Consonance counted
Small numbers sound calm.
Sound both notes of a 2:1 pair together and they melt into one. A pair that settles like that is called consonant. 3:2 keeps a little shimmer, 4:3 a little more. Move to 9:8, two notes a single step apart, and the blend turns to grinding.
The Pythagoreans measured all of this with fractions and noticed that calm arrived with the smallest numbers. They could rank the pairs by ear and put a fraction to every rank, with nothing underneath to say why the ranking holds.
Lacking a cause, Greek thinkers promoted the pattern into cosmology and tuned the planets themselves to the same fractions, a music of the spheres said to surround us unheard.
The physical cause stayed unknown for two thousand years. Discovery 7 answers it.
Play the five pairs in order, from octave to semitone. Listen for the octave to fuse, the fifth and fourth to shimmer, and the close pairs to grow rough.