Congratulations, you’ve done the same thing Steve Reich started doing a few decades ago. It’s called “phasing”. The cool thing, in his opinion, is how things progress through these various stages of cohesiveness and chaos.
The rest of this is going to be a little abrasive, because I highly recommend you do some more research before making claims like you have here. You touch on a number of things that have been discussed at length in a number of academic and non-academic circles for quite some time, and there’s no scarcity of literature on the matter(s). Indeed, Wikipedia is a great resource for such things; I used the hell out of it when I was just starting to seriously explore melody, harmony, and the realms beyond. I’m going to be hard on you, and I’ll pull no punches–because I have faith that, if you’re really interested in music, you’ll be able to handle it; being able to handle people telling you, “You’re fucking stupid, and you have no talent,” is probably the most valuable asset you can possibly have in this (or any) artistic endeavor. So without further ado, here’s where you majorly fucked up in the few paragraphs I took the time to read.
First, people who think “music is a sequence of numbers” tend to make really shitty music–because they’re doing math, not composition. Don’t get me wrong, numbers are a great way to get ideas and to get those creative juices flowing, but when you do math instead of making creative decisions based on the psychoacoustics of the thing, you kind of miss the whole point. If written and/or performed well, music can convey ideas to anyone with the capacity for hearing; it speaks across all language barriers, and seems to grab us in the most intimate way possible. This is how millions of people can walk around thinking a song was written just for them–that it’s “their” song–though the composer probably has no fucking clue that they even exist.
So, “if 40,000 numbers create a second of sound…” is a gargantuan ‘if’, because they don’t; numbers aren’t a creative but a descriptive unit. They are abstract objects, whereas oscillations are not (or at least the phenomenon we signify with the word ‘oscillation’). You can say that A4 is any thing oscillating at a rate of 440 times per second, but that’s still descriptive and, moreover, is only true for that intonation. I can take 111hz for my A1, and thus my A4 would be 444hz, which, in my opinion, is a cooler number than 440. Would you be able to tell the difference without the two notes being sounded simultaneously? If we were, for instance, in the middle of nowhere, and the only thing we had was an acoustic guitar (also assuming neither of us had perfect pitch), I could generate my harmonic series just about anywhere, and unless you had some highly trained ears, you’d never know the difference (because the frequency ratios would be more or less equivalent to the equally tempered scale that takes A1 as 110hz).
The next part of what’s wrong with what you wrote stems from an inadequate understanding of how one graphs a function. If we’re dealing with oscillations, and we’re going to address the waveform–which makes it easy and two-dimensional (rather than four)–then assuming we have a simple, timbre-less wave (I’ll briefly explain what timbre is and why this further complicates your error/s in the next paragraph), then we should be well aware that any line segment is composed of an infinite number of points. This is why when you indicate that a number x is greater than 3 and less than or equal to 4, you notate it (3,4], and not [3.1,4], or [3.01,4], or [3.001,4], ad infinitum. I think it’s pretty obvious that 40,000 isn’t equal to infinity, so even saying, “40,000 numbers create 1x10^-99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999th of a millisecond of sound,” is just not correct–even if numbers were a creative unit (which they aren’t).
Unfortunately, it gets worse for you, because no musical sound is a ‘single line’; this is because of timbre, which informs you that the same note sounds remarkably different when coming from the human vocal chords, a violin, a grand piano, the hum of an engine, a blue whale, or a flatulent elephant. The waveform of a given timbre is composed of a number of waves, but still only represents the thing; the best recording of a grand piano on the best speakers still can’t give you every overtone you’d hear were you standing next to the thing, because there isn’t a grand piano inside your speakers. This gets into the harmonic series. You see, if I hit C1 on a grand piano, I’m not just hearing C1, but also C2, G2, C3, E3, G3, and so on, each successive vibratory mode being less audible than the last. The relative prevalence of certain overtones more or less constitutes the tone color. There are entire books devoted to this aspect of acoustics, so instead of trying to condense a few millennia of human knowledge into a few paragraphs, I’m going to advise you to take a course in the basics of music theory, which will be good for you anyway.
(For the sake of being thorough, timbre may also refer to the approach to playing an instrument, which still bears upon the brief definition above, but is a little more subtle, as two performers can evoke different timbres from the same instrument.)
“You could draw an entire landscape of all the valleys and mountains corresponding to the intensities of the frequencies and harmonics and how they change in time and then convert it back to sound, another form of image to sound generator, another way to actually draw music, to paint it by using the fourier series, the fourier transform of sound, by creating an imaginary fourier series, an imaginary series of sine and cosine values with intensities and how they vary in time and creating a spectrogram, a spectrograph, a sonogram of the sound and inverting it directly back to sound again, through software and machines, whatever…”
Remove every occurrence of the word “music” in that paragraph, replace it with the word “sound”, and I’ll have no problem with it.
Incidentally, you may like Varese and his floating “sound objects” in Arcana.
[youtube]http://www.youtube.com/watch?v=wu-bIPtZgE4[/youtube]
The first time I heard that piece, I thought “Hey, here’s someone who’s lost his fucking mind.” After hearing some of his explorations into the realm of electronics, I revised my opinion of the piece to “Hey, here’s someone who’s lost his fucking mind, but didn’t have the right instruments to express it, and tried to make due.”
Or Ives’ Concord Sonata:
[youtube]http://www.youtube.com/watch?v=RXPSU1gOjL0[/youtube]
The only problem with this spectrum of “music” is that anyone with an understanding of the musical notation of rhythm and harmony (and often, some serious virtuosity at a given instrument), but absolutely no creative musical talent could write this sort of thing and say, “Hey, don’t bitch at me because you’re too stupid to understand it; look, I’ll play it exactly the same every time. I intend to do that–therefor it’s creative–and, because you don’t understand it, it’s esoteric and brilliant and so ahead of its time–and god knows I just transcribed a recording of my tone-deaf, delirious Aunt beating the hell out of her cats on my piano in between my improvisation on ideas similar to Debussy, Scriabin, Stravinsky, Prokofiev, et al., but you can’t say anything because you’ll be a fucking Nazi, you fucking Nazi pig.” When they carted Nietzsche off to the loony-bin, they said he was banging away at the piano like a madman. How do they know he wasn’t anticipating “the future of music”?
When does music become simply drawing on staves? When does esotericism become an excuse for having no talent? Those are the questions. I consider Ives’ piece to be an example of marginal talent with a shit-ton of academic intellectualization as filler–but as I said, I may just be a stupid fucking Nazi.
I’ll leave you with Leo Ornstein’s Suicide In An Airplane, which I hold to be an absolutely brilliant work of art.
[youtube]http://www.youtube.com/watch?v=xYACtB0qWJY[/youtube]