Just look at the Wikipedia entry on tuning, for example: http://en.wikipedia.org/wiki/Musical_tuning
Do you think that was all created by non-musicians while 'most of the finest musicians in history' cowered in the corner afraid of the magic being broken?
We covered it more deeply (including, gasp, math) in a higher-level electronic music class.
It's probably true that many fine musicians won't think much about the mathematical side of music very often at all (practically speaking, this knowledge is not necessary to master an instrument), but certainly anyone who's gone through an academic music education will have covered it, quite possibly more than once.
Go read "How Equal Temperament Destroyed Harmony". By a musician, for musicians. I would add there are a number of conductors and musicians that insist on playing compositions in their original tunings.
> Musical culture seems to resist illumination
And I'm sure elsewhere in cyberspace at this precise moment some musician is lamenting the ability of scientists to understand their craft. Plus ca change...
I'm speaking as a musician when I say that we resist illumination. I've raised this topic with many teachers and peers and there is a sort of disbelief in the connection between the artistic experience of music and the underlying mathematics.
I don't think this is because musicians are ignorant luddites, I think it's because the emotional response to music is primal and not at all intuitive. Why do we feel so strongly about harmonically related tones? It doesn't sound like anything, in the way a painting or a sculpture looks like something. Abstract art is a relatively recent invention, yet music has been almost purely abstract for as long as anyone remembers.
This is true, but I think the answer is far more mundane. Musicians operate at a couple of levels of abstraction above that SO answer, so such details become irrelevant to them.
Imagine if the standard introduction to programming was a course on Java or PHP. Pretty soon you'd have a plethora of programmers who didn't know a thing about pointers or any of the old tricks programmers used to do with assembly. Wait... that's already happened :)
Musical culture seems to resist illumination, perhaps fearing that the "magic" will somehow be broken. The irony is that music is, in a sense, a mathematical illusion, but revealing the trick only makes it more fascinating.
I will add one important point that hasn't really been made: The purpose of equal temperament may have originally been to "change keys without retuning", but it also essentially allows you to play in 12 different keys at the same time. This has been exploited to great lengths as source of musical novelty and is absolutely fundamental to modern music.