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In music, a ditone ((ラテン語:ditonus), from , "of two tones") is the interval of a major third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also called a comma-redundant major third; the smallest is the interval with a ratio of 100:81, also called a comma-deficient major third.〔Abraham Rees, "Ditone, Ditonum", in ''The Cyclopædia, or Universal Dictionary of Arts, Sciences, and Literature. In Thirty-Nine Volumes'', vol. 12 (London: Longman, Hurst, Rees, Orme, & Brown, 1819) (paginated ).〕 ==Pythagorean tuning== The Pythagorean ditone is the major third in Pythagorean tuning, which has an interval ratio of 81:64,〔James Murray Barbour, ''Tuning and Temperament: A Historical Survey'' (East Lansing: Michigan State College Press, 1951): v. Paperback reprint (Mineola, NY: Dover Books, 2004). ISBN 978-0-486-43406-3.〕 which is 407.82 cents. The Pythagorean ditone is evenly divisible by two major tones (9/8 or 203.91 cents) and is wider than a just major third (5/4, 386.31 cents) by a syntonic comma (81/80, 21.51 cents). Because it is a comma wider than a "perfect" major third of 5:4, it is called a "comma-redundant" interval.〔Abraham Rees, "Inconcinnous", in ''The Cyclopædia, or Universal Dictionary of Arts, Sciences, and Literature. In Thirty-Nine Volumes'', vol. 13 (London: Longman, Hurst, Rees, Orme, & Brown, 1819) (paginated ).〕 "The major third that appears commonly in the () system (C–E, D–F, etc.) is more properly known as the Pythagorean ditone and consists of two major and two minor semitones (2M+2m). This is the interval that is extremely sharp, at 408c (the ''pure'' major third is only 386c)."〔Jeffrey T. Kite-Powell, ''A Performer's Guide to Renaissance Music'', second edition, revised and expanded; Publications of the Early Music Institute (Bloomington and Indianapolis: Indiana University Press, 2007), p.281. ISBN 978-0-253-34866-1.〕 It may also be thought of as four justly tuned fifths minus two octaves. The prime factorization of the 81:64 ditone is 3^4/2^6 (or 3/1 * 3/1 * 3/1 * 3/1 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ditone」の詳細全文を読む スポンサード リンク
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