Dicot - Revision history

FloraC: No septimal dicot anymore!

2026-05-29T10:11:53Z

No septimal dicot anymore!

← Older revision		Revision as of 10:11, 29 May 2026
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	'''Dicot''' is an [[exotemperament]] that [[tempering out\|tempers out]] [[25/24]]. It is also the first fully prototypical [[ploidacot/Dicot\|dicot]] temperament. It tempers [[6/5]] and [[5/4]] into the same [[neutral third]] interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of [[5-limit]] harmonies without fully representing them in its greater accuracy, with [[mos scale]]s [[3L 4s]] and [[7L 3s]].		'''Dicot''' is an [[exotemperament]] that [[tempering out\|tempers out]] [[25/24]]. It is also the first fully prototypical [[ploidacot/Dicot\|dicot]] temperament. It tempers [[6/5]] and [[5/4]] into the same [[neutral third]] interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of [[5-limit]] harmonies without fully representing them in its greater accuracy, with [[mos scale]]s [[3L 4s]] and [[7L 3s]].

	It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.		It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], called ''[[mujannabic]]'', though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.

	Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the [[6:7:8]] chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.		Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the [[6:7:8]] chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.
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	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

			[[Category:Dicot\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Exotemperaments]]		[[Category:Exotemperaments]]
	[[Category:Dicot family]]		[[Category:Dicot family]]
	~~[[Category:Mint temperaments]]~~
	~~[[Category:Keemic temperaments]]~~

Overthink: add it in the infobox then

2026-05-22T15:07:29Z

add it in the infobox then

← Older revision		Revision as of 15:07, 22 May 2026
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	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Dicot		\| Title = Dicot
	\| Subgroups = 2.3.5		\| Subgroups = 2.3.5, 2.3.5.11
	\| Comma basis = [[25/24]]		\| Comma basis = [[25/24]] (2.3.5);<br>[[25/24]], [[45/44]] (2.3.5.11)
	\| Edo join 1 = 3 \| Edo join 2 = 7		\| Edo join 1 = 7 \| Edo join 2 = 10
	\| Mapping = 1; 2 1		\| Mapping = 1; 2 1 5
	\| Generators = 6/5 \| Generators tuning = 351.1 \| Optimization method = CWE		\| Generators = 6/5 \| Generators tuning = 351.1 \| Optimization method = CWE
	\| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]		\| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]
	\| Pergen = (P8, P5/2)		\| Pergen = (P8, P5/2)
	\| Odd limit 1 = 5 \| Mistuning 1 = 35.3 \| Complexity 1 = 3		\| Odd limit 1 = 5 \| Mistuning 1 = 35.3 \| Complexity 1 = 3
	\| Odd limit 2 = 5~~-limit 9~~ \| Mistuning 2 = 35.3 \| Complexity 2 = 7		\| Odd limit 2 = 2.3.5.11 15 \| Mistuning 2 = 35.3 \| Complexity 2 = 7
	}}		}}
	{{About\|the regular temperament\|the ploidacot signature\|Ploidacot/Dicot}}		{{About\|the regular temperament\|the ploidacot signature\|Ploidacot/Dicot}}

FloraC: /* Tunings */ + basic norm-based tunings

2026-05-22T07:45:47Z

Tunings: + basic norm-based tunings

@@ Line 42: / Line 42: @@
 == Tunings ==
 === Norm-based tunings ===
-{{Todo|complete section|inline=1}}
+{| class="wikitable mw-collapsible mw-collapsed"
 === Tuning spectrum ===

Overthink: /* Tuning spectrum */ more edo tunings; links

2026-05-21T01:05:25Z

Tuning spectrum: more edo tunings; links

← Older revision		Revision as of 01:05, 21 May 2026
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	\| '''[[4edo\|1\4]]''' \|\| \|\| '''300.000''' \|\| '''Lower bound of 5-odd-limit diamond monotone'''		\| '''[[4edo\|1\4]]''' \|\| \|\| '''300.000''' \|\| '''Lower bound of 5-odd-limit diamond monotone'''
	\|-		\|-
	\| \|\| 5/3 \|\| 315.641 \|\| Full comma		\| \|\| [[5/3]] \|\| 315.641 \|\| Full comma
	\|-		\|-
	\| \|\| 9/5 \|\| 339.199 \|\| 2/3-comma		\| [[11edo\|3\11]] \|\| \|\| 327.273 \|\| 11c val
			\|-
			\| \|\| [[9/5]] \|\| 339.199 \|\| 2/3-comma
	\|-		\|-
	\| '''[[7edo\|2\7]]''' \|\| \|\| '''342.857''' \|\| '''Lower bound of 5-limit 9-odd-limit diamond monotone'''		\| '''[[7edo\|2\7]]''' \|\| \|\| '''342.857''' \|\| '''Lower bound of 5-limit 9-odd-limit diamond monotone'''
	\|-		\|-
	\| \|\| 27/20 \|\| 343.910 \|\| 3/5-comma		\| \|\| [[27/20]] \|\| 343.910 \|\| 3/5-comma
	\|-		\|-
	\| [[24edo\|7\24]] \|\| \|\| 350.000 \|\| 24c val		\| [[24edo\|7\24]] \|\| \|\| 350.000 \|\| 24c val
	\|-		\|-
	\| \|\| 3/2 \|\| 350.978 \|\| 1/2-comma		\| \|\| [[3/2]] \|\| 350.978 \|\| 1/2-comma
	\|-		\|-
	\| [[17edo\|5\17]] \|\| \|\| 352.941 \|\|		\| [[17edo\|5\17]] \|\| \|\| 352.941 \|\|
	\|-		\|-
	\| \|\| 45/32 \|\| 358.045 \|\| 2/5-comma		\| \|\| [[45/32]] \|\| 358.045 \|\| 2/5-comma
	\|-		\|-
	\| [[10edo\|3\10]] \|\| \|\| 360.000 \|\|		\| [[10edo\|3\10]] \|\| \|\| 360.000 \|\|
	\|-		\|-
	\| \|\| 15/8 \|\| 362.756 \|\| 1/3-comma		\| \|\| [[15/8]] \|\| 362.756 \|\| 1/3-comma
			\|-
			\| [[13edo\|4\13]] \|\| \|\| 369.231 \|\|
	\|-		\|-
	\| \|\| 5/4 \|\| 386.314 \|\| Untempered tuning		\| \|\| [[5/4]] \|\| 386.314 \|\| Untempered tuning
	\|-		\|-
	\| '''[[3edo\|1\3]]''' \|\| \|\| '''400.000''' \|\| '''Upper bound of 5-odd-limit, <br>and 5-limit 9-odd-limit diamond monotone'''		\| '''[[3edo\|1\3]]''' \|\| \|\| '''400.000''' \|\| '''Upper bound of 5-odd-limit, <br>and 5-limit 9-odd-limit diamond monotone'''

Overthink: link

2026-02-09T22:53:35Z

link

← Older revision		Revision as of 22:53, 9 February 2026
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	It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.		It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.

	Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.		Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the [[6:7:8]] chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.

	For technical data, see [[Dicot family #Dicot]].		For technical data, see [[Dicot family #Dicot]].

FloraC at 10:19, 9 February 2026

2026-02-09T10:19:37Z

← Older revision		Revision as of 10:19, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Dicot		\| Title = Dicot
	\| Subgroups = 2.3.5		\| Subgroups = 2.3.5
	\| Comma basis = [[25/24]]		\| Comma basis = [[25/24]]
	\| Edo join 1 = 3 \| Edo join 2 = 7		\| Edo join 1 = 3 \| Edo join 2 = 7
			\| Mapping = 1; 2 1
	\| Generators = 6/5 \| Generators tuning = 351.1 \| Optimization method = CWE		\| Generators = 6/5 \| Generators tuning = 351.1 \| Optimization method = CWE
	\| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]		\| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]
	~~\| Mapping = 1; 2 1~~
	\| Pergen = (P8, P5/2)		\| Pergen = (P8, P5/2)
	\| Odd limit 1 = 5 \| Mistuning 1 = 35.3 \| Complexity 1 = 3		\| Odd limit 1 = 5 \| Mistuning 1 = 35.3 \| Complexity 1 = 3

FloraC: Cleanup on infobox

2026-02-09T09:06:50Z

Cleanup on infobox

← Older revision		Revision as of 09:06, 9 February 2026
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	\| Comma basis = [[25/24]]		\| Comma basis = [[25/24]]
	\| Edo join 1 = 3 \| Edo join 2 = 7		\| Edo join 1 = 3 \| Edo join 2 = 7
	\| ~~Generator~~ = 6/5 \| ~~Generator~~ tuning = 351.~~086~~ \| Optimization method = CWE		\| Generators = 6/5 \| Generators tuning = 351.1 \| Optimization method = CWE
	\| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]		\| MOS scales = [[3L 1s]], [[3L 4s]], [[7L 3s]]
	\| Mapping = 1; 2 1		\| Mapping = 1; 2 1
	\| Pergen = (P8, P5/2)		\| Pergen = (P8, P5/2)
	\| Odd limit 1 = 5 \| Mistuning 1 = 35.3 \| Complexity 1 = 3		\| Odd limit 1 = 5 \| Mistuning 1 = 35.3 \| Complexity 1 = 3
	\| Odd limit 2 = (5-limit) 9 \| Mistuning 2 = 35.3 \| Complexity 2 = 7		\| Odd limit 2 = 5-limit 9 \| Mistuning 2 = 35.3 \| Complexity 2 = 7
	}}		}}
	{{About\|the regular temperament\|the ploidacot signature\|Ploidacot/Dicot}}		{{About\|the regular temperament\|the ploidacot signature\|Ploidacot/Dicot}}

FloraC: /* Tunings */ correction

2026-01-11T09:55:56Z

Tunings: correction

← Older revision		Revision as of 09:55, 11 January 2026
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	== Tunings ==		== Tunings ==
	=== Norm-based tunings ===		=== Norm-based tunings ===
	{{~~todo~~\|complete section\|inline=1}}		{{Todo\|complete section\|inline=1}}
	=== Tuning ~~Spectrum~~ ===
			=== Tuning spectrum ===
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
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	\| '''[[4edo\|1\4]]''' \|\| \|\| '''300.000''' \|\| '''Lower bound of 5-odd-limit diamond monotone'''		\| '''[[4edo\|1\4]]''' \|\| \|\| '''300.000''' \|\| '''Lower bound of 5-odd-limit diamond monotone'''
	\|-		\|-
	\| \|\| 6/5 \|\| 315.641 \|\| Full comma		\| \|\| 5/3 \|\| 315.641 \|\| Full comma
	\|-		\|-
	\| \|\| 9/5 \|\| 339.199 \|\| 2/3-comma		\| \|\| 9/5 \|\| 339.199 \|\| 2/3-comma
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	\| [[17edo\|5\17]] \|\| \|\| 352.941 \|\|		\| [[17edo\|5\17]] \|\| \|\| 352.941 \|\|
	\|-		\|-
	\| \|\| 27/20 \|\| 358.~~405~~ \|\| 2/5-comma		\| \|\| 45/32 \|\| 358.045 \|\| 2/5-comma
	\|-		\|-
	\| [[10edo\|3\10]] \|\| \|\| 360.000 \|\|		\| [[10edo\|3\10]] \|\| \|\| 360.000 \|\|
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	\| \|\| 5/4 \|\| 386.314 \|\| Untempered tuning		\| \|\| 5/4 \|\| 386.314 \|\| Untempered tuning
	\|-		\|-
	\| '''[[3edo\|1\3]]''' \|\| \|\| '''400.000''' \|\| '''Upper bound of 5-odd-limit, <br>5-limit 9-odd-limit diamond monotone'''		\| '''[[3edo\|1\3]]''' \|\| \|\| '''400.000''' \|\| '''Upper bound of 5-odd-limit, <br>and 5-limit 9-odd-limit diamond monotone'''
	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

Overthink: + tunings section

2026-01-11T00:44:50Z

+ tunings section

@@ Line 39: / Line 39: @@
 |}
 <nowiki/>* In 5-limit CWE tuning
 [[Category:Rank-2 temperaments]]

FloraC: - pointless rhetorics

2025-11-22T16:11:44Z

- pointless rhetorics

← Older revision		Revision as of 16:11, 22 November 2025
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	{{About\|the regular temperament\|the ploidacot signature\|Ploidacot/Dicot}}		{{About\|the regular temperament\|the ploidacot signature\|Ploidacot/Dicot}}

	'''Dicot''' is an [[exotemperament]] that [[tempering out\|tempers out]] [[25/24]]. It is also the first fully prototypical [[ploidacot/Dicot\|dicot]] temperament. It tempers [[6/5]] and [[5/4]] into the same [[neutral third]] interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of [[5-limit]] harmonies without fully representing them in its greater accuracy.		'''Dicot''' is an [[exotemperament]] that [[tempering out\|tempers out]] [[25/24]]. It is also the first fully prototypical [[ploidacot/Dicot\|dicot]] temperament. It tempers [[6/5]] and [[5/4]] into the same [[neutral third]] interval, which, when the fifth is tuned pure, is [[sqrt(3/2)]]. It is useful to represent the structure of [[5-limit]] harmonies without fully representing them in its greater accuracy, with [[mos scale]]s [[3L 4s]] and [[7L 3s]].

	It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.		It can be extended by tempering out [[15/14]] and [[36/35]] in the [[7-limit]], though this could turn the [[3L 4s]] [[mos]] into a [[4L 3s]] [[mos]]. This makes [[7/6]] and [[9/7]] equated to the neutral third, viewing [[6:7:9]] as a tertian chord.

	Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.		Another notable extension of dicot is [[decimal]], which splits the octave in two for [[7/5]][[~]][[10/7]] by tempering out [[50/49]], and equates [[7/6]] and [[8/7]] to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.

	~~As an exotemperament, dicot represents [[3L 4s]] and [[7L 3s]], and fittingly, [[Ploidacot/Dicot\|dicot]].~~

	For technical data, see [[Dicot family #Dicot]].		For technical data, see [[Dicot family #Dicot]].