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A septimal comma is a small musical interval in Just intonation that contains the number seven in its prime factorization. It is based on the seventh partial of the harmonic series. This partial is a flat + a septimal comma (50 + 41 cents). The comma is approximately 41 cents. It is used to tune an interval justly so that is sounds more "in tune." A pythagorean seventh would be slightly too big. Use of septimal commas introduces new intervals that extend tuning beyond common-practice, extending music to the 7-limit, including the 7/6 septimal minor third, the 7/5 septimal tritone and the 8/7 septimal major second. Composers who made extensive use of these intervals include Harry Partch and Ben Johnston. Johnston uses a "7" as an accidental to indicate a note is lowered 49 cents, or an upside down seven ("ㄥ" or "") to indicate a note is raised 49 cents (36/35).〔John Fonville. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.113, ''Perspectives of New Music'', Vol. 29, No. 2 (Summer, 1991), pp. 106-137.〕 ==Specific commas== The 64/63 septimal comma (), also known as ''Archytas' Comma'', is the interval equal to the difference between a major and septimal whole tone (with 9/8 and 8/7 ratios, respectively). Alternatively, it can be viewed as the difference between the 16/9 Pythagorean minor seventh (the composition of two 4/3 perfect fourths) and the 7/4 harmonic seventh.〔Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. ISBN 0-521-85387-7.〕 Its size is 27.264 cents, slightly larger than the Pythagorean comma. The composition of the septimal comma and the syntonic comma is 36/35, known as the ''septimal diesis''.〔 Its size is 48.8 cents, making it practically a quarter tone. The septimal diesis appears as the difference between many septimal intervals and their 5-limit counterparts: the minor seventh (9/5) and the seventh harmonic (7/4),〔 the 8/7 septimal whole tone and the 10/9 minor whole tone, the 7/6 septimal minor third and the 6/5 minor third, the 9/7 septimal major third and the 5/4 major third, and many more. Other septimal commas include 49/48 (occasionally called the ''slendro diesis''〔) (), which commonly appears as the difference between a ratio with 7 in the denominator and another with 7 in the numerator, like 8/7 and 7/6; and 50/49, called the ''tritonic diesis'',〔 because it is the difference between the two septimal tritones, 7/5 and 10/7, or ''Erlich's decatonic comma'', because it plays an important role in the ten-tone scales of Paul Erlich (the intervals are tempered so that 50/49 vanishes). The septimal kleisma and the septimal semicomma are smaller septimal commas. 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「septimal comma」の詳細全文を読む スポンサード リンク
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