Pure supposition but
Anyone who was a musician with a multi-stringed instrument could not fail to notice that a string with a fundamental 2/3 of another were somehow related. And if that perspicacious muso/mathematician were to set the two strings at 1/2 and 1/3 distance (at the correct respective tensions) the result would be a eureka moment. Even geniuses can miss the obvious - but old Pythy?

Didn't J S Bach spot just these kind of relationships?


Or am I being a lyre?

I'll get my toga....