247edo - Revision history

Hotcrystal0: that -> where

2026-03-06T01:52:47Z

that -> where

← Older revision		Revision as of 01:52, 6 March 2026
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	{{ED intro}}		{{ED intro}}

	[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo ~~that~~ the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].		[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo where the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].

	The [[wart_notation\|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning\|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{c}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the {{nowrap\|31 & 61e}} temperament known as [[hemivalentino]].		The [[wart_notation\|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning\|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{c}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the {{nowrap\|31 & 61e}} temperament known as [[hemivalentino]].

ArrowHead294 at 17:44, 20 February 2025

2025-02-20T17:44:08Z

← Older revision		Revision as of 17:44, 20 February 2025
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	[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].		[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].

	The [[wart_notation\|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning\|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{~~cent~~}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the [[hemivalentino]] ~~temperament (31 & 61e)~~.		The [[wart_notation\|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning\|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{c}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the {{nowrap\|31 & 61e}} temperament known as [[hemivalentino]].

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

Francium: changed EDO intro to ED intro

2025-02-20T17:12:11Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:12, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].		[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].

Recentlymaterialized: 247cg

2024-10-30T01:38:21Z

247cg

← Older revision		Revision as of 01:38, 30 October 2024
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	{{EDO intro}}		{{EDO intro}}

	[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). ~~Using~~ the [[~~patent val~~]], ~~it tempers out [[126/125]], [[243/242]] and [[1029/1024]] in~~ the ~~11-limit , so it~~ [[~~support~~]]~~s the ''hemivalentino'' temperament (31 & 61e)~~.		[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].

	~~As every other step~~ of the ~~monstrous~~ [[~~494edo~~]], 247edo ~~can be used~~ in the ~~2.9.15.21~~ [[~~subgroup~~]].		The [[wart_notation\|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning\|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{cent}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the [[hemivalentino]] temperament (31 & 61e).

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

FloraC: Expand on theory; +subsets and supersets

2024-03-22T15:32:49Z

Expand on theory; +subsets and supersets

← Older revision		Revision as of 15:32, 22 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''247 equal divisions of the octave''' ('''247EDO'''), or the '''247(-tone) equal temperament''' ('''247TET''', '''247ET''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO~~\|equal division of the octave]] into 247 parts of 4.8583 [[cent]]s each.~~		{{EDO intro}}

	~~== Theory ==~~		[[Prime harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit\|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family\|compton fifth]]). Using the [[patent val]], it tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit , so it [[support]]s the ''hemivalentino'' temperament (31 & 61e).
	~~In 247EDO, 144 degree represents~~ [[3/2]] ~~(2.36¢ flat)~~, ~~80 degree represents~~ [[5/4]] ~~(2.35¢ sharp)~~, ~~199 degree represents~~ [[7/4]] ~~(2.02¢ flat)~~, and ~~113 degree represents~~ [[11/8]] ~~(2.33¢ flat). 247EDO~~ lacks consistency to the 5 and higher odd~~-limit~~. It is the largest ~~number EDO~~ that ~~interval representing~~ 3/2 is flatter than that of [[~~12EDO~~]] (700¢, [[Compton family\|compton]] ~~fifth~~). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit ~~patent mapping~~, so it [[support]]s the ''hemivalentino'' temperament (31&61e).
			As every other step of the monstrous [[494edo]], 247edo can be used in the 2.9.15.21 [[subgroup]].

			=== Odd harmonics ===
	{{Harmonics in equal\|247\|columns=15}}		{{Harmonics in equal\|247\|columns=15}}

	[[~~Category:Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		=== Subsets and supersets ===
			Since 247 factors into {{factorization\|247}}, 247edo contains [[13edo]] and [[19edo]] as its subsets. 494edo, which doubles it, provides excellent correction to all the lower prime harmonics.

BudjarnLambeth at 07:29, 25 January 2024

2024-01-25T07:29:45Z

← Older revision		Revision as of 07:29, 25 January 2024
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	== Theory ==		== Theory ==
	In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family\|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&61e).		In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family\|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&61e).
	{{Harmonics in equal\|247}}		{{Harmonics in equal\|247\|columns=15}}

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

BudjarnLambeth: Harmonics template

2024-01-25T07:28:59Z

Harmonics template

← Older revision		Revision as of 07:28, 25 January 2024
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	== Theory ==		== Theory ==
	In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family\|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&61e).		In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family\|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&61e).
	{{~~Odd harmonics~~ in ~~edo~~\|~~edo=~~247~~\|prec=2~~}}		{{Harmonics in equal\|247}}

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

Plumtree: Infobox ET added

2022-10-04T21:27:37Z

Infobox ET added

← Older revision		Revision as of 21:27, 4 October 2022
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			{{Infobox ET}}
	The '''247 equal divisions of the octave''' ('''247EDO'''), or the '''247(-tone) equal temperament''' ('''247TET''', '''247ET''') when viewed from a [[regular temperament]] perspective, is the [[EDO\|equal division of the octave]] into 247 parts of 4.8583 [[cent]]s each.		The '''247 equal divisions of the octave''' ('''247EDO'''), or the '''247(-tone) equal temperament''' ('''247TET''', '''247ET''') when viewed from a [[regular temperament]] perspective, is the [[EDO\|equal division of the octave]] into 247 parts of 4.8583 [[cent]]s each.

Fredg999 category edits: Sort key

2022-07-03T18:56:05Z

Sort key

← Older revision		Revision as of 18:56, 3 July 2022
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	{{Odd harmonics in edo\|edo=247\|prec=2}}		{{Odd harmonics in edo\|edo=247\|prec=2}}

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

Cmloegcmluin: link to new page for Supports

2022-01-25T18:15:57Z

link to new page for Supports

← Older revision		Revision as of 18:15, 25 January 2022
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	== Theory ==		== Theory ==
	In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family\|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it ~~supports~~ the ''hemivalentino'' temperament (31&61e).		In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family\|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&61e).
	{{Odd harmonics in edo\|edo=247\|prec=2}}		{{Odd harmonics in edo\|edo=247\|prec=2}}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]