luuIntroduction to Computer Music (2009) [pdf]
https://composerprogrammer.com/introductiontocomputermusic.pdf
I often see people frame music as mathematical manipulation or try to approach music making from a “first principles” approach, where those principles are mathematics and physics. But watching musicians talk about making music, I seldom see any discussion of the underlying math, and instead see discussions of timbres, instruments, and stylistic/historical influences; musicians who make good music seems to believe “first principles” involves historical knowledge and a well-listened ear, and nothing involving math. My question is: Is thinking about music as applied mathematics a good way to create good music? Or is it just the most easily digestible model of music for the crowd on this site?
Wonderful question. I suspect it's partially the culture issue you point to, but also a practical issue of composition. If we decompose sound into the basic waveforms, similar to the subject pdf on page 18, we then have parts that we can reassemble. We can take the defense-funded DSP math of the likes of a John Cooley or a John Tukey and build an engine for assembling the parts of sound.
All this being said, I think that's a process of convenience and a historical path not a absolute constraint. We have some more flexible means of communicating with the machines today. And I strongly encourage someone to work on a new UI for computer music. "Jazz trio piano, upright bass, and drums. start drummer laid-back, piano blowing over the changes, then piano on top."