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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tonality diamond ： ウィキペディア英語版 Tonality diamond In music theory and tuning, a tonality diamond is a two-dimensional diagram of ratios in which one dimension is the Otonality and one the Utonality.〔Rasch, Rudolph (2000). "A Word or Two on the Tunings of Harry Partch", ''Harry Partch: An Anthology of Critical Perspectives'', p.28. Dunn, David, ed. ISBN 90-5755-065-2.〕 Thus the n-limit tonality diamond ("limit" here is in the sense of odd limit, not prime limit) is an arrangement in diamond-shape of the set of rational numbers ''r'', , such that the odd part of both the numerator and the denominator of ''r'', when reduced to lowest terms, is less than or equal to the fixed odd number ''n''. Equivalently, the diamond may be considered as a set of pitch classes, where a pitch class is an equivalence class of pitches under octave equivalence. The tonality diamond is often regarded as comprising the set of consonances of the n-limit. Although originally invented by Max Friedrich Meyer,〔("Musical Mathematics: Meyer's Diamond" ), ''Chrysalis-Foundation.org''.〕 the tonality diamond is now most associated with Harry Partch. ==The diamond arrangement== Partch arranged the elements of the tonality diamond in the shape of a rhombus, and subdivided into (n+1)2/4 smaller rhombuses. Along the upper left side of the rhombus are placed the odd numbers from 1 to n, each reduced to the octave (divided by the minimum power of 2 such that ). These intervals are then arranged in ascending order. Along the lower left side are placed the corresponding reciprocals, 1 to 1/n, also reduced to the octave (here, ''multiplied'' by the minimum power of 2 such that ). These are placed in descending order. At all other locations are placed the product of the diagonally upper- and lower-left intervals, reduced to the octave. This gives all the elements of the tonality diamond, with some repetition. Diagonals sloping in one direction form Otonalities and the diagonals in the other direction form Utonalities. One of Partch's instruments, the diamond marimba, is arranged according to the tonality diamond. 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「Tonality diamond」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.