176edo - Revision history

FloraC: /* Regular temperament properties */ simplify

2026-06-28T10:10:17Z

Regular temperament properties: simplify

← Older revision		Revision as of 10:10, 28 June 2026
Line 75:		Line 75:
	\| 115.91		\| 115.91
	\| 77/72		\| 77/72
	\| [[~~Mercy]] / [[countermiracle~~]] / counterbenediction / countermanna		\| [[Countermiracle]] / counterbenediction / countermanna
	\|-		\|-
	\| 1		\| 1
Line 93:		Line 93:
	\| 497.73		\| 497.73
	\| 4/3		\| 4/3
	\| [[~~Gary]] / [[cotoneum~~]]		\| [[Cotoneum]]
	\|-		\|-
	\| 1		\| 1
Line 114:		Line 114:
	\|-		\|-
	\| 4		\| 4
	\| ~~73\176<br>(~~15\176)		\| 15\176
	\| ~~497.73<br>(~~102.27)		\| 102.27
	\| ~~4/3<br>(~~35/33)		\| 35/33
	\| [[Unlit]]		\| [[Unlit]]
	\|-		\|-
	\| 8		\| 8
	\| ~~73\176<br>(~~7\176)		\| 7\176
	\| ~~497.73<br>(~~47.73)		\| 47.73
	\| ~~4/3<br>(~~36/35)		\| 36/35
	\| [[Twilight]]		\| [[Twilight]]
	\|-		\|-
	\| 8		\| 8
	\| ~~83\176<br>(~~5\176)		\| 5\176
	\| ~~565.91<br>(~~34.09)		\| 34.09
	\| ~~168/121<br>(~~55/54)		\| 55/54
	\| [[Octowerck]] (176f) / octowerckis (176)		\| [[Octowerck]] (176f) / octowerckis (176)
	\|-		\|-
	\| 11		\| 11
	\| ~~73\176<br>(~~7\176)		\| 7\176
	\| ~~497.73<br>(~~47.73)		\| 47.73
	\| ~~4/3<br>(~~36/35)		\| 36/35
	\| [[Hendecatonic (temperament)\|Hendecatonic]]		\| [[Hendecatonic (temperament)\|Hendecatonic]]
	\|-		\|-
	\| 22		\| 22
	\| ~~73\176<br>(~~1\176)		\| 1\176
	\| ~~497.73<br>(~~6.82)		\| 6.82
	\| ~~4/3<br>(~~385/384)		\| 385/384
	\| [[Icosidillic~~]] / [[major arcana~~]]		\| [[Icosidillic]]
	\|}		\|}
	<nowiki/>* ~~[[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and~~ [[normal forms #Minimal-generator form\|minimal form]] ~~in parentheses if distinct~~		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

	[[Category:Countermiracle]]		[[Category:Countermiracle]]

FloraC: Update link

2026-04-05T12:18:14Z

Update link

← Older revision		Revision as of 12:18, 5 April 2026
Line 135:		Line 135:
	\| 497.73<br>(47.73)		\| 497.73<br>(47.73)
	\| 4/3<br>(36/35)		\| 4/3<br>(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic (temperament)\|Hendecatonic]]
	\|-		\|-
	\| 22		\| 22

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:53Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
Line 143:		Line 143:
	\| [[Icosidillic]] / [[major arcana]]		\| [[Icosidillic]] / [[major arcana]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	[[Category:Countermiracle]]		[[Category:Countermiracle]]

FloraC: Cleanup and update

2025-03-16T14:02:21Z

Cleanup and update

← Older revision		Revision as of 14:02, 16 March 2025
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 176 factors into {{~~Factorisation~~\|~~176~~}}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.		Since 176 factors into primes as {{nowrap\| 2<sup>4</sup> × 11 }}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 19:		Line 19:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 26:		Line 26:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 279 -176 }}		\| {{Monzo\| 279 -176 }}
	\| {{~~mapping~~\| 176 279 }}		\| {{Mapping\| 176 279 }}
	\| −0.100		\| −0.100
	\| 0.100		\| 0.100
Line 34:		Line 34:
	\| 2.3.5		\| 2.3.5
	\| 78732/78125, {{monzo\| 41 -20 -4 }}		\| 78732/78125, {{monzo\| 41 -20 -4 }}
	\| {{~~mapping~~\| 176 279 409 }}		\| {{Mapping\| 176 279 409 }}
	\| −0.400		\| −0.400
	\| 0.432		\| 0.432
Line 41:		Line 41:
	\| 2.3.5.7		\| 2.3.5.7
	\| 6144/6125, 10976/10935, 50421/50000		\| 6144/6125, 10976/10935, 50421/50000
	\| {{~~mapping~~\| 176 279 409 494 }}		\| {{Mapping\| 176 279 409 494 }}
	\| −0.243		\| −0.243
	\| 0.463		\| 0.463
Line 48:		Line 48:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 441/440, 3388/3375, 6144/6125, 8019/8000		\| 441/440, 3388/3375, 6144/6125, 8019/8000
	\| {{~~mapping~~\| 176 279 409 494 609 }}		\| {{Mapping\| 176 279 409 494 609 }}
	\| −0.250		\| −0.250
	\| 0.414		\| 0.414
Line 55:		Line 55:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 351/350, 364/363, 441/440, 2197/2187, 3146/3125		\| 351/350, 364/363, 441/440, 2197/2187, 3146/3125
	\| {{~~mapping~~\| 176 279 409 494 609 651 }}		\| {{Mapping\| 176 279 409 494 609 651 }}
	\| −0.123		\| −0.123
	\| 0.473		\| 0.473
Line 65:		Line 65:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 99:		Line 99:
	\| 565.91		\| 565.91
	\| 13/9		\| 13/9
	\| [[~~Tricot]] / [[trident~~]]		\| [[Alphatrident]]
	\|-		\|-
	\| 2		\| 2
Line 114:		Line 114:
	\|-		\|-
	\| 4		\| 4
	\| 73\176<br />(15\176)		\| 73\176<br>(15\176)
	\| 497.73<br />(102.27)		\| 497.73<br>(102.27)
	\| 4/3<br />(35/33)		\| 4/3<br>(35/33)
	\| [[~~Undim~~]]		\| [[Unlit]]
	\|-		\|-
	\| 8		\| 8
	\| 73\176<br />(7\176)		\| 73\176<br>(7\176)
	\| 497.73<br />(47.73)		\| 497.73<br>(47.73)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Twilight]]		\| [[Twilight]]
	\|-		\|-
	\| 8		\| 8
	\| 83\176<br />(5\176)		\| 83\176<br>(5\176)
	\| 565.91<br />(34.09)		\| 565.91<br>(34.09)
	\| 168/121<br />(55/54)		\| 168/121<br>(55/54)
	\| [[Octowerck]] (176f) / octowerckis (176)		\| [[Octowerck]] (176f) / octowerckis (176)
	\|-		\|-
	\| 11		\| 11
	\| 73\176<br />(7\176)		\| 73\176<br>(7\176)
	\| 497.73<br />(47.73)		\| 497.73<br>(47.73)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|-		\|-
	\| 22		\| 22
	\| 73\176<br />(1\176)		\| 73\176<br>(1\176)
	\| 497.73<br />(6.82)		\| 497.73<br>(6.82)
	\| 4/3<br />(385/384)		\| 4/3<br>(385/384)
	\| [[Icosidillic]] / [[major arcana]]		\| [[Icosidillic]] / [[major arcana]]
	\|}		\|}

ArrowHead294 at 19:25, 20 February 2025

2025-02-20T19:25:23Z

← Older revision		Revision as of 19:25, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 14:50, 16 January 2025

2025-01-16T14:50:34Z

← Older revision		Revision as of 14:50, 16 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~The '''176 equal divisions of the octave''' ('''176edo'''), or the '''176(-tone) equal temperament''' ('''176tet''', '''176et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO~~\|equal division of the octave]] into 176 parts of about 6.82 [[cent]]s each, a size close to [[243/242]], the rastma.~~		{{EDO intro}}

	== Theory ==		== Theory ==
	176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo\| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.		176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo\| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]], and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.

	176edo tempers the [[64/63\|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[bicommatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.		176edo tempers the [[64/63\|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[bicommatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 176 factors into ~~2<sup>4</sup> × 11~~, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.		Since 176 factors into {{Factorisation\|176}}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 19:		Line 19:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve stretch (¢)		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 28:		Line 28:
	\| {{monzo\| 279 -176 }}		\| {{monzo\| 279 -176 }}
	\| {{mapping\| 176 279 }}		\| {{mapping\| 176 279 }}
	\| ~~−0~~.100		\| −0.100
	\| 0.100		\| 0.100
	\| 1.47		\| 1.47
Line 35:		Line 35:
	\| 78732/78125, {{monzo\| 41 -20 -4 }}		\| 78732/78125, {{monzo\| 41 -20 -4 }}
	\| {{mapping\| 176 279 409 }}		\| {{mapping\| 176 279 409 }}
	\| ~~−0~~.400		\| −0.400
	\| 0.432		\| 0.432
	\| 6.34		\| 6.34
Line 42:		Line 42:
	\| 6144/6125, 10976/10935, 50421/50000		\| 6144/6125, 10976/10935, 50421/50000
	\| {{mapping\| 176 279 409 494 }}		\| {{mapping\| 176 279 409 494 }}
	\| ~~−0~~.243		\| −0.243
	\| 0.463		\| 0.463
	\| 6.79		\| 6.79
Line 49:		Line 49:
	\| 441/440, 3388/3375, 6144/6125, 8019/8000		\| 441/440, 3388/3375, 6144/6125, 8019/8000
	\| {{mapping\| 176 279 409 494 609 }}		\| {{mapping\| 176 279 409 494 609 }}
	\| ~~−0~~.250		\| −0.250
	\| 0.414		\| 0.414
	\| 6.08		\| 6.08
Line 56:		Line 56:
	\| 351/350, 364/363, 441/440, 2197/2187, 3146/3125		\| 351/350, 364/363, 441/440, 2197/2187, 3146/3125
	\| {{mapping\| 176 279 409 494 609 651 }}		\| {{mapping\| 176 279 409 494 609 651 }}
	\| ~~−0~~.123		\| −0.123
	\| 0.473		\| 0.473
	\| 6.93		\| 6.93
Line 65:		Line 65:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br>per 8ve		! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>ratio*		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 114:		Line 114:
	\|-		\|-
	\| 4		\| 4
	\| 73\176<br>(15\176)		\| 73\176<br />(15\176)
	\| 497.73<br>(102.27)		\| 497.73<br />(102.27)
	\| 4/3<br>(35/33)		\| 4/3<br />(35/33)
	\| [[Undim]]		\| [[Undim]]
	\|-		\|-
	\| 8		\| 8
	\| 73\176<br>(7\176)		\| 73\176<br />(7\176)
	\| 497.73<br>(47.73)		\| 497.73<br />(47.73)
	\| 4/3<br>(36/35)		\| 4/3<br />(36/35)
	\| [[Twilight]]		\| [[Twilight]]
	\|-		\|-
	\| 8		\| 8
	\| 83\176<br>(5\176)		\| 83\176<br />(5\176)
	\| 565.91<br>(34.09)		\| 565.91<br />(34.09)
	\| 168/121<br>(55/54)		\| 168/121<br />(55/54)
	\| [[Octowerck]] (176f) / octowerckis (176)		\| [[Octowerck]] (176f) / octowerckis (176)
	\|-		\|-
	\| 11		\| 11
	\| 73\176<br>(7\176)		\| 73\176<br />(7\176)
	\| 497.73<br>(47.73)		\| 497.73<br />(47.73)
	\| 4/3<br>(36/35)		\| 4/3<br />(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|-		\|-
	\| 22		\| 22
	\| 73\176<br>(1\176)		\| 73\176<br />(1\176)
	\| 497.73<br>(6.82)		\| 497.73<br />(6.82)
	\| 4/3<br>(385/384)		\| 4/3<br />(385/384)
	\| [[Icosidillic]] / [[major arcana]]		\| [[Icosidillic]] / [[major arcana]]
	\|}		\|}
	<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Countermiracle]]		[[Category:Countermiracle]]

FloraC: /* Theory */ update

2025-01-13T13:38:31Z

Theory: update

← Older revision		Revision as of 13:38, 13 January 2025
Line 5:		Line 5:
	176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo\| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.		176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo\| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.

	176edo tempers the [[64/63\|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[~~commatic~~]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.		176edo tempers the [[64/63\|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[bicommatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 176 factors into ~~{{factorization\|176}}~~, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.		Since 176 factors into 2<sup>4</sup> × 11, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: /* Regular temperament properties */ cleanup and update

2025-01-13T13:27:22Z

Regular temperament properties: cleanup and update

← Older revision		Revision as of 13:27, 13 January 2025
Line 19:		Line 19:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 65:		Line 65:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 105:		Line 105:
	\| 20.45		\| 20.45
	\| 81/80		\| 81/80
	\| [[~~Commatic~~]]		\| [[Bicommatic]]
	\|-		\|-
	\| 2		\| 2
Line 114:		Line 114:
	\|-		\|-
	\| 4		\| 4
	\| 73\176<br />(15\176)		\| 73\176<br>(15\176)
	\| 497.73<br />(102.27)		\| 497.73<br>(102.27)
	\| 4/3<br />(35/33)		\| 4/3<br>(35/33)
	\| [[Undim]]		\| [[Undim]]
	\|-		\|-
	\| 8		\| 8
	\| 73\176<br />(7\176)		\| 73\176<br>(7\176)
	\| 497.73<br />(47.73)		\| 497.73<br>(47.73)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Twilight]]		\| [[Twilight]]
	\|-		\|-
	\| 8		\| 8
	\| 83\176<br />(5\176)		\| 83\176<br>(5\176)
	\| 565.91<br />(34.09)		\| 565.91<br>(34.09)
	\| 168/121<br />(55/54)		\| 168/121<br>(55/54)
	\| [[Octowerck]] (176f) / octowerckis (176)		\| [[Octowerck]] (176f) / octowerckis (176)
	\|-		\|-
	\| 11		\| 11
	\| 73\176<br />(7\176)		\| 73\176<br>(7\176)
	\| 497.73<br />(47.73)		\| 497.73<br>(47.73)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|-		\|-
	\| 22		\| 22
	\| 73\176<br />(1\176)		\| 73\176<br>(1\176)
	\| 497.73<br />(6.82)		\| 497.73<br>(6.82)
	\| 4/3<br />(385/384)		\| 4/3<br>(385/384)
	\| [[Icosidillic]] / [[major arcana]]		\| [[Icosidillic]] / [[major arcana]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Countermiracle]]		[[Category:Countermiracle]]

AthiTrydhen at 20:37, 1 December 2024

2024-12-01T20:37:51Z

← Older revision		Revision as of 20:37, 1 December 2024
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 176 factors into {{factorization\|176}}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 44, and 88 }}.		Since 176 factors into {{factorization\|176}}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 44, and 88 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

Lucius Chiaraviglio: /* Theory */ Add link to ruthenium temperament

2024-11-21T23:17:00Z

Theory: Add link to ruthenium temperament

← Older revision		Revision as of 23:17, 21 November 2024
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	176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo\| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.		176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo\| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.

	It [[support]]s the [[bison]] temperament and the [[commatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.		176edo tempers the [[64/63\|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[commatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 176 factors into {{factorization\|176}}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 44, and 88 }}.		Since 176 factors into {{factorization\|176}}, 176edo has subset edos {{EDOs\| 2, 4, 8, 11, 22, 44, and 88 }}.

	== Regular temperament properties ==		== Regular temperament properties ==