6656/6655 - Revision history

Eliora: /* Temperaments */

2026-09-06T20:57:05Z

Temperaments

← Older revision		Revision as of 20:57, 6 September 2026
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	== Temperaments ==		== Temperaments ==
	By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13 ~~o fthe~~ comma Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].		By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13, the subgroup of the comma. Although 1789edo has a unique position due to its number of steps being a hallmark year of the {{W\|French Revolution}}, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].

	The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.		The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.

Eliora: /* Temperaments */ typo

2026-09-06T17:10:58Z

Temperaments: typo

← Older revision		Revision as of 17:10, 6 September 2026
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	== Temperaments ==		== Temperaments ==
	By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is ~~consistence~~ to distance 2 on the subgroup 2.5.11.13 o fthe comma Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].		By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13 o fthe comma Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].

	The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.		The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.

Eliora: /* Temperaments */

2026-09-05T23:33:02Z

Temperaments

← Older revision		Revision as of 23:33, 5 September 2026
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	The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.		The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.

	See [[The Jacobins#Jacobin]] for technical data.		See [[The Jacobins#Jacobin]] for technical data.

	== Etymology ==		== Etymology ==

Eliora: /* Temperaments */

2026-09-05T23:32:56Z

Temperaments

← Older revision		Revision as of 23:32, 5 September 2026
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	By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistence to distance 2 on the subgroup 2.5.11.13 o fthe comma Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].		By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistence to distance 2 on the subgroup 2.5.11.13 o fthe comma Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].

	The 17-limit factorization shows us a natural path of extension. See [[The Jacobins#Jacobin]] for technical data.		The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.

			See [[The Jacobins#Jacobin]] for technical data.

	== Etymology ==		== Etymology ==

Eliora: /* Temperaments */ not putting temperaments in main pages and minus duplicate data (already addressed in The Jacobins)

2026-09-05T23:32:02Z

Temperaments: not putting temperaments in main pages and minus duplicate data (already addressed in The Jacobins)

@@ Line 9: / Line 9: @@
 == Temperaments ==
-By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].
+By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistence to distance 2 on the subgroup 2.5.11.13 o fthe comma Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].
-The 17-limit factorization shows us a natural path of extension, also given below.
+The 17-limit factorization shows us a natural path of extension. See [[The Jacobins#Jacobin]] for technical data.
 == Etymology ==

Fredg999: Expand etymology

2026-07-12T05:59:20Z

Expand etymology

← Older revision		Revision as of 05:59, 12 July 2026
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	== Etymology ==		== Etymology ==
	This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki \| ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>.		This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki \| ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>. An hypothesis is that "jacobin" refers to the {{w\|Jacobins}}, a political group founded in 1789 during the French Revolution, since this comma is tempered out by [[1789edo]], a tuning which, furthermore, is [[consistent]] to distance 2 in the 2.5.11.13-subgroup-limited [[13-odd-limit]], reinforcing the importance of this comma in this tuning.

	== See also ==		== See also ==
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	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]
	{{Todo\|add etymology\|comment=I know it's something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name "jacobin" uniquely fit this particular comma?}}

FloraC: Complete data

2026-02-25T06:52:33Z

Complete data

← Older revision		Revision as of 06:52, 25 February 2026
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 3 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 3 \|\| ]]
	\|}		\|}
			: mapping generators: ~2, ~3, ~5, ~7, ~11

	: ~~mapping generators~~: ~2, ~3, ~5, ~7, ~11		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9887{{c}}, ~3/2 = 701.9663{{c}}, ~5/4 = 386.3430{{c}}, ~7/4 = 968.8484{{c}}, ~11/8 = 551.3967{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9661{{c}}, ~5/4 = 386.3383{{c}}, ~7/4 = 968.8455{{c}}, ~11/8 = 551.3980{{c}}

	{{Optimal ET sequence\|legend=1\| 15, 22, 26, 31f, 37, 39df, 41, 46, 63, 72, 87, 111, 152f, 183, 198, 224, 270, 494, 764, 1012, 1084, 1236, 1506, 2814, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816ee }}		{{Optimal ET sequence\|legend=1\| 15, 22, 26, 31f, 37, 39df, 41, 46, 63, 72, 87, 111, 152f, 183, 198, 224, 270, 494, 764, 1012, 1084, 1236, 1506, 2814, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816ee }}

			[[Badness]] (Sintel): 0.416

	==== Septendecimal jacobin ====		==== Septendecimal jacobin ====
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	\|}		\|}

	Optimal ~~ET sequence~~: {{Optimal ET sequence\| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}		Optimal tunings:
			* WE: ~2 = 1199.9890{{c}}, ~3/2 = 701.9675{{c}}, ~5/4 = 386.3466{{c}}, ~7/4 = 968.8454{{c}}, ~11/8 = 551.3945{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9670{{c}}, ~5/4 = 386.3410{{c}}, ~7/4 = 968.8434{{c}}, ~11/8 = 551.3964{{c}}

			{{Optimal ET sequence\|legend=0\| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}

			Badness (Sintel): 0.239

	== Etymology ==		== Etymology ==

FloraC: Cleanup

2026-02-25T06:47:16Z

Cleanup

← Older revision		Revision as of 06:47, 25 February 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''6656/6655''', the '''jacobin comma''', [~~https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 apparently named] by~~ [~~[Gene Ward Smith~~]] ~~in 2014, is a~~ [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] ~~interval~~ of about 0.26{{cent}}. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]] ([[13/5]]). In terms of commas, it is the difference between [[364/363]] and [[385/384]], between [[2080/2079]] and [[3025/3024]] as well as between [[4096/4095]] and [[10648/10647]]. In the 17-limit, it factors neatly into ([[12376/12375]])([[14400/14399]]).		'''6656/6655''', the '''jacobin comma''', is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] [[comma]] of about 0.26{{cent}}. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]] ([[13/5]]).

			In terms of commas, it is the difference between [[364/363]] and [[385/384]], between [[2080/2079]] and [[3025/3024]] as well as between [[4096/4095]] and [[10648/10647]]. In the [[17-limit]], it factors neatly into ([[12376/12375]])⋅([[14400/14399]]).

	== Temperaments ==		== Temperaments ==
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	Optimal ET sequence: {{Optimal ET sequence\| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}		Optimal ET sequence: {{Optimal ET sequence\| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}

			== Etymology ==
			This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki \| ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>.

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

			== References ==

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]
			{{Todo\|add etymology\|comment=I know it's something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name "jacobin" uniquely fit this particular comma?}}
	{{~~todo~~\|add etymology\|comment=I know ~~it’s~~ something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name ~~“jacobin”~~ uniquely fit this particular comma?}}

Jdood: added 13/5 to "13/10 naiadic + an octave)

2025-12-22T06:09:59Z

added 13/5 to "13/10 naiadic + an octave)

← Older revision		Revision as of 06:09, 22 December 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''6656/6655''', the '''jacobin comma''', [https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 apparently named] by [[Gene Ward Smith]] in 2014, is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26{{cent}}. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]]. In terms of commas, it is the difference between [[364/363]] and [[385/384]], between [[2080/2079]] and [[3025/3024]] as well as between [[4096/4095]] and [[10648/10647]]. In the 17-limit, it factors neatly into ([[12376/12375]])([[14400/14399]]).		'''6656/6655''', the '''jacobin comma''', [https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 apparently named] by [[Gene Ward Smith]] in 2014, is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26{{cent}}. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]] ([[13/5]]). In terms of commas, it is the difference between [[364/363]] and [[385/384]], between [[2080/2079]] and [[3025/3024]] as well as between [[4096/4095]] and [[10648/10647]]. In the 17-limit, it factors neatly into ([[12376/12375]])([[14400/14399]]).

	== Temperaments ==		== Temperaments ==

BudjarnLambeth at 03:34, 4 November 2024

2024-11-04T03:34:00Z

← Older revision		Revision as of 03:34, 4 November 2024
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	[[Category:Jacobin]]		[[Category:Jacobin]]
			[[Category:Commas with unknown etymology]]

			{{todo\|add etymology\|comment=I know it’s something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name “jacobin” uniquely fit this particular comma?}}