Posted 22 July 2006, 18:58
A mensuration canon in just intonation based on Terence McKenna’s TimeWave Zero. Revised 22 July 2006.
Duration: 4 minutes, 56 seconds.
Terence McKenna was one of the more interesting counter-cultural thinkers to emerge in the Sixties. His novelty theory is largely based on a mathematical construct called the TimeWave, which has its origin in a particular arrangement of the I Ching called the King Wen sequence. While McKenna’s explanation of the TimeWave is interesting, a paper by physicist John Sheliak (page context) provides a clearer and more mathematically rigorous account.
I have no opinion on novelty theory per se, but I have for several years been fascinated by the form of the TimeWave that Sheliak calls the Tri-Level Bi-Directional Wave (see Figure 4 in the McKenna article and Figure 10 in the Sheliak article). Without getting into too many details, the essence of it is a sequence of 64 integers, superimposed upon itself. One layer is a single cycle, which defines one period of the overall wave; the next layer is two cycles; the third layer is six cycles. Actually, each layer consists of two sequences: the original sequence and a retrograde-inversion of the original sequence, so there are six lines altogether. It made sense to me to see this object in musical terms, where each integer represents a note in some scale, and each of the three layers represents a two-voice sequence of those pitches in time. So I decided to translated the wave into sound, but first I had to choose an appropriate musical language.
Within any cycle of the TimeWave, the set of integers has a very small range, between 1 and 6. Since seven-note scales or modes are so frequently used in music around the world, I decided that I would limit myself to something in that domain. Something about the “contrapuntal” structure of the wave reminded me of Gamelan, which led me to make my first attempt using a pelog scale and bell- or gong-like timbres. But I don’t have access to convincing gamelan sounds, nor do I have a deep understanding of gamelan, so I abandoned that approach. I eventually settled on a scale similar to the following:
C D E♭ F♯ G A B♭ C
which contains some of my favorite intervals: the minor third, the augmented fourth and the flat seventh. There are a number of ways to express this scale in just intonation, and this is the one I chose:
1/1 9/8 7/6 7/5 3/2 5/3 7/4 2/1
Each two-voice sequence is presented in its own octave, where the slowest single-cycle line is in a lower octave, the two-cycle line is one octave higher in pitch, and the six-cycle line is another octave higher.
I’m a little embarrassed to admit that it didn’t occur to me for quite a while that the structure of the music that emerged can be considered a mensuration canon, which is a type of canon where the different voices play the same music at different speeds. My flimsy excuse for this belated realization is that it’s been 28 years since I studied music in college.
The piece starts (and ends) with a slightly reverb-processed sine-wave choir that plays the minor seventh chord that is implied by the scale. Before the full six-voice canon begins, you hear one complete cycle at the highest octave and speed.
I wrote the piece using Steven Yi’s excellent program blue as a front-end to Csound 5.0. Blue’s Microtonal Piano Roll feature allowed me to work directly with the scale I built in Scala, and the very cool BlueX7 feature made it very easy to use Russell Pinkston’s DX7 emulation instrument designs for Csound.
The piece is dedicated to the memory of Terence McKenna, whom I wish I had met, and also to John Sheliak, with gratitude for his willingness to discuss the TimeWave through an email conversation.
Revised, 22 July 2006: In the process of preparing an eight-channel version of the piece, I made a new stereo version that makes a much better use of space relative to the orginal version. Each sequence now starts with the two voices on separate sides of the stereo field, which then cross-pan to swap places. The cross-pan recurs for each repetition of the sequence.
Update, 23 September 2006: The eight-channel version of TimeWave Canon was played last night (22 September 2006) as part of the final concert of the third annual Mid-Autumn Harvest Moon Festival at Concordia University in Montreal. Thanks to Kevin Austin at Concordia for encouraging me to participate, and also to Mark Corwin, Yves Chigon, the students, and everyone else who made this event so collegial and congenial.
Update, 31 October 2008: Updated the link to the Sheliak paper to go directly to the PDF in its new location, and added a link to the page on which it is now found.
Copyright © 2006, Dave Seidel. Some rights reserved. This work is licensed under a Creative Commons Attribution License.