720edo - 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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	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		\|}
	<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:Schismic]]		[[Category:Schismic]]
	[[Category:Octant]]		[[Category:Octant]]

FloraC: Text replacement - "Category:Schismatic" to "Category:Schismic"

2026-01-07T09:11:51Z

Text replacement - "Category:Schismatic" to "Category:Schismic"

← Older revision		Revision as of 09:11, 7 January 2026
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	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:~~Schismatic~~]]		[[Category:Schismic]]
	[[Category:Octant]]		[[Category:Octant]]

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:30:34Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:30, 17 April 2025
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	\| 701.667		\| 701.667
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|-		\|-
	\| 8		\| 8

Sintel: fix helmholtz link

2025-04-16T15:36:26Z

fix helmholtz link

← Older revision		Revision as of 15:36, 16 April 2025
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	\| 701.667		\| 701.667
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|-		\|-
	\| 8		\| 8

ArrowHead294 at 22:57, 20 February 2025

2025-02-20T22:57:31Z

← Older revision		Revision as of 22:57, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|720~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:02, 15 January 2025

2025-01-15T16:02:00Z

← Older revision		Revision as of 16:02, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	720edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).		720edo is the 14th [[superabundant edo]], and also the 6th factorial edo ({{nowrap\|720 {{=}} 1 × 2 × 3 × 4 × 5 × 6 {{=}} 6!}}), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).

	Since {{nowrap\|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.		Since {{nowrap\|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.
Line 50:		Line 50:
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		\|}
	<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:Schismatic]]		[[Category:Schismatic]]
	[[Category:Octant]]		[[Category:Octant]]

Eliora: /* Subsets and supersets */

2024-11-25T01:24:42Z

Subsets and supersets

← Older revision		Revision as of 01:24, 25 November 2024
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	720edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out~~{{clarify}}~~.		720edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).

	Since {{nowrap\|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.		Since {{nowrap\|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.

ArrowHead294: Partial undo

2024-11-16T13:14:14Z

Partial undo

← Older revision		Revision as of 13:14, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{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
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	\| 130/99<br />(?)		\| 130/99<br />(?)
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	~~{{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

	[[Category:Schismatic]]		[[Category:Schismatic]]
	[[Category:Octant]]		[[Category:Octant]]

ArrowHead294: /* Regular temperament properties */

2024-11-16T01:50:07Z

Regular temperament properties

← Older revision		Revision as of 01:50, 16 November 2024
Line 17:		Line 17:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 49:		Line 42:
	\| 130/99<br />(?)		\| 130/99<br />(?)
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

	[[Category:Schismatic]]		[[Category:Schismatic]]
	[[Category:Octant]]		[[Category:Octant]]

ArrowHead294 at 01:12, 16 November 2024

2024-11-16T01:12:11Z

← Older revision		Revision as of 01:12, 16 November 2024
Line 13:		Line 13:
	720edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out{{clarify}}.		720edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out{{clarify}}.

	Since 720 = 72 × 10, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.		Since {{nowrap\|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.

	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+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
	\|-		\|-
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	\|-		\|-
	\| 8		\| 8
	\| 421\720<br>(61\720)		\| 421\720<br />(61\720)
	\| 701.667<br>(101.667)		\| 701.667<br />(101.667)
	\| 4/3<br>(36/35)		\| 4/3<br />(36/35)
	\| [[Octant]]		\| [[Octant]]
	\|-		\|-
	\| 80		\| 80
	\| 421\720<br>(7\720)		\| 421\720<br />(7\720)
	\| 701.667<br>(11.667)		\| 701.667<br />(11.667)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Octogintic]]		\| [[Octogintic]]
	\|-		\|-
	\| 80		\| 80
	\| 283\720<br>(4\720)		\| 283\720<br />(4\720)
	\| 471.667<br>(6.667)		\| 471.667<br />(6.667)
	\| 130/99<br>(?)		\| 130/99<br />(?)
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		\|}
	~~<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}}

	[[Category:Schismatic]]		[[Category:Schismatic]]
	[[Category:Octant]]		[[Category:Octant]]