> A 12 TET chromatic is 2^(1/12), and a 12 TET fifth would be 2^(7/12). A perfect fifth is a 3:2 ratio. Those numbers are slightly different, and that’s enough to understand it.
Note this this is normally called the "Pythagorean comma".
Yes, thanks! And that article points at the “problem” setup in the article: the syntonic or diatonic comma, or the discrepancy between four stacked perfect fifths and two octaves plus a major third.
I like how the Pythagorean comma simplifies to 3^12 / 2^19 - pure powers of three vs pure powers of two. That makes it so obvious (to me anyway) why we can’t have perfect fifths.
Note this this is normally called the "Pythagorean comma".
https://en.wikipedia.org/wiki/Pythagorean_comma