# 9edϕ

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Prime factorization
3
Step size
92.5656¢
Octave
13\9edϕ (1203.35¢)

(convergent)
Twelfth
21\9edϕ (1943.88¢) (→7\3edϕ)
Consistency limit
4
Distinct consistency limit
3

← 8edϕ | 9edϕ | 10edϕ → |

^{2}(convergent)

9 equal divisions of acoustic phi (9edϕ) is a tuning system that evenly divides ϕ into 9 parts of approximately 92.566 cents each. This scale is closely related to 13edo, but slightly stretched. The result is an equal 13-tone-per-octave scale where acoustic phi is justly intonated, and the octave equivalence is 1203.353 cents.

! 9edphi.scl ! 9 equal divisions of acoustic phi 9 ! 92.565588 185.131177 277.696765 370.262354 462.827942 555.393531 647.959119 740.524708 833.090296

! 13tet_phi-stretched.scl ! 13-tone-per-octave with acoustic phi justly intonated 13 ! 92.565588 185.131177 277.696765 370.262354 462.827942 555.393531 647.959119 740.524708 833.090296 925.655885 1018.221473 1110.787062 1203.35265

## Logarithmic phi

As a coïncidence, 9 equal divisions of acoustic phi has a very close approximation of logarithmic phi on its 21th step, with only +2.2 cents of error.