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| == Musical applications == | | == Musical applications == |
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| Phi taken as a musical ratio (ϕ*f where f=1/1) is about 833.1 cents. This is sometimes called "acoustical phi".
| | The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. |
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| As the ratios of successive terms of the Fibonacci sequence converge on phi, the just intonation intervals 3/2, 5/3, 8/5, 13/8, 21/13, ... converge on ~833.1 cents.
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| "Logarithmic phi", or 1200*ϕ cents = 1941.6 cents (or, octave-reduced, 741.6 cents) is also useful as a generator, for example in [[Erv Wilson]]'s "Golden Horagrams".
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| == Additional reading ==
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| * [[Generating a scale through successive divisions of the octave by the Golden Ratio]]
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| * [[Phi as a Generator]]
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| * [[sqrtphi]], a temperament based on the square root of phi (~416.5 cents) as a generator
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| * [[Golden meantone]]
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| * [[833 Cent Golden Scale (Bohlen)]]
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| * [http://dkeenan.com/Music/NobleMediant.txt The Noble Mediant: Complex ratios and metastable musical intervals], by [[Margo Schulter]] and [[David Keenan]]
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| * [http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm 5- to 9-tone, octave-repeating scales from Wilson's Golden Horagrams of the Scale Tree], by [[David Finnamore]]
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