72ed5 - Revision history

ArrowHead294 at 15:00, 16 July 2025

2025-07-16T15:00:58Z

← Older revision		Revision as of 15:00, 16 July 2025
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	* [[80ed6]] – relative ed6		* [[80ed6]] – relative ed6
	* [[87ed7]] – relative ed7		* [[87ed7]] – relative ed7
			* [[107ed11]] – relative ed11
	* [[111ed12]] – relative ed12		* [[111ed12]] – relative ed12
			* [[138ed22]] – relative ed22
	* [[204ed96]] – close to the zeta-optimized tuning for 31edo		* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

	[[Category:31edo]]		[[Category:31edo]]

ArrowHead294: /* See also */

2025-06-10T13:31:34Z

FloraC: Note consistency and tuning tendency

2025-03-24T12:37:53Z

Note consistency and tuning tendency

← Older revision		Revision as of 12:37, 24 March 2025
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	== Theory ==		== Theory ==
	72ed5 is related to [[31edo]], but with the 5/1 rather than the [[2/1]] being just. The octave is slightly compressed (about 0.3372 cents). ~~This tuning~~ has a meantone ~~fifth~~ as the number of divisions of the 5th harmonic is multiple of 4.		72ed5 is related to [[31edo]], but with the 5/1 rather than the [[2/1]] being just. The octave is slightly compressed (about 0.3372 cents). Like 31edo, 72ed5 is [[consistent]] through the [[integer limit\|12-integer-limit]], but it has a flat tendency, with [[prime harmonic]]s 2, [[3/1\|3]], [[7/1\|7]], and [[11/1\|11]] all tuned flat. It [[support]]s [[meantone]] as the number of divisions of the 5th harmonic is multiple of 4.

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

FloraC: /* Theory */ +subsets and supersets

2025-03-24T12:26:26Z

Theory: +subsets and supersets

← Older revision		Revision as of 12:26, 24 March 2025
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	{{Harmonics in equal\|72\|5\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|72\|5\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|72\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 72ed5 (continued)}}		{{Harmonics in equal\|72\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 72ed5 (continued)}}

			=== Subsets and supersets ===
			72 is a [[largely composite]] number. Since it factors into primes as {{nowrap\| 2<sup>3</sup> × 3<sup>2</sup> }}, 72ed5 has subset ed5's {{EDs\|equave=5\| 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36 }}.

	== Intervals ==		== Intervals ==

FloraC: Cleanup (2/2)

2025-03-24T12:24:04Z

Cleanup (2/2)

Show changes

FloraC: Cleanup (1/)

2025-03-24T12:04:20Z

Cleanup (1/)

← Older revision		Revision as of 12:04, 24 March 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 72 equal parts''' (72ed5) is related to [[31edo\|31 edo]], but with the 5/1 rather than the 2/1 being just. The octave is slightly compressed (about 0.3372 cents) and the step size is about 38.6988 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.		{{ED intro}}

	== ~~Harmonics~~ ==		== Theory ==
	~~{{harmonics in equal\|72\|~~5\|1~~\|columns~~=~~8\|prec~~=~~2}}~~		72ed5 is related to [[31edo]], but with the 5/1 rather than the [[2/1]] being just. The octave is slightly compressed (about 0.3372 cents). This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.
	{{~~harmonics~~ in equal\|72\|5\|1\|~~columns~~=8\|~~start=9\|prec~~=2}}
	~~31edo for comparison:~~		=== Harmonics ===
	{{~~harmonics~~ in equal\|31\|~~columns=8~~\|~~prec=2~~\|intervals=integer~~\|collapsed=1}}~~		{{Harmonics in equal\|72\|5\|1\|intervals=integer\|columns=11}}
	~~{{harmonics in equal\|31~~\|columns=8\|start=9\|~~prec~~=2\|~~intervals=integer\|collapsed=1~~}}		{{Harmonics in equal\|72\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 72ed5 (continued)}}

	== Intervals ==		== Intervals ==
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	\|}		\|}

	[[~~Category:Ed5~~]]		== See also ==
	[[~~Category:Edonoi~~]]		* [[18edf]] – relative edf
	~~{{todo\|expand}}~~		* [[31edo]] – relative edo
			* [[49edt]] – relative edt
			* [[80ed6]] – relative ed6
			* [[87ed7]] – relative ed7
			* [[111ed12]] – relative ed12
			* [[39cET]]

BudjarnLambeth: Replace ultra wide tables with 2 less wide ones for phone users

2024-12-22T04:12:00Z

Replace ultra wide tables with 2 less wide ones for phone users

← Older revision		Revision as of 04:12, 22 December 2024
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	== Harmonics ==		== Harmonics ==
	{{harmonics in equal\|72\|5\|1\|columns=15\|prec=2}}		{{harmonics in equal\|72\|5\|1\|columns=8\|prec=2}}
			{{harmonics in equal\|72\|5\|1\|columns=8\|start=9\|prec=2}}
	31edo for comparison:		31edo for comparison:
	{{harmonics in equal\|31\|columns=15\|prec=2\|intervals=integer\|collapsed=1}}		{{harmonics in equal\|31\|columns=8\|prec=2\|intervals=integer\|collapsed=1}}
			{{harmonics in equal\|31\|columns=8\|start=9\|prec=2\|intervals=integer\|collapsed=1}}

	== Intervals ==		== Intervals ==

BudjarnLambeth: Todo table

2024-12-22T04:10:02Z

Todo table

← Older revision		Revision as of 04:10, 22 December 2024
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	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
	\|-		\|-
	! \| degree		! \| degree
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	[[Category:Ed5]]		[[Category:Ed5]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			{{todo\|expand}}

ArrowHead294 at 00:53, 15 September 2024

2024-09-15T00:53:23Z

← Older revision		Revision as of 00:53, 15 September 2024
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	== Harmonics ==		== Harmonics ==
	{{harmonics in equal\|72\|5\|1\|columns=15}}		{{harmonics in equal\|72\|5\|1\|columns=15\|prec=2}}
	31edo for comparison:		31edo for comparison:
	{{harmonics in equal\|31\|intervals=integer\|collapsed=1}}		{{harmonics in equal\|31\|columns=15\|prec=2\|intervals=integer\|collapsed=1}}

	== Intervals ==		== Intervals ==

ArrowHead294 at 00:52, 15 September 2024

2024-09-15T00:52:41Z

← Older revision		Revision as of 00:52, 15 September 2024
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	== Harmonics ==		== Harmonics ==
	{{harmonics in equal\|72\|5\|1}}		{{harmonics in equal\|72\|5\|1\|columns=15}}
	31edo for comparison:		31edo for comparison:
	{{harmonics in equal\|31\|intervals=integer\|collapsed=1}}		{{harmonics in equal\|31\|intervals=integer\|collapsed=1}}

← Older revision		Revision as of 13:31, 10 June 2025
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	* [[87ed7]] – relative ed7		* [[87ed7]] – relative ed7
	* [[111ed12]] – relative ed12		* [[111ed12]] – relative ed12
			* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

			[[Category:31edo]]