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Bohlen-pierce ScaleThe Bohlen-Pierce scale (BP scale) is a musical scale that offers an alternative to the 12-tone equal temperament typical in western music. It was independently discovered by Heinz Bohlen, Kees van Prooijen, and also John R. Pierce. Pierce, who, with Max V. Mathews and others, published his discovery in 1984, renamed the scale the Bohlen-Pierce scale after learning of Bohlen's earlier publication. While most scales have octave-equivalence, the BP scale instead has tritave equivalence. This means that its pitch classes are based on the interval 3:1 (tritave or "perfect 12th" in diatonic nomenclature) rather than the 2:1 (octave). Thus the scale contains many consonant harmonies. Though Bohlen originally expressed the BP scale in just intonation, a tempered form of the scale, which divides the tritave into 13 equal steps, has become the most popular form. In it, 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 12-tone equal temperament (3:5:7 = 1:1.66:2.33 and 4:5:6 = 2:2.5:3 = 1:1.25:1.5). This tempered BP scale can be seen as an approximation of a just intonation system based only on ratios of odd whole numbers, similar to the spectra of instruments such as the clarinet which consist of primarily the odd harmonics. External link
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