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In music, the septimal minor third , also called the ''subminor third'' (e.g., by Helmholtz〔Hermann L. F Von Helmholtz (2007). On the Sensations of Tone, p.195. ISBN 1-60206-639-6.〕〔Royal Society (Great Britain) (1880, digitized Feb 26, 2008). ''Proceedings of the Royal Society of London, Volume 30'', p.531. Harvard University.〕), is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies.〔Partch, Harry (1979). ''Genesis of a Music'', p.68. ISBN 0-306-80106-X.〕 In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5. In 24-tone equal temperament five quarter tones approximate the septimal minor third at 250 cents (). The septimal minor third may be derived in the harmonic series from the seventh harmonic, and as such is in inharmonic ratios with all notes in the regular 12TET scale, with the exception of the fundamental and the octave.〔Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. ISBN 0-252-03120-2. "Among the most striking intervals are...the narrow 7:6 subminor third...The seventh harmonic...was problematic in all Western tuning systems. The interval it forms with the sixth harmonic (subminor third ) is smaller than a minor third but larger than a major second. To cite a specific example: the seventh harmonic of C lies partway between A and B-flat. Sounding with the sixth harmonic (G), it forms a 7:6 subminor third of 267 cents--33 cents smaller than the equal-tempered minor third, itself 16 cents smaller than the pure 6:5 minor third. This 7:6 interval is thus nearly a quarter tone smaller than the pure minor third (33 + 16 = 49 cents)."〕 It has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using it in place of the minor third is called a septimal minor or subminor triad . In the meantone era the interval made its appearance as the alternative minor third in remote keys, under the name augmented second. Tunings of the meantone fifth in the neighborhood of quarter-comma meantone will give three septimal minor thirds among the twelve minor thirds of the tuning; since the wolf fifth appears with an ordinary minor third, this entails there are three septimal minor triads, eight ordinary minor triads and one triad containing the wolf fifth arising from an ordinary minor third followed by a septimal major third. Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents, or an upside down seven ("ㄥ") to indicate a note is raised 49 cents.〔Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", ''Perspectives of New Music'', Vol. 29, No. 1. (Winter, 1991), pp. 176-211.〕 The position of this note also appears on the scale of the Moodswinger. Yuri Landman indicated the harmonic positions of his instrument in a color dotted series. The septimal minor third position is cyan blue as well as the other knotted positions of the seventh harmonic (5/7, 4/7, 3/7, 2/7 and 1/7 of the string length of the open string).〔("Moodswinger" ), ''oddmusic homepage''〕 ==In equal temperament and non-Western scales== Twelve-tone equal temperament (12-TET), as commonly used in Western music, does not provide a good approximation for this interval, and quarter tones (24-TET) do not match it well either. 19-TET, 22-TET, 31-TET, 41-TET, 53-TET, and 72-TET each offer successively better matches (measured in cents difference) to this interval. Several non-Western and just intonation tunings, such as the 43-tone scale developed by Harry Partch, do feature the (exact) septimal minor third. 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 minor third」の詳細全文を読む スポンサード リンク
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