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Harry Partch's 43-tone scale
The 43-tone scale is a just intonation scale with 43 pitches in each octave, invented and used by Harry Partch.
The first of Partch's "four concepts" is "The scale of musical intervals begins with absolute consonance (1 to 1) and gradually progresses into an infinitude of dissonance, the consonance of the intervals decreasing as the odd numbers of their ratios increase."〔Partch 1974, 87.〕 Almost all of Partch's music is written in the 43-tone scale, and although most of his instruments can play only subsets of the full scale, he used it as an all-encompassing framework.
==Construction==
Partch chose the 11 limit (i.e. all rational numbers with odd factors of numerator and denominator not exceeding 11) as the basis of his music, because the 11th harmonic is the first that is utterly foreign to Western ears. The seventh harmonic is poorly approximated by 12-tone equal temperament, but it appears in ancient Greek scales, is well-approximated by meantone temperament, and it is familiar from the barbershop quartet;〔Abbott, Lynn (1992): Play That Barber Shop Chord: A Case for the African-American Origin of Barbershop Harmony. American Music 10, no. 3 (1992), 289–325.〕〔Döhl, Frédéric (2014): From Harmonic Style to Genre. The Early History (1890s–1940s) of the Uniquely American Musical Term Barbershop. American Music 32, no. 2, 123–171.〕 the ninth harmonic is comparatively well approximated by equal temperament and it exists in Pythagorean tuning (because 3 × 3 = 9); but the 11th harmonic falls right in the middle between two pitches of 12-tone equal temperament (551.3 cents). Although theorists like Hindemith and Schoenberg have suggested that the 11th harmonic is implied by, e.g. F in the key of C, Partch's opinion is that it is simply too far out of tune, and "if the ear does not realize an implication, it does not exist."
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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