John Carlos Baez on Nostr: If you're playing medieval music, you can easily avoid the wolf fifth: just don't ...

If you're playing medieval music, you can easily avoid the wolf fifth: just don't play one of the two fifths that contains the tritone!

A more practical problem concerns the
'third' - the third note in the scale. Ideally this vibrates 5/4 as fast as the first. But in Pythagorean tuning it vibrates 81/64 times as fast. That's annoyingly high!

Sure, 81/64 is a rational number. But it's not the really *simple* rational number our ears are hoping for when we hear a third.

Indeed, Pythagorean tuning punishes the ear with some very complicated fractions. The first, fourth, fifth and octave are great. But the rest of the notes are not. There's no way that 243/128 sounds better than an irrational number!

(19/n)