Dicot family - Revision history

FloraC: Restore key category

2026-10-23T13:25:58Z

Restore key category

← Older revision		Revision as of 13:25, 23 October 2026
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	[[Category:Dicot family\| ]] <!-- main article -->		[[Category:Dicot family\| ]] <!-- main article -->
			[[Category:Dicot\| ]] <!-- key article -->
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Catalogs of rank-2 temperaments]]		[[Category:Catalogs of rank-2 temperaments]]

FloraC: /* Dicot */ - links to geryon ({8/7, 25/21}, deleted), replace with ternary and quad

2026-10-20T09:45:17Z

Dicot: - links to geryon ({8/7, 25/21}, deleted), replace with ternary and quad

← Older revision		Revision as of 09:45, 20 October 2026
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* ''[[~~Geryon~~]]'' → [[Very low accuracy temperaments #~~Geryon~~\|Very low accuracy temperaments]]		* ''[[Ternary]]'' → [[Very low accuracy temperaments #Ternary\|Very low accuracy temperaments]]
			* ''[[Quad]]'' → [[Very low accuracy temperaments #Quad\|Very low accuracy temperaments]]
	* ''[[Jamesbond]]'' → [[Whitewood family #Jamesbond\|Whitewood family]]		* ''[[Jamesbond]]'' → [[Whitewood family #Jamesbond\|Whitewood family]]

FloraC: Text replacement - "Gencom mapping: {{mapping| " to "{{Mapping|legend=4| "

2026-09-30T17:43:25Z

Text replacement - "Gencom mapping: {{mapping| " to "{{Mapping|legend=4| "

← Older revision		Revision as of 17:43, 30 September 2026
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	Subgroup val mapping: {{mapping\| 1 1 2 2 \| 0 2 1 5 }}		Subgroup val mapping: {{mapping\| 1 1 2 2 \| 0 2 1 5 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 1 2 0 2 \| 0 2 1 0 5 }}		{{Mapping\|legend=4\| 1 1 2 0 2 \| 0 2 1 0 5 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup val mapping: {{mapping\| 1 1 2 2 4 \| 0 2 1 5 -1 }}		Subgroup val mapping: {{mapping\| 1 1 2 2 4 \| 0 2 1 5 -1 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 1 2 0 2 4 \| 0 2 1 0 5 -1 }}		{{Mapping\|legend=4\| 1 1 2 0 2 4 \| 0 2 1 0 5 -1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:06Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:33, 24 September 2026
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	Comma list: 15/14, 22/21, 25/24		Comma list: 15/14, 22/21, 25/24

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 2 2 \| 0 2 1 3 5 }}		{{Mapping\|legend=0\| 1 1 2 2 2 \| 0 2 1 3 5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 15/14, 25/24, 33/32		Comma list: 15/14, 25/24, 33/32

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 2 4 \| 0 2 1 3 -2 }}		{{Mapping\|legend=0\| 1 1 2 2 4 \| 0 2 1 3 -2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 15/14, 25/24, 33/32, 40/39		Comma list: 15/14, 25/24, 33/32, 40/39

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 2 4 4 \| 0 2 1 3 -2 -1 }}		{{Mapping\|legend=0\| 1 1 2 2 4 4 \| 0 2 1 3 -2 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 21/20, 25/24, 33/32		Comma list: 21/20, 25/24, 33/32

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 3 4 \| 0 2 1 -1 -2 }}		{{Mapping\|legend=0\| 1 1 2 3 4 \| 0 2 1 -1 -2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 14/13, 21/20, 25/24, 33/32		Comma list: 14/13, 21/20, 25/24, 33/32

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 3 4 4 \| 0 2 1 -1 -2 -1 }}		{{Mapping\|legend=0\| 1 1 2 3 4 4 \| 0 2 1 -1 -2 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 28/27, 35/33		Comma list: 25/24, 28/27, 35/33

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 1 2 \| 0 2 1 6 5 }}		{{Mapping\|legend=0\| 1 1 2 1 2 \| 0 2 1 6 5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 45/44, 64/63		Comma list: 25/24, 45/44, 64/63

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 4 2 \| 0 2 1 -4 5 }}		{{Mapping\|legend=0\| 1 1 2 4 2 \| 0 2 1 -4 5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 40/39, 45/44, 64/63		Comma list: 25/24, 40/39, 45/44, 64/63

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 4 2 4 \| 0 2 1 -4 5 -1 }}		{{Mapping\|legend=0\| 1 1 2 4 2 4 \| 0 2 1 -4 5 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 22/21, 25/24, 33/32		Comma list: 22/21, 25/24, 33/32

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 4 4 \| 0 2 1 -4 -2 }}		{{Mapping\|legend=0\| 1 1 2 4 4 \| 0 2 1 -4 -2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 22/21, 25/24, 33/32, 40/39		Comma list: 22/21, 25/24, 33/32, 40/39

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 4 4 4 \| 0 2 1 -4 -2 -1 }}		{{Mapping\|legend=0\| 1 1 2 4 4 4 \| 0 2 1 -4 -2 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 35/33, 64/63		Comma list: 25/24, 35/33, 64/63

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 4 5 \| 0 2 1 -4 -5 }}		{{Mapping\|legend=0\| 1 1 2 4 5 \| 0 2 1 -4 -5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 35/33, 40/39, 64/63		Comma list: 25/24, 35/33, 40/39, 64/63

	~~Mapping:~~ {{~~mapping~~\| 1 1 2 4 5 4 \| 0 2 1 -4 -5 -1 }}		{{Mapping\|legend=0\| 1 1 2 4 5 4 \| 0 2 1 -4 -5 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 45/44, 49/48		Comma list: 25/24, 45/44, 49/48

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

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 45/44, 49/48, 91/90		Comma list: 25/24, 45/44, 49/48, 91/90

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

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 33/32, 49/48		Comma list: 25/24, 33/32, 49/48

	~~Mapping:~~ {{~~mapping~~\| 2 0 3 4 10 \| 0 2 1 1 -2 }}		{{Mapping\|legend=0\| 2 0 3 4 10 \| 0 2 1 1 -2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 35/33, 49/48		Comma list: 25/24, 35/33, 49/48

	~~Mapping:~~ {{~~mapping~~\| 2 0 3 4 7 \| 0 2 1 1 0 }}		{{Mapping\|legend=0\| 2 0 3 4 7 \| 0 2 1 1 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 25/24, 45/44, 99/98		Comma list: 25/24, 45/44, 99/98

	~~Mapping:~~ {{~~mapping~~\| 1 -1 1 -3 -3 \| 0 4 2 9 10 }}		{{Mapping\|legend=0\| 1 -1 1 -3 -3 \| 0 4 2 9 10 }}

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

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

	Optimal tunings:		Optimal tunings:

FloraC: Recategorize

2026-08-14T11:54:51Z

Recategorize

← Older revision		Revision as of 11:54, 14 August 2026
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	Badness (Sintel): 1.54		Badness (Sintel): 1.54

			[[Category:Dicot family\| ]] <!-- main article -->
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:~~Dicot family\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

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]]