...The Pythagoreans in particular believed that the world was composed musically, and that the heavens caused harmony in their revolutions, and that our soul is formed according to the same laws, and that it is awakened and its powers vivified by songs and instrumental music.
The ancient Greeks (and the Renaissance writers like Zarlino who brought the ancients to the... early modernists) believed that the movement of heavenly bodies was just like the movement of musical tones and harmonies. This was called musica universalis or music of the universe (as opposed to music of the body--singing--and instrumental music). I've always been moved by this idea and wondered what these sounds would be--not just harmonically, but timbally as well (Just to clarify, you can't really HEAR musica universalis. In addition to it having always been more metaphorical, sound doesn't exist in the vacuum of space. Don't tell George Lucas.). I don't know if I've been unduly influenced by Star Trek IV, but when I close my eyes and see Jupiter whoosh past Saturn, I hear whale song.
Many cultures and religions place special meaning on certain numbers, but I don't know of any that do the same with ratios. I think if we're talking about harmony of the spheres, then we need to get to the ratios of the movements of the planets. I can't really get into it here, but I would really like to explore these harmonies sometime.
Over the past week I've enjoyed reading about the mythical beginnings of music. The Greeks said Pythagoras first heard music in hammers striking anvils. The Jews and Christians said it was Jubal in a similar story. I prefer J.R.R. Tolkien's version from The Silmarillion, and I'll leave it in parting since it reminds me of the Pythagoreans.