Modus - Revision history

ArrowHead294 at 21:00, 16 April 2026

2026-04-16T21:00:20Z

← Older revision		Revision as of 21:00, 16 April 2026
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	\| Generators tuning = 176.8		\| Generators tuning = 176.8
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]		\| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 13.6 \| Complexity 1 = 20		\| Odd limit 1 = 9 \| Mistuning 1 = 13.6 \| Complexity 1 = 20
	\| Odd limit 2 = 13 \| Mistuning 2 = 16.7 \| Complexity 2 = 20		\| Odd limit 2 = 13 \| Mistuning 2 = 16.7 \| Complexity 2 = 20
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	The '''modus''' [[regular temperament\|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.		The '''modus''' [[regular temperament\|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.

	In addition to the tetracot comma, modus tempers out [[64/63]], making it a member of the [[archytas clan]]. As such, septimal intervals are tempered together with Pythagorean intervals; in particular, a stack of two perfect fifths [[octave reduction\|octave reduced]] represents [[8/7]][[~]][[9/8]] at 8 generator steps. Modus also tempers out [[4375/4374]], making it a [[ragismic microtemperaments\|ragismic temperament]]. In the 11- and 13-limit it can be viewed as a [[weak extension]] of [[suhajira]] as well.		In addition to the tetracot comma, modus tempers out [[64/63]], making it a member of the [[archytas clan]]. As such, septimal intervals are tempered together with Pythagorean intervals; in particular, a stack of two perfect fifths [[octave reduction\|octave reduced]] represents {{nowrap\|[[8/7]][[~]][[9/8]]}} at 8 generator steps. Modus also tempers out [[4375/4374]], making it a [[ragismic microtemperaments\|ragismic temperament]]. In the 11- and 13-limit it can be viewed as a [[weak extension]] of [[suhajira]] as well.

	Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -5 generator steps.		Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at −5 generator steps.

	Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group \| ''Guaranteed meantone successor'']</ref>.		Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group \| ''Guaranteed meantone successor'']</ref>.

FloraC: Move its history here

2026-04-16T15:32:00Z

Move its history here

← Older revision		Revision as of 15:32, 16 April 2026
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	Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -5 generator steps.		Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -5 generator steps.

			Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group \| ''Guaranteed meantone successor'']</ref>.

	See [[Tetracot family #Modus]] for technical data.		See [[Tetracot family #Modus]] for technical data.
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	== Music ==		== Music ==
	See [[Tetracot #Music]].		See [[Tetracot #Music]].

			== References ==

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

FloraC: /* Tunings */ + note

2026-04-15T12:31:04Z

Tunings: + note

← Older revision		Revision as of 12:31, 15 April 2026
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	\|		\|
	\|}		\|}
			<nowiki/>* Besides the octave

	== Music ==		== Music ==

FloraC: /* Tunings */ + norm-based tunings

2026-04-15T12:29:55Z

Tunings: + norm-based tunings

@@ Line 116: / Line 116: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"

FloraC: Complete tuning spectrum

2026-04-15T12:26:03Z

Complete tuning spectrum

Show changes

FloraC: Complete interval table

2026-04-15T12:12:37Z

Complete interval table

← Older revision		Revision as of 12:12, 15 April 2026
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	== Interval chain ==		== Interval chain ==
	{\| class="wikitable ~~right~~-1 right-2"		{\| class="wikitable center-1 right-2"
	\|-		\|-
	! #		! #
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	\|-		\|-
	\| 0		\| 0
	\| 0.00		\| 0.0
	\| '''1/1'''		\| '''1/1'''
	\|-		\|-
	\| 1		\| 1
	\| 176.95		\| 176.9
	\| 10/9, 11/10		\| 10/9, 11/10
	\|-		\|-
	\| 2		\| 2
	\| 353.91		\| 353.7
	\| 11/9, '''16/13'''		\| 11/9, '''16/13'''
	\|-		\|-
	\| 3		\| 3
	\| 530.86		\| 530.6
	\| 15/11		\| 15/11
	\|-		\|-
	\| 4		\| 4
	\| 707.81		\| 707.5
	\| '''3/2'''		\| '''3/2'''
	\|-		\|-
	\| 5		\| 5
	\| 884.77		\| 884.4
	\| 5/3		\| 5/3
	\|-		\|-
	\| 6		\| 6
	\| 1061.72		\| 1061.2
	\| 11/6, 13/7, 24/13		\| 11/6, 13/7, 24/13
	\|-		\|-
	\| 7		\| 7
	\| 38.67		\| 38.1
	\| 36/35, 40/39, 45/44, 55/54		\| 36/35, 40/39, 45/44, 55/54
	\|-		\|-
	\| 8		\| 8
	\| 215.63		\| 215.0
	\| '''8/7''', '''9/8'''		\| '''8/7''', '''9/8'''
	\|-		\|-
	\| 9		\| 9
	\| ~~392~~.58		\| 391.9
	\| '''5/4'''		\| '''5/4'''
	\|-		\|-
	\| 10		\| 10
	\| ~~569~~.53		\| 568.7
	\| '''11/8''', 18/13		\| '''11/8''', 18/13
	\|-		\|-
	\| 11		\| 11
	\| ~~746~~.49		\| 745.6
	\| 20/13		\| 20/13
	\|-		\|-
	\| 12		\| 12
	\| ~~923~~.44		\| 922.5
	\| 12/7, 22/13		\| 12/7, 22/13
	\|-		\|-
	\| 13		\| 13
	\| ~~1100~~.39		\| 1099.4
	\| 15/8, 40/21		\| 15/8, 40/21
	\|-		\|-
	\| 14		\| 14
	\| 77.35		\| 76.2
	\| 22/21, 25/24, 27/26		\| 22/21, 25/24, 27/26
	\|-		\|-
	\| 15		\| 15
	\| ~~254~~.30		\| 253.1
	\| 15/13		\| 15/13
	\|-		\|-
	\| 16		\| 16
	\| ~~431~~.25		\| 430.0
	\| 9/7		\| 9/7
	\|-		\|-
	\| 17		\| 17
	\| ~~608~~.20		\| 606.8
	\| 10/7		\| 10/7
	\|-		\|-
	\| 18		\| 18
	\| ~~785~~.16		\| 783.7
	\| 11/7		\| 11/7
	\|-		\|-
	\| 19		\| 19
	\| ~~962~~.11		\| 960.6
	\|		\| 45/26
	\|-		\|-
	\| 20		\| 20
	\| ~~1139~~.06		\| 1137.5
	\| 27/14		\| 27/14
	\|-
	~~\| 21~~
	~~\| 116.02~~
	~~\| 15/14~~
	\|}		\|}
	<nowiki/>* in 13-limit ~~POTE~~ tuning		<nowiki/>* in 13-limit CWE tuning

	== Tunings ==		== Tunings ==

FloraC: Birth

2026-04-15T12:05:16Z

Birth

Show changes

FloraC at 13:52, 23 November 2025

2025-11-23T13:52:43Z

← Older revision		Revision as of 13:52, 23 November 2025
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	#redirect [[Tetracot family #Modus]]		#redirect [[Tetracot family #Modus]]

	[[Category:~~Temperaments~~]]		[[Category:Rank-2 temperaments]]
	[[Category:Tetracot family]]		[[Category:Tetracot family]]
			[[Category:Archytas clan]]
			[[Category:Ragismic microtemperaments]]

Xenwolf: replace {{IoT}} by plain categorization

2022-03-01T19:29:21Z

replace {{IoT}} by plain categorization

← Older revision		Revision as of 19:29, 1 March 2022
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	#redirect [[Tetracot family #Modus]]		#redirect [[Tetracot family #Modus]]

			[[Category:Temperaments]]
	[[Category:Tetracot family]]		[[Category:Tetracot family]]
	~~{{IoT}}~~

Xenwolf at 22:06, 1 June 2021

2021-06-01T22:06:10Z

← Older revision		Revision as of 22:06, 1 June 2021
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	[[Category:Tetracot family]]		[[Category:Tetracot family]]
	~~[[Category:Temperament]]~~		{{IoT}}