2nd- to 4th-octave temperaments

2-, 3- and 4edo are much less used as scales, rather as chords. In many 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
• Alteraugment
• Ternary

4th-octave temperaments:

• Diminished family
• Undim family
• Quad