9edϕ

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 is stretched by 3.353 cents.

← 8edϕ

9edϕ

10edϕ →

Prime factorization	32
Step size	92.5656 ¢
Octave	13\9edϕ (1203.35 ¢) (convergent)
Twelfth	21\9edϕ (1943.88 ¢) (→ 7\3edϕ)
Consistency limit	4
Distinct consistency limit	4

! 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

9edϕ has a very close approximation of logarithmic phi on its 21st step, with only +2.2 cents of error. This is because 9edϕ is related to 13edo, which is a Fibonacci edo.