The Pythagorean Scale
by Eric W. Weisstein

Pythagoras (570-504 BC) is usually credited with discovering that vibrating strings with lengths the ratios of small whole numbers of each other produced a pleasing harmony. The Pythagorean scale consists of only two intervals: 9:8 (the second) and 256:243, and is also known as the Lydian mode. The intervals were chosen and then the gaps filled in with hemitones, where a hemitone equals a ratio of 256:243. Note that a hemitone is significantly less than half a Pythagorean tone (sqrt(9/8) = 1.0606). The Pythagorean Scale contains four fifths and five fourths, more commensurabilities than can be attained from any other eight notes (Jeans 1938, p. 168).

tonic 1:1   9:8   81:64   4:3   3:2   27:16   243:128   2:1
ratio   9:8 9:8 256:243 9:8 9:8 9:8 256:243  

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Date this article was posted to 10/3/1999
(Note that this date does not necessarily correspond to the date the article was written)

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