392edo - 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"

2026-03-13T13:32:40Z

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 92:		Line 92:
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (5-limit)
	\|}		\|}
	<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

2025-02-21T06:27:50Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:27, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|392~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:01:07Z

Theory: cleanup

← Older revision		Revision as of 16:01, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. It [[tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].		392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. As an equal temperament, it [[tempering out\|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 ([[varunisma]]), 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 823543/819200 ([[quince comma]]) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	392 factors into ~~{{factorisation\|392}}~~, with subset edos {{EDOs\|2, 4, 7, 8, 14, 28, 49, 56, 98, and 196}}.		392 factors into 2<sup>3</sup> × 7<sup>2</sup>, with subset edos {{EDOs\| 2, 4, 7, 8, 14, 28, 49, 56, 98, and 196 }}.

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

ArrowHead294 at 18:46, 15 January 2025

2025-01-15T18:46:21Z

← Older revision		Revision as of 18:46, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].		392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. It [[tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	392 factors into ~~2<sup>3</sup> × 7<sup>2</sup>~~, with subset edos {{EDOs\|2, 4, 7, 8, 14, 28, 49, 56, 98, and 196}}.		392 factors into {{factorisation\|392}}, with subset edos {{EDOs\|2, 4, 7, 8, 14, 28, 49, 56, 98, and 196}}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 92:		Line 92:
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (5-limit)
	\|}		\|}
	<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

2024-11-16T13:02:54Z

Partial undo

← Older revision		Revision as of 13:02, 16 November 2024
Line 12:		Line 12:

	== 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		\| 2.3
Line 41:		Line 50:
	\| 0.2335		\| 0.2335
	\| 7.63		\| 7.63
	~~{{comma basis end}~~}		\|}

	=== 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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	\| 4/3<br />(105/104)		\| 4/3<br />(105/104)
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (5-limit)
	~~{{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 02:45, 16 November 2024

2024-11-16T02:45:50Z

← Older revision		Revision as of 02:45, 16 November 2024
Line 12:		Line 12:

	== 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		\| 2.3
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	\| 0.2335		\| 0.2335
	\| 7.63		\| 7.63
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| 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
	\| 185\392<br>(11\392)		\| 185\392<br />(11\392)
	\| 566.33<br>(33.67)		\| 566.33<br />(33.67)
	\| 104/75<br>(55/54)		\| 104/75<br />(55/54)
	\| [[Octowerck]] (392f)		\| [[Octowerck]] (392f)
	\|-		\|-
	\| 28		\| 28
	\| 163\392<br>(5\392)		\| 163\392<br />(5\392)
	\| 498.98<br>(15.31)		\| 498.98<br />(15.31)
	\| 4/3<br>(105/104)		\| 4/3<br />(105/104)
	\| [[Oquatonic]] (5-limit)		\| [[Oquatonic]] (5-limit)
	\|}		{{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: +11-limit commas

2024-01-01T09:30:37Z

+11-limit commas

← Older revision		Revision as of 09:30, 1 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. The equal temperament [[tempering out\|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit. It [[support]]s [[qak]] and [[octowerck]].		392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. The equal temperament [[tempering out\|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	\| {{monzo\| -621 392 }}		\| {{monzo\| -621 392 }}
	\| {{mapping\| 392 621 }}		\| {{mapping\| 392 621 }}
	\| 0.2948		\| +0.2948
	\| 0.2949		\| 0.2949
	\| 9.63		\| 9.63
Line 32:		Line 32:
	\| {{monzo\| 8 14 -13 }}, {{monzo\| -49 28 2 }}		\| {{monzo\| 8 14 -13 }}, {{monzo\| -49 28 2 }}
	\| {{mapping\| 392 621 910 }}		\| {{mapping\| 392 621 910 }}
	\| 0.2826		\| +0.2826
	\| 0.2414		\| 0.2414
	\| 7.89		\| 7.89
Line 39:		Line 39:
	\| 321489/320000, 420175/419904, 703125/702464		\| 321489/320000, 420175/419904, 703125/702464
	\| {{mapping\| 392 621 910 1100 }}		\| {{mapping\| 392 621 910 1100 }}
	\| 0.3437		\| +0.3437
	\| 0.2343		\| 0.2343
	\| 7.65		\| 7.65
Line 46:		Line 46:
	\| 441/440, 8019/8000, 41503/41472, 703125/702464		\| 441/440, 8019/8000, 41503/41472, 703125/702464
	\| {{mapping\| 392 621 910 1100 1356 }}		\| {{mapping\| 392 621 910 1100 1356 }}
	\| 0.2922		\| +0.2922
	\| 0.2335		\| 0.2335
	\| 7.63		\| 7.63

FloraC: Review

2024-01-01T09:28:00Z

Review

← Older revision		Revision as of 09:28, 1 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	392et is consistent to the [[7-odd-limit]]~~, although it has~~ a flat tendency in the prime ~~harmonics~~. It tempers out the parakleisma in the 5-limit; ~~184528125~~/~~184473632~~, [[703125/702464]], ~~95703125/95551488~~ and ~~420175~~/~~419904~~ in the 7-limit. ~~392edo supports~~ [[~~misneb~~]].		392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. The equal temperament [[tempering out\|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit. It [[support]]s [[qak]] and [[octowerck]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 13:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|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
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-621 392}}		\| {{monzo\| -621 392 }}
	\|{{mapping\|392 621}}		\| {{mapping\| 392 621 }}
	\| 0.2948		\| 0.2948
	\| 0.2949		\| 0.2949
	\| 9.63		\| 9.63
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|8 14 -13}}, {{monzo\|-49 28 2}}		\| {{monzo\| 8 14 -13 }}, {{monzo\| -49 28 2 }}
	\|{{mapping\|392 621 910}}		\| {{mapping\| 392 621 910 }}
	\| 0.2826		\| 0.2826
	\| 0.2414		\| 0.2414
	\| 7.89		\| 7.89
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|321489/320000, 420175/419904, 703125/702464		\| 321489/320000, 420175/419904, 703125/702464
	\|{{mapping\|392 621 910 1100}}		\| {{mapping\| 392 621 910 1100 }}
	\| 0.3437		\| 0.3437
	\| 0.2343		\| 0.2343
	\| 7.65		\| 7.65
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|441/440, 8019/8000, 41503/41472, ~~1265625~~/~~1261568~~		\| 441/440, 8019/8000, 41503/41472, 703125/702464
	\|{{mapping\|392 621 910 1100 1356}}		\| {{mapping\| 392 621 910 1100 1356 }}
	\| 0.2922		\| 0.2922
	\| 0.2335		\| 0.2335
Line 55:		Line 55:
	\|+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
	\|-		\|-
	\|1		\| 1
	\|37\392		\| 37\392
	\|113.27		\| 113.27
	\|16/15		\| 16/15
	\|[[Misneb]]		\| [[Misneb]] (5-limit)
	\|-		\|-
	\|1		\| 1
	\|103\392		\| 103\392
	\|315.31		\| 315.31
	\|6/5		\| 6/5
	\|[[Parakleismic]]		\| [[Parakleismic]] (5-limit)
	\|-		\|-
	\|1		\| 1
	\|149\392		\| 149\392
	\|456.12		\| 456.12
	\|125/96		\| 125/96
	\|[[Qak]]		\| [[Qak]]
	\|-		\|-
	\|8		\| 8
	\|185\392<br>(11\392)		\| 185\392<br>(11\392)
	\|566.33<br>(33.67)		\| 566.33<br>(33.67)
	\|104/75<br>(55/54)		\| 104/75<br>(55/54)
	\|[[Octowerck]]		\| [[Octowerck]] (392f)
	\|-		\|-
	\|28		\| 28
	\|163\392<br>(5\392)		\| 163\392<br>(5\392)
	\|498.98<br>(15.31)		\| 498.98<br>(15.31)
	\|4/3<br>(105/104)		\| 4/3<br>(105/104)
	\|[[Oquatonic]]		\| [[Oquatonic]] (5-limit)
	\|}		\|}

	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium at 16:52, 19 December 2023

2023-12-19T16:52:44Z

← Older revision		Revision as of 16:52, 19 December 2023
Line 90:		Line 90:
	\|[[Oquatonic]]		\|[[Oquatonic]]
	\|}		\|}

			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium: /* Rank-2 temperaments */ +octowerk; +oquatonic

2023-12-19T16:07:12Z

Rank-2 temperaments: +octowerk; +oquatonic

@@ Line 77: / Line 77: @@
 |125/96
 |[[Qak]]
 |}