On a minor point of pedantry, Harry Partch developed his 43-tone scale as an alternative to what he regarded as the abomination of the 12-tone tempered Western scale. Indeed, the only of his instruments designed to play the 43-tone scale were his retuned harmoniums and his adapted guitars & violas. His mathematics were Pythagorean, taken to extremes so that he could use pure intervals that you couldn't find in Western music. His music otherwise is perfectly 'tonal', though his writing for voice was concerned with the 'intonation' of the vernacular spoken voice rather than with singing per se, but a lot of it is surprisingly tuneful and folksy. Here's his setting of various hitch-hiker inscriptions collected from graffito during his travels which is infused with the humour and playfulness of his admittedly eccentric genius. The spoken voice here is Partch himself.

http://www.youtube.com/watch?v=rRXDYgYQYXM