# The "well-tempered scale"



## millionrainbows (Jun 23, 2012)

> The well tempered scale is divided equally in tones, whereas the original schema was based on perfect 5ths.


Actually, the 12 notes of our Western octave (even before equal temperament) we arrived at by a Pythagoran-derived procedure of "stacking" or projecting fifths. After 12 cycles of fifths, the starting point almost coincided with the end point of 12; but not quite, and this is called "The Pythagoran comma."

Still, the net result was that the "circle" of the octave was closed, and the Western octave is still based on 12 notes arrived at by the 12-division of fifths. The modern tempered fifth is off by only 2 cents (a cent is 1/100th of a semitone), and this is negligible. Our Western system is still based on root movement by fifths. The fifth is the favored interval. By contrast, major thirds are sharp by a full 14 cents! That is very audible, but we seem to have gotten used to it. The fifth is the more important interval anyway, because it creates stability in triads.


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