Just Intonation (Part 3)

Last time I said a bit about ‘just intonation’: that is, tuning where the most important notes have frequency ratios that are simple fractions. I focused on the historically important case of ‘5-limit tuning’, where the frequency ratios are products of powers of primes ≤ 5.

I went a long way toward getting some popular scales in 5-limit tuning. I started by drawing a chart called a ‘Tonnetz’ where going east multiplies the frequency by 3/2, and going roughly northeast multiplies the frequency ...