3rd-octave temperaments - Revision history

Xenllium at 05:04, 23 February 2026

2026-02-23T05:04:25Z

← Older revision		Revision as of 05:04, 23 February 2026
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	There are nonetheless other less common temperaments which divide the octave in three.		There are nonetheless other less common temperaments which divide the octave in three.

			Temperaments discussed elsewhere are:
			* [[Augmented family]]
			* [[Misty family]]
			* [[Landscape microtemperaments]]
			* [[Very low accuracy temperaments #Alteraugment\|Alteraugment]]
			* [[Very low accuracy temperaments #Ternary\|Ternary]]

	== Argument ==		== Argument ==

Xenllium at 05:58, 21 February 2026

2026-02-21T05:58:41Z

@@ Line 10: / Line 10: @@
 == Argument ==
-Argument temperament tempers out the [[1372/1331]] comma in the 2.7.11 subgroup. Subgroup: 2.7.11
+Argument temperament tempers out [[1372/1331]] in the 2.7.11 subgroup.
 [[Comma list]]: 1372/1331
@@ Line 25: / Line 27: @@
 [[Badness]] (Sintel): 0.475
 {{Navbox fractional-octave}}
 {{Todo| review }}

Xenllium: Created page with "{{Infobox fractional-octave|3}}3edo is much less used as a scale, rather as a chord. In many diatonic-based interval region schemes, one step of 3edo is known as a major third, and the stacking of them is the augmented triad. 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..."

2026-02-21T02:24:48Z

Created page with "{{Infobox fractional-octave|3}}3edo is much less used as a scale, rather as a chord. In many diatonic-based interval region schemes, one step of 3edo is known as a major third, and the stacking of them is the augmented triad. 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..."

New page

{{Infobox fractional-octave|3}}[[3edo]] is much less used as a scale, rather as a chord. In many [[5L 2s|diatonic-based]] [[interval region]] schemes, one step of 3edo is known as a major third, and the stacking of them is the augmented triad.

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 a collection of rank-3 temperaments tempering it out.

There are nonetheless other less common temperaments which divide the octave in three.

== Argument ==
Argument temperament tempers out the [[1372/1331]] comma in the 2.7.11 subgroup. Subgroup: 2.7.11

[[Comma list]]: 1372/1331

{{Mapping|legend=2| 3 0 2 | 0 1 1 }}

: sval mapping generators: ~14/11, ~7

[[Optimal tuning]]s:
* [[CTE]]: ~14/11 = 400.000{{c}} (1\3), ~8/7 = 238.126{{c}}
* [[CWE]]: ~14/11 = 400.000{{c}} (1\3), ~8/7 = 237.253{{c}}

{{Optimal ET sequence|legend=1| 6, 9, 15 }}

[[Badness]] (Sintel): 0.475

{{Navbox fractional-octave}}

{{Todo| review }}