Sean Breheny wrote:
>
> LOL,Wagner! The scale developed over a long period of time, initiallt
> based, IIRC, on the notes produced when you took a certain length of string
> and plucked it while holding it at certain fractions of its length.
===================

The theorem underlying the modern scale was set forth by Pythagoras, a
Greek philosopher/mathemetician in the 6th century B.C. He discovered
that the major consonances (sounds that harmonize well) were the octave,
perfect fifth and perfect fourth. Perfect fourth and fifth being the
notes four and five up from the fundamental. The length of the strings
relate to the fundamental in the ratios of 1:2 (octave), 3:2 (fifth) and
4:3 (fourth).
The perfect scale was found to not be workable when used in a number of
different keys, and J.S. Bach demonstrated the versatility of the
equal-tempered scale when he wrote 'The Well-Tempered Clavier', a series
of pieces written in a succession of keys.

Harley L. Miller     hmiller@sound.net