Starscape comma

The starscape comma is a 7-limit unnoticeable comma, with a ratio of 645700815/645657712, a monzo of [-4 17 1 -9⟩, and a size of 0.11557 cents. It is tempered out in temperaments such as domain and supermajor.

Temperament

Tempering this comma out gives starscape temperament.

Starscape (2019 & 171 & 3125)

Subgroup: 2.3.5.7

Commas: 645700815/645657712

Mapping: [⟨1 0 4 0], ⟨0 1 1 2], ⟨0 0 -9 -1]]

POTE generators: ~3 = 1901.9514, ~9/7 = 435.0711

Vals: 171, 342, 1848, 2019, 2783, 2954, 3125, 3296, 4973, 5144

Badness: 0.000545

Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-4%2C17%2C1%2C-9%3E&page=2&limit=7

Domain

Subgroup: 2.3.5.7

Comma list: 250047/250000, 645700815/645657712

Mapping: [⟨3 -3 -9 -8], ⟨0 17 35 36]]

Wedgie: ⟨⟨51 105 108 48 28 -44]]

POTE generator: ~10/9 = 182.467

Optimal GPV sequence: 171, 1164, 1335, 1506, 1677, 1848, 2019, 2190, 11943, 13962, 15981, 18000, 20019, 22038

Badness: 0.013979

Supermajor

Subgroup: 2.3.5.7

Comma list: 4375/4374, 52734375/52706752

Mapping: [⟨1 15 19 30], ⟨0 -37 -46 -75]]

Wedgie: ⟨⟨37 46 75 -13 15 45]]

POTE generator: ~9/7 = 435.082

Optimal GPV sequence: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214

Badness: 0.010836

See also

• Unnoticeable comma