Law of Octaves
CD-R release: Sublimation
Posted 28 October 2008, 03:19
Epimoric dream music. For Greg Schiemer and Warren Burt.
The initial spark for “Unstill Light” was a piece by Greg Schiemer called Tempered Dekanies and his related article Tempered Dekanies: Chorus effect using microtonal intervals based on just intonation. As described in the paper, and heard in the piece, Greg came up with an Csound instrument design that is based on the Risset harmonic glissandi. This was intriguing, as I have used a similar instrument in several of my pieces; however, Greg added a couple of new wrinkles, once of which is particularly interesting: using superparticular (or epimoric) ratios to determine the frequency differences between the stacked oscillator tones that together produce the output of the instrument. I immediately wanted to explore that idea, and I ended up writing something that is entirely based on epimoric ratios and uses a version of Greg’s Risset instrument (modified to produce a different effect from the one he used in his piece).
Fundamentally, the piece is based on the superparticular series 3/2, 4/3, 5/4, 6/5, 7/6, 9/8. If you treat these numbers as musical intervals relative to a “root” (1/1) pitch, they get progressively narrower as one moves through the series (3/2 is a just perfect fifth, 9/8 is a just major second, and the others fail in between). Then for each number in the series I computed the ratio that is the “harmonic mean” between that number and 1/1, giving the series 5/4, 7/6, 9/8, 11/10, 13/12, 15/14, 17/16 (note that these are all superparticular as well). Finally, I made two more series that consist of the the reciprocals of the two original series. If we stack up all four series, add in the 1/1 pitch, and look at it in table form, the columns form the chords that are the harmonic basis of the piece (top-to-bottom = high-to-low pitch):
The chords get narrower and more closely-voiced as they progress, converging on the central root pitch.
However, the chords are not simply played as blocks. Except for the central 1/1 pitch, which remains constant, the horizontal voices are offset from one another, so that the chords change gradually, one note at a time.
Getting back my modified Schiemer/Risset instrument, I didn’t employ Greg’s use of envelopes to vary the pitch offsets, using constant offsets instead. I also decided to use much smaller ratios (based on twin primes 1021 and 1023) for the oscillator offsets, resulting in a 2:1 beating pattern (DAH-dit, DAH-dit). Since the duration of the beats depends on the pitch, two or more voices at different pitches played together creates a rhythmic counterpoint. Different lines come in and out of sync with one another, sounding at times like arpeggios.
The chords played on the pulsating Scheimer/Risset instrument have no added effects, but they are backed with a reverb-processed drone. The only sound source used is a precision sine wave generator.
Thanks very much to Greg Schiemer for his music, for corresponding with me about his work, and for allowing me to study his Csound code. I also dedicate “Unstill Light” to Warren Burt, another source of inspiration.
Copyright © 2008, Dave Seidel. Some rights reserved. This work is licensed under a Creative Commons Attribution License.