56ed5 - Revision history

ArrowHead294: /* See also */

2025-06-25T19:18:29Z

2025-06-19T15:24:39Z

Theory

← Older revision		Revision as of 15:24, 19 June 2025
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	== Theory ==		== Theory ==
	56ed5 is related to 24edo, but with the 5th harmonic rather than the [[2/1\|octave]] being just. The octave is compressed by about 5.8{{c}}, a ~~deviation that despite being~~ small ~~is enough to be~~ significant. This tuning has a [[meantone]] fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a [[hyperpyth]], tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.		56ed5 is related to 24edo, but with the 5th harmonic rather than the [[2/1\|octave]] being just. The octave is compressed by about 5.8{{c}}, a small but significant deviation. This tuning has a [[meantone]] fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a [[hyperpyth]], tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.

	=== Harmonics ===		=== Harmonics ===

2025-06-18T18:10:06Z

2025-06-18T18:06:25Z

← Older revision		Revision as of 18:06, 18 June 2025
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	== Theory ==		== Theory ==
	56ed5 is related to 24edo, but with the 5th harmonic rather than the [[2/1\|octave]] being just. The octave is about 5.~~87 cents compressed~~. This tuning has a [[meantone]] fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a [[hyperpyth]], tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.		56ed5 is related to 24edo, but with the 5th harmonic rather than the [[2/1\|octave]] being just. The octave is compressed by about 5.8{{c}}, a deviation that despite being small is enough to be significant. This tuning has a [[meantone]] fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a [[hyperpyth]], tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.

	=== Harmonics ===		=== Harmonics ===
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	* [[62ed6]] – relative ed6		* [[62ed6]] – relative ed6
	* [[86ed12]] – relative ed12		* [[86ed12]] – relative ed12

			[[Category:24edo]]

2025-05-27T10:27:19Z

Intervals: style

← Older revision		Revision as of 10:27, 27 May 2025
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	== Intervals ==		== Intervals ==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable center-1 right-2 mw-collapsible"
	~~\|+ Intervals of 56ed5~~
	\|-		\|-
	! #		! #

2025-05-27T10:24:20Z

+ see also

2025-05-27T10:19:14Z

Cleanup & expand

2024-12-23T14:47:56Z

Intervals

← Older revision		Revision as of 14:47, 23 December 2024
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	==Intervals==		==Intervals==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
	\|+ Intervals of ~~56ed6~~		\|+ Intervals of 56ed5
	\|-		\|-
	! \| degree		! \| degree

2024-12-22T04:08:48Z

Todo collapsible

← Older revision		Revision as of 04:08, 22 December 2024
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	==Intervals==		==Intervals==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 56ed6
	\|-		\|-
	! \| degree		! \| degree
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	\| collapsed = 1		\| collapsed = 1
	}}		}}

			{{todo\|expand}}

2024-10-06T01:29:57Z

Harmonics

← Older revision		Revision as of 01:29, 6 October 2024
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	'''[[Ed5\|Division of the 5th harmonic]] into 56 equal parts''' (56ed5) is related to [[24edo\|24 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 49.7556 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a [[hyperpyth]], tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.		'''[[Ed5\|Division of the 5th harmonic]] into 56 equal parts''' (56ed5) is related to [[24edo\|24 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 49.7556 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning is also a [[hyperpyth]], tempering out 135/133, 171/169, 225/221, and 1521/1445 in the patent val.

			==Intervals==
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
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	\|}		\|}

	~~[[Category:Ed5]]~~		== Harmonics ==
	~~[[Category:Edonoi]]~~		{{Harmonics in equal
			\| steps = 56
			\| num = 5
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 56
			\| num = 5
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

← Older revision		Revision as of 19:18, 25 June 2025
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	* [[38edt]] – relative edt		* [[38edt]] – relative edt
	* [[62ed6]] – relative ed6		* [[62ed6]] – relative ed6
			* [[83ed11]] – relative ed11
	* [[86ed12]] – relative ed12		* [[86ed12]] – relative ed12
	* [[198ed304]] – close to the zeta-optimized tuning for 24edo		* [[198ed304]] – close to the zeta-optimized tuning for 24edo

	[[Category:24edo]]		[[Category:24edo]]

← Older revision		Revision as of 18:10, 18 June 2025
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	* [[62ed6]] – relative ed6		* [[62ed6]] – relative ed6
	* [[86ed12]] – relative ed12		* [[86ed12]] – relative ed12
			* [[198ed304]] – close to the zeta-optimized tuning for 24edo

	[[Category:24edo]]		[[Category:24edo]]