Pythagorean tuning generates all notes from factors 3 and 2 alone.

Evidence

New notes are thus generated with the factors 3n/2n, and extra factors of 1/2 are introduced to bring the result back down to the first octave; thus the factors generating new notes are of the form 3n/2m. Only factors of 3, always in the numerator, and 2, always in the denominator, are involved. If we stop at three in the generation of notes, we have arrived at 3-limit Just intonation. — Eric J. Heller, Why You Hear What You Hear- An…, 2360

Categorization

• DEFINE: Defines the technical construction rule (3^n/2^m factors) that underlies 3-limit Just intonation — essential vocabulary for the why-question.