Composing In n Dimensions

(In Search Of My Muse #1.03 )

Frequency = Color = Space/time

An old Vedic doctrine postulates, that there is a static supersonic sound, without vibrations, somewhere in the Universe: this is the time-base of all natural events occurring on Earth and elsewhere...

Also, this doctrine holds that the ultimate quality of any sound potential is silence. At the finite level, sounds generate different degrees of vibrations that create light and dimensions. Every vibration has its own volume and structure that varies in accordance with the density of the sound.

Furthermore, it holds that time is relative and has no objective reality: it is always conceived in relation to its antecedents and sequence events. Space, like time, is also considered to be relative, as it is constructed on the basis of relation and position

On that subject, I still remember, vividly, the day when David Wessel stunned me and the other students, during a lecture at the I.R.C.A.M, by declaring, very matter-of-factly : "In essence, there is only one parameter in music: Frequency!"

Surprising as it may be, this fact is not new to serialist composers: their serial system unifies all frequencies, harmonics and time intervals in a coherent way.

n Dimensions Table

Alas, due to space restrictions, the above non-linear table had to be compressed in a linear way. (Note: The real table should be spread over four octaves vertically and horizontally !).... Anyhow, this main table shows (in the Y dimension) the first 16 harmonics (H1 to H16) of a given fundamental note (Fo) belonging to a chromatic scale (shown in the X dimension). Notice that the odd numbers harmonics are shown in a Grey box. Also, the relative amplitude of each harmonic is shown in an adjacent box to the right of the harmonic number.

A sub-table, located under the main table shows, on the X plane, a color spectrum chart  vs. a "Modulo 12" sequence of numbers corresponding to the chromatic scale (in Blue).

Slide-ruler A shows the tonal intervals for a standard seven notes-per-octave diatonic scale (Red dots), as well as a pentatonic scale (White Dots). There is also a Tonic scale using intervals by whole-tones (Dark-Green dots) .

Slide-ruler B shows the usual duration and rests symbols, using the conventional notation system : it can be used to quickly estimate the durations/rests or "accelerations/decelerations"- ratios between a pivot frequency and any other frequency in the scale. If needed, you can also use this slider to select, arbitrarily or randomly, a given value of duration/ rest for each note in the scale.

For example, if you want to know the intervals of a diatonic scale in F, place the cursor of slide-ruler A (Red dot in Black box) under the Blue F note in the chromatic scale and read on: i.e. F, G, A, A#, C and so on...

Reading the chart vertically (on a Y plane), you discover that F has a aqua color spectrum and has a value of 5 on the "Modulo 12" dodecaphonic scale. Then, you can read the first 16 harmonics of tone F (i.e. F0, F1, C2, F2, A2, C3, E3, F3, G3, A3, B3, C4, C#4, D#4, E4 and F4), as well as the relative amplitude of each harmonic (Hn) vs. the fundamental (Fo.).

Evidently, this chart can also be used for other purposes: i.e. chords building or morphing according to the harmonics series (on a Y plane), morphing of several timbres together (on an X/Y plane) and -in conjunction with slide-ruler B- one can interpolate duration relationships and positioning between two tones in space/time (on a virtual Z plane).

Now, If you have access to a pan-tone color chart - and if the whole chart is expanded in a non-linear way -, you can calculate the approximate hue of each harmonic number vs. the primary colors. This will help you to better understand, on a musical and poetic level, the relationships existing between color hues and timbre colors (soundscapes).

Since Antiquity, composers have known the emotional and subliminal qualities of individual tones and/or notes: DO (strong, firm), RE (rousing, hopeful), MI (steady, calm), FA (desolate, awe-inspiring), SOL (grand, bright), LA (sad, weeping), TI piercing, sensitive)... Keep in mind, that sharpening the pitches in high notes leads to a brighter and joyous music, while flattening the pitch to deep notes conveys a feeling of solemness.

André

(Extracts from 'Ye Olde Timer's Analogue Cookbook' by André C. Stordeur)

André Stordeur has taught analog modular synthesis since 1973. He studied with David Wessel at the I.R.C.A.M, in Paris, and with American composer Morton Subotnick.