2nd- to 4th-octave temperaments - Revision history

Xenllium at 02:13, 4 July 2026

2026-07-04T02:13:02Z

← Older revision		Revision as of 02:13, 4 July 2026
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	* One step of 4edo is known as a minor third, and the stacking of them is the diminished seventh chord.		* One step of 4edo is known as a minor third, and the stacking of them is the diminished seventh chord.

	Usage of the [[5/4]] major third as one step of 3edo by tempering out [[128/125]], and therefore using 3edo as a augmented triad produced by stacking two major thirds is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Augmented family]] for a collection of such temperaments. [[24/19]] is much closer to 1/3-octave than 5/4, and while it is not a microtemperament, a lot of equal divisions support it. An interval closer to 1\3 is [[63/50]], with the associated comma being the landscape comma. See [[Landscape family]] for the family of rank-3 temperaments tempering it out. There are nonetheless other less common temperaments which divide the octave in three.		Usage of [[7/5]] or [[10/7]] as one step of 2edo by tempering out [[50/49]], and therefore using 2edo as a tritone is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Jubilismic clan]] or [[Jubilismic family]] for a collection of such temperaments. Other interpretations as one step of 2edo include [[Diaschismic family\|diaschismic]] (tempering out [[2048/2025]]), [[semitonismic]] (tempering out [[289/288]]), and [[kalismic]] (tempering out [[9801/9800]]).

			Usage of the [[5/4]] major third as one step of 3edo by tempering out [[128/125]], and therefore using 3edo as an augmented triad produced by stacking two major thirds is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Augmented family]] for a collection of such temperaments. [[24/19]] is much closer to 1/3-octave than 5/4, and while it is not a microtemperament, a lot of equal divisions support it. An interval closer to 1\3 is [[63/50]], with the associated comma being the landscape comma. See [[Landscape family]] for the family of rank-3 temperaments tempering it out. There are nonetheless other less common temperaments which divide the octave in three.

	Usage of the [[6/5]] minor third as one step of 4edo by tempering out [[648/625]], and therefore using 4edo as a diminished seventh chord produced by stacking three minor thirds is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Diminished family]] for a collection of such temperaments. [[19/16]], the 19th harmonic octave-reduced, is much closer to quarter-octave than 6/5, and while it is not a microtemperament, a lot of equal divisions support it. An interval closer to 1\4 is [[25/21]], with the associated comma being the dimcomp comma. See [[Dimcomp family]] for the family of rank-3 temperaments tempering it out. There are nonetheless other less common temperaments which divide the octave in four.		Usage of the [[6/5]] minor third as one step of 4edo by tempering out [[648/625]], and therefore using 4edo as a diminished seventh chord produced by stacking three minor thirds is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Diminished family]] for a collection of such temperaments. [[19/16]], the 19th harmonic octave-reduced, is much closer to quarter-octave than 6/5, and while it is not a microtemperament, a lot of equal divisions support it. An interval closer to 1\4 is [[25/21]], with the associated comma being the dimcomp comma. See [[Dimcomp family]] for the family of rank-3 temperaments tempering it out. There are nonetheless other less common temperaments which divide the octave in four.

			2nd-octave temperaments:
			* [[Diaschismic family\|Diaschismic temperaments]]
			* [[Vishnuzmic family\|Vishnuzmic temperaments]]
			* [[Jubilismic clan\|Jubilismic temperaments]]
			* [[Varunismic temperaments]]
			* [[Lokismic temperaments]]
			* [[Nimona\|Nimona temperament]]
			* [[Very low accuracy temperaments #Antitonic\|Antitonic]]

	3rd-octave temperaments:		3rd-octave temperaments:
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	* [[Very low accuracy temperaments #Alteraugment\|Alteraugment]]		* [[Very low accuracy temperaments #Alteraugment\|Alteraugment]]
	* [[Very low accuracy temperaments #Ternary\|Ternary]]		* [[Very low accuracy temperaments #Ternary\|Ternary]]
			* [[No-fives subgroup temperaments #Deviaug\|Deviaug]]

	4th-octave temperaments:		4th-octave temperaments:
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	* [[Undim family]]		* [[Undim family]]
	* [[Very low accuracy temperaments #Quad\|Quad]]		* [[Very low accuracy temperaments #Quad\|Quad]]
			* [[No-threes subgroup temperaments #Berylic\|Berylic]]

	[[Category:Fractional-octave temperaments\|#]] <!-- 1-digit number -->		[[Category:Fractional-octave temperaments\|#]] <!-- 1-digit number -->

FloraC: + category

2026-07-02T12:57:00Z

+ category

← Older revision		Revision as of 12:57, 2 July 2026
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	* [[Undim family]]		* [[Undim family]]
	* [[Very low accuracy temperaments #Quad\|Quad]]		* [[Very low accuracy temperaments #Quad\|Quad]]

			[[Category:Fractional-octave temperaments\|#]] <!-- 1-digit number -->

FloraC: Merge of 3rd- and 4th-octave temperaments

2026-07-02T12:54:35Z

Merge of 3rd- and 4th-octave temperaments

New page

[[2edo|2-]], [[3edo|3-]] and [[4edo]] are much less used as scales, rather as chords. In many [[5L 2s|diatonic-based]] [[interval region]] schemes:
* One step of 2edo is known as a tritone.
* One step of 3edo is known as a major third, and the stacking of them is the augmented triad.
* One step of 4edo is known as a minor third, and the stacking of them is the diminished seventh chord.

Usage of the [[5/4]] major third as one step of 3edo by tempering out [[128/125]], and therefore using 3edo as a augmented triad produced by stacking two major thirds is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Augmented family]] for a collection of such temperaments. [[24/19]] is much closer to 1/3-octave than 5/4, and while it is not a microtemperament, a lot of equal divisions support it. An interval closer to 1\3 is [[63/50]], with the associated comma being the landscape comma. See [[Landscape family]] for the family of rank-3 temperaments tempering it out. There are nonetheless other less common temperaments which divide the octave in three.

Usage of the [[6/5]] minor third as one step of 4edo by tempering out [[648/625]], and therefore using 4edo as a diminished seventh chord produced by stacking three minor thirds is one of the features of standard Western music theory, and is supported by [[12edo]]. See [[Diminished family]] for a collection of such temperaments. [[19/16]], the 19th harmonic octave-reduced, is much closer to quarter-octave than 6/5, and while it is not a microtemperament, a lot of equal divisions support it. An interval closer to 1\4 is [[25/21]], with the associated comma being the dimcomp comma. See [[Dimcomp family]] for the family of rank-3 temperaments tempering it out. There are nonetheless other less common temperaments which divide the octave in four.

3rd-octave temperaments:
* [[Augmented family]]
* [[Misty family]]
* [[Landscape microtemperaments]]
* [[Very low accuracy temperaments #Alteraugment|Alteraugment]]
* [[Very low accuracy temperaments #Ternary|Ternary]]

4th-octave temperaments:
* [[Diminished family]]
* [[Undim family]]
* [[Very low accuracy temperaments #Quad|Quad]]