various computer editing techniques to bring the score to a point of readability without straying too far from not only the transcription but also the ideas in the original composition. Through this process, I resolved the problems inherent to notated improvisation, which can be inadequate - the piece is not a mere transcription, it is a reflected combination of transcribed improvisation and intentional notation.

Variations on the Orange Cycle is a challenging piece for a performer. Pianist Lois Svard, who recorded it for Lovely Music, did a labor of love with it. One year after the Lovely Music release came out, in 1999, Variations on the Orange Cycle was is included in Chamber Music America Magazine's Century List of the Best of the 20th Century,compiled by Frank Oteri, along with works of similar length by Steve Reich, John Adams, Alvin Singleton and Leo Ornstein. That was eight years after the piece was composed.


The Gaia Cycle

After the Variations, I continued my research on the earth tone, and experimented with pitch set to match the yearly rotation of the earth, C# at 136 Hz, which brings the reference pitch to A=432, much lower than the standard A440. I also tuned my piano to a more natural tuning, an eighteen century well temperament, Vallotti Young. The piece was first developed on the piano.

The Gaia Cycle matrix I developed over time, from which Tronik Involutions is derived, is a musical mandala revolving around the Earth Tone, the sound corresponding to the earth's yearly cycle around the sun. It is composed of 12 five-minute sections corresponding to the year cycle (represented by the twelve astrological signs), 12 hexagrams of the I Ching, and a sequence of twelve different tonal centers/key signatures. The 'Earth Tone' or frequency corresponding to the earth's rotation around the sun, was established by Cousto at 136.1 Hz. Consequently, the piece is not in A 440 reference pitch, but slightly lower.

Equal temperament is systematically avoided and replaced by just intonation or Vallotti tunings, sometimes in combination within the same piece (poly microtonality).

The Gaia Cycle is a continuation of my exploration of the experience of time, which I started with Variations on the Orange Cycle, as it connects to universal time and human perception of life cycles. Both works are "Earth Works"- they are based on earth tones, the 24-hour tone (Variations) and the yearly tone (Tronik).

The piece stemmed from the possibilities offered by the principle that any cycle can be expressed in terms of frequency, therefore sound, and that any frequency can be transposed to a perceptible range by way of octave transposition - the same way a child sings a melody along with an adult in what appears to be unison, even though the child sings one octave higher.

The choice of the Earth Tone as a basis for a new body of work reflects an effort to ground the music to a holistic reference pitch. This low C# coincidentally happens to be the "Sa" or universal tonic of Indian music.

The general structure of the work is focused on a key change dynamic which follows a similar logic to that of J.S. Bach's Well Tempered Klavier: It uses the succession of sharps and flats as a hierarchical device. However, the keys used in The Gaia Cycle are expanded tonalities including elements of Western and non-Western modes. Unlike Vivaldi's Four Seasons, The Gaia Cycle does not attempt to literally translate the mood of any particular time of the year - after all, on the global scale, winter in Australia is summer in Canada. It expresses a desire to communicate the vitality of the experience of time, and to maintain an awareness of climactic, psychic and social influences affecting the musical stream.

This is how the correspondence between the year cycle, the I Ching hexagrams sequence 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, Earth. The first key signature is a modified C# minor (with the addition of an occasional A#). C# minor has four sharps (F, C, G, D).

In clockwise motion, the next hexagram, Return, is formed of 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 we are in F# minor.

The next hexagram, Approach, has two Yangs under four Yins - and one less sharp again (F, C): B minor. And so on. Heaven, which is all Yang lines, 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. There is a underlying dynamic of transformation between each part. A logic of mutation is established.

At the micro level, in Tronik Involutions, the basic tone and its harmonics define the scale for a piece and an improvisation is developed around that scale. There is a difference between a scale and a mode. A mode is a scale plus a myth. It contains cultural references. In UMI, there is modulation not into another key but into atonality or poly tonailty 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 can be modified. The important consideration is how one particular accidental can change the entire 'rasa' or mood of the piece. 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.


The Rainbow matrix and Symphony 2001

Symphony 2001 was commissioned by the Bozeman Symphony Society as a celebration of the Millennium. The "uplifting" aspect was essential and I was asked to do a happy piece... a rather unusual request for me. As I started to meditate on the different aspect of the millennium, what I saw was: once the millennium has passed and everyone is still alive, it is wonderful to see the sun rise again; the light of the sun...the continuation of life. Millennium or apocalypse? There are mixed emotions related to the occurrence: fears, superstitions, prophecies, enthusiasm.

The symphony relates the magic and superstitions surrounding the millennium, the predictions of doom, and the idea of universal time, and gratitude for the gift of life. Symphony 2001 could be nicknamed 'Rainbow Symphony', as the seven successive ascending tonal centers are correlated to the light spectrum.

There is a fairly close mathematical correspondence between the frequency of each pure color of the spectrum and certain musical frequencies. Thus the idea of setting each movement to a color of the rainbow and corresponding tonal center.

The tonal structure of Symphony 2001 follows this hierarchy: there are seven movements to match the seven colors of the rainbow. The tonal center for the first movement is G-violet (405 Hz/396 Angström), the second movement A-indigo (433 Hz/440 Angström), the third movement B-blue (473 Hz/495 Angström), the fourth movement C-green (527 Hz/528 Angström), the fifth movement D-yellow (580 Hz/594 Angström), the sixth movement E-orange(597 Hz/660 Angström) and the seventh movement F-red (700 Hz/704 Angström). Structurally, the light of the sun: the light spectrum with its seven colors of the rainbow provides the macro-matrix for the symphony. The general structure is ascending, corresponding to the sunlight/sunrise theme, and within the movements, there are recurrent ascending structures. Within these tonal centers, there are modulations, melodic and rhythmic elements relating to the emotional aspects of the millennium. The general effect is progressively going from low to high, from the first to the seventh movement.

Copyright Elodie Lauten 2007