106edo - Revision history

Overthink: /* Theory */ Removed confusing MMTM sentence from years ago

2025-11-18T22:41:49Z

Theory: Removed confusing MMTM sentence from years ago

← Older revision		Revision as of 22:41, 18 November 2025
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	Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament. Unfortunately, it is now only consistent to the [[5-odd-limit]] due to 7/5 being closer to 51 steps rather than its patent val mapping of 52 steps. A superset of 53edo with much a higher consistency limit is [[159edo]].		Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament. Unfortunately, it is now only consistent to the [[5-odd-limit]] due to 7/5 being closer to 51 steps rather than its patent val mapping of 52 steps. A superset of 53edo with much a higher consistency limit is [[159edo]].

	The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo~~. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]]~~.		The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo.

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

Overthink: Note about inconsistency

2025-11-18T00:53:08Z

Note about inconsistency

← Older revision		Revision as of 00:53, 18 November 2025
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	== Theory ==		== Theory ==
	Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.		Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament. Unfortunately, it is now only consistent to the [[5-odd-limit]] due to 7/5 being closer to 51 steps rather than its patent val mapping of 52 steps. A superset of 53edo with much a higher consistency limit is [[159edo]].

	The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]].		The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]].

Yourmusic Productions: Add lumatone mapping link.

2025-07-24T05:26:59Z

Add lumatone mapping link.

← Older revision		Revision as of 05:26, 24 July 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Instruments ==
			* [[Lumatone mapping for 106edo]]

	== See also ==		== See also ==

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:16:50Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:16, 11 April 2025
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	== Theory ==		== Theory ==
	Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.

	The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]].		The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]].

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:41:06Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:41, 11 April 2025
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	== Theory ==		== Theory ==
	Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament.		Since 106 = 2 × 53, 106edo is closely related to [[53edo]], and is [[contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], [[1600000/1594323]], [[2109375/2097152]] in the [[5-limit]], 3125/3087, [[225/224]], 4000/3969, [[1728/1715]], [[2430/2401]], [[4375/4374]] in the 7-limit) as the [[patent val]] for 53edo. In the 11-limit it also tempers out [[243/242]], [[3025/3024]] and [[9801/9800]], so that it [[support]]s [[spectacle]] temperament and [[borwell]] temperament. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]].		The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]].

ArrowHead294 at 16:47, 18 February 2025

2025-02-18T16:47:39Z

← Older revision		Revision as of 16:47, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|106~~}}		{{ED intro}}

	== Theory ==		== Theory ==

BudjarnLambeth: /* Prime harmonics */ Added collapsed 53edo table for comparison

2024-01-25T09:41:57Z

Prime harmonics: Added collapsed 53edo table for comparison

← Older revision		Revision as of 09:41, 25 January 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|106\|columns=16}}		{{Harmonics in equal\|106\|columns=16}}

			53edo for comparison:
			{{Harmonics in equal\|53\|collapsed=1\|columns=16}}

	== Intervals ==		== Intervals ==

BudjarnLambeth: Added interval table

2024-01-20T00:55:27Z

Added interval table

← Older revision		Revision as of 00:55, 20 January 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|106\|columns=16}}		{{Harmonics in equal\|106\|columns=16}}

			== Intervals ==
			{{Interval table}}

	== See also ==		== See also ==

Eliora: /* Scales */

2023-05-30T21:13:31Z

Scales

Show changes

Plumtree: Infobox ET now computes most parameters automatically

2022-10-04T16:01:14Z

Infobox ET now computes most parameters automatically

← Older revision		Revision as of 16:01, 4 October 2022
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	{{Infobox ET		{{Infobox ET}}
	~~\| Prime factorization = 2 × 53~~
	~~\| Step size = 11.32075¢~~
	~~\| Fifth = 62\106 (701.89¢) (→[[53edo\|31\53]])~~
	~~\| Semitones = 10:8 (113.21¢ : 90.57¢)~~
	~~\| Consistency = 5~~
	}}
	{{EDO intro\|106}}		{{EDO intro\|106}}