I realize that some people know this stuff and some places teach it as part of an advanced music education, it's just remarkably uncommon considering how fundam

I realize that some people know this stuff and some places teach it as part of an advanced music education, it's just remarkably uncommon considering how fundamental it is. I would have meticulously qualified my earlier generalization but I foolishly assumed that my hyperbole would not be taken literally. 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.