It's important to remember that there is no real "bottom-up" when it comes to music theory. Sure there's a couple of rough audio-acoustic rules like how simple fractions of frequences sound more harmonious because there's less beating, but those rules are few and don't get you far.
They're equivalent to noting that, say, vowel sounds with similar formants are harder to distinguish. That's true, but there's no way to reason up from that all the way to Shakespeare and Dickens.
The way to look at music theory is that it's like linguistics for sound. It doesn't say "here are the rules that are required to generate X". It says "people have already generated X, Y, and Z (using whatever intuitive cultural processes and/or academic learning they had) and here are the patterns we observe about the result."
People creating music are not outputting new provable theorems derived generatively from the axiomatic rules of music theory. Music theory cannot disprove a song.
People just make stuff they and others like (or don't). And then music theorists try to find the common threads that link it to better understand how the world of music fits together. It is descriptive and not prescriptive.
Knowing theory can help you write music because it can take information you already have in your intuitive "ear" and move it to your front cortex or somewhere more accessible to your hands. But many other musicians skip this step entirely and just connect their hands straight to their intuition though tons of practice. Either path is valid for producing beautiful music.
Expanding on your comment about vowels, I don't think it's fair to say that music is completely arbitrary in the same way as, say, language. Whereas for language we can be pretty confident in saying that it really is truly arbitrary, e.g. see the birth and development of Nicaraguan Sign Language: https://en.wikipedia.org/wiki/Nicaraguan_Sign_Language
To put this another way, two hypothetical languages developed in complete isolation from each other would be completely different. Two musical traditions developed in complete isolation would be different, but not completely different. There is still an underlying theory that unifies them to some extent. This is why music theory exists as a useful topic of study, even if it is not sufficient for writing aesthetically pleasing music. Whereas I know of no equivalent for linguistics: linguistics is truly a descriptive field, it can only describe what exists, not predict what properties a new language can/should have.
Your claim about linguistics here is subject a great deal controversy in the linguistics world. The question of whether there is, for example, a deep grammar that is shared across all languages, is a matter of long lasting and deep debate (these days it seems to be leaning to "no", but the debate is not over).
So... I agree with your point about music, but I'm not sure you're right to try to contrast it with language in this respect.
> Two musical traditions developed in complete isolation would be different, but not completely different. There is still an underlying theory that unifies them to some extent.
What theory do you have in mind? My (limited) understanding is that across cultures there is wide variance in rhythms, time signatures, how many tones span each octave and what emotions are associated with different intervals and chords.
They're equivalent to noting that, say, vowel sounds with similar formants are harder to distinguish. That's true, but there's no way to reason up from that all the way to Shakespeare and Dickens.
The way to look at music theory is that it's like linguistics for sound. It doesn't say "here are the rules that are required to generate X". It says "people have already generated X, Y, and Z (using whatever intuitive cultural processes and/or academic learning they had) and here are the patterns we observe about the result."
People creating music are not outputting new provable theorems derived generatively from the axiomatic rules of music theory. Music theory cannot disprove a song.
People just make stuff they and others like (or don't). And then music theorists try to find the common threads that link it to better understand how the world of music fits together. It is descriptive and not prescriptive.
Knowing theory can help you write music because it can take information you already have in your intuitive "ear" and move it to your front cortex or somewhere more accessible to your hands. But many other musicians skip this step entirely and just connect their hands straight to their intuition though tons of practice. Either path is valid for producing beautiful music.