||NOTES ON THE CONTINUOUS PERIODIC COMPOSITE SOUND WAVEFORM ENVIRONMENT REALIZATIONS OF MAP OF 49S DREAM THE TWO SYSTEMS OF ELEVEN SETS OF GALACTIC INTERVALS ORNAMENTAL LIGHTYEARS TRACERY BY LA MONTE YOUNG
MAP OF 49S DREAM THE TWO SYSTEMS OF ELEVEN SETS OF GALACTIC INTERVALS ORNAMENTAL LIGHTYEARS TRACERY consists of a total environmental set of frequency structures of sound and light-a collaboration of my work with light projections and designs created by Marian Zazeela. Although the work is a section of THE TORTOISE, HIS DREAMS AND JOURNEYS it is different from the previous sections and will have its own subsections, each of which will receive an individual title. A major difference is that all work on this section has taken place since I began to write 2-3PM 12XI 663:43AM 28 X11 66 FOR JOHN CAGE FROM VERTICAL HEARING OR HEARING IN THE PRESENT TENSE which I have since revised under the title THE TWO SYSTEMS OF ELEVEN CA TEGORIES 1:07:40 AM 3 X 67—. I have concentrated primarily on selected intervals from categories Al, 131, and A2, B2, X=5 from the latter work.
THE TWO SYSTEMS OF ELEVEN CATEGORIES applies to sets of concurrent generating frequencies which are integral multiples of a common fundamental and outlines a means for achieving graduated degrees of control over which frequencies will be present within a complex of such concurrent generating frequencies and their associated combination frequencies. Generating frequencies are defined to he the prime, or zeroth order; combination frequencies from which all higher order combination frequencies are derived. The nth order (N 0) combination frequencies are defined to be the sum and difference frequencies produced by all lower order combination frequencies. This control is achieved by categorizing sets of concurrent generating frequencies according to the specific generating and combination frequencies to be excluded.
Consider the premise that in determining the relationship of two or more frequencies the brain can best analyze information of a periodic nature. Since chords in which any pair of frequency components must he represented by some irrational fraction (such as those required for any system of equal temperament) produce composite sound waveforms that are infinitely non-repeating, only an infinite number of lifetimes of listening could possibly yield the precise analysis of the intervallic relationship. Consequently the human auditory mechanism could be best expected to analyse the intervallic relationships between the frequency components of chords in which every pair of components can be represented by some rational fraction, since only these harmonically related frequencies produce periodic composite sound waveforms.
As sources for the frequency environments I have selected sine waves since they have only one frequency component. These are produced by frequency generators tuned both by ear and with an oscilloscope which continuously displays the generator frequency ratios with lissajous and intensity modulated ring patterns. Most recently I have been using a Moog Synthesizer with ultra-stable variable frequency sine wave oscillators designed for my work.
To my knowledge there have been no previous studies of the long-term effects of continuous periodic composite sound waveforms on people. (long-term is defined to be longer than a few hours in this case.)
My past work in music with sounds of long duration slowly led in this direction until it became possible for me to develop a situation allowing the study of truly continuous sounds by establishing continuous frequency environments with electronic instruments. I have maintained an environment of constant periodic sound waveforms at my studio and home continuously since September 1966. The only exceptions have been that I sometimes, but not always, turn off the equipment when no one will be in the environment at all, and when listening to other music. Also, I sometimes turn it off to test the acoustical situation for spurious (incidental) sounds, and to study the contrasts of such extended periods of sound with periods of silence.
The sets of frequency ratios listened to are often played continuously 24 hours a day for several weeks or months. Marian Zazeela and I have worked and lived in this environment, and varied groups of people have been invited to listen and report their reactions to the frequencies. Although in 1957 I was originally drawn to work with sounds of long duration by intuition alone, my work of this nature has led to the formulation of three principles which suggest further study:
1. Tuning is a function of time. Since tuning an interval establishes the relationship of two frequencies in time, the degree of precision is proportional to the duration of the analysis, i.e. to the duration of tuning. Therefore, it is necessary to sustain the frequencies for longer periods if higher standards of precision are to be achieved. The fact that this information is not generally known to musicians may be one reason that only a few examples of pitches of long duration such as organum, pedal point, and the drone are to be found in music. On the other hand, astronomers have known for some time that if a measurement or comparison is to be made of two orbits which involve many years of time, the degree of precision of the measurement will be proportional to the duration for which the measurement is made. (1)
2. Consider the possibility that the number of complete cycles of a periodic composite waveform is a primary factor in recognizing an interval and/or in determining the degree of precision in tuning once the interval has been recognized. If this were the case, ratios comprised of lower frequencies (such as 52.5 Hz: 30 Hz=7:4) would have to be sustained for longer periods of time than the identical ratios comprised of higher frequencies (such as 840 Hz:480 Hz=7:4), in order to produce an equivalent number of complete cycles of their periodic composite waveforms.
3. In the tradition of modal music, a fixed tonic is continued as a drone or frequently repeated, and a limited set of frequencies with intervallic relationships established in reference to the tonic is repeated in various melodic permutations throughout a performance in a particular mode. Generally, a specific mood or psychological state is attributed to each of the modes. The place theory of pitch identification postulates that each time the same frequency is repeated it is received at the same fixed place on the basilar membrane and transmitted to the same fixed point in the cerebral cortex presumably by the same fiber or neuron of the auditory nerve. The volley theory of pitch perception assumes that a sequence of electrical impulses is sent traveling along specified neurons of the auditory nerve. For frequencies up to about 2000 Hz only, these produce a more or less complete reproduction of the frequency of the vibratory motion of the basilar membrane in the case of a single sine wave and a more or less distorted reproduction of the complete waveform for more complex signals. It is presumed that this reproduction will he best for sounds at lower frequencies and less good for higher frequencies since an individual neuron cannot fire faster than 300 Hz. At lower frequencies a group of neurons working together would be able to supply several pulses per cycle whereas at higher frequencies they could only supply one every several cycles. The assumptions of place theory and volley theory suggest that when a specific set of harmonically related fre quencies is continuous, as is often the case in my music, it could more definitively produce (or simulate) a psychological state that may be re ported by the listener since the set of harmonically related frequencies will continuously trigger a specific set of the auditory neurons which in turn will continuously perform the same operation of transmitting a periodic pattern of impulses to the corresponding set of fixed points in the cerebral cortex. When these states are sustained over longer periods of time they may provide greater opportunity to define the psychological characteristics of the ratios of the frequencies to each other. (2)
(1) A notable example of the application of principles 1 and 3 is the classical music of India which has nearly always included a sustained drone and has evolved and actually practices the most highly developed system of modal scales and moods related to modes in the history of music.
Copyright © La Monte Young, 1969
From Aspen Magazone No. 8. Accessed 12.04.2007 from http://www.ubu.com/aspen/aspen8/waveform.html