Associated temperament - Revision history

FloraC: Update

2025-09-06T14:12:56Z

Update

← Older revision		Revision as of 14:12, 6 September 2025
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	\| [[28/27]]		\| [[28/27]]
	\| [[15edo]]		\| [[15edo]]
	\| [[~~Blacksmith~~]]		\| [[Blackwood]]
	\| 28/27, [[49/48]]		\| 28/27, [[49/48]]
	\|-		\|-
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	\| [[36/35]]		\| [[36/35]]
	\| [[12edo]]		\| [[12edo]]
	\| [[Diminished]]		\| [[Diminished (temperament)\|Diminished]]
	\| 36/35, [[50/49]]		\| 36/35, [[50/49]]
	\|-		\|-
Line 170:		Line 170:
	\| 33/32		\| 33/32
	\| [[16edo]]		\| [[16edo]]
	\| [[Armodue]]		\| [[Armodue (temperament)\|Armodue]]
	\| 33/32, 36/35, 45/44		\| 33/32, 36/35, 45/44
	\|-		\|-
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	\| 40/39		\| 40/39
	\| [[15edo]]		\| [[15edo]]
	\| [[~~Blacksmith~~]]		\| [[Blackwood]]
	\| 28/27, 40/39, 49/48, 55/54		\| 28/27, 40/39, 49/48, 55/54
	\|-		\|-

Bcmills at 15:26, 23 August 2024

2024-08-23T15:26:08Z

← Older revision		Revision as of 15:26, 23 August 2024
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	\| [[36/35]]		\| [[36/35]]
	\| [[12edo]]		\| [[12edo]]
	\| [[Dominant]]		\| [[Dominant (temperament)\|Dominant]]
	\| 36/35, [[64/63]]		\| 36/35, [[64/63]]
	\|-		\|-

FloraC: -typo

2024-03-13T05:07:41Z

-typo

← Older revision		Revision as of 05:07, 13 March 2024
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	In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit\|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET\|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[~~cocmma~~ basis]] for the rank-2 temperament.		In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit\|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET\|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[comma basis]] for the rank-2 temperament.

	== 7-limit ==		== 7-limit ==

BudjarnLambeth: Update a temperament name from catcall to catnip

2024-01-30T02:22:43Z

Update a temperament name from catcall to catnip

← Older revision		Revision as of 02:22, 30 January 2024
Line 1:		Line 1:
	In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit\|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET\|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[~~comma~~ basis]] for the rank-2 temperament.		In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit\|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET\|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[cocmma basis]] for the rank-2 temperament.

	== 7-limit ==		== 7-limit ==
Line 195:		Line 195:
	\| 56/55		\| 56/55
	\| [[36edo]]		\| [[36edo]]
	\| [[~~Catcall~~]]		\| [[Catnip]]
	\| 56/55, 81/80, 128/125		\| 56/55, 81/80, 128/125
	\|-		\|-

Fredg999: In RTT, misc. edits

2022-08-01T05:58:41Z

In RTT, misc. edits

← Older revision		Revision as of 05:58, 1 August 2022
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	By an '''associated temperament''' to a ''p''-limit [[comma]] is ~~meant~~ a ~~[[harmonic limit\|~~''p''-limit]] [[regular ~~temperament\|~~temperament]] [[~~temper out\|~~tempering out]] that comma which shares the same [[optimal patent val]] as the [[~~Rank and~~ codimension~~\|codimension one~~]] temperament tempering out that comma. By definition, the [[optimal patent val]] defines the unique [[ET\|rank ~~one~~]] associated temperament. For [[rank ~~two temperaments~~]], it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank ~~two~~ temperament, and a [[comma basis]] for the rank ~~two~~ temperament.		In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit\|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET\|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[comma basis]] for the rank-2 temperament.

	== 7-limit ==		== 7-limit ==

Fredg999 category edits: Removing from Category:Temperament using Cat-a-lot

2022-03-01T01:31:14Z

Removing from Category:Temperament using Cat-a-lot

← Older revision		Revision as of 01:31, 1 March 2022
Line 439:		Line 439:

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Temperament]]~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: +14641/14580 and 1573/1568

2022-01-08T16:27:57Z

+14641/14580 and 1573/1568

← Older revision		Revision as of 16:27, 8 January 2022
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	\| [[Septisuperfourth]]		\| [[Septisuperfourth]]
	\| 540/539, 4000/3993, 5632/5625		\| 540/539, 4000/3993, 5632/5625
			\|-
			\| 14641/14580
			\| [[410edo]]
			\| [[Floral]]
			\| 2401/2400, 9801/9800, 14641/14580
	\|-		\|-
	\| 243/242		\| 243/242
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	\| [[Subsemifourth]]		\| [[Subsemifourth]]
	\| 540/539, 847/845, 1375/1372, 1575/1573		\| 540/539, 847/845, 1375/1372, 1575/1573
			\|-
			\| 1573/1568
			\| [[323edo]]
			\| [[Stockhausenic]]
			\| 676/675, 1001/1000, 1375/1372, 4096/4095
	\|-		\|-
	\| 325/324		\| 325/324

FloraC: Simplify links

2022-01-08T16:10:43Z

Simplify links

Show changes

Cmloegcmluin: unhyphenate "comma basis"

2021-11-12T20:20:19Z

unhyphenate "comma basis"

← Older revision		Revision as of 20:20, 12 November 2021
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	By an '''associated temperament''' to a ''p''-limit [[comma]] is meant a [[prime limit\|''p''-limit]] [[regular temperament\|temperament]] [[temper out\|tempering out]] that comma which shares the same [[optimal patent val]] as the [[Rank and codimension\|codimension one]] temperament tempering out that comma. By definition, the [[optimal patent val]] defines the unique [[ET\|rank one]] associated temperament. For [[rank two temperaments]], it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a [[comma-basis]] for the rank two temperament.		By an '''associated temperament''' to a ''p''-limit [[comma]] is meant a [[prime limit\|''p''-limit]] [[regular temperament\|temperament]] [[temper out\|tempering out]] that comma which shares the same [[optimal patent val]] as the [[Rank and codimension\|codimension one]] temperament tempering out that comma. By definition, the [[optimal patent val]] defines the unique [[ET\|rank one]] associated temperament. For [[rank two temperaments]], it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a [[comma basis]] for the rank two temperament.

	== 7-limit ==		== 7-limit ==

Cmloegcmluin: add links

2021-11-08T23:05:07Z

add links

← Older revision		Revision as of 23:05, 8 November 2021
Line 1:		Line 1:
	By an '''associated temperament''' to a ''p''-limit comma is meant a ''p''-limit temperament tempering out that comma which shares the same [[optimal patent val]] as the [[Rank and codimension\|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a comma basis for the rank two temperament.		By an '''associated temperament''' to a ''p''-limit [[comma]] is meant a [[prime limit\|''p''-limit]] [[regular temperament\|temperament]] [[temper out\|tempering out]] that comma which shares the same [[optimal patent val]] as the [[Rank and codimension\|codimension one]] temperament tempering out that comma. By definition, the [[optimal patent val]] defines the unique [[ET\|rank one]] associated temperament. For [[rank two temperaments]], it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a [[comma-basis]] for the rank two temperament.

	== 7-limit ==		== 7-limit ==