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A quarter tone , is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone. Many composers are known for having written music including quarter tones or the quarter-tone scale (24 equal temperament), first proposed by 19th-century music theorist Mikha'il Mishaqah,〔Touma, Habib Hassan (1996). ''The Music of the Arabs'', p.16. Trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.〕 and in 1823 by the German theorist Heinrich Richter,〔Julian Rushton., "Quarter-Tone", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).〕 including: Pierre Boulez, Julián Carrillo, Mildred Couper, George Enescu, Alberto Ginastera, Gérard Grisey, Alois Hába, Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Ammar El Sherei, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Alexandrovich Wyschnegradsky, and Iannis Xenakis (see List of quarter tone pieces). ==Types of quarter tones== The term ''quarter tone'' can refer to a number of different intervals, all very close in size. For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g., D–E).〔Julian Rushton, "Quarter-tone", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).〕 In the quarter tone scale, also called 24 tone equal temperament (24-TET), the quarter tone is 50 cents, or a frequency ratio of 21/24 or approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). In this scale the quarter tone is the smallest step. A semitone is thus made of two steps, and three steps make a three-quarter tone or neutral second, half of a minor third. In just intonation the quarter tone can be represented by the septimal quarter tone, 36:35 (48.77 cents), or by the undecimal quarter tone, 33:32 (53.27 cents), approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone. This just ratio is also the difference between a minor third (6:5) and septimal minor third (7:6). Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, slightly smaller. 72-TET also has equally tempered quarter-tones, and indeed contains 3 quarter tone scales, since 72 is divisible by 24. Composer Ben Johnston, to accommodate the just septimal quarter tone, uses a small "7" () as an accidental to indicate a note is lowered 49 cents, or an upside down "(unicode:∠)" () 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.〕 or a ratio of 36/35.〔Fonville, John (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", p.114, ''Perspectives of New Music'', Vol. 29, No. 2, pp. 106-137.〕 Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33/32, or 53 cents.〔 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「Quarter tone」の詳細全文を読む スポンサード リンク
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