User:Eliora/Phi to the phi: Difference between revisions

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'''Phi to the phi''' is the interval, which if used as an interval of equivalence, equates [[acoustic phi]] with [[logarithmic phi]]. The interval measures 1347.9684152 cents, making it a neutral ninth.

'''Phi to the phi''' is the interval, which if used as an interval of equivalence, equates [[acoustic phi]] with [[logarithmic phi]] - in other words, when this interval is divided by logarithmic phi, the result is acoustic phi. The interval measures 1347.9684152 cents, making it a neutral ninth.

== Theory ==

Golden ratio raised to the power of itself is equal to about 2.1784.

Concoctic scales made of two Fibonacci numbers (8&13, 13&21, 21&34, etc.) have both the amount of notes to the period approaching phi. and a generator that increasingly approaches logarithimic phi. ~~When~~ phi to the phi is used as an interval of equivalence, the generator also approaches the acoustic phi.

Concoctic scales made of two Fibonacci numbers (8&13, 13&21, 21&34, etc.) have both the amount of notes to the period approaching phi. and a generator that increasingly approaches logarithimic phi. In this case, phi to the phi is used as an interval of equivalence, and the generator also approaches the acoustic phi.

=== Useful divisions ===

21edφ<sup>φ</sup> - not only it has an interval 13\21 approaching acoustic phi, it also corresponds to 18.6948edo, which makes it sound quite close to the Rectified Hebrew's 19-tone scale (18.579-edo). It has a very precise major third (as opposed to conventional 19edo's precise minor third of 6/5) and a superpythagorean fifth of 706 cents.

[[Category:Edonoi]]

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-'''Phi to the phi''' is the interval, which if used as an interval of equivalence, equates [[acoustic phi]] with [[logarithmic phi]]. The interval measures 1347.9684152 cents, making it a neutral ninth.
+'''Phi to the phi''' is the interval, which if used as an interval of equivalence, equates [[acoustic phi]] with [[logarithmic phi]] - in other words, when this interval is divided by logarithmic phi, the result is acoustic phi. The interval measures 1347.9684152 cents, making it a neutral ninth.
 == Theory ==
 Golden ratio raised to the power of itself is equal to about 2.1784.
-Concoctic scales made of two Fibonacci numbers (8&13, 13&21, 21&34, etc.) have both the amount of notes to the period approaching phi. and a generator that increasingly approaches logarithimic phi. When phi to the phi is used as an interval of equivalence, the generator also approaches the acoustic phi.
+Concoctic scales made of two Fibonacci numbers (8&13, 13&21, 21&34, etc.) have both the amount of notes to the period approaching phi. and a generator that increasingly approaches logarithimic phi. In this case, phi to the phi is used as an interval of equivalence, and the generator also approaches the acoustic phi.
 === Useful divisions ===
 edφ<sup>φ</sup> - not only it has an interval 13\21 approaching acoustic phi, it also corresponds to 18.6948edo, which makes it sound quite close to the Rectified Hebrew's 19-tone scale (18.579-edo). It has a very precise major third (as opposed to conventional 19edo's precise minor third of 6/5) and a superpythagorean fifth of 706 cents.
 [[Category:Edonoi]]