The Syntonic Comma

Tuning systems in music is the subject where you get mad at irrational numbers. Nothing works perfectly—and it’s not your fault: it’s math’s fault. You’re left pushing around lumps in the carpet.

An ‘octave’ is the chord where the high note vibrates 2 times as fast as the low note. In a ‘perfect fifth’ it vibrates 3/2 times as fast. In a ‘perfect fourth’ it vibrates 4/3 as fast. In a ‘major third’ it vibrates 5/4 as fast. Our ears love these simple fractions.

But if you go up 4 perfect f...