9edϕ: Difference between revisions

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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.

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>

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<pre>

! ~~13-tet_phi~~-stretched.scl

! 13tet_phi-stretched.scl

!

13-tone-per-octave with acoustic phi justly intonated

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1203.35265

</pre>

== 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.

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-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.
+{{Infobox ET}}
+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.
+{{Harmonics in cet|92.5656|columns=15}}
 <pre>
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 <pre>
-! 13-tet_phi-stretched.scl
+! 13tet_phi-stretched.scl
 !
 -tone-per-octave with acoustic phi justly intonated
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 .35265
 </pre>
+== Logarithmic phi ==
+edϕ 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.