174edo - Revision history

Hotcrystal0: flat

2026-01-21T18:32:54Z

flat

← Older revision		Revision as of 18:32, 21 January 2026
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	174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

	The 174b val flat fifth is a meantone fifth very close to the [[quarter-comma meantone]] fifth, being only 0.027 cents ~~below~~ it.		The 174b val flat fifth is a meantone fifth very close to the [[quarter-comma meantone]] fifth, being only 0.027 cents flat of it.

	=== Odd harmonics ===		=== Odd harmonics ===

Hotcrystal0 at 18:30, 21 January 2026

2026-01-21T18:30:25Z

← Older revision		Revision as of 18:30, 21 January 2026
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	== Theory ==		== Theory ==
	174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

			The 174b val flat fifth is a meantone fifth very close to the [[quarter-comma meantone]] fifth, being only 0.027 cents below it.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Sectioning following similar pages and misc. improvements

2025-11-07T16:17:58Z

Sectioning following similar pages and misc. improvements

← Older revision		Revision as of 16:17, 7 November 2025
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	{{ED intro}}		{{ED intro}}

			== Theory ==
	174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

	== Odd harmonics ==		=== Odd harmonics ===
	{{Harmonics in equal\|174}}		{{Harmonics in equal\|174}}

	== Subsets and supersets ==		=== Subsets and supersets ===
	Since 174 factors into {{~~factorization~~\|~~174~~}}, 174edo has subset edos {{EDOs\| 2, 3, 6, 29, 58, and 87 }}.		Since 174 factors into primes as {{nowrap\| 2 × 3 × 29 }}, 174edo has subset edos {{EDOs\| 2, 3, 6, 29, 58, and 87 }}.

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

Lucius Chiaraviglio: Fix section headings; add interval table

2025-11-07T09:56:07Z

Fix section headings; add interval table

← Older revision		Revision as of 09:56, 7 November 2025
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	174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

	=== Odd harmonics ===		== Odd harmonics ==
	{{Harmonics in equal\|174}}		{{Harmonics in equal\|174}}

	=== Subsets and supersets ===		== Subsets and supersets ==
	Since 174 factors into {{factorization\|174}}, 174edo has subset edos {{EDOs\| 2, 3, 6, 29, 58, and 87 }}.		Since 174 factors into {{factorization\|174}}, 174edo has subset edos {{EDOs\| 2, 3, 6, 29, 58, and 87 }}.

			== Intervals ==
			{{Interval table}}

ArrowHead294 at 19:24, 20 February 2025

2025-02-20T19:24:57Z

← Older revision		Revision as of 19:24, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

FloraC: Adopt template: EDO intro; +subsets and supersets; -redundant categories

2024-04-25T10:30:11Z

Adopt template: EDO intro; +subsets and supersets; -redundant categories

← Older revision		Revision as of 10:30, 25 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''174edo''' is the [[~~EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		{{EDO intro}}

	==~~Harmonics~~==		174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1\|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|174}}		{{Harmonics in equal\|174}}
	{{~~stub~~}}
	~~[[Category:Equal divisions of the octave~~\|~~###]] <!--~~ 3~~-digit number -->~~		=== Subsets and supersets ===
			Since 174 factors into {{factorization\|174}}, 174edo has subset edos {{EDOs\| 2, 3, 6, 29, 58, and 87 }}.

BudjarnLambeth: /* Harmonics */

2024-01-25T06:52:11Z

Harmonics

← Older revision		Revision as of 06:52, 25 January 2024
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	==Harmonics==		==Harmonics==
	{{Harmonics in equal\|~~174edo~~}}		{{Harmonics in equal\|174}}
	{{stub}}		{{stub}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Added table of harmonics

2024-01-25T06:51:59Z

Added table of harmonics

← Older revision		Revision as of 06:51, 25 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''174edo''' is the [[EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		'''174edo''' is the [[EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

			==Harmonics==
			{{Harmonics in equal\|174edo}}
	{{stub}}		{{stub}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Marked as stub

2024-01-04T01:54:04Z

Marked as stub

← Older revision		Revision as of 01:54, 4 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''174edo''' is the [[EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		'''174edo''' is the [[EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.
			{{stub}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:12:22Z

Infobox ET added

← Older revision		Revision as of 21:12, 4 October 2022
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			{{Infobox ET}}
	'''174edo''' is the [[EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.		'''174edo''' is the [[EDO\|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->