Mutt - Revision history

Overthink: fix this

2026-02-14T01:40:37Z

fix this

← Older revision		Revision as of 01:40, 14 February 2026
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	The other remarkable property explains its name: it is supported by the standard val for [[768edo]]. Since dividing the octave into 768 = 12 × 64 parts is what some systems use for defining pitch (using the coarse, but not the fine, conceptual "pitch wheel" of [[MIDI]]), mutt is a temperament which accords to this kind of MIDI unit, hence the acronym "MIDI unit tempered tuning", or "mutt", as was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_53634.html#53850 Yahoo! Tuning Group \| ''Retuning using midi to produce beatless music - You gotta be kidding!'']</ref>.		The other remarkable property explains its name: it is supported by the standard val for [[768edo]]. Since dividing the octave into 768 = 12 × 64 parts is what some systems use for defining pitch (using the coarse, but not the fine, conceptual "pitch wheel" of [[MIDI]]), mutt is a temperament which accords to this kind of MIDI unit, hence the acronym "MIDI unit tempered tuning", or "mutt", as was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_53634.html#53850 Yahoo! Tuning Group \| ''Retuning using midi to produce beatless music - You gotta be kidding!'']</ref>.

	The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].		The fact that the smallest proper mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].

	See [[Horwell temperaments]] for technical data.		See [[Horwell temperaments]] for technical data.

VectorGraphics: Phase out wedgies

2025-06-12T04:04:52Z

Phase out wedgies

← Older revision		Revision as of 04:04, 12 June 2025
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	== 7-limit ==		== 7-limit ==
	Commas: 65625/65536, 250047/250000		Commas: 65625/65536, 250047/250000

	~~Wedgie: <<21 3 -36 -44 -116 -92\|\|~~

	Mapping: [<3 5 7 8\|, <0 -7 -1 12\|]		Mapping: [<3 5 7 8\|, <0 -7 -1 12\|]

FloraC: - parent category

2025-04-28T14:26:58Z

- parent category

← Older revision		Revision as of 14:26, 28 April 2025
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	[[Category:Mutt\| ]] <!-- main article -->		[[Category:Mutt\| ]] <!-- main article -->
	~~[[Category:Temperaments]]~~
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Horwell temperaments]]		[[Category:Horwell temperaments]]
	[[Category:Landscape microtemperaments]]		[[Category:Landscape microtemperaments]]

FloraC: The data here is out of date but there's still something to be integrated to the data page. Restore link

2025-04-20T13:14:17Z

The data here is out of date but there's still something to be integrated to the data page. Restore link

← Older revision		Revision as of 13:14, 20 April 2025
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	The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].		The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].

			See [[Horwell temperaments]] for technical data.

	== 5-limit ==		== 5-limit ==

Lériendil at 23:24, 19 April 2025

2025-04-19T23:24:21Z

← Older revision		Revision as of 23:24, 19 April 2025
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	The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].		The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].

	~~See [[Horwell temperaments]] for technical data.~~

	== 5-limit ==		== 5-limit ==
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	[[Category:Mutt\| ]] <!-- main article -->		[[Category:Mutt\| ]] <!-- main article -->
	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Horwell temperaments]]		[[Category:Horwell temperaments]]
	[[Category:Landscape microtemperaments]]		[[Category:Landscape microtemperaments]]

FloraC: Cleanup, +naming history

2024-11-12T17:36:40Z

Cleanup, +naming history

← Older revision		Revision as of 17:36, 12 November 2024
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	~~The~~ '''~~mutt~~''' temperament ~~has~~ two remarkable properties. In the 5-limit, the mutt comma reduces the lattice of pitch classes to three parallel strips of major thirds. The strips are three fifths (or three minor thirds, if you prefer) wide. In other words, tempering via mutt reduces the 5-limit to monzos of the form {{monzo\| a b c }}, where b is -1, 0 or 1. In the 7-limit, the [[landscape comma]] 250047/250000 reduces the entire 7-limit to three layers of the 5-limit; everything in the 7-limit can be written {{monzo\| a b c d }}, where d is -1, 0, or +1. Putting these facts together, we discover that mutt reduces the 7-limit to nine infinite chains of major thirds. In mutt, everything in the 7-limit can be written {{monzo\| a b c d }}; where both b and d are in the range from -1 to 1, so that \|b\| ~~<=~~ 1 and \|d\| ~~<=~~ 1.		'''Mutt''' is the [[regular temperament\|temperament]] [[tempering out]] the [[horwell comma]] and the [[landscape comma]] in the 7-limit. [[Gene Ward Smith]] noted two remarkable properties of this temperament<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12028.html#12037 Yahoo! Tuning Group \| ''mutt microtemperament'']</ref>. In the [[5-limit]], the [[mutt comma]] reduces the lattice of pitch classes to three parallel strips of major thirds. The strips are three fifths (or three minor thirds, if you prefer) wide. In other words, tempering via mutt reduces the 5-limit to monzos of the form {{monzo\| ''a'' ''b'' ''c'' }}, where ''b'' is -1, 0 or 1. In the 7-limit, the landscape comma 250047/250000 reduces the entire 7-limit to three layers of the 5-limit; everything in the 7-limit can be written {{monzo\| ''a'' ''b'' ''c'' ''d'' }}, where ''d'' is -1, 0, or +1. Putting these facts together, we discover that mutt reduces the 7-limit to nine infinite chains of major thirds. In mutt, everything in the 7-limit can be written {{monzo\| ''a'' ''b'' ''c'' ''d'' }}; where both ''b'' and ''d'' are in the range from -1 to 1, so that \|''b''\| ≤ 1 and \|''d''\| ≤ 1.

	The other remarkable property explains its name: it is supported by the standard val for ~~768 equal~~. Since dividing the octave into 768 = 12 × 64 parts is what some systems use for defining pitch (using the coarse, but not the fine, conceptual "pitch wheel" of ~~midi~~) mutt is a temperament which accords to this kind of ~~midi~~ unit, hence the acronym ~~Midi Unit Tempered Tuning~~, or "mutt".		The other remarkable property explains its name: it is supported by the standard val for [[768edo]]. Since dividing the octave into 768 = 12 × 64 parts is what some systems use for defining pitch (using the coarse, but not the fine, conceptual "pitch wheel" of [[MIDI]]), mutt is a temperament which accords to this kind of MIDI unit, hence the acronym "MIDI unit tempered tuning", or "mutt", as was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_53634.html#53850 Yahoo! Tuning Group \| ''Retuning using midi to produce beatless music - You gotta be kidding!'']</ref>.

	The fact that the smallest ~~MOS~~ is 84 and the generator is about the 14 cent difference between the 400 cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in ~~768 equal~~ to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].		The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].

	~~From a~~ [~~http://tech.groups.yahoo.com/group/tuning-math/message/12037 posting~~] ~~on tuning-math~~.		See [[Horwell temperaments]] for technical data.

	== 5-limit ==		== 5-limit ==
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	MOS: 84, 87, 171		MOS: 84, 87, 171

	== ~~See also~~ ==		== Notes ==
	* [[Horwell temperaments]]
	* [[Landscape microtemperaments]]
	* [[Mutt comma]]

	[[Category:Mutt\| ]] <!-- main article -->		[[Category:Mutt\| ]] <!-- main article -->

FloraC: +categories

2024-11-12T16:06:03Z

+categories

← Older revision		Revision as of 16:06, 12 November 2024
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	[[Category:Mutt\| ]] <!-- main article -->		[[Category:Mutt\| ]] <!-- main article -->
			[[Category:Temperaments]]
			[[Category:Horwell temperaments]]
			[[Category:Landscape microtemperaments]]

FloraC: FloraC moved page Mutt temperament to Mutt: Following other similar pages

2024-11-12T16:05:18Z

FloraC moved page Mutt temperament to Mutt: Following other similar pages

← Older revision	Revision as of 16:05, 12 November 2024
(No difference)

Fredg999 category edits: Categories, sort key

2023-03-05T04:32:53Z

Categories, sort key

← Older revision		Revision as of 04:32, 5 March 2023
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	* [[Mutt comma]]		* [[Mutt comma]]

	~~[[Category:Theory]]~~		[[Category:Mutt\| ]] <!-- main article -->
	[[Category:Mutt]]

Xenllium at 11:58, 8 April 2021

2021-04-08T11:58:35Z

← Older revision		Revision as of 11:58, 8 April 2021
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	From a [http://tech.groups.yahoo.com/group/tuning-math/message/12037 posting] on tuning-math.		From a [http://tech.groups.yahoo.com/group/tuning-math/message/12037 posting] on tuning-math.

	= 5-limit =		== 5-limit ==

	Comma: {{monzo\| -44 -3 21 }} (the [[mutt comma]])		Comma: {{monzo\| -44 -3 21 }} (the [[mutt comma]])

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	Poptimal generator: 9\771		Poptimal generator: 9\771

	TOP period: 400.~~023~~		TOP period: ~98304/78125 = 400.0227

	TOP generator: ~5/4 = 386.~~016~~ or 14.~~007~~		TOP generator: ~5/4 = 386.0017 or 14.0210

	MOS: 84, 87, 171, 429, 600, 771		MOS: 84, 87, 171, 429, 600, 771, 942, 1113, 1284, 1455

	== 7-limit ==		== 7-limit ==
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	9-limit poptimal generator: 2\171		9-limit poptimal generator: 2\171

	TOP period: ~63/50 = 400.~~025~~		TOP period: ~63/50 = 400.0352

	TOP generator: ~5/4 = 385.~~990~~ or ~126/125 = 14.~~035~~		TOP generator: ~5/4 = 385.9987 or ~126/125 = 14.0365

	MOS: 84, 87, 171		MOS: 84, 87, 171

			== See also ==
			* [[Horwell temperaments]]
			* [[Landscape microtemperaments]]
			* [[Mutt comma]]

	[[Category:Theory]]		[[Category:Theory]]
	~~[[Category:Temperament family]]~~
	[[Category:Mutt]]		[[Category:Mutt]]
	~~[[Category:Rank 2]]~~

	~~{{todo\|review}}~~