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The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal tempered diatonic scale. The interval 3:1 (often called by a new name, ''tritave'') serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent. The BP scale divides the tritave into 13 steps, either equal tempered (the most popular form), or in a justly tuned version. Compared with octave-repeating scales, the BP scale's intervals are more consonant with certain types of acoustic spectra. The scale was independently described by Heinz Bohlen, Kees van Prooijen and John R. Pierce. Pierce, who, with Max Mathews and others, published his discovery in 1984, renamed the Pierce 3579b scale and its chromatic variant the ''Bohlen–Pierce scale'' after learning of Bohlen's earlier publication. Bohlen had proposed the same scale based on consideration of the influence of combination tones on the Gestalt impression of intervals and chords. The intervals between BP scale pitch classes are based on odd integer frequency ratios, in contrast with the intervals in diatonic scales, which employ both odd and even ratios found in the harmonic series. Specifically, the BP scale steps are based on ratios of integers whose factors are 3, 5, and 7. Thus the scale contains consonant harmonies based on the odd harmonic overtones 3/5/7/9 (). The chord formed by the ratio 3:5:7 () serves much the same role as the 4:5:6 chord (a major triad ) does in diatonic scales (3:5:7 = 1:1.66:2.33 and 4:5:6 = 2:2.5:3 = 1:1.25:1.5). ==Chords and modulation== 3:5:7's intonation sensitivity pattern is similar to 4:5:6's (the just major chord), more similar than that of the minor chord.〔Mathews; Pierce (1989). pp. 165–66.〕 This similarity suggests that our ears will also perceive 3:5:7 as harmonic. The 3:5:7 chord may thus be considered the major triad of the BP scale. It is approximated by an interval of 6 equal-tempered BP semitones () on bottom and an interval of 4 equal-tempered semitones on top (semitones: 0,6,10; ). A minor triad is thus 6 semitones on top and 4 semitones on bottom (0,4,10; ). 5:7:9 is the first inversion of the major triad (0,4,7; ).〔Mathews; Pierce (1989). p. 169.〕 A study of chromatic triads formed from arbitrary combinations of the 13 tones of the chromatic scale among twelve musicians and twelve untrained listeners found 0,1,2 (semitones) to be the most dissonant chord () but 0,11,13 () was considered the most consonant by the trained subjects and 0,7,10 () was judged most consonant by the untrained subjects.〔Mathews; Pierce (1989). p. 171.〕 Every tone of the Pierce 3579b scale is in a major and minor triad except for tone II of the scale. There are thirteen possible keys. Modulation is possible through changing a single note, moving note II up one semitone causes the tonic to rise to what was note III (semitone: 3), which thus may be considered the dominant. VIII (semitone: 10) may be considered the subdominant.〔 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「Bohlen–Pierce scale」の詳細全文を読む スポンサード リンク
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