User:Eufalesio/Telicity - Revision history

Eufalesio at 20:13, 5 January 2026

2026-01-05T20:13:43Z

← Older revision		Revision as of 20:13, 5 January 2026
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	\|-		\|-
	\|		\|
	\|		\|(1)
	\|2		\|2
	\|3		\|3
	\|4		\|4
	\|		\|(5)
	\|-		\|-
	\|		\|(1)
	\|3		\|3
	\|'''5'''		\|'''5'''
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	\|'''8'''		\|'''8'''
	\|'''''10'''''		\|'''''10'''''
	\|		\|(12)
	\|		\|(14)
	\|		\|16
	\|-		\|-
	\|		\|(2)
	\|		\|(7)
	\|'''12'''		\|'''12'''
	\|17		\|17
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	\|'''31'''		\|'''31'''
	\|''36''		\|''36''
	\|		\|(41)
	\|		\|'''46'''
	\|		\|51
	\|-		\|-
	\|		\|(17)
	\|		\|(29)
	\|'''41'''		\|'''41'''
	\|		\|(53)
	\|		\|'''65'''
	\|		\|77
	\|-		\|-
	\|		\|
	\|		\|(12)
	\|'''53'''		\|'''53'''
	\|'''94'''		\|'''94'''
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	\|176		\|176
	\|-		\|-
	\|		\|(24)
	\|'''65'''		\|'''(65)'''
	\|''106''		\|''106''
	\|147		\|147
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	\|229		\|229
	\|-		\|-
	\|77		\|(77)
	\|'''118'''		\|'''118'''
	\|'''''159'''''		\|'''''159'''''
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	\|'''224'''		\|'''224'''
	\|''265''		\|''265''
	\|		\|(306)
	\|		\|347
	\|		\|388
	\|-		\|-
	\|		\|(200)
	\|		\|(253)
	\|306		\|306
	\|359		\|359
	\|		\|412
	\|		\|465
	\|-		\|-
	\|		\|506
	\|559		\|559
	\|''612''		\|''612''
	\|		\|(665)
	\|		\|718
	\|		\|771
	\|-		\|-
	\|		\|(53)
	\|		\|(359)
	\|665		\|665
	\|971		\|971

Eufalesio at 20:04, 5 January 2026

2026-01-05T20:04:10Z

← Older revision		Revision as of 20:04, 5 January 2026
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	\|CFD+1		\|CFD+1
	\|CFD+2		\|CFD+2
	\|~~CDF~~+3		\|CFD+3
	\|-		\|-
	\|		\|

Eufalesio at 20:03, 5 January 2026

2026-01-05T20:03:30Z

Show changes

Overthink: /* Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos */ fix link

2026-01-01T04:20:02Z

Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos: fix link

← Older revision		Revision as of 04:20, 1 January 2026
Line 78:		Line 78:
	\|'''[[5edo\|5]]'''		\|'''[[5edo\|5]]'''
	\|'''[[12edo\|12]]''' [<nowiki/>[[24edo\|'''24''']]]		\|'''[[12edo\|12]]''' [<nowiki/>[[24edo\|'''24''']]]
	\|'''[[53edo\|53]]''' [<nowiki/>[[~~1590edo~~\|'''159''']]]		\|'''[[53edo\|53]]''' [<nowiki/>[[159edo\|'''159''']]]
	3-k		3-k
	\|[[306edo\|306]] ''[<nowiki/>[[612edo\|'''612''']]]''		\|[[306edo\|306]] ''[<nowiki/>[[612edo\|'''612''']]]''

Eufalesio: Added links to every telic edo and then some

2025-12-30T18:54:05Z

Added links to every telic edo and then some

← Older revision		Revision as of 18:54, 30 December 2025
Line 55:		Line 55:

	Of those, 12, 53, 665 are multitelic, because they have a k-strength value greater than one; being 2, 3, and 11 respectively, which means that [[24edo\|24]], [[106edo\|106]], [[159edo\|159]], [[1330edo\|1330]], [[1995edo\|1995]], [[2660edo\|2660]], [[3325edo\|3325]], [[3990edo\|3990]], [[4655edo\|4655]], [[5320edo\|5320]], [[5985edo\|5985]], [[6650edo\|6650]], and [[7315edo\|7315]] are also 3-2 telic.		Of those, 12, 53, 665 are multitelic, because they have a k-strength value greater than one; being 2, 3, and 11 respectively, which means that [[24edo\|24]], [[106edo\|106]], [[159edo\|159]], [[1330edo\|1330]], [[1995edo\|1995]], [[2660edo\|2660]], [[3325edo\|3325]], [[3990edo\|3990]], [[4655edo\|4655]], [[5320edo\|5320]], [[5985edo\|5985]], [[6650edo\|6650]], and [[7315edo\|7315]] are also 3-2 telic.

			A naïve way find if an edo is p-2 telic, multiply the relative error of that prime by the edo. If the error is less than 50%, it is telic.

	== Applications ==		== Applications ==
Line 73:		Line 75:
	\|+		\|+
	\|3-2 telic		\|3-2 telic
	\| ~~rowspan="5" \|1~~		\|[[2edo\|2]]
	\|2		\|'''[[5edo\|5]]'''
	\|'''5'''		\|'''[[12edo\|12]]''' [<nowiki/>[[24edo\|'''24''']]]
	\|'''12''' [24]		\|'''[[53edo\|53]]''' [<nowiki/>[[1590edo\|'''159''']]]
	\|'''53''' [159]
	3-k		3-k
	\|306 [''612'']		\|[[306edo\|306]] ''[<nowiki/>[[612edo\|'''612''']]]''
	\|'''665''' [7315]		\|'''[[665edo\|665]]''' [<nowiki/>[[7315edo\|'''7315''']]]
	11-k		11-k
	\|15601 ''[78005]''		\|[[15601edo\|'''15601''']] ''[<nowiki/>[[78005edo\|'''78005''']]]''
	\|31867		\|[[31867edo\|31867]]
	\|79335		\|[[79335edo\|79335]]
	\|190537		\|[[190537edo\|190537]]
	28-k		28-k
	\|-		\|-
	\|5-2 telic		\|5-2 telic
	\|3 [12]		\|[[3edo\|3]] [<nowiki/>[[12edo\|'''12''']]]
	4-k		4-k
	\|28		\|[[28edo\|28]]
	\|59 [118]		\|[[59edo\|59]] [<nowiki/>[[118edo\|'''118''']]]
	\|146		\|[[146edo\|146]]
	2-k		2-k
	\|'''643'''		\|'''[[643edo\|643]]'''
	3-k		3-k
	\|4004		\|[[4004edo\|4004]]
	\|8651		\|[[8651edo\|8651]]
	\|12655		\|[[12655edo\|12655]]
	\|21306		\|[[21306edo\|21306]]
	2-k		2-k
	\|97879		\|[[97879edo\|97879]]
	9-k		9-k
	\|-		\|-
	\|7-2 telic		\|7-2 telic
	\|5 [10, '~~'15~~'']		\|'''[[5edo\|5]]''' ['''[[10edo\|10]]''']
	\|'''26''' [~~52,~~ ''130'']		2-k
	\|109 ~~[218~~]		\|'''[[26edo\|26]]''' [''[[130edo\|'''130''']]'']
	~~\|571~~		2-k
			\|[[109edo\|109]]
	2-k		2-k
	\|2964		\|[[571edo\|571]]
			2-k
			\|[[2964edo\|2964]]
	15-k		15-k
	\|91313		\|[[91313edo\|91313]]
	2-k		2-k
	\|453601		\|[[453601edo\|453601]]
	4-k		4-k
	\|		\|
Line 122:		Line 126:
	\|-		\|-
	\|11-2 telic		\|11-2 telic
	\|2		\|[[2edo\|2]]
	3-k		3-k
	\|13 [26]		\|[[13edo\|13]] [<nowiki/>[[26edo\|'''26''']]]
	\|37		2-k
			\|[[37edo\|37]]
	13-k		13-k
	\|986		\|[[986edo\|986]]
	\|1935		\|[[1935edo\|1935]]
	\|4856		\|[[4856edo\|4856]]
	\|16503		\|[[16503edo\|16503]]
	12-k		12-k
	\|		\|
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	\|-		\|-
	\|13-2 telic		\|13-2 telic
	\|1		\|[[3edo\|3]]
	\|3		\|[[7edo\|'''7''']]
	\|7		\|'''[[10edo\|10]]''' [<nowiki/>[[50edo\|'''50''']], [[80edo\|'''80''']], ''[[130edo\|'''130''']], [[270edo\|'''270''']]'']
	\|10 [50, 80, ''130, 270'']~~ ~~
	11-k		11-k
	\|227 [908]		\|[[227edo\|227]] [<nowiki/>[[908edo\|908]]]
	11-k		11-k
	\|5458		\|[[5458edo\|5458]]
	4-k		4-k
	\|54353		\|[[54353edo\|54353]]
	74-k		74-k
			\|
	\|		\|
	\|		\|
	\|		\|
	\|}		\|}
	Bolded edos are notable. Edos in brackets are notable telic edo multiples, due to high consistency or accuracy of their intervals. If italicized, the edo is a multiple of the telic edo but beyond its k-strength range.		1edo and 0edo excluded. Bolded telic edos are notable. Edos in brackets are notable telic edo multiples, due to high consistency or accuracy of their intervals. If italicized, the edo is a multiple of the telic edo but beyond its k-strength range.

			Of these, the only edos ''(that I know so far)'' that are telic in many primes are 5edo (7-3-2 telic) 12edo (5-3-2 telic), and 26edo (11-7-2 telic).

	WIP		WIP

Overthink: /* ARTICLE START */ Used level 1 header

2025-12-30T01:30:21Z

ARTICLE START: Used level 1 header

← Older revision		Revision as of 01:30, 30 December 2025
Line 7:		Line 7:
	––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––		––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

	== '''ARTICLE START''' ==		= '''ARTICLE START''' =
	'''Telicity''' is a property of both [[equal temperament]]s and [[comma]]s and how they relate to each other. An edo is p-2 '''telic''' when it tempers a comma in 2.p subgroup for a prime p, and that comma is smaller than half an edostep.		'''Telicity''' is a property of both [[equal temperament]]s and [[comma]]s and how they relate to each other. An edo is p-2 '''telic''' when it tempers a comma in 2.p subgroup for a prime p, and that comma is smaller than half an edostep.

Overthink: /* Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos */ oops

2025-12-30T01:29:38Z

Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos: oops

← Older revision		Revision as of 01:29, 30 December 2025
Line 107:		Line 107:
	\|7-2 telic		\|7-2 telic
	\|5 [10, ''15'']		\|5 [10, ''15'']
	\|[[26]] [52, ''130'']		\|'''26''' [52, ''130'']
	\|109 [218]		\|109 [218]
	\|571		\|571

Overthink: /* Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos */ bold 26 (listed in 2-11 telic)

2025-12-30T01:29:16Z

Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos: bold 26 (listed in 2-11 telic)

← Older revision		Revision as of 01:29, 30 December 2025
Line 107:		Line 107:
	\|7-2 telic		\|7-2 telic
	\|5 [10, ''15'']		\|5 [10, ''15'']
	\|26 [52, ''130'']		\|[[26]] [52, ''130'']
	\|109 [218]		\|109 [218]
	\|571		\|571

Eufalesio: How could I forget 118edo??

2025-12-29T18:53:45Z

How could I forget 118edo??

← Older revision		Revision as of 18:53, 29 December 2025
Line 92:		Line 92:
	4-k		4-k
	\|28		\|28
	\|59		\|59 [118]
	\|146		\|146
	2-k		2-k

Eufalesio: TBA semiconvergents and make the table nicer

2025-12-29T18:45:11Z

TBA semiconvergents and make the table nicer

← Older revision		Revision as of 18:45, 29 December 2025
Line 69:		Line 69:
	Scale sizes for edos that have semiconvergent or non-telic convergent generators may generate proper but never strictly proper, or improper scales ''(I hypothesize this)''		Scale sizes for edos that have semiconvergent or non-telic convergent generators may generate proper but never strictly proper, or improper scales ''(I hypothesize this)''

	=== Table of P-2 telic edos ===		=== Table of P-2 telic, non-telic P-2 convergent, and semiconvergent edos ===
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	\|3-2 telic		\|3-2 telic
	\| rowspan="4" \|1		\| rowspan="5" \|1
	\|2		\|2
	\|5		\|'''5'''
	\|12		\|'''12''' [24]
	~~2-strong~~		\|'''53''' [159]
	\|53		3-k
	3-~~strong~~		\|306 [''612'']
	\|306		\|'''665''' [7315]
	\|665		11-k
	11-~~strong~~		\|15601 ''[78005]''
	\|15601
	\|31867		\|31867
	\|79335		\|79335
	\|190537		\|190537
	28-~~strong~~		28-k
	\|-		\|-
	\|5-2 telic		\|5-2 telic
	\|3		\|3 [12]
	4-~~strong~~		4-k
	\|28		\|28
	\|59		\|59
	\|146		\|146
	2-~~strong~~		2-k
	\|643		\|'''643'''
	3-~~strong~~		3-k
	\|4004		\|4004
	\|8651		\|8651
	\|12655		\|12655
	\|21306		\|21306
	2-~~strong~~		2-k
	\|97879		\|97879
	9-~~strong~~		9-k
	\|-		\|-
	\|7-2 telic		\|7-2 telic
	\|5		\|5 [10, ''15'']
	~~2-strong~~		\|26 [52, ''130'']
	\|26		\|109 [218]
	~~2-strong~~
	\|109
	~~2-strong~~
	\|571		\|571
	2-~~strong~~		2-k
	\|~~2694~~		\|2964
	15-~~strong~~		15-k
	\|91313		\|91313
	2-~~strong~~		2-k
	\|453601		\|453601
	4-~~strong~~		4-k
	\|		\|
	\|		\|
Line 127:		Line 123:
	\|11-2 telic		\|11-2 telic
	\|2		\|2
	3-~~strong~~		3-k
	\|13		\|13 [26]
	\|37		\|37
	13-~~strong~~		13-k
	\|986		\|986
	\|1935		\|1935
	\|4856		\|4856
	\|16503		\|16503
	12-~~strong~~		12-k
			\|
			\|
			\|
			\|-
			\|13-2 telic
			\|1
			\|3
			\|7
			\|10 [50, 80, ''130, 270'']
			11-k
			\|227 [908]
			11-k
			\|5458
			4-k
			\|54353
			74-k
	\|		\|
	\|		\|
	\|		\|
	\|}		\|}
			Bolded edos are notable. Edos in brackets are notable telic edo multiples, due to high consistency or accuracy of their intervals. If italicized, the edo is a multiple of the telic edo but beyond its k-strength range.

	WIP		WIP

← Older revision		Revision as of 04:20, 1 January 2026
Line 78:		Line 78:
	\|'''[[5edo\|5]]'''		\|'''[[5edo\|5]]'''
	\|'''[[12edo\|12]]''' [<nowiki/>[[24edo\|'''24''']]]		\|'''[[12edo\|12]]''' [<nowiki/>[[24edo\|'''24''']]]
	\|'''[[53edo\|53]]''' [<nowiki/>[[~~1590edo~~\|'''159''']]]		\|'''[[53edo\|53]]''' [<nowiki/>[[159edo\|'''159''']]]
	3-k		3-k
	\|[[306edo\|306]] ''[<nowiki/>[[612edo\|'''612''']]]''		\|[[306edo\|306]] ''[<nowiki/>[[612edo\|'''612''']]]''