1920edo - 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"

2026-03-13T13:30:05Z

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 13:30, 13 March 2026
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	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|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

	== Music ==		== Music ==

FloraC: Expand the harmonics table a little. Misc. cleanup

2025-10-02T16:14:05Z

Expand the harmonics table a little. Misc. cleanup

← Older revision		Revision as of 16:14, 2 October 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1920\|columns=9}}		{{Harmonics in equal\|1920\|columns=11}}
	{{Harmonics in equal\|1920\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 1920edo (continued)}}		{{Harmonics in equal\|1920\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 1920edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
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	\|+ 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
	\|-		\|-
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	\|-		\|-
	\| 30		\| 30
	\| 583\1920<br />(7\1920)		\| 583\1920<br>(7\1920)
	\| 364.375<br />(4.375)		\| 364.375<br>(4.375)
	\| 216/175<br />(385/384)		\| 216/175<br>(385/384)
	\| [[Zinc]]		\| [[Zinc]]
	\|-		\|-
	\| 60		\| 60
	\| 583\1920<br />(7\1920)		\| 583\1920<br>(7\1920)
	\| 364.375<br />(4.375)		\| 364.375<br>(4.375)
	\| 216/175<br />(385/384)		\| 216/175<br>(385/384)
	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: /* Theory */ +some commas; misc. cleanup

2025-03-07T07:54:31Z

Theory: +some commas; misc. cleanup

← Older revision		Revision as of 07:54, 7 March 2025
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	== Theory ==		== Theory ==
	1920edo is [[consistency\|distinctly consistent]] through the [[25-odd-limit]], and in terms of 23-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], only [[1578edo\|1578]] and [[1889edo\|1889]] are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31-, 37-, 41-, 43- and 47-limit, nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for [[interval size measure]].		1920edo is [[consistency\|distinctly consistent]] through the [[25-odd-limit]], and in terms of [[23-limit]] [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], only [[1578edo\|1578]] and [[1889edo\|1889]] are both smaller and with a lower relative error. In the [[29-limit]], only 1578 beats it, and in the [[31-limit\|31-]], [[37-limit\|37-]], [[41-limit\|41-]], [[43-limit\|43-]] and [[47-limit]], nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for [[interval size measure]].

			As a micro- (or nano-) temperament, it is a [[landscape]] system in the [[7-limit]], [[tempering out]] [[250047/250000]], and in the [[11-limit]] it tempers out [[9801/9800]]. Beyond that, it tempers out [[10648/10647]] in the [[13-limit]]; [[5832/5831]] and [[14400/14399]] in the [[17-limit]]; [[4200/4199]], [[5985/5984]], and 6860/6859 in the [[19-limit]]; and [[3381/3380]] in the 23-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1920\|columns=15}}		{{Harmonics in equal\|1920\|columns=9}}
			{{Harmonics in equal\|1920\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 1920edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1920 factors into {{~~factorization~~\|~~1920~~}}, 1920edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960 }}.		Since 1920 factors into {{nowrap\| 2<sup>7</sup> × 3 × 5 }}, 1920edo has subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960 }}.

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

ArrowHead294 at 14:11, 20 February 2025

2025-02-20T14:11:15Z

← Older revision		Revision as of 14:11, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1920~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:07, 15 January 2025

2025-01-15T16:07:03Z

← Older revision		Revision as of 16:07, 15 January 2025
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	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	\|}		\|}
	<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

	== Music ==		== Music ==

ArrowHead294: Partial undo

2024-11-16T13:16:40Z

Partial undo

← Older revision		Revision as of 13:16, 16 November 2024
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	=== 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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	\| 216/175<br />(385/384)		\| 216/175<br />(385/384)
	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	~~{{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

	== Music ==		== Music ==

ArrowHead294 at 01:43, 16 November 2024

2024-11-16T01:43:50Z

← Older revision		Revision as of 01:43, 16 November 2024
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	=== 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
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	\| 216/175<br />(385/384)		\| 216/175<br />(385/384)
	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:04, 16 November 2024

2024-11-16T01:04:29Z

← Older revision		Revision as of 01:04, 16 November 2024
Line 16:		Line 16:
	=== 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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	\|-		\|-
	\| 30		\| 30
	\| 583\1920<br>(7\1920)		\| 583\1920<br />(7\1920)
	\| 364.375<br>(4.375)		\| 364.375<br />(4.375)
	\| 216/175<br>(385/384)		\| 216/175<br />(385/384)
	\| [[Zinc]]		\| [[Zinc]]
	\|-		\|-
	\| 60		\| 60
	\| 583\1920<br>(7\1920)		\| 583\1920<br />(7\1920)
	\| 364.375<br>(4.375)		\| 364.375<br />(4.375)
	\| 216/175<br>(385/384)		\| 216/175<br />(385/384)
	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	\|}		\|}
	~~<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}}

	== Music ==		== Music ==

FloraC: /* Regular temperament properties */ the ratio is found

2024-07-21T10:10:21Z

Regular temperament properties: the ratio is found

← Older revision		Revision as of 10:10, 21 July 2024
Line 33:		Line 33:
	\| 583\1920<br>(7\1920)		\| 583\1920<br>(7\1920)
	\| 364.375<br>(4.375)		\| 364.375<br>(4.375)
	\| 216/175<br>(?)		\| 216/175<br>(385/384)
	\| [[Zinc]]		\| [[Zinc]]
	\|-		\|-
Line 39:		Line 39:
	\| 583\1920<br>(7\1920)		\| 583\1920<br>(7\1920)
	\| 364.375<br>(4.375)		\| 364.375<br>(4.375)
	\| 216/175<br>(?)		\| 216/175<br>(385/384)
	\| [[Neodymium]] / [[neodymium magnet]]		\| [[Neodymium]] / [[neodymium magnet]]
	\|}		\|}

FloraC: Table title

2023-10-30T12:21:57Z

Table title

← Older revision		Revision as of 12:21, 30 October 2023
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	=== 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
			\|-
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-