I am motivated to write a program(s?) that would allow the user to:

“hear” a triangle — e.g., in two-dimensional space (x=time, y=pitch)
- presumably would need only 2 voices (i.e., only 0, 1, or 2 intersections are possible between an arbitrary straight line and an arbitrary triangle)
draw and “hear” a triangle

The logical continuation of this idea is toward an intuitive graphic notation system outside the bounds of standard musical notation (e.g., notes, rests).

And indeed, that terrain has been trodden by composers of this era. Cage mentions a diagram that stretched across the wall near Schillinger (1895-1943)’s ceiling: “all the scales, Oriental and Occidental, that had been in general us, each in its own color plotted against, no one of them identical with, a black one, the latter the scale as it would have been had it been physically based on the overtone series”. Schillinger was a contemporary of Rachmaninoff and Stravinsky, also an émigré from Russia. Schillinger created what later became known as the Schillinger System, evidently a monumental effort; and indeed, The Berklee College of Music began as the “Schillinger House” in 1945, where the system survived in the curriculum until the early 1970s. This system begins with a highly mathematical treatment of rhythm.

Silence

I have been reading from John Cage’s Silence: Lectures and Writings. What a mind!

From the Forward

Poetry is not prose simply because poetry is in one or another way formalized. It is not poetry by reason of its content or ambiguity but by reason of its allowing musical elements (time, sound) to be introduced into the world of words. Thus, traditionally, information no matter how stuffy (e.g., the sutras and shastras of India) was transmitted in poetry. It was easier to grasp that way. Karl Shapiro may have been thinking along these lines when he wrote his Essay on Rime in poetry.

What I do, I do not wish to be blamed on Zen, though without my engagement with Zen (attendance at lectures by Alan Watts and D. T. Suzuki, reading of the literature) I doubt whether I would have done what I have done.

From The Future of Music: Credo

Whereas in the past, the point of disagreement has been between dissonance and consonance, it will be, in the immediate future, between noise and so-called musical sounds.

The principle of form will be our only constant connection with the past. Although the great form of the future will not be as it was in the past, at one time the fugue and at another the sonata, it will be related to these as they are to each other: through the principle of organization or man’s common ability to think.

Most inventors of electrical musical instruments have attempted to imitate eighteenth- and nineteenth-century instruments, just as early automobile designers copied the carriage. The Novachord and the Solovox are examples of this desire to imitate the past rather than construct the future.

Schoenberg’s method assigns to each material, in a group of equal materials, its function with respect to the group. (Harmony assigned to each material, in a group of unequal materials, its function with respect to the fundamental or most important material in the group.) Schoenberg’s method is analogous to a society in which the emphasis is on the group and the integration of the individual in the group.

From Experimental Music

sounds: those that are notated and those that are not

There is no such thing as an empty space or an empty time.

Examples cited: glass houses of Mies van der Rohe and Richard Lippold’s wire sculptures.

Try as we may to make silence, we cannot.

Give up walking in order to fly

This fearlessness only follows if, at the parting of the ways, where it is realize that sounds occur whether intended or not, one turns in the direction of those he does not intend. This turning is psychological and seems at first to be giving up everything that belongs to humanity—for a musician, the giving up of music. The psychological turning leads to the world of nature, where, gradually or suddenly, one sees that humanity and nature, not separate, are in this world together; that nothing was lost when everything was given away. In fact, everything is gained. In musical terms, any sounds may occur in any combination and in any continuity.

A total sound-space, the limits of which are ear-determined only, the position of a particular sound being the result of five determinants:

frequency or pitch
amplitude or loudness
overtone structure or timbre
duration
morphology (how the sound begins, goes on, and dies away) (I think this was later called “envelope”? -MG)

One may take advantage of the appearance of images without visible transition in distant places, which is a way of saying “television”, if one is willing to stay home instead of going to a theatre. Or one may fly if one is able to give up walking.

Musical habits include scales, modes, theories of counterpoint and harmony, and the study of the timbres, singly and in combination of a limited number of sound-producing mechanisms. In mathematical terms, these all concern discrete steps. They resemble walking—in the case of pitches, on steppingstones twelve in number.

He was moved greatly by the advent of magnetic tape recording (early contribitions by Pierre Schaeffer. It opened up all the possibilities to imitate nature more closely.

This cautious stepping is not characteristic of the possibilities of magnetic tape, which is revealing to us that musical action or existence can occur at any point or along any line or curve or what have you in total sound-space; that we are, in fact, technologically equipped to transform our contemporary awareness of nature’s manner of operation into art.

One has a choice. If he does not wish to give up his attempts to control sound, he may complicate his technique to an approximation of the new possibilities and awareness. (I use the word “approximation” because the measuring mind can never finally measure nature.) Or one may give up the desire to control sound, clear his mind of music, and set about discovering means of to let the sounds be themselves rather than vehicles for man-made theories or expressions of human sentiments.

Hearing sounds which are just sounds immediately sets the theorizing mind to theorizing, and the emotions of human beings are continually aroused by encounters with nature.

Sounds, when allowed to be themselves, do not require those who hear them to do so unfeelingly. The opposite is what is meant by response ability.

Donna Haraway also writes about “response ability”.

Those involved with the composition of experimental music find ways and means to remove themselves from the activities of the sounds they make… the composer resembles the maker of a camera who allows someone else to take a picture.

It goes without saying that dissonances and noises are welcome in this new music. But so is the dominant seventh chord if it happens to put in an appearance.

We are concerned with the coexistence of dissimilars, and the central point where fusion occurs are many: the ears of the listeners wherever they are. This disharmony, to paraphrase Bergson’s statement about disorder (there is mention of it here), is simply harmony to which many are unaccustomed.