I’m in a similar boat to you when it comes to math. And more and more I’ve been looking to up my math skills as I also think it’ll improve my skill in SC and open up many new possibilities compositionally and creatively.

I’m also comfortable with various synthesis techniques, but the underlying math behind them is I think important to knowing and intuiting how to set up controls, modulations, interconnections, etc.

I recently picked up Musimathics by Gareth Loy, and have recently begun going through it. I’m still early stages in the first book, and want to read them in order, but it’s really vol 2 that I’m interested in going through, I think many relevant concepts will be introduced there, but I also think that vol 1 lays the foundation. I haven’t gotten far enough into it yet to see whether it’s a use resource, but it seems like the books were written to speak toward this exactly, so I hope so! There also seem to be a lot of references to Curtis Roads’s Computer Music Tutorial, and various other resources of this sort. I’m not sure if the math is clearly laid out there, but at least the formulas are discussed. Depending on the complexity of the formulas, it may be possible to work backward, maybe not.

Personally I think compositionally, with some foundational algebra under your belt and an understanding of synthesis, you’ve got a lot of tools already inherently there in helping make sense of the math, because you know about how this math is actually implemented. If looking at a formula that describes filter behavior, for instance, you already know what many of those variables represent. Often seeing which variables are used can also be informative for thinking about how to structure a synth compositionally, as the math has helped inform many concepts of common synthesizer controls, layouts, etc.

I think where the math knowledge comes in though are examples like how to set up control structures for say FM synths when you want them to be more harmonically cohesive, versus not.

One of Nick Collins’s SC tutorials on synthesis goes into some of the math, and some of the common means of control, and also references a Max/MSP tutorial that references Roads, Chowning, and Moore. Collins sort of hints at it, and the Max tutorial goes into it just a bit more, about the difference in Chowning and Roads’s harmonicity index formula, vs Moore’s and ultimately opting for Moore’s:

In this tutorial we use Moore’s definition because that way whenever the harmonicity ratio is an integer the result will be a harmonic tone with *Fc* as the fundamental.

I think it does take an appreciable understanding of math, not to understand why *they* chose one over the other, but just knowing that it’s possible to choose, of knowing thee distinction, of figuring out one versus the other on your own. And the ramifications of choosing Chowning’s versus Moore’s, or if you chose the wrong one, even know that it’s possible to correct and switch to another… My natural inclination would have been some sort of down chain brute strength method, and who knows what that means - that could derail the entire patch, and would certainly take a lot of energy, where actually switching numerator and denominator is a simple thing, with huge ramifications!

As for learning other languages after learning a first one… I personally think that the basic syntactical requirements of a language is the easy part. It’s truly the ability to think through a problem programmatically, and to layout and define functionality in this way which is the hard part and not language specific at all. So ideas such as signal flow, problem solving, etc these are the real concepts that must be understood to learn. Sure every language has its quirks, and the more you learn about each language’s syntactical structure will certainly inform and inspire specific types of use, but I think the underlying principals of how to think in this way are much more difficult and generally universal. Maybe there are larger divides between object oriented languages and non-, but all the languages you listed are, and so will function similarly for the most part.