The Nexus - Revision history

FloraC: Finalize the data

2026-09-17T08:35:46Z

Finalize the data

← Older revision		Revision as of 08:35, 17 September 2026
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	Subgroup-val mapping: {{mapping\| 3 0 8 23 \| 0 2 1 -5 }}		Subgroup-val mapping: {{mapping\| 3 0 8 23 \| 0 2 1 -5 }}

	Optimal ~~tuning (POTE)~~: ~121/96 = 400.0000{{c}}, ~1331/768 = 951.~~4814~~{{c}}		Optimal tunings:
			* WE: ~121/96 = 399.8965{{c}}, ~1331/768 = 951.2352{{c}}
			* CWE: ~121/96 = 400.0000{{c}}, ~1331/768 = 951.4779{{c}}

	{{Optimal ET sequence\|legend=0\| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }}		{{Optimal ET sequence\|legend=0\| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }}

	Badness (~~Smith~~): 2.~~70 × 10<sup>-3</sup>~~		Badness (Sintel): 0.613

	=== Trilobite ===		=== Trilobite ===
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	Subgroup-val mapping: {{mapping\| 3 0 8 42 \| 0 2 1 -13 }}		Subgroup-val mapping: {{mapping\| 3 0 8 42 \| 0 2 1 -13 }}

	Optimal ~~tuning (POTE)~~: ~121/96 = 400.0000{{c}}, ~1331/768 = ~~950~~.~~7810~~{{c}}		Optimal tunings:
			* WE: ~121/96 = 400.0489{{c}}, ~1331/768 = 950.8972{{c}}
			* CWE: ~121/96 = 400.0000{{c}}, ~1331/768 = 951.7766{{c}}

	{{Optimal ET sequence\|legend=0\| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }}		{{Optimal ET sequence\|legend=0\| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }}

	Badness (~~Smith~~): 1.~~65 × 10<sup>-3</sup>~~		Badness (Sintel): 0.724

	[[Category:Commatic realms]]		[[Category:Commatic realms]]
	[[Category:The Nexus\| ]] <!-- main article -->		[[Category:The Nexus\| ]] <!-- main article -->
	[[Category:Nexus]]		[[Category:Nexus]]

FloraC: Merge; fix typo

2026-09-17T08:17:18Z

Merge; fix typo

@@ Line 56: / Line 56: @@
 == Rank-2 temperaments ==
-Rank-2 temperaments in the Nexus include [[septienenalimmal clan #Hemiennealimmal|hemiennealimmal]], [[misty family #Hemimist|hemimist]], [[schismatic family #Hemiterm|hemiterm]], [[schismatic family #Altinex|altinex]], [[canopic clan #Mirkat|mirkat]], [[kleismic family #Tritikleismic|tritikleismic]], [[vulture family #Terture|terture]], and [[landscape microtemperaments #Avicenna|avicenna]].
+Rank-2 temperaments in the Nexus include [[septiennealimmal clan #Hemiennealimmal|hemiennealimmal]], [[misty family #Hemimist|hemimist]], [[schismatic family #Hemiterm|hemiterm]], [[schismatic family #Altinex|altinex]], [[canopic clan #Mirkat|mirkat]], [[kleismic family #Tritikleismic|tritikleismic]], [[vulture family #Terture|terture]], and [[landscape microtemperaments #Avicenna|avicenna]].
 Considered below is the 2.3.11-subgroup temperament tribilo.
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 [[Badness]] (Sintel): 0.127
 [[Category:Commatic realms]]
 [[Category:The Nexus| ]] <!-- main article -->
 [[Category:Nexus]]

FloraC: - duplicate data; various cleanup

2026-09-17T08:14:19Z

- duplicate data; various cleanup

← Older revision		Revision as of 08:14, 17 September 2026
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	== Rank-4 temperaments ==		== Rank-4 temperaments ==
	~~{{main\|~~ Nexus ~~family }}~~		See [[Catalog of rank-4 temperaments #Nexus (1771561/1769472)]].

	The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.		The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.

	~~=== Nexus ===~~

	~~The parent temperament for the Nexus is Nexus temperament itself. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.~~

	~~Subgroup: 2.3.5.7.11~~

	~~[[Comma list]]: [[1771561/1769472]]~~

	~~[[Mapping]]: [{{val\| 3 0 0 0 8}}, {{val\| 0 2 0 0 1}}, {{val\| 0 0 1 0 0}}, {{val\| 0 0 0 1 0}}]~~

	~~Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1~~

	~~[[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966~~

	~~{{Optimal ET sequence\|legend=1\| 9, 15, 24, 33cd, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}~~

	~~[[Badness]]: 0.588 × 10<sup>-6</sup>~~

	== Rank-3 temperaments ==		== Rank-3 temperaments ==
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	Temperaments not discussed here include:		Temperaments not discussed here include:
	* ''[[Tyr]]''~~, {~~3025/3024~~, 102487/102400}~~ → [[~~Lehmerismic temperaments~~ #Tyr]]		* ''[[Tyr]]'' (+3025/3024) → [[Landscape family #Tyr]]

	=== Schisnex ===		=== Schisnex ===
	~~This temperament~~ adds the [[~~schisma~~]] to the list of tempered out ~~commas on account of~~ the ~~schisma being an unnoticeable comma~~ for ~~adding the 5-limit to the mix~~.		Named by [[Aura]] in 2021, schisnex adds the [[nexus comma]] to the list of commas tempered out. Thus the generator for [[7/1\|7]] is indepedent.

	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 32805/32768, 1771561/1769472		[[Comma list]]: 32805/32768, 1771561/1769472

	~~[[Mapping]]: [~~{{~~val~~\| 3 0 45 0 8 ~~}}, {{val~~\| 0 2 -16 0 1 ~~}}, {{val~~\| 0 0 0 1 0 }}]		{{Mapping\|legend=1\| 3 0 45 0 8 \| 0 2 -16 0 1 \| 0 0 0 1 0 }}
			: mapping generators: ~121/96, ~1331/768, ~7

	[[~~POTE generator~~]]s: ~1331/768 = 950.~~8701~~, ~7/4 = 968.~~5689~~		[[Optimal tuning]]s:
			* [[WE]]: ~121/96 = 400.0305{{c}}, ~1331/768 = 950.9426{{c}}, ~7/4 = 968.6428{{c}}
			: [[error map]]: {{val\| +0.092 -0.070 -0.022 -0.000 -0.131 }}
			* [[CWE]]: ~121/96 = 400.0000{{c}}, ~1331/768 = 950.8678{{c}}, ~7/4 = 968.6270{{c}}
			: error map: {{val\| 0.000 -0.219 -0.199 -0.199 -0.450 }}

	{{Optimal ET sequence\|legend=1\| 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce }}		{{Optimal ET sequence\|legend=1\| 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce, 5703bbcddeeee }}

	[[Badness]]: 5.~~155 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 6.19

	=== Nexiquart ===		=== Nexiquart ===
	This temperament can be seen as adding the [[quartisma]] to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix.		This temperament can be seen as adding the [[quartisma]] to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix.

	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 19712/19683, 1771561/1769472		[[Comma list]]: 19712/19683, 1771561/1769472

	~~[[Mapping]]: [~~{{~~val~~\| 3 0 0 -32 8 ~~}}, {{val~~\| 0 2 0 17 1 ~~}}, {{val~~\| 0 0 1 0 0 }}]		{{Mapping\|legend=1\| 3 0 0 -32 8 \| 0 2 0 17 1 \| 0 0 1 0 0 }}
			: mapping generators: ~121/96, ~1331/768, ~5

	[[~~POTE generator~~]]s: ~1331/768 = 951.~~1077~~, ~5/4 = 386.~~3748~~		[[Optimal tuning]]s:
			* [[WE]]: ~121/96 = 399.9912{{c}}, ~1331/768 = 951.0868{{c}}, ~5/4 = 386.3663{{c}}
			: [[error map]]: {{val\| -0.026 +0.219 -0.000 -0.069 -0.301 }}
			* [[CWE]]: ~121/96 = 400.0000{{c}}, ~1331/768 = 951.1062{{c}}, ~5/4 = 386.3573{{c}}
			: error map: {{val\| 0.000 +0.257 +0.044 -0.021 -0.212 }}

	{{Optimal ET sequence\|legend=1\| 24, 48d, 87d, 111, 159, 246, 270, 1215, 1485, 1755, 2025, 2295b }}		{{Optimal ET sequence\|legend=1\| 24, 48d, 87d, 111, 159, 246, 270, 1215, 1485, 1755, 2025, 2295b }}

	[[Badness]]: 6.~~275 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 7.54

	== Rank-2 temperaments ==		== Rank-2 temperaments ==
	Rank-2 temperaments in the Nexus include [[~~Ragismic microtemperaments~~ #Hemiennealimmal\|hemiennealimmal]], [[~~Misty~~ family #Hemimist\|hemimist]], [[~~Schismatic~~ family #Hemiterm\|hemiterm]], [[~~Schismatic~~ family #Altinex\|altinex]], [[~~Mirkwai~~ clan #Mirkat\|mirkat]], [[~~Kleismic~~ family #Tritikleismic\|tritikleismic]], [[~~Landscape microtemperaments~~ #Terture\|terture]], and [[~~Landscape~~ microtemperaments #Avicenna\|avicenna]].		Rank-2 temperaments in the Nexus include [[septienenalimmal clan #Hemiennealimmal\|hemiennealimmal]], [[misty family #Hemimist\|hemimist]], [[schismatic family #Hemiterm\|hemiterm]], [[schismatic family #Altinex\|altinex]], [[canopic clan #Mirkat\|mirkat]], [[kleismic family #Tritikleismic\|tritikleismic]], [[vulture family #Terture\|terture]], and [[landscape microtemperaments #Avicenna\|avicenna]].

	Considered below is the 2.3.11 subgroup temperament tribilo.		Considered below is the 2.3.11-subgroup temperament tribilo.

	=== Tribilo ===		=== Tribilo ===
	~~{{Main\| Nexus clan }}~~		Tribilo is the pure rank-2 2.3.11-subgroup temperament that tempers out the nexus comma – its name comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]].

	~~Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma – its name comes from the nexus comma being referred to as the "tribilo comma" in~~ [[~~color notation~~]].		[[Subgroup]]: 2.3.11

	~~Subgroup~~: 2.3.11

	[[Comma list]]: 1771561/1769472		[[Comma list]]: 1771561/1769472

	~~[[Sval]] [[mapping]]: [~~{{~~val~~\| 3 0 8 ~~}}, {{val~~\| 0 2 1 }}]		{{Mapping\|legend=2\| 3 0 8 \| 0 2 1 }}
			: mapping generators: ~121/96, ~1331/768
	~~Sval~~ mapping generators: ~121/96, ~1331/768

	[[~~POTE generator~~]]: ~1331/768 = 950.~~9518~~		[[Optimal tuning]]s:
			* [[WE]]: ~121/96 = 400.0154{{c}}, ~1331/768 = 950.9883{{c}}
			* [[CWE]]: ~121/96 = 400.0000{{c}}, ~1331/768 = 950.9685{{c}}

	{{Optimal ET sequence\|legend=1\| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }}		{{Optimal ET sequence\|legend=1\| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }}

	Badness:		[[Badness]] (Sintel): 0.127

	[[Category:Commatic realms]]		[[Category:Commatic realms]]
	[[Category:The Nexus\| ]] <!-- main article -->		[[Category:The Nexus\| ]] <!-- main article -->
	[[Category:Nexus]]		[[Category:Nexus]]

VectorGraphics at 04:41, 12 June 2025

2025-06-12T04:41:12Z

← Older revision		Revision as of 04:41, 12 June 2025
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	Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1		Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1

	~~{{Multival\|legend=1\|rank=4\| 6 0 0 3 -16 }}~~

	[[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966		[[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966
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	[[Mapping]]: [{{val\| 3 0 45 0 8 }}, {{val\| 0 2 -16 0 1 }}, {{val\| 0 0 0 1 0 }}]		[[Mapping]]: [{{val\| 3 0 45 0 8 }}, {{val\| 0 2 -16 0 1 }}, {{val\| 0 0 0 1 0 }}]

	~~{{Multival\|legend=1\|rank=3\| 0 6 0 -48 0 -3 -90 0 16 -173 }}~~

	[[POTE generator]]s: ~1331/768 = 950.8701, ~7/4 = 968.5689		[[POTE generator]]s: ~1331/768 = 950.8701, ~7/4 = 968.5689
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	[[Mapping]]: [{{val\| 3 0 0 -32 8 }}, {{val\| 0 2 0 17 1 }}, {{val\| 0 0 1 0 0 }}]		[[Mapping]]: [{{val\| 3 0 0 -32 8 }}, {{val\| 0 2 0 17 1 }}, {{val\| 0 0 1 0 0 }}]

	~~{{Multival\|legend=1\|rank=3\| 6 0 0 -51 -3 0 -64 16 0 -168 }}~~

	[[POTE generator]]s: ~1331/768 = 951.1077, ~5/4 = 386.3748		[[POTE generator]]s: ~1331/768 = 951.1077, ~5/4 = 386.3748

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

" to "{{Technical data page}}"

2025-04-13T13:45:49Z

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

← Older revision		Revision as of 13:45, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	'''The Nexus''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[nexus comma]] – the unnoticeable comma with the ratio 1771561/1769472, and a monzo of {{monzo\|-16 -3 0 0 6}}. Among the known branches of this collection are nexus, schisnex, nexiquart, altinex, and tribilo.		'''The Nexus''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[nexus comma]] – the unnoticeable comma with the ratio 1771561/1769472, and a monzo of {{monzo\|-16 -3 0 0 6}}. Among the known branches of this collection are nexus, schisnex, nexiquart, altinex, and tribilo.

BudjarnLambeth: {{Technical data page}}

2025-04-13T10:38:09Z

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

← Older revision		Revision as of 10:38, 13 April 2025
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			{{Technical data page}}<br><br>
	'''The Nexus''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[nexus comma]] – the unnoticeable comma with the ratio 1771561/1769472, and a monzo of {{monzo\|-16 -3 0 0 6}}. Among the known branches of this collection are nexus, schisnex, nexiquart, altinex, and tribilo.		'''The Nexus''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[nexus comma]] – the unnoticeable comma with the ratio 1771561/1769472, and a monzo of {{monzo\|-16 -3 0 0 6}}. Among the known branches of this collection are nexus, schisnex, nexiquart, altinex, and tribilo.

BudjarnLambeth: /* Rank-4 temperaments */

2024-02-24T06:06:10Z

Rank-4 temperaments

← Older revision		Revision as of 06:06, 24 February 2024
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	== Rank-4 temperaments ==		== Rank-4 temperaments ==
	{{main\| Nexus family }}		{{main\| Nexus family }}


	The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.		The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.

BudjarnLambeth: /* Rank-4 temperaments */

2024-02-24T06:06:02Z

Rank-4 temperaments

← Older revision		Revision as of 06:06, 24 February 2024
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	== Rank-4 temperaments ==		== Rank-4 temperaments ==
			{{main\| Nexus family }}


	The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.		The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.
	~~{{main\| Nexus family }}~~

	=== Nexus ===		=== Nexus ===

BudjarnLambeth: Made heading style consistent with the rest of the wiki

2024-02-24T06:05:36Z

Made heading style consistent with the rest of the wiki

← Older revision		Revision as of 06:05, 24 February 2024
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	Because the nexus comma is the difference between (121/96)<sup>3</sup> and 2/1, all nexus temperaments divide 2/1 into three equal parts of (approximately) 400 cents.		Because the nexus comma is the difference between (121/96)<sup>3</sup> and 2/1, all nexus temperaments divide 2/1 into three equal parts of (approximately) 400 cents.

	= Rank-4 temperaments =		== Rank-4 temperaments ==
	The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.		The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.
			{{main\| Nexus family }}

	== Nexus ==		=== Nexus ===
	~~{{main\| Nexus family }}~~

	The parent temperament for the Nexus is Nexus temperament itself. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.		The parent temperament for the Nexus is Nexus temperament itself. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.
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	[[Badness]]: 0.588 × 10<sup>-6</sup>		[[Badness]]: 0.588 × 10<sup>-6</sup>

	= Rank-3 temperaments =		== Rank-3 temperaments ==
	From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived.		From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived.

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	* ''[[Tyr]]'', {3025/3024, 102487/102400} → [[Lehmerismic temperaments #Tyr]]		* ''[[Tyr]]'', {3025/3024, 102487/102400} → [[Lehmerismic temperaments #Tyr]]

	== Schisnex ==		=== Schisnex ===
	This temperament adds the [[schisma]] to the list of tempered out commas on account of the schisma being an unnoticeable comma for adding the 5-limit to the mix.		This temperament adds the [[schisma]] to the list of tempered out commas on account of the schisma being an unnoticeable comma for adding the 5-limit to the mix.

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	[[Badness]]: 5.155 × 10<sup>-3</sup>		[[Badness]]: 5.155 × 10<sup>-3</sup>

	== Nexiquart ==		=== Nexiquart ===
	This temperament can be seen as adding the [[quartisma]] to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix.		This temperament can be seen as adding the [[quartisma]] to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix.

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	[[Badness]]: 6.275 × 10<sup>-3</sup>		[[Badness]]: 6.275 × 10<sup>-3</sup>

	= Rank-2 temperaments =		== Rank-2 temperaments ==
	Rank-2 temperaments in the Nexus include [[Ragismic microtemperaments #Hemiennealimmal\|hemiennealimmal]], [[Misty family #Hemimist\|hemimist]], [[Schismatic family #Hemiterm\|hemiterm]], [[Schismatic family #Altinex\|altinex]], [[Mirkwai clan #Mirkat\|mirkat]], [[Kleismic family #Tritikleismic\|tritikleismic]], [[Landscape microtemperaments #Terture\|terture]], and [[Landscape microtemperaments #Avicenna\|avicenna]].		Rank-2 temperaments in the Nexus include [[Ragismic microtemperaments #Hemiennealimmal\|hemiennealimmal]], [[Misty family #Hemimist\|hemimist]], [[Schismatic family #Hemiterm\|hemiterm]], [[Schismatic family #Altinex\|altinex]], [[Mirkwai clan #Mirkat\|mirkat]], [[Kleismic family #Tritikleismic\|tritikleismic]], [[Landscape microtemperaments #Terture\|terture]], and [[Landscape microtemperaments #Avicenna\|avicenna]].

	Considered below is the 2.3.11 subgroup temperament tribilo.		Considered below is the 2.3.11 subgroup temperament tribilo.

	== Tribilo ==		=== Tribilo ===
	{{Main\| Nexus clan }}		{{Main\| Nexus clan }}

Aura at 18:44, 17 June 2023

2023-06-17T18:44:07Z

← Older revision		Revision as of 18:44, 17 June 2023
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	== Tribilo ==		== Tribilo ==
	{{Main\| ~~Tribilo family~~ }}		{{Main\| Nexus clan }}

	Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma – its name comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]].		Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma – its name comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]].

The Nexus - Revision history

FloraC: Finalize the data

FloraC: Merge; fix typo

FloraC: - duplicate data; various cleanup

VectorGraphics at 04:41, 12 June 2025

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

BudjarnLambeth: {{Technical data page}}

BudjarnLambeth: /* Rank-4 temperaments */

BudjarnLambeth: /* Rank-4 temperaments */

BudjarnLambeth: Made heading style consistent with the rest of the wiki

Aura at 18:44, 17 June 2023

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

" to "{{Technical data page}}"