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. | ||
== Theory == | == Theory == | ||
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=== Useful divisions === | === 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]] | [[Category:Edonoi]] | ||
Revision as of 16:16, 8 November 2022
| Interval information |
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.