1944edo - 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"

2026-03-13T13:33:17Z

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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	\| [[Jamala]]		\| [[Jamala]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T06:18:51Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:18, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1944~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:02, 15 January 2025

2025-01-15T16:02:30Z

← Older revision		Revision as of 16:02, 15 January 2025
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	\| [[Jamala]]		\| [[Jamala]]
	\|}		\|}
	<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

2024-11-16T13:20:19Z

Partial undo

← Older revision		Revision as of 13:20, 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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	\| 73205/53248<br />(?)		\| 73205/53248<br />(?)
	\| [[Jamala]]		\| [[Jamala]]
	~~{{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 01:35, 16 November 2024

2024-11-16T01:35:14Z

← Older revision		Revision as of 01:35, 16 November 2024
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	== 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
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	\| 73205/53248<br />(?)		\| 73205/53248<br />(?)
	\| [[Jamala]]		\| [[Jamala]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:52, 16 November 2024

2024-11-16T00:52:19Z

← Older revision		Revision as of 00:52, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\|-		\|-
	\| 24		\| 24
	\| 944\1944<br>(53\1944)		\| 944\1944<br />(53\1944)
	\| 582.716<br>(32.716)		\| 582.716<br />(32.716)
	\| 7/5<br>(?)		\| 7/5<br />(?)
	\| [[Chromium]] (1944d)		\| [[Chromium]] (1944d)
	\|-		\|-
	\| 72		\| 72
	\| 892\1944<br>(1\1944)		\| 892\1944<br />(1\1944)
	\| 550.617<br>(0.617)		\| 550.617<br />(0.617)
	\| 73205/53248<br>(?)		\| 73205/53248<br />(?)
	\| [[Jamala]]		\| [[Jamala]]
	\|}		\|}
	~~<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}}

Eliora: /* Theory */

2024-02-24T22:50:33Z

Theory

← Older revision		Revision as of 22:50, 24 February 2024
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	== Theory ==		== Theory ==
	1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1\|7]] is about halfway between its steps. In the 5-limit, it [[tempering out\|tempers out]] the [[luna comma]], {{monzo\| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system, tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament.		1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1\|7]] is about halfway between its steps. In the 5-limit, it [[tempering out\|tempers out]] the [[luna comma]], {{monzo\| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament, providing a tuning close to [[POTE]] tuning.

	In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.		In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1944 factors into {{factorization\|1944}}, 1944edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972 }}.		Since 1944 factors into {{factorization\|1944}}, 1944edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972 }}.

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

FloraC: Rework theory; +subsets and supersets

2023-10-30T12:19:29Z

Rework theory; +subsets and supersets

← Older revision		Revision as of 12:19, 30 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far. In the 5-limit, it ~~does temper~~ out the [[luna comma]], {{monzo\| 38 -2 -15 }}. In the 1944d val in the 7-limit, it is a [[landscape]] system, tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament.		1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1\|7]] is about halfway between its steps. In the 5-limit, it [[tempering out\|tempers out]] the [[luna comma]], {{monzo\| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system, tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament.

	In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.		In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.
Line 9:		Line 9:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1944}}		{{Harmonics in equal\|1944}}

			=== Subsets and supersets ===
			Since 1944 factors into {{factorization\|1944}}, 1944edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

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

2023-10-15T14:04:27Z

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

← Older revision		Revision as of 14:04, 15 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1944}}		{{EDO intro\|1944}}

	== Theory ==		== Theory ==
	1944edo is consistent in the 5-limit to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far. In the 5-limit, it does temper out the [[luna]] ~~comma~~, {{monzo\|38 -2 -15}}. In the 1944d val in the 7-limit, it is a landscape system, tempering out 250047/250000, and as a consequence it tunes the 24th-octave [[chromium]] temperament.		1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far. In the 5-limit, it does temper out the [[luna comma]], {{monzo\| 38 -2 -15 }}. In the 1944d val in the 7-limit, it is a [[landscape]] system, tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament.

	In higher limits, 1944edo is a tuning for the [[~~Jamala~~]] temperament in the 2.5.11.13.19.41.47 subgroup, for which 1944edo provides good approximation (except for the 13th harmonic) ~~and which is named after an [[wikipedia:Jamala\|artist]] who performed a [[wikipedia:1944 (song)\|song about the same year as the edo number]]~~. Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.		In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|1944}}		{{Harmonics in equal\|1944}}

	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods<br>per 8ve		! Periods<br>per 8ve
	!Generator~~<br>(reduced)~~		! Generator*
	!Cents<br>~~(reduced)~~		! Cents*
	~~!Associated ratio~~		! Associated<br>Ratio
	!Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|313\1944		\| 313\1944
	\|193.210		\| 193.210
	\|262144/234375		\| 262144/234375
	\|[[Luna]] (5-limit)		\| [[Luna]] (5-limit)
	\|-		\|-
	\|24		\| 24
	\|944\1944<br>(53\1944)		\| 944\1944<br>(53\1944)
	\|582.716<br>(32.716)		\| 582.716<br>(32.716)
	\|7/5<br>(?)		\| 7/5<br>(?)
	\|[[Chromium]] (1944d)		\| [[Chromium]] (1944d)
	\|-		\|-
	\|72		\| 72
	\|892\1944<br>(1\1944)		\| 892\1944<br>(1\1944)
	\|550.617<br>(0.617)		\| 550.617<br>(0.617)
	\|73205/53248<br>(?)		\| 73205/53248<br>(?)
	\|[[Jamala]]		\| [[Jamala]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Eliora: /* Regular temperament properties */

2023-07-10T22:53:15Z

Regular temperament properties

← Older revision		Revision as of 22:53, 10 July 2023
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	{{harmonics in equal\|1944}}		{{harmonics in equal\|1944}}
	== Regular temperament properties ==		== Regular temperament properties ==
			=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods<br>per 8ve		!Periods<br>per 8ve