Just Intonation (Part 2)

Now let’s dive into the beauties of 5-limit tuning—that is, tuning systems with frequency ratios that are products of powers of only the primes 2, 3 and 5:

We’ve already tackled 3-limit tuning, where we only got to use the primes 2 and 3. Since multiplying the frequency by 2 merely raises a tone by an octave, giving a tone that sounds ‘just the same, only higher’, we were freed to focus on powers of 3/2. Multiplying the frequency by 3/2 raises a tone by a fifth, so we got a diagram called ...