595/594 - Revision history

FloraC: /* Temperaments */ update data

2026-03-22T10:35:00Z

Temperaments: update data

@@ Line 37: / Line 37: @@
 == Temperaments ==
 Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic''' temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic''' temperament, enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support these temperaments below.
 === Dakotismic ===
@@ Line 58: / Line 84: @@
 : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2950{{c}}, ~5/4 = 386.0705{{c}}, ~7/4 = 968.4704{{c}}, ~11/8 = 551.8578{{c}}, ~13/8 = 840.5277{{c}}
+[[Optimal tuning]]s:
 {{Optimal ET sequence|legend=1| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*
@@ Line 64: / Line 92: @@
 <nowiki>*</nowiki> [[optimal patent val]]: [[861edo|861]]
-=== Dakotic ===
+[[Badness]] (Sintel): 0.478
 == Etymology ==

FloraC: + see also

2026-03-22T10:30:08Z

+ see also

← Older revision		Revision as of 10:30, 22 March 2026
Line 88:		Line 88:
	== Etymology ==		== Etymology ==
	The dakotisma was named by [[Praveen Venkataramana]] in 2022 in honor of [[Scott Dakota]]'s pioneering study of this comma and of its role in 311et.		The dakotisma was named by [[Praveen Venkataramana]] in 2022 in honor of [[Scott Dakota]]'s pioneering study of this comma and of its role in 311et.

			== See also ==
			* [[List of superparticular intervals]]

	[[Category:Dakotismic]]		[[Category:Dakotismic]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FloraC: Cleanup

2026-03-22T10:29:34Z

Cleanup

← Older revision		Revision as of 10:29, 22 March 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''595/594''', the '''dakotisma''', is a [[small comma\|small]] [[17-limit]] [[comma]] measuring about 2.91 [[cent]]s. ~~Named after [[Scott Dakota]], it~~ is one of the simplest commas tempered out in [[311edo\|311et]], a highly notable general-purpose equal temperament.		'''595/594''', the '''dakotisma''', is a [[small comma\|small]] [[17-limit]] [[comma]] measuring about 2.91 [[cent]]s. It is one of the simplest commas [[tempering out\|tempered out]] in [[311edo\|311et]], a highly notable general-purpose equal temperament.

	== Commatic relations ==		== Commatic relations ==
	This comma identifies itself as the difference between the following superparticular pairs:		This comma identifies itself as the difference between the following superparticular pairs:

	* [[34/33]] and [[36/35]]		* [[34/33]] and [[36/35]]
	* [[85/84]] and [[99/98]]		* [[85/84]] and [[99/98]]
Line 37:		Line 36:

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic ~~temperament~~''', or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic ~~temperament~~''', enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support these temperaments below.		Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic''' temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic''' temperament, enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support these temperaments below.

	=== Dakotismic ===		=== Dakotismic ===
Line 57:		Line 56:
	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
	\|}		\|}

	: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2950{{c}}, ~5/4 = 386.0705{{c}}, ~7/4 = 968.4704{{c}}, ~11/8 = 551.8578{{c}}, ~13/8 = 840.5277{{c}}

	{{Optimal ET sequence\|legend=1\| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*		{{Optimal ET sequence\|legend=1\| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*
Line 69:		Line 67:
	[[Subgroup]]: 2.3.5.7.11.17		[[Subgroup]]: 2.3.5.7.11.17

	[[~~Sval~~]] [[mapping]]: <br>		[[Subgroup-val\|Subgroup val]] [[mapping]]: <br>
	{\| class="right-all"		{\| class="right-all"
	\|-		\|-
Line 82:		Line 80:
	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]
	\|}		\|}
			: mapping generators: ~2, ~3, ~5, ~7, ~11

	~~: sval mapping generators: ~2, ~3, ~5, ~7, ~11~~		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2950{{c}}, ~5/4 = 386.0705{{c}}, ~7/4 = 968.4704{{c}}, ~11/8 = 551.8578{{c}}

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578

	{{Optimal ET sequence\|legend=1\| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}		{{Optimal ET sequence\|legend=1\| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}

BudjarnLambeth at 01:50, 16 November 2024

2024-11-16T01:50:28Z

← Older revision		Revision as of 01:50, 16 November 2024
Line 93:		Line 93:

	[[Category:Dakotismic]]		[[Category:Dakotismic]]
			[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

Francium: Added color name

2023-09-07T16:26:30Z

Added color name

← Older revision		Revision as of 16:26, 7 September 2023
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = dakotisma		\| Name = dakotisma
			\| Color name = 17o1uzy2, soluzoyo 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: /* Temperaments */ formatting

2023-08-13T12:24:23Z

Temperaments: formatting

← Older revision		Revision as of 12:24, 13 August 2023
Line 42:		Line 42:

	[[Mapping]]: <br>		[[Mapping]]: <br>
	[~~{{val~~\| 1 0 0 0 0 0 1 ~~}}<br>~~		{\| class="right-all"
	~~{{val~~\| 0 1 0 0 0 0 3 ~~}}<br>~~		\|-
	~~{{val~~\| 0 0 1 0 0 0 -1 ~~}}<br>~~		\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| ],
	~~{{val~~\| 0 0 0 1 0 0 -1 ~~}}<br>~~		\|-
	~~{{val~~\| 0 0 0 0 1 0 1 ~~}}<br>~~		\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 3 \|\| ],
	~~{{val~~\| 0 0 0 0 0 1 0 }}]		\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
			\|}

	~~Mapping~~ generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277
Line 61:		Line 69:

	[[Sval]] [[mapping]]: <br>		[[Sval]] [[mapping]]: <br>
	[~~{{val~~\| 1 0 0 0 0 1 ~~}}<br>~~		{\| class="right-all"
	~~{{val~~\| 0 1 0 0 0 3 ~~}}<br>~~		\|-
	~~{{val~~\| 0 0 1 0 0 -1 ~~}}<br>~~		\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| ],
	~~{{val~~\| 0 0 0 1 0 -1 ~~}}<br>~~		\|-
	~~{{val~~\| 0 0 0 0 1 1 }}]		\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 3 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]
			\|}

	~~Sval~~ mapping generators: ~2, ~3, ~5, ~7, ~11		: sval mapping generators: ~2, ~3, ~5, ~7, ~11

	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578

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

2023-05-07T18:43:16Z

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

← Older revision		Revision as of 18:43, 7 May 2023
Line 53:		Line 53:
	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277

	{{~~Val list~~\|legend=1\| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*		{{Optimal ET sequence\|legend=1\| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*

	<nowiki>*</nowiki> [[optimal patent val]]: [[861edo\|861]]		<nowiki>*</nowiki> [[optimal patent val]]: [[861edo\|861]]
Line 71:		Line 71:
	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578

	{{~~Val list~~\|legend=1\| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}		{{Optimal ET sequence\|legend=1\| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}

	== Etymology ==		== Etymology ==

FloraC: /* Temperaments */ +subgroup temp

2023-02-23T11:24:54Z

Temperaments: +subgroup temp

← Older revision		Revision as of 11:24, 23 February 2023
Line 36:		Line 36:

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic temperament''', or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic temperament''', enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support ~~this temperament~~ below.		Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic temperament''', or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic temperament''', enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support these temperaments below.

			=== Dakotismic ===
	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

	[[Mapping]]:		[[Mapping]]: <br>
	<br>[{{val\| 1 0 0 0 0 0 1 }},		[{{val\| 1 0 0 0 0 0 1 }}<br>
	<br>{{val\| 0 1 0 0 0 0 3 }},		{{val\| 0 1 0 0 0 0 3 }}<br>
	<br>{{val\| 0 0 1 0 0 0 -1 }},		{{val\| 0 0 1 0 0 0 -1 }}<br>
	<br>{{val\| 0 0 0 1 0 0 -1 }},		{{val\| 0 0 0 1 0 0 -1 }}<br>
	<br>{{val\| 0 0 0 0 1 0 1 }},		{{val\| 0 0 0 0 1 0 1 }}<br>
	<br>{{val\| 0 0 0 0 0 1 0 }}]		{{val\| 0 0 0 0 0 1 0 }}]

	Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13		Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

			[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277

	{{Val list\|legend=1\| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*		{{Val list\|legend=1\| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*

	<nowiki>*</nowiki> [[optimal patent val]]: [[861edo\|861]]		<nowiki>*</nowiki> [[optimal patent val]]: [[861edo\|861]]

			=== Dakotic ===
			[[Subgroup]]: 2.3.5.7.11.17

			[[Sval]] [[mapping]]: <br>
			[{{val\| 1 0 0 0 0 1 }}<br>
			{{val\| 0 1 0 0 0 3 }}<br>
			{{val\| 0 0 1 0 0 -1 }}<br>
			{{val\| 0 0 0 1 0 -1 }}<br>
			{{val\| 0 0 0 0 1 1 }}]

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

			[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578

			{{Val list\|legend=1\| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}

	== Etymology ==		== Etymology ==

FloraC: +subgroup temp; +link

2023-02-18T16:00:41Z

+subgroup temp; +link

← Older revision		Revision as of 16:00, 18 February 2023
Line 36:		Line 36:

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic temperament''', ~~and enables~~ the ~~related essentially tempered~~ chords. You may find a list of good equal temperaments that support this temperament below.		Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic temperament''', or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic temperament''', enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support this temperament below.

	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

FloraC: +source of the name

2023-02-18T10:39:20Z

+source of the name

← Older revision		Revision as of 10:39, 18 February 2023
Line 53:		Line 53:

	<nowiki>*</nowiki> [[optimal patent val]]: [[861edo\|861]]		<nowiki>*</nowiki> [[optimal patent val]]: [[861edo\|861]]

			== Etymology ==
			The dakotisma was named by [[Praveen Venkataramana]] in 2022 in honor of [[Scott Dakota]]'s pioneering study of this comma and of its role in 311et.

	[[Category:Dakotismic]]		[[Category:Dakotismic]]