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.
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.