364edo - Revision history

FloraC: /* Regular temperament properties */ +1 temp

2026-05-15T12:54:59Z

Regular temperament properties: +1 temp

← Older revision		Revision as of 12:54, 15 May 2026
Line 114:		Line 114:
	\|-		\|-
	\| 2		\| 2
	\| 57\364		\| 125\364<br>(57\364)
	\| 187.91		\| 412.09<br>(187.91)
	\| 49/44		\| 80/63<br>(49/44)
	\| [[Semiwitcher]]		\| [[Semiwitcher]]
			\|-
			\| 2
			\| 151\364<br>(31\364)
			\| 497.80<br>(102.20)
			\| 4/3<br>(35/33)
			\| [[Gariwizmic]]
	\|-		\|-
	\| 4		\| 4

FloraC: General cleanup. + second harmonics table

2026-05-15T12:48:33Z

General cleanup. + second harmonics table

← Older revision		Revision as of 12:48, 15 May 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	364edo is [[consistent]] through the [[21-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 ([[wizma]]) in the [[7-limit]] ([[support]]ing [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[9801/9800]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]]; [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], [[10985/10976]], and 14641/14625 in the [[13-limit]]; [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], [[2431/2430]], [[4914/4913]], [[5832/5831]], and 8624/8619 in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], and [[1729/1728]] in the [[19-limit]].		364edo is [[consistent]] through the [[21-odd-limit]] with good average accuracy.

			As an equal temperament, it [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 ([[wizma]]) in the [[7-limit]] ([[support]]ing [[fifthplus]] and [[oquatonic]]); [[1375/1372]], [[6250/6237]], [[9801/9800]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]]; [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], [[10985/10976]], and 14641/14625 in the [[13-limit]]; [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], [[2431/2430]], [[4914/4913]], [[5832/5831]], and 8624/8619 in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], and [[1729/1728]] in the [[19-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|364}}		{{Harmonics in equal\|364\|columns=11}}
			{{Harmonics in equal\|364\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 364edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 364 factors into 2<sup>2</sup> × 7 × 13, 364edo has subset edos {{EDOs\| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}.		Since 364 factors into primes as {{nowrap\| 2<sup>2</sup> × 7 × 13 }}, 364edo has subset edos {{EDOs\| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}.

	=== Miscellany ===		=== Miscellany ===
Line 20:		Line 23:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
Line 27:		Line 30:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 577 -364 }}		\| {{Monzo\| 577 -364 }}
	\| {{~~mapping~~\| 364 577 }}		\| {{Mapping\| 364 577 }}
	\| −0.0766		\| −0.0766
	\| 0.0766		\| 0.0766
Line 35:		Line 38:
	\| 2.3.5		\| 2.3.5
	\| 1600000/1594323, {{monzo\| -65 0 28 }}		\| 1600000/1594323, {{monzo\| -65 0 28 }}
	\| {{~~mapping~~\| 364 577 845 }}		\| {{Mapping\| 364 577 845 }}
	\| +0.0350		\| +0.0350
	\| 0.1698		\| 0.1698
Line 42:		Line 45:
	\| 2.3.5.7		\| 2.3.5.7
	\| 65625/65536, 390625/388962, 420125/419904		\| 65625/65536, 390625/388962, 420125/419904
	\| {{~~mapping~~\| 364 577 845 1022 }}		\| {{Mapping\| 364 577 845 1022 }}
	\| −0.0098		\| −0.0098
	\| 0.1662		\| 0.1662
Line 49:		Line 52:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 1375/1372, 6250/6237, 19712/19683, 41503/41472		\| 1375/1372, 6250/6237, 19712/19683, 41503/41472
	\| {{~~mapping~~\| 364 577 845 1022 1259 }}		\| {{Mapping\| 364 577 845 1022 1259 }}
	\| +0.0366		\| +0.0366
	\| 0.1753		\| 0.1753
Line 56:		Line 59:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625		\| 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625
	\| {{~~mapping~~\| 364 577 845 1022 1259 1347 }}		\| {{Mapping\| 364 577 845 1022 1259 1347 }}
	\| +0.0245		\| +0.0245
	\| 0.1622		\| 0.1622
Line 63:		Line 66:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197		\| 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197
	\| {{~~mapping~~\| 364 577 845 1022 1259 1347 1488 }}		\| {{Mapping\| 364 577 845 1022 1259 1347 1488 }}
	\| +0.0022		\| +0.0022
	\| 0.1599		\| 0.1599
Line 70:		Line 73:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728		\| 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728
	\| {{~~mapping~~\| 364 577 845 1022 1259 1347 1488 1546 }}		\| {{Mapping\| 364 577 845 1022 1259 1347 1488 1546 }}
	\| +0.0257		\| +0.0257
	\| 0.1620		\| 0.1620
Line 80:		Line 83:
	\|+ 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
	\|-		\|-
Line 90:		Line 93:
	\| 339.56		\| 339.56
	\| 243/200		\| 243/200
	\| [[~~Amity]] / [[paramity~~]]		\| [[Paramity]]
	\|-		\|-
	\| 1		\| 1
Line 96:		Line 99:
	\| 412.09		\| 412.09
	\| 80/63		\| 80/63
	\| [[~~Witch~~]]		\| [[Witcher]]
	\|-		\|-
	\| 1		\| 1
Line 114:		Line 117:
	\| 187.91		\| 187.91
	\| 49/44		\| 49/44
	\| [[~~Semiwitch~~]]		\| [[Semiwitcher]]
	\|-		\|-
	\| 4		\| 4
Line 123:		Line 126:
	\|-		\|-
	\| 13		\| 13
	\| 151\364<br />(11\364)		\| 151\364<br>(11\364)
	\| 497.80<br />(36.26)		\| 497.80<br>(36.26)
	\| 4/3<br />(?)		\| 4/3<br>(?)
	\| [[Aluminium]]		\| [[Aluminium]]
	\|-		\|-
	\| 26		\| 26
	\| 151\364<br />(11\364)		\| 151\364<br>(11\364)
	\| 497.80<br />(36.26)		\| 497.80<br>(36.26)
	\| 4/3<br />(?)		\| 4/3<br>(?)
	\| [[Iron]]		\| [[Iron]]
	\|-		\|-
	\| 28		\| 28
	\| 151\364<br />(5\364)		\| 151\364<br>(5\364)
	\| 497.80<br />(16.48)		\| 497.80<br>(16.48)
	\| 4/3<br />(105/104)		\| 4/3<br>(105/104)
	\| [[Oquatonic]]		\| [[Oquatonic]]
	\|-		\|-
	\| 91		\| 91
	\| 151\364<br />(3\364)		\| 151\364<br>(3\364)
	\| 497.80<br />(3.30)		\| 497.80<br>(3.30)
	\| 4/3<br />(176/175)		\| 4/3<br>(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==
	* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30		* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30

ArrowHead294 at 22:42, 20 February 2025

2025-02-20T22:42:38Z

← Older revision		Revision as of 22:42, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|364~~}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 29:		Line 29:
	\| {{monzo\| 577 -364 }}		\| {{monzo\| 577 -364 }}
	\| {{mapping\| 364 577 }}		\| {{mapping\| 364 577 }}
	\| -0.0766		\| −0.0766
	\| 0.0766		\| 0.0766
	\| 2.32		\| 2.32
Line 43:		Line 43:
	\| 65625/65536, 390625/388962, 420125/419904		\| 65625/65536, 390625/388962, 420125/419904
	\| {{mapping\| 364 577 845 1022 }}		\| {{mapping\| 364 577 845 1022 }}
	\| -0.0098		\| −0.0098
	\| 0.1662		\| 0.1662
	\| 5.04		\| 5.04

FloraC: /* Theory */ cleanup

2025-01-17T16:04:41Z

Theory: cleanup

← Older revision		Revision as of 16:04, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	364edo is [[consistent]] through the [[21-odd-limit]]. It [[tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 (wizma) in the [[7-limit]] (~~supporting~~ [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]] ~~(as well as [[9801/9800]])~~; [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], ~~and 14641/14625 in the [[13-limit]] (as well as~~ [[4096/4095]], [[4225/4224]], ~~and~~ [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], ~~and 8624/8619 in the [[17-limit]] (as well as~~ [[2431/2430]], [[4914/4913]], ~~and~~ [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].		364edo is [[consistent]] through the [[21-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 ([[wizma]]) in the [[7-limit]] ([[support]]ing [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[9801/9800]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]]; [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], [[10985/10976]], and 14641/14625 in the [[13-limit]]; [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], [[2431/2430]], [[4914/4913]], [[5832/5831]], and 8624/8619 in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], and [[1729/1728]] in the [[19-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|364~~\|columns=11~~}}		{{Harmonics in equal\|364}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 364 factors into ~~{{factorization\|364}}~~, 364edo has subset edos {{EDOs\| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}.		Since 364 factors into 2<sup>2</sup> × 7 × 13, 364edo has subset edos {{EDOs\| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}.

	=== ~~Miscellaneous properties~~ ===		=== Miscellany ===
	364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after.		364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after.

ArrowHead294 at 14:47, 16 January 2025

2025-01-16T14:47:34Z

← Older revision		Revision as of 14:47, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	364edo is [[consistent]] through the [[21-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], and 8624/8619 in the [[17-limit]] (as well as [[2431/2430]], [[4914/4913]], and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].		364edo is [[consistent]] through the [[21-odd-limit]]. It [[tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], and 8624/8619 in the [[17-limit]] (as well as [[2431/2430]], [[4914/4913]], and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===

ArrowHead294 at 14:47, 16 January 2025

2025-01-16T14:47:20Z

Show changes

ArrowHead294 at 14:44, 16 January 2025

2025-01-16T14:44:02Z

Show changes

ArrowHead294 at 12:12, 16 November 2024

2024-11-16T12:12:20Z

← Older revision		Revision as of 12:12, 16 November 2024
Line 15:		Line 15:

	== 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 65:		Line 74:
	\| 0.1620		\| 0.1620
	\| 4.91		\| 4.91
	~~{{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
Line 129:		Line 145:
	\| 4/3<br />(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	~~{{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

	== Scales ==		== Scales ==
	* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30		* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30

ArrowHead294 at 05:22, 16 November 2024

2024-11-16T05:22:06Z

← Older revision		Revision as of 05:22, 16 November 2024
Line 15:		Line 15:

	== 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
	\| {{monzo\| 577 -364 }}		\| {{monzo\| 577 -364 }}
	\| {{mapping\| 364 577 }}		\| {{mapping\| 364 577 }}
	\| -0.0766		\| −0.0766
	\| 0.0766		\| 0.0766
	\| 2.32		\| 2.32
Line 42:		Line 34:
	\| 65625/65536, 390625/388962, 420125/419904		\| 65625/65536, 390625/388962, 420125/419904
	\| {{mapping\| 364 577 845 1022 }}		\| {{mapping\| 364 577 845 1022 }}
	\| -0.0098		\| −0.0098
	\| 0.1662		\| 0.1662
	\| 5.04		\| 5.04
Line 73:		Line 65:
	\| 0.1620		\| 0.1620
	\| 4.91		\| 4.91
	\|}		{{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
Line 121:		Line 107:
	\|-		\|-
	\| 13		\| 13
	\| 151\364<br>(11\364)		\| 151\364<br />(11\364)
	\| 497.80<br>(36.26)		\| 497.80<br />(36.26)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Aluminium]]		\| [[Aluminium]]
	\|-		\|-
	\| 26		\| 26
	\| 151\364<br>(11\364)		\| 151\364<br />(11\364)
	\| 497.80<br>(36.26)		\| 497.80<br />(36.26)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Iron]]		\| [[Iron]]
	\|-		\|-
	\| 28		\| 28
	\| 151\364<br>(5\364)		\| 151\364<br />(5\364)
	\| 497.80<br>(16.48)		\| 497.80<br />(16.48)
	\| 4/3<br>(105/104)		\| 4/3<br />(105/104)
	\| [[Oquatonic]]		\| [[Oquatonic]]
	\|-		\|-
	\| 91		\| 91
	\| 151\364<br>(3\364)		\| 151\364<br />(3\364)
	\| 497.80<br>(3.30)		\| 497.80<br />(3.30)
	\| 4/3<br>(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		{{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}}

	== Scales ==		== Scales ==
	* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30		* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30

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

2023-11-09T15:14:01Z

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

← Older revision		Revision as of 15:14, 9 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	364edo is consistent through the [[21-odd-limit]], [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }}; ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 (horwell), 390625/388962 ([[~~Dimcomp~~ comma~~\|dimcomp~~]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and 41503/41472 in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], 1275/1274, 2025/2023, and 8624/8619 in the [[17-limit]] (as well as 2431/2430, 4914/4913, and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].		364edo is [[consistent]] through the [[21-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], and 8624/8619 in the [[17-limit]] (as well as [[2431/2430]], [[4914/4913]], and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].

	~~364 is divisible by, and thus contains sub-edos {{EDOs\|1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182}}~~.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|364\|columns=11}}		{{Harmonics in equal\|364\|columns=11}}

			=== Subsets and supersets ===
			Since 364 factors into {{factorization\|364}}, 364edo has subset edos {{EDOs\| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}.

	=== Miscellaneous properties ===		=== Miscellaneous properties ===
	364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these ~~EDos~~ are sought after.		364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after.

	== 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]]		! 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]] (¢)
Line 26:		Line 27:
	\| 2.3		\| 2.3
	\| {{monzo\| 577 -364 }}		\| {{monzo\| 577 -364 }}
	\| [{{~~val~~\| 364 577 }}]		\| {{mapping\| 364 577 }}
	\| -0.0766		\| -0.0766
	\| 0.0766		\| 0.0766
Line 33:		Line 34:
	\| 2.3.5		\| 2.3.5
	\| 1600000/1594323, {{monzo\| -65 0 28 }}		\| 1600000/1594323, {{monzo\| -65 0 28 }}
	\| [{{~~val~~\| 364 577 845 }}]		\| {{mapping\| 364 577 845 }}
	\| +0.0350		\| +0.0350
	\| 0.1698		\| 0.1698
Line 40:		Line 41:
	\| 2.3.5.7		\| 2.3.5.7
	\| 65625/65536, 390625/388962, 420125/419904		\| 65625/65536, 390625/388962, 420125/419904
	\| [{{~~val~~\| 364 577 845 1022 }}]		\| {{mapping\| 364 577 845 1022 }}
	\| -0.0098		\| -0.0098
	\| 0.1662		\| 0.1662
Line 47:		Line 48:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 1375/1372, 6250/6237, 19712/19683, 41503/41472		\| 1375/1372, 6250/6237, 19712/19683, 41503/41472
	\| [{{~~val~~\| 364 577 845 1022 1259 }}]		\| {{mapping\| 364 577 845 1022 1259 }}
	\| +0.0366		\| +0.0366
	\| 0.1753		\| 0.1753
Line 54:		Line 55:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625		\| 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625
	\| [{{~~val~~\| 364 577 845 1022 1259 1347 }}]		\| {{mapping\| 364 577 845 1022 1259 1347 }}
	\| +0.0245		\| +0.0245
	\| 0.1622		\| 0.1622
Line 61:		Line 62:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197		\| 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197
	\| [{{~~val~~\| 364 577 845 1022 1259 1347 1488 }}]		\| {{mapping\| 364 577 845 1022 1259 1347 1488 }}
	\| +0.0022		\| +0.0022
	\| 0.1599		\| 0.1599
Line 68:		Line 69:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728		\| 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728
	\| [{{~~val~~\| 364 577 845 1022 1259 1347 1488 1546 }}]		\| {{mapping\| 364 577 845 1022 1259 1347 1488 1546 }}
	\| +0.0257		\| +0.0257
	\| 0.1620		\| 0.1620
Line 78:		Line 79:
	\|+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
	\|-		\|-
Line 137:		Line 138:
	\| [[Oquatonic]]		\| [[Oquatonic]]
	\|-		\|-
	\|91		\| 91
	\| 151\364<br>(3\364)		\| 151\364<br>(3\364)
	\| 497.80<br>(3.30)		\| 497.80<br>(3.30)
	\| 4/3<br>(176/175)		\| 4/3<br>(176/175)
	\|[[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
			<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:Equal divisions of~~ the octave\|~~###~~]]

	== Scales ==		== Scales ==
			* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30
	* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30~~<!-- 3-digit number -->~~