Wilschisma - Revision history

FloraC: Name change followup. Cleanup.

2026-03-03T10:13:54Z

Name change followup. Cleanup.

← Older revision		Revision as of 10:13, 3 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''wilschisma''' ({{monzo\|legend=1\| 13 -12 1 0 0 1 }}, [[ratio]]: 532480/531441) is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] (also 2.3.5.13-[[subgroup]]) [[comma]] measuring about 3.38 [[cent]]s. It is the difference between the wilsorma ([[65/64]]) and the [[Pythagorean comma]], hence the name. The wilschisma can be viewed as a counterpart of the [[symbiotic comma]] – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[~~schismina~~]].		The '''wilschisma''' ({{monzo\|legend=1\| 13 -12 1 0 0 1 }}, [[ratio]]: 532480/531441) is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] (also [[2.3.5.13 subgroup\|2.3.5.13-]][[subgroup]]) [[comma]] measuring about 3.38 [[cent]]s. It is the difference between the wilsorma ([[65/64]]) and the [[Pythagorean comma]], hence the name. The wilschisma can be viewed as a counterpart of the [[symbiotic comma]] – while the symbiotic comma connects [[7/1\|7]] and [[11/1\|11]], the wilschisma connects [[5/1\|5]] and [[13/1\|13]], and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[minisma]].

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 13-limit results in the rank-5 '''wilschismic temperament'''. You may find a list of good equal temperaments that support this temperament below. Adding the [[ibnsinma]] and thus the [[symbiotic comma]] to the comma list gives symbiotic (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), with virtually no additional error, so it is highly recommendable. Otherwise, retracting it to the 2.3.5.13 subgroup gives the rank-3 '''will temperament'''.		[[Tempering out]] this comma in the full 13-limit results in the rank-5 '''wilschismic temperament'''. You may find a list of good equal temperaments that support this temperament below. Adding the [[ibnsinma]] and thus the [[symbiotic comma]] to the comma list gives symbiotic (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), with virtually no additional error, so it is highly recommendable. Otherwise, retracting it to the 2.3.5.13 subgroup gives the rank-3 '''will temperament'''.

	=== Wilschismic ===		=== Wilschismic ===

FloraC: +etymology. Recategorize

2024-11-04T16:44:10Z

+etymology. Recategorize

← Older revision		Revision as of 16:44, 4 November 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''wilschisma''' (~~monzo:~~ {{monzo\| 13 -12 1 0 0 1 }}, ratio: 532480/531441) is a 13-limit (also 2.3.5.13 subgroup) [[~~unnoticeable~~ comma]] measuring about 3.38 [[cent]]s. It is the difference between the wilsorma ([[65/64]]) and the [[Pythagorean comma]], hence the name. The wilschisma can be viewed as a counterpart of the [[symbiotic comma]] – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[schismina]].		The '''wilschisma''' ({{monzo\|legend=1\| 13 -12 1 0 0 1 }}, [[ratio]]: 532480/531441) is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] (also 2.3.5.13-[[subgroup]]) [[comma]] measuring about 3.38 [[cent]]s. It is the difference between the wilsorma ([[65/64]]) and the [[Pythagorean comma]], hence the name. The wilschisma can be viewed as a counterpart of the [[symbiotic comma]] – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[schismina]].

	== Temperaments ==		== Temperaments ==
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	{{Mapping\|legend=2\| 1 0 0 -13 \| 0 1 0 12 \| 0 0 1 -1 }}		{{Mapping\|legend=2\| 1 0 0 -13 \| 0 1 0 12 \| 0 0 1 -1 }}

	[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.2227, ~5/4 = 386.2658

	{{Optimal ET sequence\|legend=1\| 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf }}		{{Optimal ET sequence\|legend=1\| 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf }}
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	[[Badness]]: 0.132 × 10<sup>-3</sup>		[[Badness]]: 0.132 × 10<sup>-3</sup>

	== ~~See also~~ ==		== Etymology ==
	* [[~~Unnoticeable comma~~]]		This comma was named by [[Flora Canou]] in 2021 for its relationship with the wilsorma and Pythagorean comma.

	[[Category:Wilschismic]]		[[Category:Wilschismic]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named for other reasons]]

BudjarnLambeth at 02:58, 4 November 2024

2024-11-04T02:58:04Z

← Older revision		Revision as of 02:58, 4 November 2024
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	[[Category:Wilschismic]]		[[Category:Wilschismic]]
			[[Category:Commas with unknown etymology]]

FloraC: /* Temperaments */ formatting

2023-07-19T12:36:05Z

Temperaments: formatting

← Older revision		Revision as of 12:36, 19 July 2023
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	[[Mapping]]: <br>		[[Mapping]]: <br>
	[~~{{val~~\| 1 0 0 0 0 -13 }}, ~~<br>~~		{\| class="right-all"
	~~{{val~~\| 0 1 0 0 0 12 }}, ~~<br>~~		\|-
	~~{{val~~\| 0 0 1 0 0 -1 }}, ~~<br>~~		\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| -13 \|\| ],
	~~{{val~~\| 0 0 0 1 0 0 }}, ~~<br>~~		\|-
	~~{{val~~\| 0 0 0 0 1 0 }}]		\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 12 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
			\|}

	~~Mapping~~ generators: ~2, ~3, ~5, ~7, ~11		: mapping generators: ~2, ~3, ~5, ~7, ~11

	{{Optimal ET sequence\|legend=1\| 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef }}		{{Optimal ET sequence\|legend=1\| 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef }}
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	[[Comma list]]: 532480/531441		[[Comma list]]: 532480/531441

	~~[[Sval]] [[mapping]]: [~~{{~~val~~\| 1 0 0 -13 ~~}}, {{val~~\| 0 1 0 12 ~~}}, {{val~~\| 0 0 1 -1 }}]		{{Mapping\|legend=2\| 1 0 0 -13 \| 0 1 0 12 \| 0 0 1 -1 }}

	[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658		[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:21:57Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:21, 7 May 2023
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	Mapping generators: ~2, ~3, ~5, ~7, ~11		Mapping generators: ~2, ~3, ~5, ~7, ~11

	{{~~Val list~~\|legend=1\| 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef }}		{{Optimal ET sequence\|legend=1\| 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef }}

	=== Will ===		=== Will ===
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	[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658		[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658

	{{~~Val list~~\|legend=1\| 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf }}		{{Optimal ET sequence\|legend=1\| 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf }}

	[[Badness]]: 0.132 × 10<sup>-3</sup>		[[Badness]]: 0.132 × 10<sup>-3</sup>

TallKite at 05:28, 19 January 2023

2023-01-19T05:28:53Z

← Older revision		Revision as of 05:28, 19 January 2023
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	\| Ratio = 532480/531441		\| Ratio = 532480/531441
	\| Name = wilschisma		\| Name = wilschisma
			\| Color name = s3oy2, sathoyo 2nd,<br>Sathoyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T18:06:36Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 18:06, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 532480/531441		\| Ratio = 532480/531441
	~~\| Monzo = 13 -12 1 0 0 1~~
	~~\| Cents = 3.38137~~
	\| Name = wilschisma		\| Name = wilschisma
	\| ~~Color name =~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}
	The '''wilschisma''' (monzo: {{monzo\| 13 -12 1 0 0 1 }}, ratio: 532480/531441) is a 13-limit (also 2.3.5.13 subgroup) [[unnoticeable comma]] measuring about 3.38 [[cent]]s. It is the difference between the wilsorma ([[65/64]]) and the [[Pythagorean comma]], hence the name. The wilschisma can be viewed as a counterpart of the [[symbiotic comma]] – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[schismina]].		The '''wilschisma''' (monzo: {{monzo\| 13 -12 1 0 0 1 }}, ratio: 532480/531441) is a 13-limit (also 2.3.5.13 subgroup) [[unnoticeable comma]] measuring about 3.38 [[cent]]s. It is the difference between the wilsorma ([[65/64]]) and the [[Pythagorean comma]], hence the name. The wilschisma can be viewed as a counterpart of the [[symbiotic comma]] – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[schismina]].
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	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]

	~~[[Category:13-limit]]~~
	~~[[Category:Small commas]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Wilschismic]]		[[Category:Wilschismic]]

FloraC: Correction

2022-09-02T00:09:53Z

Correction

← Older revision		Revision as of 00:09, 2 September 2022
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	[[Comma list]]: 532480/531441		[[Comma list]]: 532480/531441

	[[~~Mapping~~]]: [{{val\| 1 ~~0 0~~ 0 0 -13 }}, {{val\| 0 1 ~~0 0~~ 0 12 }}, {{val\| 0 0 1 ~~0 0~~ -1 }}]		[[Sval]] [[mapping]]: [{{val\| 1 0 0 -13 }}, {{val\| 0 1 0 12 }}, {{val\| 0 0 1 -1 }}]

	[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658		[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658

FloraC: +wilschismic and will

2022-09-02T00:09:07Z

+wilschismic and will

@@ Line 11: / Line 11: @@
 == Temperaments ==
-Tempering out this comma in the full 13-limit results in the rank-5 wilschismic temperament.
+Tempering out this comma in the full 13-limit results in the rank-5 '''wilschismic temperament'''. You may find a list of good equal temperaments that support this temperament below. Adding the [[ibnsinma]] and thus the [[symbiotic comma]] to the comma list gives symbiotic (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), with virtually no additional error, so it is highly recommendable. Otherwise, retracting it to the 2.3.5.13 subgroup gives the rank-3 '''will temperament'''.
 == See also ==

Fredg999 category edits: Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

2022-03-20T22:01:56Z

Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

← Older revision		Revision as of 22:01, 20 March 2022
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	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:Small commas]]		[[Category:Small commas]]
	[[Category:Unnoticeable ~~comma~~]]		[[Category:Unnoticeable commas]]
	[[Category:Wilschismic]]		[[Category:Wilschismic]]