# Phi to the phi

Expression | [math]\varphi^{\varphi}[/math] |

Size in cents | 1347.9684¢ |

Name | phi to the phi |

Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.56492 bits |

**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. 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^{φ} - 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.