Simple whole-number ratios that rule musical intervals were extended into a cosmic harmony doctrine

Evidence

The universality and beauty of musical intervals such as the octave (2:1) and the perfect fifth (3:2) is bonded to simple ratios of small whole numbers, as Pythagoras realized. Philosophers could not stop here. Not only music, but the whole universe must be built on the divine whole number ratios: the Divine Harmony. Even the planets emitted harmonious tones, which we are told only Pythagoras could hear. — Eric J. Heller, Why You Hear What You Hear- An…, 918

Categorization

• XREF: Connects to the earlier discussion of musical intervals as small-integer ratios and to Kepler’s later planetary-harmony work.