# Keemic family

The keemic family of rank-3 temperaments are planar temperaments tempering out the keema, 875/864.

## Supermagic

Subgroup: 2.3.5.7

Comma list: 875/864

Mapping[1 0 0 5], 0 1 0 3], 0 0 1 -3]]

mapping generators: ~2, ~3, ~5

Mapping to lattice: [0 0 -1 3], 0 1 1 0]]

Lattice basis:

6/5 length = 0.8879, 3/2 length = 1.3391
Angle (6/5, 3/2) = 77.834

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8733, ~5/4 = 380.4684

[[1 0 0 0, [0 1 0 0, [5/4 3/4 1/4 -1/4, [5/4 3/4 -3/4 3/4]
eigenmonzo (unchanged-interval) basis: 2.3.7/5

Projection pair: 7 864/125

Scales: supermagic15

## Undecimal supermagic

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384

Mapping[1 0 0 5 2], 0 1 0 3 -2], 0 0 1 -3 2]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.1985, ~5/4 = 381.5394

Scales: supermagic15

## Supernatural

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/243

Mapping[1 0 2 -1 0], 0 5 1 12 0], 0 0 0 0 1]]

mapping generators: ~2, ~5, ~11

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 380.3520, ~11/8 = 547.5758