# User:VIxen/Temperament proposals

# Not logged in the main namespace

## Kibi

This temperament is heavily tailored towards 19-limit use with the 33/19 equave, inspired by that the smallest 19-limit superparticular is (91/10) × (33/19)^{-4}. It was named after minor planet 3319.

In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103h & 354), and a Fokker block of 23 notes per equave is available, corresponding to the 29g val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.

Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103h val.

Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.011 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 969/968, 1275/1274, 1521/1520, 4200/4199, 6175/6171

Mapping: [⟨1 0 23 29 26 23 36 19], ⟨0 1 0 0 1 0 -1 2], ⟨0 0 -30 -38 -35 -28 -44 -26]]

Mapping generators: ~2, ~3, ~266/165

Optimal ET sequence: 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840

Badness: 1.78 × 10^{-3}