Dicot family - Revision history

FloraC: /* Dicot */ update a link

2026-06-08T11:41:50Z

Dicot: update a link

← Older revision		Revision as of 11:41, 8 June 2026
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon\|Very low accuracy temperaments]]		* ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon\|Very low accuracy temperaments]]
	* ''[[Jamesbond]]'' → [[~~7th-octave temperaments~~ #Jamesbond\|~~7th-octave temperaments~~]]		* ''[[Jamesbond]]'' → [[Whitewood family #Jamesbond\|Whitewood family]]

	The rest are considered in each sections below.		The rest are considered in each sections below.

FloraC: Decanonicalize septimal dicot. - 2.3.5.11-subgroup eudicot (no need for explicit documentation if it's canonical)

2026-05-29T10:09:06Z

Decanonicalize septimal dicot. - 2.3.5.11-subgroup eudicot (no need for explicit documentation if it's canonical)

← Older revision		Revision as of 10:09, 29 May 2026
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	{{Mapping\|legend=1\| 1 1 2 \| 0 2 1 }}		{{Mapping\|legend=1\| 1 1 2 \| 0 2 1 }}

	: mapping generators: ~2, ~5/4		: mapping generators: ~2, ~5/4

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	=== Overview to extensions ===		=== Overview to extensions ===
	==== 7-limit extensions ====		==== 7-limit extensions ====
	The second comma of the ~~[[normal forms #Normal forms for commas\|normal~~ comma list]] defines which [[7-limit]] family member we are looking at. ~~Septimal dicot~~ adds [[36/35]], flattie adds [[21/20]], sharpie adds [[28/27]], and dichotic adds [[64/63]], all retaining the same period and generator.		The second comma of the comma list defines which [[7-limit]] family member we are looking at. Mujannabic adds [[36/35]], flattie adds [[21/20]], sharpie adds [[28/27]], and dichotic adds [[64/63]], all retaining the same period and generator.

	The dicot comma, 25/24, factors into the 7-limit as ([[49/48]])⋅([[50/49]]). Since [[49/48]] is the difference between [[8/7]] and [[7/6]], and [[50/49]] is the difference between [[7/5]] and [[10/7]], it makes sense to extend dicot to temper them all out, leading to decimal, a weak extension where the octave and twelfth are split in halves. Other weak extensions include sidi, which adds [[245/243]], and jamesbond, which adds [[16/15]]. Here sidi uses 14/9 as a generator, with two of them making up the combined [[5/2]][[~]][[12/5]] neutral tenth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.		The dicot comma, 25/24, factors into the 7-limit as ([[49/48]])⋅([[50/49]]). Since [[49/48]] is the difference between [[8/7]] and [[7/6]], and [[50/49]] is the difference between [[7/5]] and [[10/7]], it makes sense to extend dicot to temper them all out, leading to decimal, a weak extension where the octave and twelfth are split in halves. Other weak extensions include sidi, which adds [[245/243]], and jamesbond, which adds [[16/15]]. Here sidi uses 14/9 as a generator, with two of them making up the combined [[5/2]][[~]][[12/5]] neutral tenth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.
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	In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.		In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.

	An alternative identity is 25/24 = ([[33/32]])⋅([[100/99]]), and tempering out these commas leads to the 2.3.5.11 ~~version~~ of ~~eudicot~~.		An alternative identity is 25/24 = ([[33/32]])⋅([[100/99]]), and tempering out these commas leads to the 2.3.5.11-subgroup restriction of some of the temperaments below.

	=== ~~Dicot (~~2.3.5.11 subgroup) ===		=== 2.3.5.11 subgroup ===
	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

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	Badness (Sintel): 0.536		Badness (Sintel): 0.536

	==~~= Eudicot (2.3.5.11 subgroup) =~~==		== Mujannabic ==
	~~Subgroup: 2.3.5.11~~		Mujannabic extends dicot such that [[7/6]] and [[9/7]] are also conflated with 5/4~6/5. Although 5/4–6/5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the utility of this extension despite the relatively poor accuracy.

	~~Comma list: 25~~/~~24, 33~~/32

	~~Subgroup val mapping: {{mapping\| 1 1 2 4 \| 0 2 1 -2 }}~~

	~~Gencom mapping: {{mapping\| 1 1 2 0 4 \| 0 2 1 0 -2 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1209.224{{c}}, ~5/4 ~~= 347.612{{c}}~~
	* CWE: ~2 = 1200.000{{c}}, ~5/~~4 = 346.056{{c}}~~

	~~{{Optimal ET sequence\|legend=0\| 3, 4, 7, 45cceee }}~~

	~~Badness (Sintel): 0.493~~

	~~==== 2.3.~~5.~~11.13 subgroup ====~~
	~~Subgroup: 2.3.~~5~~.11.13~~

	~~Comma list: 25~~/~~24, 33~~/32, 40/39

	~~Subgroup val mapping: {{mapping\| 1 1 2 4 4 \| 0 2 1 -2 -1 }}~~

	~~Gencom mapping: {{mapping\| 1 1 2 0 4 4 \| 0 2 1 0 -2 -1 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1205.934{{c}}, ~5/~~4 = 349.530{{c}}~~
	* CWE: ~2 = 1200.~~000{{c}}, ~5/4 = 348.213{{c}}~~

	~~{{Optimal ET sequence\|legend=0\| 3, 4, 7 }}~~

	~~Badness (Sintel): 0~~.~~575~~

	~~== Septimal dicot ==~~
	~~{{Main\| Dicot }}~~

	~~Septimal~~ dicot ~~is the extension where~~ [[~~7/6~~]] ~~and [~~[~~9/7]] are also conflated into 5~~/~~4~6~~/5. ~~Although 5~~/~~4~6~~/~~5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the canonicity of this extension, despite the relatively poor accuracy~~.		Mujannabic was known as ''septimal dicot'' in earlier materials such as [[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Flattie ==		== Flattie ==
	This temperament used to be known as ''flat''. Unlike ~~septimal dicot~~ where 7/6 is added to the neutral third, here [[8/7]] is added instead.		This temperament used to be known as ''flat''. Unlike mujannabic where 7/6 is added to the neutral third, here [[8/7]] is added instead.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Overthink: /* 11-limit */ fix

2026-03-04T22:41:44Z

11-limit: fix

← Older revision		Revision as of 22:41, 4 March 2026
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1209.621{{c}}, ~14/11 = 772.376{{c}}		* WE: ~2 = 1209.621{{c}}, ~11/7 = 772.376{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~14/11 = 772.247{{c}}		* CWE: ~2 = 1200.000{{c}}, ~11/7 = 772.247{{c}}

	{{Optimal ET sequence\|legend=0\| 3, 11c, 14c }}		{{Optimal ET sequence\|legend=0\| 3, 11c, 14c }}

Xenllium at 21:28, 4 March 2026

2026-03-04T21:28:58Z

← Older revision		Revision as of 21:28, 4 March 2026
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	In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.		In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.

	An alternative identity is 25/24 = ([[33/32]])⋅([[100/99]]), and tempering out these commas leads to eudicot ~~(named by [[Xenllium]] in 2026)~~.		An alternative identity is 25/24 = ([[33/32]])⋅([[100/99]]), and tempering out these commas leads to the 2.3.5.11 version of eudicot.

	=== 2.3.5.11 subgroup ===		=== Dicot (2.3.5.11 subgroup) ===
	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

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	Badness (Sintel): 0.536		Badness (Sintel): 0.536

	=== Eudicot ===		=== Eudicot (2.3.5.11 subgroup) ===
	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

FloraC: - redundant category

2026-03-04T08:42:15Z

- redundant category

← Older revision		Revision as of 08:42, 4 March 2026
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Dicot family\| ]] <!-- main article -->		[[Category:Dicot family\| ]] <!-- main article -->
	~~[[Category:Dicot\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Review

2026-03-04T08:41:42Z

Review

← Older revision		Revision as of 08:41, 4 March 2026
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	In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.		In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.

	An alternative identity 25/24 = ([[33/32]])⋅([[100/99]]) ~~also makes sense to temper~~ out ~~in the 11-limit, leading~~ to ~~some undecimal extensions as~~ eudicot.		An alternative identity is 25/24 = ([[33/32]])⋅([[100/99]]), and tempering out these commas leads to eudicot (named by [[Xenllium]] in 2026).

	=== 2.3.5.11 ~~dicot~~ ===		=== 2.3.5.11 subgroup ===
	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

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	Badness (Sintel): 0.536		Badness (Sintel): 0.536

	=== ~~2.3.5.11 eudicot~~ ===		=== Eudicot ===
	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

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	* CWE: ~2 = 1200.000{{c}}, ~5/4 = 346.056{{c}}		* CWE: ~2 = 1200.000{{c}}, ~5/4 = 346.056{{c}}

	{{Optimal ET sequence\|legend=0\| 3, 4, 7 }}		{{Optimal ET sequence\|legend=0\| 3, 4, 7, 45cceee }}

	Badness (Sintel): 0.493		Badness (Sintel): 0.493
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	== Sidi ==		== Sidi ==
	Sidi tempers out 245/243, and splits 5/2~12/5 in two. Its ploidacot is beta-tetracot. This relates it to [[squares]], to which it can be used as a simpler alternative. 14edo in the 14c val can be used as a tuning, in which case it is identical to squares, however.		Sidi tempers out [[245/243]], and splits [[5/2]][[~]][[12/5]] in two. Its [[ploidacot]] is beta-tetracot. This relates it to [[squares]], to which it can be used as a simpler alternative. 14edo in the 14c val can be used as a tuning, in which case it is identical to squares, however.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Sida ==		== Sida ==
	~~Sida~~ is described as {{nowrap\|3 & 14c}} temperment, and tempers out 1323/1280 and 4000/3969. Its ploidacot is beta-tetracot.		Named by [[Xenllium]] in 2026, sida is described as the {{nowrap\| 3 & 14c }} temperment, and tempers out [[1323/1280]] and [[4000/3969]]. Its [[ploidacot]] is beta-tetracot, the same as [[#Sidi\|sidi]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	[[Comma list]]: 25/24, 1323/1280		[[Comma list]]: 25/24, 1323/1280

	{{Mapping\|legend=1\| 1 ~~3 3~~ 1 \| 0 -4 -2 5 }}		{{Mapping\|legend=1\| 1 -1 1 6 \| 0 4 2 -5 }}
			: mapping generators: ~2, ~32/21
	: mapping generators: ~2, ~21~~/16~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1209.021{{c}}, ~21~~/16~~ = ~~430~~.~~723~~{{c}}		* [[WE]]: ~2 = 1209.021{{c}}, ~32/21 = 778.298{{c}}
	: [[error map]]: {{val\| +9.021 +2.216 -20.696 -6.188 }}		: [[error map]]: {{val\| +9.021 +2.216 -20.696 -6.188 }}
	* [[CWE]]: ~2 = 1200.000{{c}}, ~21~~/16~~ = ~~427~~.~~215~~{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~32/21 = 772.785{{c}}
	: error map: {{val\| 0.000 -10.816 -40.744 -32.749 }}		: error map: {{val\| 0.000 -10.816 -40.744 -32.749 }}

	{{Optimal ET sequence\|legend=1\| 3~~, …~~, 11c, 14c }}		{{Optimal ET sequence\|legend=1\| 3, 11c, 14c, 45ccdd }}

	[[Badness]] (Sintel): 2.12		[[Badness]] (Sintel): 2.12
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1209.621{{c}}, ~14/11 = ~~431~~.~~245~~{{c}}		* WE: ~2 = 1209.621{{c}}, ~14/11 = 772.376{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~14/11 = ~~427~~.~~753~~{{c}}		* CWE: ~2 = 1200.000{{c}}, ~14/11 = 772.247{{c}}

	{{Optimal ET sequence\|legend=0\| 3~~, …~~, 11c, 14c }}		{{Optimal ET sequence\|legend=0\| 3, 11c, 14c }}

	Badness (Sintel): 1.54		Badness (Sintel): 1.54

Xenllium: New temperament: sida (3 & 11c)

2026-03-04T00:40:31Z

New temperament: sida (3 & 11c)

← Older revision		Revision as of 00:40, 4 March 2026
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	Badness (Sintel): 1.09		Badness (Sintel): 1.09

			== Sida ==
			Sida is described as {{nowrap\|3 & 14c}} temperment, and tempers out 1323/1280 and 4000/3969. Its ploidacot is beta-tetracot.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 25/24, 1323/1280

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

			: mapping generators: ~2, ~21/16

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1209.021{{c}}, ~21/16 = 430.723{{c}}
			: [[error map]]: {{val\| +9.021 +2.216 -20.696 -6.188 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~21/16 = 427.215{{c}}
			: error map: {{val\| 0.000 -10.816 -40.744 -32.749 }}

			{{Optimal ET sequence\|legend=1\| 3, …, 11c, 14c }}

			[[Badness]] (Sintel): 2.12

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 25/24, 33/32, 245/242

			Mapping: {{mapping\| 1 3 3 1 2 \| 0 -4 -2 5 4 }}

			Optimal tunings:
			* WE: ~2 = 1209.621{{c}}, ~14/11 = 431.245{{c}}
			* CWE: ~2 = 1200.000{{c}}, ~14/11 = 427.753{{c}}

			{{Optimal ET sequence\|legend=0\| 3, …, 11c, 14c }}

			Badness (Sintel): 1.54

	[[Category:Temperament families]]		[[Category:Temperament families]]

Xenllium at 22:57, 3 March 2026

2026-03-03T22:57:37Z

@@ Line 18: / Line 18: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1206.283{{c}}, ~6/5 = 350.420{{c}}
+* [[WE]]: ~2 = 1206.283{{c}}, ~5/4 = 350.420{{c}}
 : [[error map]]: {{val| +6.283 +5.167 -23.328 }}
 * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}}
@@ Line 46: / Line 46: @@
 In the 11-limit, we have the identity 25/24 = ([[45/44]])⋅([[55/54]]), so it makes sense to temper out all of them. This leads to the very natural subgroup temperament where [[11/9]]~[[27/22]] is mapped to the neutral third. As such, this is also the path that most of the septimal extensions take to get their 11-limit versions.
-=== 2.3.5.11 subgroup ===
+An alternative identity 25/24 = ([[33/32]])⋅([[100/99]]) also makes sense to temper out in the 11-limit, leading to some undecimal extensions as eudicot.
 Subgroup: 2.3.5.11
@@ Line 56: / Line 58: @@
 Optimal tunings:
-* WE: ~2 = 1206.750{{c}}, ~6/5 = 348.684{{c}}
+* WE: ~2 = 1206.750{{c}}, ~5/4 = 348.684{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~6/5 = 348.954{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~5/4 = 348.954{{c}}
 {{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }}
@@ Line 79: / Line 81: @@
 Badness (Sintel): 0.536
 == Septimal dicot ==

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:18:30Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:18, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Dicot family\| ]] <!-- main article -->		[[Category:Dicot family\| ]] <!-- main article -->
	[[Category:Dicot\| ]] <!-- key article -->		[[Category:Dicot\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Dicot has an article now

2025-10-21T12:15:56Z

Dicot has an article now

← Older revision		Revision as of 12:15, 21 October 2025
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	== Dicot ==		== Dicot ==
	{{~~Redirect~~\|~~Dicot\|the ploidacot signature\|Ploidacot/~~Dicot}}		{{Main\| Dicot }}

	The head of this family, dicot, is [[generator\|generated]] by a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap\|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}. Its [[ploidacot]] is the same as its name, dicot.		The head of this family, dicot, is [[generator\|generated]] by a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap\|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}. Its [[ploidacot]] is the same as its name, dicot.
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	== Septimal dicot ==		== Septimal dicot ==
			{{Main\| Dicot }}

	Septimal dicot is the extension where [[7/6]] and [[9/7]] are also conflated into 5/4~6/5. Although 5/4~6/5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the canonicity of this extension, despite the relatively poor accuracy.		Septimal dicot is the extension where [[7/6]] and [[9/7]] are also conflated into 5/4~6/5. Although 5/4~6/5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the canonicity of this extension, despite the relatively poor accuracy.