Resonant Palindrome

Posted 13 March 2005, 05:45


A variation on La Monte Young’s 1989 sine-tone installation The Romantic Symmetry (over a 60 cycle base) in Prime Time from 144 to 112 with 119. An electronic piece written and realized with Csound.

This is a revision of a piece called Symmetrical Melodic Variation on the Romantic Symmetry, originally published on 6 January 2005.

Dedicated to La Monte Young in his 70th year.

Duration: 9 minutes.

Background & Technical Details

La Monte Young’s Romantic Symmetry is a piece consisting of a chord of 22 sustained tones that express a specific set of harmonics of a 7.5 Hz fundamental frequency. All of these harmonics are prime or octaves of primes, except for 119. It is one of Young’s sine-tone installations, intended to run continuously for extended periods of time. The frequencies in the piece range from 60 Hz up to 8.64 kHz.

I have never actually heard Young’s piece as originally rendered, as it has not been recorded (or if recorded, not released) and I have had no opportunity to experience an installation of it, but I’ve been fascinated by this entire family of works as described by Kyle Gann in his article “The Outer Edge of Consonance” from the book Sound and Light: La Monte Young and Marian Zazeela (Bucknell University Press, Lewisburg 1996, ISBN 0-8387-5346-9). Gann provides a detailed analysis of the piece, including a complete list of the harmonics employed. From this I was able to easily produce a rendering of the Romantic Symmetry using Csound. Once I was able to actually hear it, I was inspired to write something that would explore some of the intervallic combinations embodied in the material of the piece. I wanted to refract the multicolored light of Young’s chord into a revolving mobile, to provide an additional way of hearing it. The result is the work presented here.

In the title Symmetrical Melodic Variation, I’m using the term “melodic” in the sense that matches my understanding of Young’s use of the term, in that the tonal materials are used horizontally rather than vertically. By “symmetrical,” I mean that I am deliberately working with the intervallic/registral symmetry inherent in Young’s arrangement of pitches. The drone note, the 127th harmonic, is the axis of symmetry in Young’s chord. I divided the remaining pitches into three “registers”. Of the four moving voices, the bottom one uses the lower seven pitches, the middle two voices use the central nine pitches minus the 127 axis, and the top voice uses the upper six pitches. Each voice uses step-wise motion, beginning and ending at the same pitch within its series. Each voice uses notes of equal duration, but each register is at a slightly different speed, so that they all start and end at the same time. The end result is that each voice, and thus the entire piece, is melodically and rhythmically symmetrical — in fact, each voice is a palindrome, which is reflected in the new title. All of the pitches used in the Romantic Symmetry are present in this piece, and there are no additional pitches added.

For the original version of the piece, I made an instrument that combines a simulation of a plucked string (using Csound’s pluck opcode) with a simple oscillator tone. I did not use a pure sine wave except for the central drone, but the other tones use relatively pure waveforms consisting of the first partial with different strengths of the 2nd, 4th, and 8th partials; since these are all octaves of the fundamental, the pitch ratios remain unmuddied.

In the revised version of the piece, I removed the pluck sound and used a simple oscillator tone. All the voices are now pure sines, except for the lowest voice, in which I added a bit of the second partial to balance it better against the higher-pitched voices. The other big change was to use a different type of reverb, using the Csound babo (“BAll-within-the-BOx”) opcode. The cool thing about this reverb is that it allows one to specify the exact dimensions of the virtual room, and well as the three-dimensional placement, within that room, of the sound source. I decided to use a room size that was a multiple of the wavelength of the fundamental frequency (7.5 Hz), to get a “tuned” resonant reverberation. I also chose to make a two-stage reverberator, where the output of the first fed into input of the second.

I am indebted to Kyle Gann, without whose writings I could not have even begun to study and explore areas of La Monte Young’s work which would otherwise have been inaccessible to me.

Notes on the Revision

I decided to revise this piece for two reasons.

First, I wasn’t really satisfied with the sound of the piece (the plucked sound was too harsh, and there was not enough “spaciousness” in the overall sound). I made the individual timbres simpler but took a different approach to overall texture over time by putting the sound within a much more resonant (virtual) space — see the penultimate paragraph in the previous section for details.

Second, I wrote this before I realized that it would become part of a series (it is the first of three, continuing with The Gemini Nebula and concluding with Passacaglia and Fugue State). After completing the other two, I felt the need to go back and make this one more consistent with the others. More specifically, I wanted simpler timbres and a greater emphasis on beating patterns and combination tones from massed sonorities. The new title is more consistent with the other pieces as well, in that it is hopefully a little more evocative and less prosaic.

Thanks to Torsten Anders for his comments.

Copyright & Licensing

Copyright © 2005, Dave Seidel. Some rights reserved. This work is licensed under a Creative Commons Attribution License.