LilyPond Music Glossary: 1.243 Pythagorean comma

## 1.243 Pythagorean comma

ES: coma pitagórica, I: comma pitagorico, F: comma pythagoricien, D: Pythagoräisches Komma, NL: komma van Pythagoras, DK: pythagoræisk komma, S: pytagoreiskt komma, FI: pytagorinen komma.

Originally, the interval by which the sum of six whole tones exceeds the octave – (9:8)^6 - 2:1 = 531441:524288, or 23.5 cents.

Modern acoustical theory defines it as the interval by which twelve fifths exceed seven octaves. To put it another way: A sequence of fifths that starts on C eventually circles back to C. However, this C is 23.5 cents higher than the C obtained by adding 7 octaves. The difference between those two pitches is the Pythagorean comma.

#### See also

cent, temperament.

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