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> 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
by thaumasiotes 8mo ago
> 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".
https://en.wikipedia.org/wiki/Pythagorean_comma https://en.wikipedia.org/wiki/Pythagorean_comma
- dahart 8mo agoYes, 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.