Augmented–cloudy equivalence continuum - Revision history

Flirora: fix typo

2025-09-15T20:52:37Z

fix typo

← Older revision		Revision as of 20:52, 15 September 2025
Line 83:		Line 83:
	\|-		\|-
	\| ∞		\| ∞
	\| [[~~AAugment~~]]		\| [[Augment]]
	\| [[128/125]]		\| [[128/125]]
	\| {{Monzo\| 7 0 -3 }}		\| {{Monzo\| 7 0 -3 }}

FloraC: Cleanup

2025-09-11T05:53:24Z

Cleanup

← Older revision		Revision as of 05:53, 11 September 2025
Line 2:		Line 2:
	The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].		The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].

	All temperaments in the continuum satisfy {{nowrap\|(128/125)<sup>''n''</sup> ~ 16807/16384}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[~~augmented~~]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[~~Just intonation~~ subgroup\|2.5.7 subgroup]] temperaments supported by [[15edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.~~0747...~~, and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\| (128/125)<sup>''n''</sup> ~ 16807/16384 }}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[augment]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[2.5.7 subgroup\|2.5.7-subgroup]] temperaments supported by [[15edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.0747…, and temperaments having ''n'' near this value tend to be the most accurate ones.

	{\| class="wikitable center-1 ~~center-2 center-4~~ center-5"		{\| class="wikitable center-1 center-5"
	\|+ style="font-size: 105%;" \| Temperaments in the continuum		\|+ style="font-size: 105%;" \| Temperaments in the continuum
	\|-		\|-
Line 19:		Line 19:
	! Monzo		! Monzo
	\|-		\|-
	\| ~~−2~~		\| −2
	\| 2 & 15		\| 2 & 15
	\| [[16807/15625]]		\| [[16807/15625]]
	\| {{Monzo\|0 0 -6 5}}		\| {{Monzo\| 0 0 -6 5 }}
	\| ~~−2~~		\| −2
	\| 15 & 14c		\| 15 & 14c
	\| [[282475249/262144000]]		\| [[282475249/262144000]]
	\| {{Monzo\|-21 0 -3 10}}		\| {{Monzo\| -21 0 -3 10 }}
	\|-		\|-
	\| ~~−1~~		\| −1
	\| 4 & 15		\| 4 & 15
	\| [[16807/16000]]		\| [[16807/16000]]
	\| {{Monzo\|-7 0 -3 5}}		\| {{Monzo\| -7 0 -3 5 }}
	\| ~~−1~~		\| −1
	\| 4 & 15		\| 4 & 15
	\| [[16807/16000]]		\| [[16807/16000]]
	\| {{Monzo\|-7 0 -3 5}}		\| {{Monzo\| -7 0 -3 5 }}
	\|-		\|-
	\| 0		\| 0
	\| Cloudy		\| Cloudy
	\| [[16807/16384]]		\| [[16807/16384]]
	\| {{Monzo\|-14 0 0 5}}		\| {{Monzo\| -14 0 0 5 }}
	\| 0		\| 0
	\| [[~~Augmented family\|Augmented~~]]		\| [[Augment]]
	\| [[128/125]]		\| [[128/125]]
	\| {{Monzo\|7 0 -3}}		\| {{Monzo\| 7 0 -3 }}
	\|-		\|-
	\| 1		\| 1
	\| [[Rainy]]		\| [[Rainy]]
	\| [[2100875/2097152]]		\| [[2100875/2097152]]
	\| {{Monzo\|-21 0 3 5}}		\| {{Monzo\| -21 0 3 5 }}
	\| 1		\| 1
	\| [[Rainy]]		\| [[Rainy]]
	\| [[2100875/2097152]]		\| [[2100875/2097152]]
	\| {{Monzo\|-21 0 3 5}}		\| {{Monzo\| -21 0 3 5 }}
	\|-		\|-
	\| 2		\| 2
	\| 37 & 15		\| 37 & 15
	\| [[268435456/262609375]]		\| [[268435456/262609375]]
	\| {{Monzo\|-28 0 6 5}}		\| {{Monzo\| -28 0 6 5 }}
	\| 2		\| 2
	\| 15 & 41		\| 15 & 41
	\| [[35309406125/34359738368]]		\| [[35309406125/34359738368]]
	\| {{Monzo\|-35 0 3 10}}		\| {{Monzo\| -35 0 3 10 }}
	\|-		\|-
	\| 3		\| 3
	\| 15 & 28		\| 15 & 28
	\|		\|
	\| {{Monzo\|-35 0 9 5}}		\| {{Monzo\| -35 0 9 5 }}
	\| 3		\| 3
	\| 15 & 51		\| 15 & 51
	\|		\|
	\| {{Monzo\|-49 0 3 15}}		\| {{Monzo\| -49 0 3 15 }}
	\|-		\|-
	\| …		\| …
Line 83:		Line 83:
	\|-		\|-
	\| ∞		\| ∞
	\| [[~~Augmented family\|Augmented~~]]		\| [[AAugment]]
	\| [[128/125]]		\| [[128/125]]
	\| {{Monzo\|7 0 -3}}		\| {{Monzo\| 7 0 -3 }}
	\| ∞		\| ∞
	\| Cloudy		\| Cloudy
	\| [[16807/16384]]		\| [[16807/16384]]
	\| {{Monzo\|-14 0 0 5}}		\| {{Monzo\| -14 0 0 5 }}
	\|}		\|}

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:44:30Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:44, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].		The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T09:34:17Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 09:34, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].		The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].

ArrowHead294 at 14:53, 18 December 2024

2024-12-18T14:53:49Z

← Older revision		Revision as of 14:53, 18 December 2024
Line 1:		Line 1:
	The '''~~augmented-cloudy~~ equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].		The '''augmented–cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|lesser dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].

	All temperaments in the continuum satisfy {{nowrap\|(128/125)<sup>''n''</sup> ~ 16807/16384}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[augmented]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[Just intonation subgroup\|2.5.7 subgroup]] temperaments supported by [[15edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.0747..., and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|(128/125)<sup>''n''</sup> ~ 16807/16384}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[augmented]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[Just intonation subgroup\|2.5.7 subgroup]] temperaments supported by [[15edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.0747..., and temperaments having ''n'' near this value tend to be the most accurate ones.

ArrowHead294 at 14:53, 18 December 2024

2024-12-18T14:53:28Z

← Older revision		Revision as of 14:53, 18 December 2024
Line 1:		Line 1:
	The '''augmented-cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].		The '''augmented-cloudy equivalence continuum''' is a continuum of 2.5.7 subgroup temperaments which equate a number of [[128/125\|dieses (128/125)]] with the [[16807/16384\|cloudy comma (16807/16384)]].

	All temperaments in the continuum satisfy (128/125)<sup>''n''</sup> ~ 16807/16384. Varying ''n'' results in different temperaments listed in the table below. It converges to [[augmented]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[Just intonation subgroup\|2.5.7 subgroup]] temperaments supported by [[15edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.0747..., and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|(128/125)<sup>''n''</sup> ~ 16807/16384}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[augmented]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[Just intonation subgroup\|2.5.7 subgroup]] temperaments supported by [[15edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.0747..., and temperaments having ''n'' near this value tend to be the most accurate ones.

	{\| class="wikitable center-1 center-2 center-4 center-5"		{\| class="wikitable center-1 center-2 center-4 center-5"
	\|+ Temperaments in the continuum		\|+ style="font-size: 105%;" \| Temperaments in the continuum
	\|-		\|-
	! rowspan="2" \| ''n''		! rowspan="2" \| ''n''
	! rowspan="2" \| Temperament		! rowspan="2" \| Temperament
	! colspan="2" \| Comma		! colspan="2" \| Comma
	! rowspan="2" \| 1 / ''n''		! rowspan="2" \| 1/''n''
	! rowspan="2" \| Temperament		! rowspan="2" \| Temperament
	! colspan="2" \| Comma		! colspan="2" \| Comma
Line 18:		Line 18:
	! Monzo		! Monzo
	\|-		\|-
	\| -2		\| −2
	\| 2 & 15		\| 2 & 15
	\| [[16807/15625]]		\| [[16807/15625]]
	\| {{Monzo\|0 0 -6 5}}		\| {{Monzo\|0 0 -6 5}}
	\| -2		\| −2
	\| 15 & 14c		\| 15 & 14c
	\| [[282475249/262144000]]		\| [[282475249/262144000]]
	\| {{Monzo\|-21 0 -3 10}}		\| {{Monzo\|-21 0 -3 10}}
	\|-		\|-
	\| -1		\| −1
	\| 4 & 15		\| 4 & 15
	\| [[16807/16000]]		\| [[16807/16000]]
	\| {{Monzo\|-7 0 -3 5}}		\| {{Monzo\|-7 0 -3 5}}
	\| -1		\| −1
	\| 4 & 15		\| 4 & 15
	\| [[16807/16000]]		\| [[16807/16000]]
Line 93:		Line 93:
	Examples of temperaments with fractional values of ''n'' not listed above:		Examples of temperaments with fractional values of ''n'' not listed above:

	* 15 & 72 (''n'' = 2/3)		* 15 & 72 ({{nowrap\|''n'' {{=}} 2/3}})
	* 379 & 4184 (''n'' = 13/12)		* 379 & 4184 ({{nowrap\|''n'' {{=}} 13/12}})
	* 410 & 3675 (''n'' = 14/13)		* 410 & 3675 ({{nowrap\|''n'' {{=}} 14/13}})
	* 851 & 1687 (''n'' = 29/27)		* 851 & 1687 ({{nowrap\|''n'' {{=}} 29/27}})
	* 441 & 1308 (''n'' = 15/14)		* 441 & 1308 ({{nowrap\|''n'' {{=}} 15/14}})
	* 68 & 15 (''n'' = 3/2)		* 68 & 15 ({{nowrap\|''n'' {{=}} 3/2}})

	== 37 & 15 ==		== 37 & 15 ==

	Commas: {{Monzo\|-28 0 6 5}} = 268435456/262609375		Commas: {{Monzo\|-28 0 6 5}} = 268435456/262609375

Line 113:		Line 112:

	== 15 & 41 ==		== 15 & 41 ==

	Commas: {{Monzo\|-35 0 3 10}} = 35309406125/34359738368		Commas: {{Monzo\|-35 0 3 10}} = 35309406125/34359738368

Line 125:		Line 123:

	== 15 & 28 ==		== 15 & 28 ==

	Commas: {{Monzo\|-35 0 9 5}} = 34359738368/32826171875		Commas: {{Monzo\|-35 0 9 5}} = 34359738368/32826171875

Line 137:		Line 134:

	== 15 & 51 ==		== 15 & 51 ==

	Commas: {{Monzo\|-49 0 3 15}} = 593445188742875/562949953421312		Commas: {{Monzo\|-49 0 3 15}} = 593445188742875/562949953421312

Line 149:		Line 145:

	== 4 & 15 ==		== 4 & 15 ==

	Commas: {{Monzo\|0 0 -6 5}} = 16807/16800		Commas: {{Monzo\|0 0 -6 5}} = 16807/16800

Line 161:		Line 156:

	== 2 & 15 ==		== 2 & 15 ==

	Commas: {{Monzo\|-7 0 -3 5}} = 16807/15625		Commas: {{Monzo\|-7 0 -3 5}} = 16807/15625

Line 173:		Line 167:

	== 15 & 14c ==		== 15 & 14c ==

	Commas: {{Monzo\|-21 0 -3 10}} = 282475249/262144000		Commas: {{Monzo\|-21 0 -3 10}} = 282475249/262144000

Line 185:		Line 178:

	== 379 & 4184 ==		== 379 & 4184 ==

	Commas: {{Monzo\|280 0 -42 -65}}		Commas: {{Monzo\|280 0 -42 -65}}

Line 197:		Line 189:

	== 410 & 3675 ==		== 410 & 3675 ==

	Commas: {{Monzo\|-301 0 45 70}}		Commas: {{Monzo\|-301 0 45 70}}

Line 209:		Line 200:

	== 441 & 1308 ==		== 441 & 1308 ==

	Commas: {{Monzo\|-322 0 48 75}}		Commas: {{Monzo\|-322 0 48 75}}

Line 221:		Line 211:

	== 851 & 1687 ==		== 851 & 1687 ==

	Commas: {{Monzo\|-623 0 93 145}}		Commas: {{Monzo\|-623 0 93 145}}

Line 233:		Line 222:

	== 68 & 15 ==		== 68 & 15 ==

	Commas: {{Monzo\|-49 0 9 10}} = 562949953421312/551709470703125		Commas: {{Monzo\|-49 0 9 10}} = 562949953421312/551709470703125

Line 245:		Line 233:

	== 15 & 72 ==		== 15 & 72 ==

	Commas: {{Monzo\|-56 0 6 15}} = 74180648592859375/72057594037927936		Commas: {{Monzo\|-56 0 6 15}} = 74180648592859375/72057594037927936

ArrowHead294: ArrowHead294 moved page Augmented-cloudy equivalence continuum to Augmented–cloudy equivalence continuum: The dash in titles like these should be an en dash, not a hyphen-minus, since "Augmented" does not modify "cloudy"

2024-12-18T14:51:34Z

ArrowHead294 moved page Augmented-cloudy equivalence continuum to Augmented–cloudy equivalence continuum: The dash in titles like these should be an en dash, not a hyphen-minus, since "Augmented" does not modify "cloudy"

← Older revision	Revision as of 14:51, 18 December 2024
(No difference)

Godtone: fix links to rainy

2024-05-26T18:02:51Z

fix links to rainy

← Older revision		Revision as of 18:02, 26 May 2024
Line 46:		Line 46:
	\|-		\|-
	\| 1		\| 1
	\| [[~~Subgroup temperaments#Rainy\|~~Rainy]]		\| [[Rainy]]
	\| [[2100875/2097152]]		\| [[2100875/2097152]]
	\| {{Monzo\|-21 0 3 5}}		\| {{Monzo\|-21 0 3 5}}
	\| 1		\| 1
	\| [[~~Subgroup temperaments#Rainy\|~~Rainy]]		\| [[Rainy]]
	\| [[2100875/2097152]]		\| [[2100875/2097152]]
	\| {{Monzo\|-21 0 3 5}}		\| {{Monzo\|-21 0 3 5}}

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

2022-02-28T20:06:45Z

Removing from Category:Temperament using Cat-a-lot

← Older revision		Revision as of 20:06, 28 February 2022
Line 257:		Line 257:

	[[Category:15edo]]		[[Category:15edo]]
	~~[[Category:Temperament]]~~
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

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

2022-02-28T20:05:57Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 20:05, 28 February 2022
Line 257:		Line 257:

	[[Category:15edo]]		[[Category:15edo]]
	~~[[Category:Theory]]~~
	[[Category:Temperament]]		[[Category:Temperament]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Augmented–cloudy equivalence continuum - Revision history

Flirora: fix typo

FloraC: Cleanup

FloraC: Text replacement - "{{Technical data page}}" to "{{Technical data page}}"

BudjarnLambeth: {{Technical data page}}

ArrowHead294 at 14:53, 18 December 2024

ArrowHead294 at 14:53, 18 December 2024

ArrowHead294: ArrowHead294 moved page Augmented-cloudy equivalence continuum to Augmented–cloudy equivalence continuum: The dash in titles like these should be an en dash, not a hyphen-minus, since "Augmented" does not modify "cloudy"

Godtone: fix links to rainy

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

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

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"