Reddit reviews Music, Cognition, and Computerized Sound: An Introduction to Psychoacoustics

If you haven't made much music in the past, I would recommend learning how to DJ while also studying the principles of audio synthesis and music theory.

DJing is a really good way of understanding what elements of a tune make it danceable and exciting - particularly as far as rhythm and harmony are concerned. Digital music production requires a pretty solid understanding of not just computer software but also a few fundamentals, including the physics of sound, the science behind audio synthesis, and then technique things such as editing, signal flow, etc.

A few books I would recommend for getting started are The Computer Music Tutorial and Musicmathics. As far as mixing and mastering is concerned, which are other essential aspects of the production process, I would recommend checking out Robert Katz's Mastering Audio.

Psychoacoustical considerations are probably what most blatantly separate the men from the boys. My recommended starter for this is Music, Cognition, and Computerized Sound by Perry Cook, who is a professor of Computer Music at Princeton.

EDIT: Also, if you don't already, start listening to and appreciating classical music - particularly stuff made after the Renaissance - in order to get an understanding of the emotional impact things such as dynamics and voicing have on the listening experience. Electronic music heavily borrows from the classical music tradition in this context. Digital music production essentially makes you a computerized Mozart, in that you can control dozens of musical voices, but with even more micromanagement potential than the typical classical music conductor can offer. You will not have a complete understanding of these musical concepts from pop/rock music alone, or even from more 'sophisticated' musical practices such as jazz.

It's a complicated question and required lots of math and music and auditory perception to fully understand.

To say that music is just math is pretty much wrong. How we hear things is not predicated by current mathematics but by how our hearing apperatus has evolved. We can try to describe our hearing mathematically but that's how we describe pretty much anything that we try to formalize.

Music on a higher level too is a kind of formalism. There is lots here, tuning systems, intervals, harmony. But there is a very trickly interplay with cultural developments and perception. It's not clear that all of what has developed say in western european music is pure cognition. Some of it may be habits or cultural preferences. So again to say that it is just math becries this complexity.

That said mathematics is our best formal structure theory out there, so it's not surprising that we can use it to model structures!

Incidentally there is a debate within the musicology community of research practicioners just how much math really means for the field. This has appeared in 2012 in a special issue of the Journal of Mathematics and Music. Discussants are Guerino Mazzola, famous for bringing heavy mathematical machinery to musicology (see his book, or should I say solid brick "Topos of Music"), Gerant Wiggins (a computer scientist, who will defend a more cognitive perspective), and Alan Marsden (who will defend space for non-mathematical musicology). If you want to learn how some practitioners in the intersection of math and musicology think, this is a place to learn about it.

There is more. Sound itself can be generated mathematically. Lots of digital signal processing (linear algebra, complex analysis, ODEs and theory of oscillators, physical simulations and PDEs etc) here. A good starting point for that stuff are Julius Smith's web books. And sound needs to be analyized (lots of autoregression, functional transforms (fourier, wavelets, etc), machine learning here). Check out the ISMIR professional society for pathways into that particular type of research and mathematical work. A good source at the interface of music, computation, and cognition is Perry Cook's book Music, Cognition, and Computerized Sound, which will give you a good view of the math of musical cognition involved (cognition of musical scales etc).

So lots and lots of stuff here. Academic programs related to this tend to be called something like Music Technology but it's not uniform.