The Jacobins - Revision history

Eliora: /* Huguenot */

2026-09-02T19:48:10Z

Huguenot

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	== Huguenot ==		== Huguenot ==
	Huguenot, named after French calvinists who fled to Ireland, tempers out the [[leprechaun comma]] together with the jacobin comma.		Huguenot, named after French calvinists who fled to Ireland, tempers out the [[4225/4224\|leprechaun comma]] together with the jacobin comma.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Eliora at 19:47, 2 September 2026

2026-09-02T19:47:37Z

← Older revision		Revision as of 19:47, 2 September 2026
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	[[Tp tuning #T2 tuning\|RMS error]]: 0.0822 cents		[[Tp tuning #T2 tuning\|RMS error]]: 0.0822 cents

			== Huguenot ==
			Huguenot, named after French calvinists who fled to Ireland, tempers out the [[leprechaun comma]] together with the jacobin comma.

			Subgroup: 2.3.5.7.11.13

			Comma list: 4225/4224, 6656/6655

			{{Mapping\|legend=1\| 1 1 4 2 2 1 \| 0 1 4 0 -3 -5 \| 0 0 -5 0 4 7 \| 0 0 0 1 0 0 }}

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.009{{c}}, ~3/2 = 701.954{{c}}, ~96/55 = 964.312{{c}}, 7/4 = 968.809{{c}}
			: [[error map]]: {{val\| 0.009, 0.008, -0.025, -0.000, 0.087, -0.102 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.953{{c}}, ~96/55 = 964.309{{c}}, 7/4 = 968.807{{c}}
			: error map: {{val\| 0.000, -0.002, -0.045, -0.019, 0.058, -0.132 }}

			[[Support]]ing [[ET]]s: {{EDOs\|87, 224, 270, 311, 494, 581, 764, 814, 1084, 1308}}

			[[Badness]]: 0.508

	== Genojacobin ==		== Genojacobin ==

Eliora at 20:13, 24 August 2026

2026-08-24T20:13:18Z

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	The main focus here will be on the 2.5.11.13 [[subgroup]], the subgroup of the comma. Besides, in the full 13-limit the jacobin comma often functions as a part of a basis of other temperaments of other families and groups, like [[vidar]].		The main focus here will be on the 2.5.11.13 [[subgroup]], the subgroup of the comma. Besides, in the full 13-limit the jacobin comma often functions as a part of a basis of other temperaments of other families and groups, like [[vidar]].

	Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments. Since 1789edo has a bad approximation to the 3rd harmonic, 2.5.7.11.13 is also the main subgroup for many temperaments, and 7-limit extensions to 2.5.11.13 temperaments are named "septimal …" after the original temperament.		Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments ― and it is consistent to distance 2 in the 2.5.11.13 subgroup, subgroup of the comma. Since 1789edo has a bad approximation to the 3rd harmonic, 2.5.7.11.13 is also the main subgroup for many temperaments, and 7-limit extensions to 2.5.11.13 temperaments are named "septimal …" after the original temperament.

	== Jacobin ==		== Jacobin ==

Eliora at 03:37, 17 August 2026

2026-08-17T03:37:54Z

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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 }}

	== Jacobin-naiadic ==		=== Jacobin-naiadic ===
	Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma. Such a mapping is realized through the fractional subgroup 2.13/10.11, which produces a basis with just one comma - namely the 6656/6655. Name given because the 13/10 interval is sometimes referred to as a "naiadic", and this name separates it from the standard diatonic framework.		Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma. Such a mapping is realized through the fractional subgroup 2.13/10.11, which produces a basis with just one comma - namely the 6656/6655. Name given because the 13/10 interval is sometimes referred to as a "naiadic", and this name separates it from the standard diatonic framework.

Eliora: /* Eternal revolutionary */ fix language id in the link

2026-08-16T01:36:44Z

Eternal revolutionary: fix language id in the link

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	== Eternal revolutionary ==		== Eternal revolutionary ==
	Described as the 91 & 1880 temperament, or 1789bd & 1880 temperament, and is named after a [[Wikipedia:ua:Вічний революціонер\|poem by Ivan Franko]] <sup>[UA, no EN]</sup> which was written in the year 1880, hence the name.		Described as the 91 & 1880 temperament, or 1789bd & 1880 temperament, and is named after a [[Wikipedia:uk:Вічний революціонер\|poem by Ivan Franko]] <sup>[UA, no EN]</sup> which was written in the year 1880, hence the name.

	Subgroup: 2.5.11.13		Subgroup: 2.5.11.13

Eliora: /* Genojacobin */ +acroquanharuk

2026-08-15T17:37:10Z

Genojacobin: +acroquanharuk

← Older revision		Revision as of 17:37, 15 August 2026
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	{{Optimal ET sequence\|legend=1\|183, 1057f, 1240, 1423, 1606, 1789, 3395 }}		{{Optimal ET sequence\|legend=1\|183, 1057f, 1240, 1423, 1606, 1789, 3395 }}

			=== Acroquanharuk ===
			Described as 183 & 1240 temperament in the full 13-limit, and named by analogy with acrosextilifourths (see below) as a more large-edo expansion upon quanharuk. 1789d val is chosen as it is simpler.

			Subgroup: 2.3.5.7.11.13

			Comma list: 729/728, 6656/6655, 1016064/1015625, 14085981/14080000

			{{Mapping\|legend=1\| 1 0 -43 -104 51 101 \| 0 5 143 337 -150 -307 }}

			Optimal tuning (CWE): ~1755/1408 = 380.323

			[[Support]]ing [[ET]]s: {{EDOs\|183, 1057f, 1240, 1403, 1789d}}

	== Onzonic ==		== Onzonic ==

BudjarnLambeth: /* Barton */ + Scott Dakota rediscovered this same temperament in 2025 and named it "hem"{{idio}}.

2025-10-02T04:31:07Z

Barton: + Scott Dakota rediscovered this same temperament in 2025 and named it "hem"{{idio}}.

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	{{See also\| Chromatic pairs #Barton }}		{{See also\| Chromatic pairs #Barton }}

	Barton may be described as the 11 & 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group \| "father" variant?]</ref>.		Barton may be described as the 11 & 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group \| "father" variant?]</ref>. [[Scott Dakota]] rediscovered this same temperament in 2025 and named it "hem"{{idio}}.

	[[Subgroup]]: 2.5.11.13		[[Subgroup]]: 2.5.11.13

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:43:00Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	'''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].		'''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T06:54:00Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 06:54, 13 April 2025
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			{{Technical data page}}<br><br>
	'''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].		'''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].

Lériendil at 20:54, 1 April 2025

2025-04-01T20:54:20Z

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	== Sextilimeans ==		== Sextilimeans ==
	Sextilimeans is like ~~sextilififths~~, but the fourth that is divided into 6 in ~~sextilififths~~ is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament.		Sextilimeans is like [[sextilifourths]], but the fourth that is divided into 6 in sextilifourths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament.

	[[Subgroup]]: 2.5.7.11.13		[[Subgroup]]: 2.5.7.11.13
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	{{Optimal ET sequence\|legend=1\|1789, 2814, }} ...		{{Optimal ET sequence\|legend=1\|1789, 2814, }} ...

	== ~~Acrosextilififths~~ ==		== Acrosextilifourths ==
	Discovered by [[Aura]] and defined as the 159 & 1619 temperament, with prefix acro- denoting the fact that it's a more precise version of ~~sextilififths~~, with fourth divided into 6 parts in 1619edo just as it is in 159edo.		Discovered by [[Aura]] and defined as the 159 & 1619 temperament, with prefix acro- denoting the fact that it's a more precise version of sextilifourths, with fourth divided into 6 parts in 1619edo just as it is in 159edo.

	[[Subgroup]]: 2.3.5.7.11.13		[[Subgroup]]: 2.3.5.7.11.13