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This book theorizes that musical scales evolve in a mathematical series of 2, 5, 7, 12, 19 tones per octave (2 + 5 = 7, 5 + 7 = 12 etc.) , closely related to the Fibonacci series in mathematics. Examples from different world cultures show that effectively equal-tempered scales are in use with 5 and 7 as well as 12 tones. In each case, the uneven spacing of pitches in the next-lower step of the series makes it possible to establish musical key centers -- for example, in the 7-tone diatonic scale within the 12-tone system. Yasser hypothesizes that a 12-tone diatonic scale is possible within a 19-tone system, and that the music of Scriabin points in that direction. I find a weakness in that hypothesis, in that the human sensory apparatus is generally able only to distinguish approximately 7 categories in any continuum. However, the 19-tone equal-tempered scale and even more so, the next step in the series, the 31-tone equal-tempered scale -- which has much better intonation very closely approximating the Baroque mean-tone system -- do allow performance of diatonic music while also including additional, intermediate pitches perceived as bent notes or blue notes. These scales also avoid thewolf tone intervals which occur in a mean-tone system which has too few pitches to close the circle of the temperament. The 31-tone scale has been implemented, and particularly in the work of Adriaan Fokker, but has not gained widespread use, and has not lead organically to the application of the supra-diatonic 12-tone scale with key centers established through unequal intervals which Yasser hypothesized.
PROBLEM OF THE RESEARCH
PLAN OF THE WORK
HISTORIC SURVEY OF CHINESE SCALES
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