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.

~~Notation proposed~~ by ~~Eliora: Cyrillic ф~~

{{Infobox Interval

| Ratio = \varphi^{\varphi}

| Cents = 1347.9684152029295

| 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]] - 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 ===

~~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.

{{Harmonics in equal|21|3418|1569|title=Approximation of harmonics in 21EdPhi^Phi}}

===== Intervals =====

== See also ==

* [[Edϕ]]

* [[EDe]]

* [[Acoustic pi]]

[[Category:Edonoi]]

[[Category:Golden ratio]]

@@ Line 1: / Line 1: @@
-'''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.
+{{Editable user page}}
-Notation proposed by Eliora: Cyrillic ф
+{{Infobox Interval
+| Ratio = \varphi^{\varphi}
+| Cents = 1347.9684152029295
+| 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]] - 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 ===
-edф, 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.
+{{Harmonics in equal|21|3418|1569|title=Approximation of harmonics in 21EdPhi^Phi}}
+===== Intervals =====
+{{Interval table|21ed3418/1569}}
+== See also ==
+* [[Edϕ]]
+* [[EDe]]
+* [[Acoustic pi]]
 [[Category:Edonoi]]
+[[Category:Golden ratio]]