472edo - Revision history

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"

2026-03-13T13:33:01Z

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 13:33, 13 March 2026
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	\| [[Octant]]		\| [[Octant]]
	\|}		\|}
	<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

ArrowHead294 at 22:38, 20 February 2025

2025-02-20T22:38:33Z

← Older revision		Revision as of 22:38, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:10, 15 January 2025

2025-01-15T18:10:51Z

← Older revision		Revision as of 18:10, 15 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|472~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
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	\| 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095		\| 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095
	\| [{{val\| 472 748 1096 1325 1633 1747 }}]		\| [{{val\| 472 748 1096 1325 1633 1747 }}]
	\| ~~−0~~.0341		\| −0.0341
	\| 0.1365		\| 0.1365
	\| 5.37		\| 5.37
Line 89:		Line 89:
	\| [[Octant]]		\| [[Octant]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T12:48:31Z

Partial undo

← Older revision		Revision as of 12:48, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
Line 36:		Line 45:
	\| 0.1365		\| 0.1365
	\| 5.37		\| 5.37
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.		Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.

	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 72:		Line 88:
	\| 4/3<br />(36/35)		\| 4/3<br />(36/35)
	\| [[Octant]]		\| [[Octant]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 03:49, 16 November 2024

2024-11-16T03:49:58Z

← Older revision		Revision as of 03:49, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
Line 41:		Line 33:
	\| 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095		\| 729/728, 1575/1573, 2200/2197, 2401/2400, 4096/4095
	\| [{{val\| 472 748 1096 1325 1633 1747 }}]		\| [{{val\| 472 748 1096 1325 1633 1747 }}]
	\| -0.0341		\| −0.0341
	\| 0.1365		\| 0.1365
	\| 5.37		\| 5.37
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.		Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.

	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 8		\| 8
	\| 196\472<br>(19\472)		\| 196\472<br />(19\472)
	\| 498.31<br>(48.31)		\| 498.31<br />(48.31)
	\| 4/3<br>(36/35)		\| 4/3<br />(36/35)
	\| [[Octant]]		\| [[Octant]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

FloraC: Cleanup; clarify the title row of the rank-2 temp table; -redundant categories

2023-11-03T06:43:18Z

Cleanup; clarify the title row of the rank-2 temp table; -redundant categories

← Older revision		Revision as of 06:43, 3 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	472edo is [[~~Enfactoring~~\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is [[consistent]] to the [[11-odd-limit]], or the no-13 29-odd-limit. In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid\|maviloid]] temperament, the [[Schismatic family #Bisesqui\|bisesqui temperament]], and the [[Schismatic family #Octant\|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.		472edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is a [[zeta peak integer edo]], [[consistent]] to the [[11-odd-limit]] or the no-13 [[29-odd-limit]].

	~~472edo is a~~ [[~~zeta peak integer edo~~]].		In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[maviloid]] temperament, the [[Schismatic family #Bisesqui\|bisesqui]] temperament, and the [[octant]] temperament. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 472 factors into ~~2<sup>3</sup> × 59~~, 472edo has subset edos {{EDOs\| 2, 4, 8, 59, 118, and 236 }}.		Since 472 factors into {{factorization\|472}}, 472edo has subset edos {{EDOs\| 2, 4, 8, 59, 118, and 236 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Octant]]		\| [[Octant]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct
	[[~~Category:Zeta~~\|~~###~~]] <!-~~- 3-digit number -->~~

Eliora: /* Rank-2 temperaments */

2023-10-22T00:16:05Z

Rank-2 temperaments

← Older revision		Revision as of 00:16, 22 October 2023
Line 51:		Line 51:
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per ~~Octave~~		! Periods<br>per 8ve
	! Generator<br>(Reduced)		! Generator<br>(Reduced)
	! Cents<br>(Reduced)		! Cents<br>(Reduced)

FloraC: /* Theory */ actually consistent to the no-13 29-odd-limit

2023-07-31T11:07:09Z

Theory: actually consistent to the no-13 29-odd-limit

← Older revision		Revision as of 11:07, 31 July 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	472edo is [[Enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is [[consistent]] to the [[11-odd-limit]]. In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid\|maviloid]] temperament, the [[Schismatic family #Bisesqui\|bisesqui temperament]], and the [[Schismatic family #Octant\|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.		472edo is [[Enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is [[consistent]] to the [[11-odd-limit]], or the no-13 29-odd-limit. In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid\|maviloid]] temperament, the [[Schismatic family #Bisesqui\|bisesqui temperament]], and the [[Schismatic family #Octant\|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

	472edo is a [[zeta peak integer edo]].		472edo is a [[zeta peak integer edo]].

FloraC: /* Theory */ quaity of higher harmonics; +subsets and supersets

2023-07-31T10:58:39Z

Theory: quaity of higher harmonics; +subsets and supersets

← Older revision		Revision as of 10:58, 31 July 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	472edo ~~is [[consistent]] to the [[11-odd-limit]]. It~~ is [[Enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid\|maviloid]] temperament, the [[Schismatic family #Bisesqui\|bisesqui temperament]], and the [[Schismatic family #Octant\|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.		472edo is [[Enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is [[consistent]] to the [[11-odd-limit]]. In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid\|maviloid]] temperament, the [[Schismatic family #Bisesqui\|bisesqui temperament]], and the [[Schismatic family #Octant\|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

	472edo is a [[zeta peak integer edo]].		472edo is a [[zeta peak integer edo]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|472\|~~columns=11~~}}		{{Harmonics in equal\|472}}

			=== Subsets and supersets ===
			Since 472 factors into 2<sup>3</sup> × 59, 472edo has subset edos {{EDOs\| 2, 4, 8, 59, 118, and 236 }}.

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

BudjarnLambeth at 06:36, 9 July 2023

2023-07-09T06:36:06Z

← Older revision		Revision as of 06:36, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|472}}		{{EDO intro\|472}}