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833 cents scale

Musical tuning scale / From Wikipedia, the free encyclopedia

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The 833 cents scale is a musical tuning and scale proposed by Heinz Bohlen[clarification needed] based on combination tones, an interval of 833.09 cents, and, coincidentally, the Fibonacci sequence.[1] The golden ratio is , which as a musical interval is 833.09 cents (Play). In the 833 cents scale this interval is taken as an alternative to the octave as the interval of repetition,[2] however the golden ratio is not regarded as an equivalent interval (notes 833.09 cents apart are not "the same" in the 833 cents scale the way notes 1200 cents apart are in traditional tunings). Other music theorists such as Walter O'Connell, in his 1993 "The Tonality of the Golden Section",[3] and Loren Temes[citation needed] appear to have also created this scale prior to Bohlen's discovery of it.

Line segments in the golden ratio ((A + B) / A = A / B = 1.618).
Stack of golden ratio (φ) intervals, measured in Hz ((11.09 + 6.854) ÷ 11.09 = 11.09 ÷ 6.854 = 1.618).
833 cents scale in 36-tet notation, with slurs indicating a golden ratio

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