192edo - Revision history

ArrowHead294 at 16:38, 20 February 2025

2025-02-20T16:38:40Z

← Older revision		Revision as of 16:38, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|192~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Fredg999: /* External links */ Misc. edits

2024-07-01T01:41:24Z

External links: Misc. edits

← Older revision		Revision as of 01:41, 1 July 2024
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/4mu.aspx ~~Tonalsoft Encyclopedia \| ''~~4mu / tetramu'']		* [http://tonalsoft.com/enc/number/4mu.aspx 4mu / tetramu] on [[Tonalsoft Encyclopedia]]

BudjarnLambeth: /* See also */ Added link to intercom scales page

2024-02-28T10:33:15Z

See also: Added link to intercom scales page

← Older revision		Revision as of 10:33, 28 February 2024
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	** [[98304edo]] (13mu tuning)		** [[98304edo]] (13mu tuning)
	** [[196608edo]] (14mu tuning)		** [[196608edo]] (14mu tuning)
			* [[Intercom scales]] (the scales listed are tuned to 192edo)

	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/4mu.aspx Tonalsoft Encyclopedia \| ''4mu / tetramu'']		* [http://tonalsoft.com/enc/number/4mu.aspx Tonalsoft Encyclopedia \| ''4mu / tetramu'']

FloraC: Rework; cleanup; +subsets and supersets; -redundant categories

2023-11-07T08:36:55Z

Rework; cleanup; +subsets and supersets; -redundant categories

← Older revision		Revision as of 08:36, 7 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|192}}		{{EDO intro\|192}}
	==Theory==
	192edo is closely related to [[96edo]], but the patent ~~vals~~ differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[~~Würschmidt family\|Würschmidt~~ comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.		== Theory ==
	=== ~~Significance in digital audio~~ ===		192edo is closely related to [[96edo]], but the [[patent val]]s differ on the mapping for [[harmonic]] [[7/1\|7]]. Using the patent val, it [[tempering out\|tempers out]] the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[würschmidt comma]], 393216/390625 and the [[unicorn comma]], 1594323/1562500 in the 5-limit; [[2401/2400]], [[3136/3125]], and 1594323/1568000 in the 7-limit; [[243/242]], [[441/440]], [[5632/5625]], and [[131769/131072]] in the 11-limit; [[676/675]], [[1287/1280]], [[1573/1568]], and 2704/2695 in the 13-limit. Using the alternative 192f val, [[351/350]], [[1001/1000]], [[1575/1573]], 3584/3575, and 5445/5408 are tempered out in the 13-limit.
	~~Its adjacent~~ step is known as '''~~Tetramu~~''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone).
			=== As a tuning standard ===
			A step of 192edo is known as a '''tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone). The internal data structure of the 4mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and two other bits which are not used.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|192}}		{{Harmonics in equal\|192}}
	==See also==
	*[[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units		=== Subsets and supersets ===
	**[[24edo]] (1mu tuning)		Since 192 factors into {{factorization\|192}}, 192edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, and 96 }}.
	**[[48edo]] (2mu tuning)
	**[[96edo]] (3mu tuning)		== See also ==
	**[[384edo]] (5mu tuning)		* [[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units
	**[[768edo]] (6mu tuning)		** [[24edo]] (1mu tuning)
	**[[1536edo]] (7mu tuning)		** [[48edo]] (2mu tuning)
	**[[3072edo]] (8mu tuning)		** [[96edo]] (3mu tuning)
	**[[6144edo]] (9mu tuning)		** [[384edo]] (5mu tuning)
	**[[12288edo]] (10mu tuning)		** [[768edo]] (6mu tuning)
	**[[24576edo]] (11mu tuning)		** [[1536edo]] (7mu tuning)
	**[[49152edo]] (12mu tuning)		** [[3072edo]] (8mu tuning)
	**[[98304edo]] (13mu tuning)		** [[6144edo]] (9mu tuning)
	**[[196608edo]] (14mu tuning)		** [[12288edo]] (10mu tuning)
			** [[24576edo]] (11mu tuning)
			** [[49152edo]] (12mu tuning)
			** [[98304edo]] (13mu tuning)
			** [[196608edo]] (14mu tuning)

	[~~[Category~~:~~Equal divisions of the octave~~\|~~###]~~] ~~<!-- 3-digit number -->~~		== External links ==
			* [http://tonalsoft.com/enc/number/4mu.aspx Tonalsoft Encyclopedia \| ''4mu / tetramu'']

Eliora: cleanup

2022-12-21T23:10:49Z

cleanup

← Older revision		Revision as of 23:10, 21 December 2022
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''192edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 192 ~~parts of 6.25 [[cent]]s each exactly. Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup>~~ = ~~16 equal divisions of the [[12edo]] semitone). It~~ is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.		{{EDO intro\|192}}
			==Theory==
			192edo is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.
			=== Significance in digital audio ===
			Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone).
			=== Odd harmonics ===
			{{harmonics in equal\|192}}
	==See also==		==See also==
	*[[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units		*[[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units

Plumtree: Infobox ET added

2022-10-04T21:17:43Z

Infobox ET added

← Older revision		Revision as of 21:17, 4 October 2022
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			{{Infobox ET}}
	'''192edo''' is the [[EDO\|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone). It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.		'''192edo''' is the [[EDO\|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone). It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.

Fredg999 category edits: Sort key

2022-07-02T21:24:02Z

Sort key

← Older revision		Revision as of 21:24, 2 July 2022
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	**[[196608edo]] (14mu tuning)		**[[196608edo]] (14mu tuning)

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

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:15Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
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	**[[196608edo]] (14mu tuning)		**[[196608edo]] (14mu tuning)

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

Xenllium at 22:17, 19 March 2019

2019-03-19T22:17:30Z

← Older revision		Revision as of 22:17, 19 March 2019
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	'''192edo''' is the [[EDO\|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.		'''192edo''' is the [[EDO\|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. Its adjacent step is known as '''Tetramu''' (fourth MIDI-resolution unit, 4mu, 2<sup>4</sup> = 16 equal divisions of the [[12edo]] semitone). It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.

			==See also==
			*[[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units
			**[[24edo]] (1mu tuning)
			**[[48edo]] (2mu tuning)
			**[[96edo]] (3mu tuning)
			**[[384edo]] (5mu tuning)
			**[[768edo]] (6mu tuning)
			**[[1536edo]] (7mu tuning)
			**[[3072edo]] (8mu tuning)
			**[[6144edo]] (9mu tuning)
			**[[12288edo]] (10mu tuning)
			**[[24576edo]] (11mu tuning)
			**[[49152edo]] (12mu tuning)
			**[[98304edo]] (13mu tuning)
			**[[196608edo]] (14mu tuning)

	[[Category:Edo]]		[[Category:Edo]]

Xenllium at 13:04, 24 December 2018

2018-12-24T13:04:19Z

← Older revision		Revision as of 13:04, 24 December 2018
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	'''192edo''' is the [[EDO\|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the ~~optimal~~ patent val, it tempers out [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400 ~~and~~ 3136/3125 in the 7-limit.		'''192edo''' is the [[EDO\|equal division of the octave]] into 192 parts of 6.25 [[cent]]s each exactly. It is closely related to [[96edo]], but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the [[pythagorean comma]], 531441/524288 in the 3-limit; the [[Würschmidt family\|Würschmidt comma]], 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.

	[[Category:Edo]]		[[Category:Edo]]