Quartismic family

The quartismic family is a family of rank-4 temperaments tempers out the quartisma- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of [24 -6 0 1 -5⟩, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see the Quartercache.

Quartismic

The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of 117440512/117406179 and a monzo of [24 -6 0 1 -5⟩. As the quartisma is an unnoticeable comma, this rank-4 temperament is a microtemperament.

Subgroup: 2.3.5.7.11

Comma list: 117440512/117406179

Mapping: [⟨1 0 0 1 5], ⟨0 1 0 1 -1], ⟨0 0 1 0 0], ⟨0 0 0 5 1]]

Mapping generators: ~2, ~3, ~5, ~33/32

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683

Template:Val list

Badness: 0.274 × 10^-6

Tridecimal quartismic

Subgroup: 2.3.5.7.11.13

Comma list: 6656/6655, 123201/123200

Mapping: [⟨1 0 0 1 5 6], ⟨0 1 0 1 -1 -3], ⟨0 0 1 0 0 1], ⟨0 0 0 5 1 3]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698

Template:Val list

Badness: 1.739 × 10^-6