Digital sound production, however. Yes. There's all kinds of thoroughly unpleasant mathematics, none of which you actually need to know unless you're writing computer music software.

(I write computer music software, and I am also a jazz musician).

- fundamentals on an instrument vs performance

- low-level graphics programming vs using a game engine

- comp sci vs software engineering

The theory side here gets to the root of things, is valid for any sort of DAW/DSP software, and has the benefit of being easier to teach. Practice is obviously more important though, especially in the arts. It's better to grope in the dark than do nothing.

As an instruction, I think clearly not, the fact that lots of musicians aren't mathematical at all but create great music seems to prove it to me.

But it is interesting to think about musicians who do seem to think about music this way. Bach is definitely a good example where the system of counterpoint is very complex. I'm not sure if she'd describe herself in these terns, but I've always got the impression Laurie Speigel thinks about music a little like that too. Then there's stuff like Coltrane's Giant Steps, where the whole piece is based around a sort of music theory "trick".

So maybe not generally, but there's definitely some awesome music out of that kind of relationship.

These aren't resources for getting started. They're more like encyclopedias for learning about DSP and tech once you've established the fundamentals of music and sequencing.

If a beginner wants practical knowledge for making records with electronic instruments I'd give them a DAW, teach them to record and sequence, teach them basic music theory, and then point them to something like Ableton's synthesis tutorials that will teach them about oscillators, envelopes, filters, LFOs, and basic sample manipulation.

That's 80% of the necessary skills right there.

It's a great way to analyse music (e.g. to categorise, understand, and communicate detail), but that does not mean it's a good way to create it. There's a lot of beauty in finding those abstractions and I think that representation appeals to a lot of people here.

Discussions about timbre, instrumentation, and stylistic influence are often symmetric to those about math. When you have 90 minutes to spare, highly recommend strapping in for a listen to https://malwebb.com/notnoi.html.

There's a lot of really incredible musicians, composers, producers, and educators that go deep on the math. There's also plenty that don't. People build mental models in different ways. That's a good thing and a big part of what makes most art interesting.

From personal experience, pattern-recognition is the most useful "applied math" skill when making music. I use it when identifying intervals between notes, and chord progressions, which you need when you're trying to get the idea out of your head and onto the instrument you're playing or song you're writing.

As another commenter below has said, "mathematics might be a useful way to understand music", but it's not how compelling music is made.

Mathematics are fundamental to scales and the harmonic series, and knowing about them will help you refine certain choices, but it's not going to help you write a dramatic melody or an emotionally resonant chord progression, or play an energizing rhythm, even if there are mathematical explanations sometimes.

Good music comes from being a good listener, having a strong sense of what's possible, where it could go, and then delivering something surprising. Telling a story with your melody and supporting the arc of that gesture with harmony that accentuates or contrasts it.

Again, there's a mathematical explanation for harmony and dissonance, but players aren't thinking that granular. They're operating at a higher level of abstraction one, two, or three levels above that: They're thinking about telling a story, evoking an emotion, and exciting an audience in the moment.

It's like telling someone they can paint a masterpiece because they understand Fe4[Fe(CN)6]3 makes an aesthetically pleasant blue pigment.

Universal in the sense that a number of rocks or a number of sheep can be doubled just as a frequency can?

The notion that there are 8 sub divisions to a doubled frequency interval isn't universal. Balinese Gamelan doesn't even neccessarily have an agreed number of "notes" in an "Octave" from one village to the next.

It's pretty much the foundational idea of any modality. No matter how you divide it up, the purest harmony is doubling or halving.

Yes thats what I meant, the doubling of frequency. It might seem trivial but the fact that doubling frequency sounds "right" to humans is actually quite interesting. Why does it sound "right"?

So yes, the 12-tone scale is a universal thing - you want both octaves and fifths in your scale.

(12 is actually too much, so usually that's pared down to something like 4 or 5 or 7 tones, this is where you get cultural variation.)

I was asking to tease out some PoV perspective, again Gamelan doesn't neccessarily have powers of two, or 12, etc divisions of a doubling (or Octave, if we're using that term); it's a non western style of percussion that has a suprising number of local variations (it's essentially near unique to Balinese culture) in divisions and tunings.

The Octave wikipedia entry includes:

  Octave equivalence is a part of most musical cultures, but is far from universal in "primitive" and early music

Cheers for the response, appreciated.

The obvious exception in the western system would be the blues scale, which arguably has 9 tones (7 equal tempered notes, plus a just tempered 3rd and 7th).

And Indian ragas break all of these rules. They have scales that don't have 8 notes, scales that don't use equal temperament, and even a few scales that don't repeat on octaves.

Math checks out.

> So yes, the 12-tone scale is a universal thing -

I don't follow the logic here though. It's certainly true that a 12-tone / Chromatic scale is ubiquitous within the Western Music tradition .. but the universe is reportedly a little larger.

Even Western Music includes exceptions like the 9-note augmented scale, though the argument can be made that it's a 12-scale with 3 bits "missing" - not a case that can be made about a non-western 7 note percussive scale.

But I suspect there’s a clear biological mechanism which makes it easy to mistake one octave for another from any source of roughly harmonic sound. This is due to the similarity in the overtones of two harmonic sounds that differ by an octave. I would be surprised if this mechanism isn’t universal, although its on various musical systems can obviously vary a lot.

Also the so-called "Western music" standardized on 12 tones very late in the process, long after the Chinese figured it out.

> a 12-scale with 3 bits "missing"

That's all scales, even the "non-Western" ones. Microtonality is added to the standard 12 tone to add tone effects. (Synthesizers in pop music do the same trick.)

https://www.huygens-fokker.org/scala/

Note also that certain musical traditions were suppressed or eradicated due to their unfortunate habit of using dissonant notes such as minor seconds, as opposed to the consonant traids favored by a particular group recently in power around the world. Happy Easter!