147edo - Revision history

Squib: /* Theory */

2026-03-02T19:35:54Z

Theory

← Older revision		Revision as of 19:35, 2 March 2026
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	147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.		147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.

	One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]] (17 & 113), which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo.		One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]] (17 & 113), which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo. Additionally, it equates a stack of three [[256/243\|pythagorean limmas]] with [[299/256]] and a stack of four with [[16/13]], tempering out 4294967296/4290323193 and the [[tridecapyth comma]].

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

Lériendil: /* Theory */

2025-08-30T06:47:08Z

Theory

← Older revision		Revision as of 06:47, 30 August 2025
Line 5:		Line 5:
	147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.		147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.

	One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]], which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo.		One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]] (17 & 113), which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo.

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

Lériendil: shoal

2025-08-30T05:02:15Z

shoal

← Older revision		Revision as of 05:02, 30 August 2025
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	== Theory ==		== Theory ==
	147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.		147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.

			One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]], which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo.

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

Lériendil at 01:38, 30 August 2025

2025-08-30T01:38:33Z

← Older revision		Revision as of 01:38, 30 August 2025
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	== Theory ==		== Theory ==
	147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament.		147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.

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

FloraC: Undo revision 204411 by FloraC (talk). Using absolute error as the standard

2025-07-28T16:22:37Z

Undo revision 204411 by FloraC (talk). Using absolute error as the standard

← Older revision		Revision as of 16:22, 28 July 2025
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	* [[Baldy17]]		* [[Baldy17]]

	~~[[Category:3-limit record edos\|###]] <!-- 3-digit number -->~~
	[[Category:Baldy]]		[[Category:Baldy]]

FloraC: + category

2025-07-12T12:46:14Z

+ category

← Older revision		Revision as of 12:46, 12 July 2025
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	* [[Baldy17]]		* [[Baldy17]]

			[[Category:3-limit record edos\|###]] <!-- 3-digit number -->
	[[Category:Baldy]]		[[Category:Baldy]]

ArrowHead294 at 17:05, 18 February 2025

2025-02-18T17:05:12Z

← Older revision		Revision as of 17:05, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|147~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Lériendil: 441 mention

2024-10-18T14:25:14Z

441 mention

← Older revision		Revision as of 14:25, 18 October 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs\| 3, 7, 21 and 49 }}.		Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs\| 3, 7, 21 and 49 }}.

			[[441edo]], which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system.

	== Scales ==		== Scales ==

FloraC: Note its accurate fifth and misc. cleanup

2024-05-18T14:46:21Z

Note its accurate fifth and misc. cleanup

← Older revision		Revision as of 14:46, 18 May 2024
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	== Theory ==		== Theory ==
	147edo [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament.		147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|147~~\|columns=11~~}}		{{Harmonics in equal\|147}}

	=== ~~Miscellaneous properties~~ ===		=== Subsets and supersets ===
	Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs\| 3, 7, 21 and 49 }}.		Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs\| 3, 7, 21 and 49 }}.

Line 16:		Line 16:
	* [[Baldy17]]		* [[Baldy17]]

	~~[[Category:147edo\| ]] <!-- main arcticle -->~~
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Baldy]]		[[Category:Baldy]]

FloraC: Link to the 41 & 106 temp; sectioning; style

2022-11-09T10:04:33Z

Link to the 41 & 106 temp; sectioning; style

← Older revision		Revision as of 10:04, 9 November 2022
Line 3:		Line 3:

	== Theory ==		== Theory ==
	147edo [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for ~~the~~ 11-limit 41&106 temperament.		147edo [[tempering out\|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament.

	~~Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs\| 3, 7, 21 and 49 }}~~.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|147\|columns=11}}		{{Harmonics in equal\|147\|columns=11}}

			=== Miscellaneous properties ===
			Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs\| 3, 7, 21 and 49 }}.

	== Scales ==		== Scales ==
	* [[~~baldy6~~]]		* [[Baldy6]]
	* [[~~baldy11~~]]		* [[Baldy11]]
	* [[~~baldy17~~]]		* [[Baldy17]]

	[[Category:147edo\| ]] <!-- main arcticle -->		[[Category:147edo\| ]] <!-- main arcticle -->
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Baldy]]		[[Category:Baldy]]