Just Intonation (Part 1)

In ‘Pythagorean tuning’ all the frequency ratios between tones are products of powers of the primes 2 and 3. I explained this system in detail here. Because the largest prime it uses is 3, we say Pythagorean tuning is a form of ‘3-limit tuning’. One can imagine other forms of 3-limit tuning, though no other is as popular.

Now I want to start talking about ‘5-limit tuning’, where we allow frequency ratios to be products of powers of 2, 3 and 5.

The most popular form of 5-limit tuning is ofte...