On Wed, 18 Jun 2008, Dennis Claxton wrote:
>> The orderliness of nature is a reality proven by Pythagoras when he
>> discovered that the musical scale (a fact of nature) is structured
>> according to simple numerical ratios.
>
> What is _the_ musical scale?
The one defined by those ratios, 2:1 (octave) 3:2 (fifth) 4:3 (fourth). AFAIK, you find them in independently discovered all over the world and at the basis of every musical tradition. What makes Chinese, middle eastern, Indian, Western and Balkan music sound so different is (a) how they deal with the problems that result from trying to keep different instruments in tune once you go beyond a single octave, and (b) what they build on this starting foundation.
You are quite right though that this results in many different musical scales or modes. The ancient Greek pentatonic scale, for example, is one no one uses today. But the universality point still holds, even if it would take a little work to express it properly.
Michael