48th-octave temperaments

48edo contains the predominating 12edo in it, dividing its step in four, as well as being a highly composite edo. Therefore, various 48th-octave temperaments make sense.

This page accommodates a number of temperaments which are otherwise difficult to catalog due to them belonging in multiple temperament families. This is buttressed by the fact that 48 is highly composite and it does contain other fractional-octave commas within itself.

70/69-48-commatic

This temperament associates the 70/69 interval with one step of 48edo, which it is closely approximated by. 48edo itself does the mapping consistently.

Subgroup: 2.3.5.7.23

Comma list: [-47 48 -48 -48 48⟩

Subgroup-val mapping: [⟨48 0 0 0 47], ⟨0 1 0 0 -1], ⟨0 0 1 0 1], ⟨0 0 0 1 1]]

sval mapping generators: ~70/69 = 1\48, ~3, ~5, ~7

Supporting ETs: 48, 96d, 144, 384, 528, 624, 720, 1056, 1152, 1776, 1920, 2544, 3696, 4320