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.
This is a companion discussion topic for the original entry at https://johncarlosbaez.wordpress.com/2023/10/30/just-intonation-part-1/