Also worth exploring in terms of modern music theory are microtonal music and atonal music, both of those are playing with incorporating the physics of notes, overtones and harmonic relationships.
Oh. It has not been my understanding that spectral music is about beat frequencies.
Beside the point: My experience of spectral music has been that it's a neat idea that seems worthy of trying out. Then, when you do it – test the hypothesis, so to say – it turns out that nope, didn't work, sounds awful.
Yes. Spectral is a bit more about composing using overtones than beat frequencies. I know the latter has been done, but I mixed them up a little, I would have described it as overtones were I to write my initial comment again.
I agree that it's not producing pleasant music to the masses. It's more of an academic exercise, but it is influencing modern music theory and bridging classical music theory with a more recent understanding of harmonics.
I can't give any links, but I've done something similar during a live show. I use a laptop and several keyboard controllers to play and loop music live, the computer providing precise timing that would otherwise make this impossible with a live band (unless everyone was on a metronome).
I've got a piece in C#m at 87 bpm [0]. I'll play a piano instrument which is being fed into a distortion (the distortion makes the beat frequency much more apparent) and slam an Ab1 and A1 at the same time. That's 55.00hz - 51.91hz [0], which gives a 3.09 hertz beating. Or a period of 323.6ms [0]. So you have two notes close together, which sounds very dissonant, they're bass notes which makes it muddy, and it's so distorted, you can barely tell what the actual notes are. But it swells up and down on the tempo like a rhythmic device.
[0] Anyone who looked up a tempo -> ms chart is going to say "WTF, that's not in time with 87 bpm." Which is correct, but because pianos are stretched tuned (and so is the virtual instrument I use), the numbers I provided aren't exactly true. I never bothered to measure the exact frequencies, but I kept adjusting things until everything sounded right by ear.
Here is good example of some one with proven jazz and classical mastery to trancend the theory he clearly knows and improvise with beat frequencies. Keith Jarrett, 'Spheres / Hymns'. He especially uses this technique between 20:00 and 30:00. See my thread below if you'd like to read more about why this composition is relevant to the parent thread.
Not remotely a canonical example, but this piece (of mine) uses Linnstrument to create rhythms and structure by detuning and retuning unison sine waves:
Do you have any links regarding this?