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In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Each step represents a frequency ratio of 21/72, or 16.67 cents, which divides the 100 cent "halftone" into 6 equal parts (100/16.6 = 6) and is thus a "twelfth-tone" (). 72 being divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, and 72, 72-tet includes those equal temperaments. This division of the octave has attracted much attention from tuning theorists, since on the one hand it subdivides the standard 12 equal temperament and on the other hand it accurately represents overtones up to the twelfth partial tone, and hence can be used for 11-limit music. It was theoreticized in the form of twelfth-tones by Alois Hába〔A. Hába: "Harmonické základy ctvrttónové soustavy". German translation: "Neue Harmonielehre des diatonischen, chromatischen Viertel-, Drittel-, Sechstel- und Zwölftel-tonsystems" by the author. Fr. Kistner & C.F.W. Siegel, Leipzig, 1927. Universal, Wien, 1978. Revised by Erich Steinhard, "Grundfragen der mikrotonalen Musik"; Bd. 3, Musikedition Nymphenburg 2001, Filmkunst-Musikverlag, München, 251 pages.〕 and Ivan Wyschnegradsky,〔I. Wyschnegradsky: ''"L'ultrachromatisme et les espaces non octaviants"'', La Revue Musicale # 290-291, pp. 71-141, Ed. Richard-Masse, Paris, 1972; ''La Loi de la Pansonorité'' (Manuscript, 1953), Ed. Contrechamps, Geneva, 1996. Preface by Pascale Criton, edited by Franck Jedrzejewski. ISBN 978-2-940068-09-8; ''Une philosophie dialectique de l'art musical'' (Manuscript, 1936), Ed. L'Harmattan, Paris, 2005, edited by Franck Jedrzejewski. ISBN 978-2-7475-8578-1.〕 who considered it as a good approach to the ''continuum'' of sound. 72-et is also cited among the divisions of the tone by Julián Carrillo, who preferred the sixteenth-tone as an approximation to continuous sound in discontinuous scales. A number of composers have made use of it, and these represent widely different points of view and types of musical practice. These include Alois Hába, Julián Carrillo, Ivan Wyschnegradsky and Iannis Xenakis. Many other composers use it freely and intuitively, such as jazz musician Joe Maneri, and classically-oriented composers such as Julia Werntz and others associated with the Boston Microtonal Society. Others, such as New York composer Joseph Pehrson are interested in it because it supports the use of miracle temperament, and still others simply because it approximates higher-limit just intonation, such as Ezra Sims and James Tenney. There was also an active Soviet school of 72 equal composers, with less familiar names: Evgeny Alexandrovich Murzin, Andrei Volkonsky, Nikolai Nikolsky, Eduard Artemiev, Alexander Nemtin, Andrei Eshpai, Gennady Gladkov, Pyotr Meshchianinov, and Stanislav Kreichi. ==Byzantine music== The 72 equal temperament is used in Byzantine music theory,〔() G. Chryssochoidis, D. Delviniotis and G. Kouroupetroglou, "A semi-automated tagging methodology for Orthodox Ecclesiastic Chant Acoustic corpora", Proceedings SMC'07, 4th Sound and Music Computing Conference, Lefkada, Greece (11–13 July 2007).〕 dividing the octave into 72 equal ''moria'', which itself derives from interpretations of the theories of Aristoxenos, who used something similar. Although the 72 equal temperament is based on irrational intervals (see above), as is the 12 tone equal temperament mostly commonly used in Western music (and which is contained as a subset within 72 equal temperament), 72 equal temperament, as a much finer division of the octave, is an excellent tuning for both representing the division of the octave according to the diatonic and the chromatic genera in which intervals are based on ratios between notes, and for representing with great accuracy many rational intervals as well as irrational intervals. 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「72 equal temperament」の詳細全文を読む スポンサード リンク
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