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pythagorean interval
In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa.〔Benson, Donald C. (2003). ''A Smoother Pebble: Mathematical Explorations'', p.56. ISBN 978-0-19-514436-9. "The frequency ratio of every Pythagorean interval is a ratio between a power of two and a power of three...confirming the Pythagorean requirements that all intervals be associated with ratios of whole numbers."〕 For instance, the perfect fifth with ratio 3/2 (equivalent to 31/21) and the perfect fourth with ratio 4/3 (equivalent to 22/31) are Pythagorean intervals.
All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above mentioned Pythagorean perfect fifth and fourth are also used in just intonation.
==Interval table==
Notice that the terms ''ditone'' and ''semiditone'' are specific for Pythagorean tuning, while ''tone'' and ''tritone'' are used generically for all tuning systems. Interestingly, despite its name, a semiditone (3 semitones, or about 300 cents) can hardly be viewed as half of a ditone (4 semitones, or about 400 cents).
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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