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]]. The interval measures 1347.9684152 cents, making it a neutral ninth.
Notation proposed by Eliora: Cyrillic ф


== Theory ==
== Theory ==
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=== Useful divisions ===
=== Useful divisions ===
8edф, 13edф, 21edф, etc.
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]]
[[Category:Edonoi]]

Revision as of 16:16, 8 November 2022

Interval information
Expression [math]\displaystyle{ \varphi^{\varphi} }[/math]
Size in cents 1347.968¢
Name phi to the phi

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.

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.

Useful divisions

21edφφ - 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.