119edo - Revision history

Overthink: /* Theory */ 119be

2026-06-14T01:57:27Z

Theory: 119be

← Older revision		Revision as of 01:57, 14 June 2026
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	119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.		119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

	Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo) and 7-limit [[mothra]].		Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo) and 7-limit [[mothra]], with the 119be val supporting 11-limit mothra with a flat tendency.

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

Lucius Chiaraviglio: /* Scales */ Approximation of Fix a/7 comma — had 2 major seconds too many, as if for a superdiatonic tuning of 157edo

2026-01-19T07:22:16Z

Scales: Approximation of Fix a/7 comma — had 2 major seconds too many, as if for a superdiatonic tuning of 157edo

← Older revision		Revision as of 07:22, 19 January 2026
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	== Scales ==		== Scales ==
	* Approximation of 2/7 comma [[meantone]]: 19 19 19 12 19 19 19 19 12		* Approximation of 2/7 comma [[meantone]]: 19 19 12 19 19 19 12
	* Approximation of half comma [[archy]]: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2		* Approximation of half comma [[archy]]: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2

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

Lériendil: "eventone" is idiosyncratic

2025-08-09T22:15:12Z

"eventone" is idiosyncratic

← Older revision		Revision as of 22:15, 9 August 2025
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	== Scales ==		== Scales ==
			* Approximation of 2/7 comma [[meantone]]: 19 19 19 12 19 19 19 19 12
	* Approximation of 2/7 comma meantone: 19 19 19 12 19 19 19 19 12		* Approximation of half comma [[archy]]: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2
	* Approximation of half comma ~~eventone~~: 23 23 2 23 23 23 2, 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2

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

Lériendil at 22:21, 20 July 2025

2025-07-20T22:21:41Z

← Older revision		Revision as of 22:21, 20 July 2025
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	119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.		119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

	Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo) and [[mothra]].		Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo) and 7-limit [[mothra]].

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

Lériendil: /* Theory */

2025-07-20T22:21:15Z

Theory

← Older revision		Revision as of 22:21, 20 July 2025
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	119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.		119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

	Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo).		Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo) and [[mothra]].

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

ArrowHead294 at 16:54, 18 February 2025

2025-02-18T16:54:17Z

← Older revision		Revision as of 16:54, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|119~~}}		{{ED intro}}
	== Theory ==		== Theory ==
	119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.		119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

Lériendil at 06:00, 15 October 2024

2024-10-15T06:00:40Z

← Older revision		Revision as of 06:00, 15 October 2024
Line 4:		Line 4:
	119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.		119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

	Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]].		Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]] in addition to supporting [[chlorine]] (by equating [[25/24]] very accurately to one step of 17edo).

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

Lériendil: added meantone mention

2024-10-15T05:59:25Z

added meantone mention

← Older revision		Revision as of 05:59, 15 October 2024
Line 4:		Line 4:
	119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.		119edo is in[[consistent]] in the 5-odd-limit, with both harmonics 3 and 5 falling halfway between steps. It does have potential as a 2.7.9.15 subgroup system. In higher limits, 2.7.15.29.37 is a strong interpretation.

	Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit.		Nonetheless, there is a number of mappings to be considered. In the 11-limit, 119edo's provides the [[optimal patent val]] for the 11-limit [[androboh]] and [[quasitemp]] temperaments. The patent val also tunes the 11-limit [[quadrawell]] temperament. 119c val tunes [[treecreeper]], [[sensus]], and [[senator]] as high as the 17-limit, while the 119b val is an extremely good approximation to [[2/7-comma meantone]].

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

BudjarnLambeth: +collapsed interval table

2024-10-02T12:44:22Z

+collapsed interval table

← Older revision		Revision as of 12:44, 2 October 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 119edo factors as {{Factorization\|119}}, it contains [[7edo]] and [[17edo]] as a subset. Hence it supports circles of fifths of those respective equal temperaments.		Since 119edo factors as {{Factorization\|119}}, it contains [[7edo]] and [[17edo]] as a subset. Hence it supports circles of fifths of those respective equal temperaments.

			== Intervals ==
			{{Interval table}}

	== Scales ==		== Scales ==

Contribution at 18:58, 19 February 2024

2024-02-19T18:58:00Z

← Older revision		Revision as of 18:58, 19 February 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|119\|columns=12}}		{{Harmonics in equal\|119\|columns=12}}
	{{Harmonics in equal\|119\|columns=12\|start=13\|collapsed=1\|title=Approximation of odd harmonics in ~~84edo~~ (continued)}}		{{Harmonics in equal\|119\|columns=12\|start=13\|collapsed=1\|title=Approximation of odd harmonics in 119edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===