Compton family - Revision history

FloraC: + distinguish notices for duodecic and duodecim. Request completion of data

2026-08-15T08:42:26Z

+ distinguish notices for duodecic and duodecim. Request completion of data

← Older revision		Revision as of 08:42, 15 August 2026
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	==== Duodecic ====		==== Duodecic ====
			{{Distinguish\|Duodecim}}

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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	=== Paly ===		=== Paly ===
	~~[[Subgroup]]: 2~~.3.5.7.11.13.17.19		{{Todo\|inline=1\|complete section\|unify precision\|comment= Sort the comma basis. Normalize the mapping. Unify the cent values in optimal tunings to 4 decimal places. Add the optimal ET sequence. <br>Add the data for the 11-, 13-, and 17-limit versions. }}

	~~[[Comma list]]~~: ~~81/80, 91/90, 51/50, 128/125, 76/75, 121/120~~		==== 19-limit ====
			Subgroup: 2.3.5.7.11.13.17.19

	~~{{Mapping\|24 38 56 48 83 108 98 102\|0 0 0 1 0 -1 0 0\|legend=1}}~~		Comma list: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120

	~~[[Optimal tuning~~\|~~Optimal tunings]]:~~		{{Mapping\| 24 38 56 48 83 108 98 102 \| 0 0 0 1 0 -1 0 0 }}

	* [[WE]]: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}		Optimal tunings:
			* WE: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}
			: error map: {{val\| -0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875 }}
			* CWE: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}
			: error map: {{val\| -0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487 }}

	: ~~[[error map]]: {{val\|-0.144 -~~2.~~183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875}}~~		Badness (Sintel): 2.383

	* [[CWE]]: ~33/32 = ~~50.000{{c}}, ~7/4~~ = ~~965.449~~{{c}}		== Duodecim ==
			{{Distinguish\|Duodecic}}

	~~: error map: {{val\|-0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487}}~~

	~~Edo join: 24 & 48cf~~

	~~[[Badness]] (Sintel): 2.383~~

	~~== Duodecim ==~~
	Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.		Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.

FloraC: Recategorize

2026-08-14T11:53:13Z

Recategorize

← Older revision		Revision as of 11:53, 14 August 2026
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	[[Badness]] (Sintel): 1.24		[[Badness]] (Sintel): 1.24

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

Zeta Function: /* Catler */ Moving temperament data

2026-08-10T16:43:22Z

Catler: Moving temperament data

← Older revision		Revision as of 16:43, 10 August 2026
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	Badness (Sintel): 1.27		Badness (Sintel): 1.27

			=== Paly ===
			[[Subgroup]]: 2.3.5.7.11.13.17.19

			[[Comma list]]: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120

			{{Mapping\|24 38 56 48 83 108 98 102\|0 0 0 1 0 -1 0 0\|legend=1}}

			[[Optimal tuning\|Optimal tunings]]:

			* [[WE]]: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}

			: [[error map]]: {{val\|-0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875}}

			* [[CWE]]: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}

			: error map: {{val\|-0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487}}

			Edo join: 24 & 48cf

			[[Badness]] (Sintel): 2.383

	== Duodecim ==		== Duodecim ==

Overthink: improve language

2026-05-04T03:50:27Z

improve language

← Older revision		Revision as of 03:50, 4 May 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo\|legend=1\| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth ~~will be that~~ of 12edo, ~~two~~ [[~~cent~~]]~~s flat~~, ~~the tuning of the larger primes is not so constrained, and the point of~~ these temperaments is to ~~improve on it~~.		The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo\|legend=1\| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth is fixed to 7 steps of 12edo, about 2{{cent}} flat of [[just]], these temperaments aim to add tunings for higher primes which are more in tune than in 12edo.

	== Compton ==		== Compton ==

Overthink: /* Catnip */ 72ce is literally contorted 36

2026-05-03T05:29:42Z

Catnip: 72ce is literally contorted 36

← Older revision		Revision as of 05:29, 3 May 2026
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	* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})		* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})

	{{Optimal ET sequence\|legend=0\| 12, 24, 36~~, 72ce~~ }}		{{Optimal ET sequence\|legend=0\| 12, 24, 36 }}

	Badness (Sintel): 1.14		Badness (Sintel): 1.14

FloraC: + commas of septimal compton. Linking

2026-03-06T12:43:10Z

+ commas of septimal compton. Linking

← Older revision		Revision as of 12:43, 6 March 2026
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	5-limit compton tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, compton is the {{nowrap\| 12 & 72 }} temperament; its [[ploidacot]] is dodecaploid acot. [[72edo]], [[84edo]] or [[240edo]] make for good tunings.		5-limit compton tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, compton is the {{nowrap\| 12 & 72 }} temperament; its [[ploidacot]] is dodecaploid acot. [[72edo]], [[84edo]] or [[240edo]] make for good tunings.

	This temperament is ~~known~~ as ''aristoxenean'' in [[Tonalsoft Encyclopedia]].		This temperament is documented as ''aristoxenean'' in [[Tonalsoft Encyclopedia]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	{{Main\| Compton }}		{{Main\| Compton }}

	In terms of the [[normal forms #Normal forms for commas\|normal comma list]], septimal compton adds 413343/409600 ({{monzo\| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]].		In terms of the [[normal forms #Normal forms for commas\|normal comma list]], septimal compton adds 413343/409600 ({{monzo\| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]]. Other important commas of this temperament are 250047/250000, the [[landscape comma]], which sets [[63/50]] to 1/3 of an octave, and 390625/388962, the [[dimcomp comma]], which sets [[25/21]] to 1/4 of an octave.

	In either the 5- or 7-limit, 240edo is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.		In either the 5- or 7-limit, 240edo is an excellent tuning, with [[81/80]] coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.

	Septimal compton is ~~known~~ as ''waage'' in [[Graham Breed]]'s [https://x31eq.com/temper/ temperament finder].		Septimal compton is catalogued as ''waage'' in [[Graham Breed]]'s [https://x31eq.com/temper/ temperament finder].

	In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]] and has a natural extension to the 13-limit. In 13-limit compton, intervals of 5, 7, 11, and 13 are off by one, two, three, and four generators, respectively. For these, 72edo can be recommended as a tuning.		In terms of the normal comma list, we may add [[8019/8000]] to get to the 11-limit version of compton, which also adds [[441/440]] and has a natural extension to the 13-limit. In 13-limit compton, intervals of 5, 7, 11, and 13 are off by one, two, three, and four generators, respectively. For these, 72edo can be recommended as a tuning.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Catler ==		== Catler ==
	In terms of the normal comma list, catler is characterized by the addition of the [[~~schisma]],~~ 32805/32768, to the Pythagorean comma, though it can also be characterized as adding 81/80, [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of 12edo. Catler can also be characterized as the {{nowrap\| 12 & 24 }} temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are [[36/35]], [[21/20]], [[15/14]], [[8/7]], [[7/6]], [[9/7]], [[7/5]], and most importantly, [[64/63]].		In terms of the normal comma list, catler is characterized by the addition of the schisma, [[32805/32768]], to the Pythagorean comma, though it can also be characterized as adding [[81/80]], [[128/125]] or [[648/625]]. In any event, the 5-limit is exactly the same as the 5-limit of 12edo. Catler can also be characterized as the {{nowrap\| 12 & 24 }} temperament. [[36edo]] or [[48edo]] are possible tunings. Possible generators are [[36/35]], [[21/20]], [[15/14]], [[8/7]], [[7/6]], [[9/7]], [[7/5]], and most importantly, [[64/63]].

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

FloraC: Fix copypasting errors

2026-03-06T12:37:26Z

Fix copypasting errors

← Older revision		Revision as of 12:37, 6 March 2026
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~16/15 = 99.8542{{c}}, ~7/4 = 975.8519{{c}} (~64/63 = 22.6896{{c}})		* WE: ~16/15 = 99.8542{{c}}, ~7/4 = 975.8519{{c}} (~64/63 = 22.6896{{c}})
	* ~~POTE~~: ~16/15 = 100.0000{{c}}, ~7/4 = 976.4125{{c}} (~64/63 = 23.5875{{c}})		* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 976.4125{{c}} (~64/63 = 23.5875{{c}})

	{{Optimal ET sequence\|legend=0\| 12, 36e, 48c }}		{{Optimal ET sequence\|legend=0\| 12, 36e, 48c }}
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~16/15 = 99.8791{{c}}, ~7/4 = 970.9614{{c}} (~64/63 = 27.8300{{c}})		* WE: ~16/15 = 99.8791{{c}}, ~7/4 = 970.9614{{c}} (~64/63 = 27.8300{{c}})
	* ~~POTE~~: ~16/15 = 100.0000{{c}}, ~7/4 = 972.2549{{c}} (~64/63 = 27.7451{{c}})		* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 972.2549{{c}} (~64/63 = 27.7451{{c}})

	{{Optimal ET sequence\|legend=0\| 12e, 36, 48c, 84c }}		{{Optimal ET sequence\|legend=0\| 12e, 36, 48c, 84c }}
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~16/15 = 99.8519{{c}}, ~7/4 = 965.7912{{c}} (~64/63 = 32.7275{{c}})		* WE: ~16/15 = 99.8519{{c}}, ~7/4 = 965.7912{{c}} (~64/63 = 32.7275{{c}})
	* ~~POTE~~: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})		* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})

	{{Optimal ET sequence\|legend=0\| 12, 24, 36, 72ce }}		{{Optimal ET sequence\|legend=0\| 12, 24, 36, 72ce }}
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~16/15 = 99.8308{{c}}, ~7/4 = 961.1391{{c}} (~40/39 = 37.1694{{c}})		* WE: ~16/15 = 99.8308{{c}}, ~7/4 = 961.1391{{c}} (~40/39 = 37.1694{{c}})
	* ~~POTE~~: ~16/15 = 100.0000{{c}}, ~7/4 = 961.1435{{c}} (~40/39 = 38.8565{{c}})		* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 961.1435{{c}} (~40/39 = 38.8565{{c}})

	{{Optimal ET sequence\|legend=0\| 12f, 24, 36f }}		{{Optimal ET sequence\|legend=0\| 12f, 24, 36f }}

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

2025-11-27T12:24:50Z

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

← Older revision		Revision as of 12:24, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Compton family\| ]] <!-- main article -->		[[Category:Compton family\| ]] <!-- main article -->
	[[Category:Compton\| ]] <!-- key article -->		[[Category:Compton\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: It's not like we're anywhere close to reviving the alt names; rewrite to reflect that. + ploidacots & misc. missing info

2025-09-19T17:58:51Z

It's not like we're anywhere close to reviving the alt names; rewrite to reflect that. + ploidacots & misc. missing info

← Older revision		Revision as of 17:58, 19 September 2025
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	{{Main\| Compton }}		{{Main\| Compton }}

	5-limit compton ~~is also known as ''aristoxenean''. It~~ tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, it is the {{nowrap\| 12 & 72 }} temperament~~, and~~ [[72edo]], [[84edo]] or [[240edo]] make for good tunings.		5-limit compton tempers out the Pythagorean comma and has a period of 1\12, so it is the 12edo circle of fifths with an independent dimension for the harmonic 5. Equivalent generators are [[5/4]], [[6/5]], [[10/9]], [[16/15]] (the [[secor]]), [[45/32]], [[135/128]] and most importantly, [[81/80]]. In terms of [[equal temperament]]s, compton is the {{nowrap\| 12 & 72 }} temperament; its [[ploidacot]] is dodecaploid acot. [[72edo]], [[84edo]] or [[240edo]] make for good tunings.

			This temperament is known as ''aristoxenean'' in [[Tonalsoft Encyclopedia]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	{{Main\| Compton }}		{{Main\| Compton }}

	~~Septimal compton is also known as ''waage''.~~ In terms of the normal list, compton adds 413343/409600 ({{monzo\| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]].		In terms of the [[normal forms #Normal forms for commas\|normal comma list]], septimal compton adds 413343/409600 ({{monzo\| -14 10 -2 1 }}) to the Pythagorean comma; however, it can also be characterized by saying it adds [[225/224]].

	In either the 5- or 7-limit, 240edo is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.		In either the 5- or 7-limit, 240edo is an excellent tuning, with 81/80 coming in at 15 cents exactly. In the 12edo, the major third is sharp by 13.686 cents, and the minor third flat by 15.641 cents; adjusting these down and up by 15 cents puts them in excellent tune.

	In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]~~. For this 72edo can be recommended as~~ a ~~tuning~~. In 11-limit compton, intervals of 5 are off by one ~~generator~~, ~~intervals of 7 are off by~~ two ~~generators~~, and ~~intervals of 11 are off by 3~~ generators.		Septimal compton is known as ''waage'' in [[Graham Breed]]'s [https://x31eq.com/temper/ temperament finder].

			In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]] and has a natural extension to the 13-limit. In 13-limit compton, intervals of 5, 7, 11, and 13 are off by one, two, three, and four generators, respectively. For these, 72edo can be recommended as a tuning.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Duodecim ==		== Duodecim ==
			Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	== Hours ==		== Hours ==
	The hours temperament has a period of 1/24 octave and tempers out the [[cataharry comma]] (19683/19600) and the mirwomo comma (33075/32768). The name ''hours'' was ~~named~~ for the reason that the period is 1/24 octave and there are 24 hours per day.		The hours temperament has a period of 1/24 octave and tempers out the [[cataharry comma]] (19683/19600) and the mirwomo comma (33075/32768). Its ploidacot is 24-ploid acot. The name ''hours'' was given for the reason that the period is 1/24 octave and there are 24 hours per day.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Gamelstearn ==		== Gamelstearn ==
	The gamelstearn temperament has a period of 1/36 octave and tempers out the [[gamelisma]] (1029/1024) and the [[stearnsma]] (118098/117649).		The gamelstearn temperament has a period of 1/36 octave and tempers out the [[gamelisma]] (1029/1024) and the [[stearnsma]] (118098/117649). Its ploidacot is 36-ploid acot.

	It used to be ~~named "~~decades".		It used to be called ''decades'', but was renamed in 2025 after the above two commas because the old name was deemed too confusing.

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

FloraC: - CTE & POTE tunings

2025-09-19T17:28:58Z

- CTE & POTE tunings

Show changes