9edϕ - Revision history

Hotcrystal0 at 00:47, 22 April 2026

2026-04-22T00:47:52Z

← Older revision		Revision as of 00:47, 22 April 2026
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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 octave is stretched by 3.353 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.

			{{Harmonics in cet\|92.5656\|columns=15}}

	<pre>		<pre>

Hotcrystal0: cleanup

2026-04-22T00:28:31Z

cleanup

← Older revision		Revision as of 00:28, 22 April 2026
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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 [[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>		<pre>

Hotcrystal0: cleanup

2026-02-17T15:14:03Z

cleanup

← Older revision		Revision as of 15:14, 17 February 2026
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	== Logarithmic phi ==		== 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.		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.

CompactStar at 00:47, 6 April 2023

2023-04-06T00:47:44Z

← Older revision		Revision as of 00:47, 6 April 2023
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			{{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 [[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 equivalence]] is 1203.353 cents.

Cmloegcmluin: add link to existing information about 9edɸ on the general page for edϕ

2023-03-06T19:48:06Z

add link to existing information about 9edɸ on the general page for edϕ

← Older revision		Revision as of 19:48, 6 March 2023
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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 [[Just intonation\|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 equivalence]] is 1203.353 cents.

	<pre>		<pre>

Contribution at 10:07, 6 March 2023

2023-03-06T10:07:44Z

← Older revision		Revision as of 10:07, 6 March 2023
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	1203.35265		1203.35265
	</pre>		</pre>

			== 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.

Contribution at 09:55, 6 March 2023

2023-03-06T09:55:46Z

← Older revision		Revision as of 09:55, 6 March 2023
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	<pre>		<pre>
	! ~~13-tet_phi~~-stretched.scl		! 13tet_phi-stretched.scl
	!		!
	13-tone-per-octave with acoustic phi justly intonated		13-tone-per-octave with acoustic phi justly intonated

Contribution at 09:47, 6 March 2023

2023-03-06T09:47:57Z

← Older revision		Revision as of 09:47, 6 March 2023
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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 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 equivalence]] is 1203.353 cents.

	<pre>		<pre>

Contribution: Created page with "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, bu..."

2023-03-06T09:45:58Z

Created page with "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, bu..."

New page

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.

<pre>
! 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
</pre>

<pre>
! 13-tet_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
</pre>