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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 Otonality and Utonality ： ウィキペディア英語版 Otonality and Utonality ''Otonality'' and ''Utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: 1/1, 2/1, 3/1,... or 1/1, 1/2, 1/3,.... == Definition == An Otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators. For example, 1/1, 5/4, and 3/2 (just major chord) form an Otonality because they can be written as 4/4, 5/4, 6/4. Every Otonality is therefore composed of members of a harmonic series. Similarly, the ratios of a Utonality share the same numerator. 7/4, 7/5, 7/6, and 1/1 (7/7) form a Utonality. Every Utonality is therefore composed of members of a subharmonic series. An Otonality corresponds to an arithmetic series of frequencies, or lengths of a vibrating string. Brass instruments naturally produce Otonalities, and indeed Otonalities are inherent in the harmonics of a single fundamental tone. Tuvan khoomei singers produce Otonalities with their vocal tracts. Utonality is the opposite, corresponding to a subharmonic series of frequencies, or an arithmetic series of wavelengths (the inverse of frequency). The ''arithmetical proportion'' "may be considered as a demonstration of Utonality ('minor tonality')."〔Partch, Harry. ''Genesis of a Music'', p.69. 2nd ed. Da Capo Press, 1974. ISBN 0-306-80106-X.〕 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「Otonality and Utonality」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.