It seemed to me, when I stumbled upon this form, not knowing it's rich history, that I had come upon something that was itself a metaphor for listening to music. The form opens with something introductory, to draw the listener in. Then it moves through some ideas, drawing the experiencer into the landscape and logic of the piece, until they reach the center of the piece, then the climax (as it's called) and then back out to the real world, the same way they went in. But the ideas are modified a bit, just as the listener has (hopefully) changed a bit by listening.
The latest chapter we're reading in Xenakis' Formalized Music is about how waveforms are not static in real life. For example, tones shift slightly on the violin. Certain partials become more or less present and drift tuning a bit. He talks about how this is a huge problem in electronic and computer music, because such forms use static waveforms, whereas live music does not. Static waveforms are uninteresting, he alleges.
Now, this is a problem with UPIC for sure. You can create "samples" that are 1/10th of a second long. A sample of somebody singing that's 1/10 of a second, repeated over and over does sound static and awful, because it doesn't conform to expectations we have about the human voice. However, I object to his characterization of analog electronic music as static. Did he listen to the same people that I did? Was he not aware of oscillator drift? If you have a problem with electronic music not changing it's tuning over the course of a note, there are several synthesizers that I could introduce you to that will drift whether you want them to or not. Alas, if only he weren't dead. Alas, if only I had a Moog.
Actually, this is a problem I have with my hardware synthesizer. It doesn't drift enough. There are many ways to work around this, most of them involving FM. You can even attach an electronic thermometer to a plug to make meandering drift (which unlike synthesized randomness, does not tend to center around 0). You can also create analog chaos, where sine 1 FM modifies sine 2, which FM modifies sine 3, which FM modifies sine 1. If chaos isn't enough variation, I don't know what is. Also, a lot of work was done at Stanford on using FM to model instruments in a convincing and less mathematically challenging way. The Yamaha DX7 was born from these efforts. One can also do phase modulation (better than FM for many applications) and even pulse width modulation (wherein you alter what percentage of square wave is spent at -1 and what percentage is spent at +1). And any analog synthesizer worth it's salt produces both noise and filtered low frequency noise which simulates randomness. Another method of changing is using envelopes to modify the amount of FM (or PM) over the course of a note and by using filters also controlled by envelopes. Enveloped filters are especially effective, however, they're not present in UPIC because Xenakis felt that they reduced richness, which he only wanted to increase.
The issues of subtle changes within electronically produced sounds was a large issue. It seems somewhat reduced in importance now, probably because of his efforts. He was extremely mathematically inclined and set up research centers to solve problems in electronic music. Also, I have spent a significant amount of the time I spend working with my synthesizer trying to introduce the kind of minute variations that Xeankis rightly characterizes as essential. However, I can't go along with how he talks about synthesizer music from the 60's. Had he not heard Pauline Oliveros or what?
The amount of applied and actual mathematics in electronic music is kind of staggering, also. I learned all these equations at one time and I can use the applications of them no problem, but it's dizzying to sit and think about all the harmonics, the different kinds of randomness and drift, etc. He's right that synthesizer music that doesn't take all those things into consideration, at least intuitively, is crap. Early electronic music is certainly not crap, doggone it. They did not have the technology then to produce that kind of crap! It takes a computer or much more advanced analog circuits to make flat, static, awful sounds! Earlier beasts could not hold a tune well enough to have this problem. A lot of effort had to go in to allowing this problem to come into being. (Similarly, a lot of work was spent on the signal to noise ratio of systems. Only with the introduction of very low noise digital technology did it become clear that a certain amount of noise is absolutely essential. Low level noise is generated by your CD player and mixed into playback. The nice thing is getting just the right amount of noise and being able to control your oscillator drift.) Maybe it doesn't seem convincing to say "this is a problem and I have some solutions" if other people also have solutions or at least workarounds.
Xenakis' sketches of his UPIC scores are framed on the wall around the lab. They're strange organic shapes, like some sort of fantastic or undersea life. I thought I should try entering in the kind of data that the system was designed for. The default waveform with UPIC is a sine wave. The first piece I posted from UPIC uses only sine waves, however it uses more of them than system supports. (The magic of overdubbing!) I created change in the piece by having the sine waves glissando (slide) around each other. They were all changing pitch in relation to each other, creating constantly changing beating patterns and thus resisting staticness.
Today, I drew a triangle wave. (ooh) It has it's own harmonics already in it, so it takes fewer of them to make a rich sound, however, the harmonics do stay in tune with each other. The richer sound plus the organic forms is nice. And because a triangle wave is one of the basic building blocks of electronic music, it is what it is. I don't feel disappointed because it doesn't hint at being a voice or violin or something without actually being it. And, again, having a large number of them going at the same time, not staying constant to each other, creates the kind of constant change that music seems to need.
Hopefully, I'll have something to post tomorrow. I cannot also post my (overly similar to Xenakis') drawing, because UPIC doesn't export art.