9edϕ: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
9 equal divisions of [[acoustic phi]] (9edϕ) is a [[tuning system]] that [[Edφ|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 [[Just intonation|justly intonated]], and the | 9 equal divisions of [[acoustic phi]] (9edϕ) is a [[tuning system]] that [[Edφ|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 [[Just intonation|justly intonated]], and the octave is stretched by 3.353 cents. | ||
<pre> | <pre> | ||
Revision as of 00:28, 22 April 2026
| ← 8edϕ | 9edϕ | 10edϕ → |
(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 is stretched by 3.353 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
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.