Re Pythagoras, Hello, Siem.

While their is a lot of mystery surrounding Pythagoras's contributions,
there is also no evidence (yet) that number was applied to tuning before
his school was founded. The cuneiform tuning tables give no hint of the
numerical relations between string lengths and pitch. His school also
seems to have been the first to discover irrational numbers and to
explore elementary number theory.

Later the tradition degenerated into mysticism.

Siemen: Greetings, welcome back to the States.

--John