Euzenius comma

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Revision as of 06:35, 26 September 2022 by Royalmilktea (talk | contribs) (interval description as a difference between two intervals)
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The euzenius comma is a 7-limit unnoticeable comma with a ratio of 78125000/78121827, a monzo of [3 -13 10 -2⟩, and a size of 0.070314 cents. It is the difference between two 6250/5103 intervals and the perfect fifth. It is tempered out in temperaments such as ennealimmal and fortune.

Temperament

Tempering this comma out gives euzenius temperament.

Euzenius (3566 & 3125 & 171)

Subgroup: 2.3.5.7

Comma list: 78125000/78121827

Mapping: [⟨1 1 0 -5], ⟨0 2 0 -13], ⟨0 0 1 5]]

POTE generators: ~6250/5103 = 350.9788, ~5 = 2786.3104

Vals: 171, 441, 612, 2954, 3125, 3566, 3737, 6250, 6520, 6691

Badness: 0.000205

Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B3%2C-13%2C10%2C-2%3E&page=2&limit=7

Ennealimmal

Subgroup: 2.3.5.7

Comma list: 2401/2400, 4375/4374

Mapping: [⟨9 1 1 12], ⟨0 2 3 2]]

Wedgie: ⟨⟨18 27 18 1 -22 -34]]

POTE generator: ~5/3 = 884.3129

Optimal GPV sequence: 27, 45, 72, 99, 171, 441, 612

Badness: 0.003610

Fortune

Subgroup: 2.3.5.7

Comma list: 78125000/78121827, [-52 17 12 -1⟩

Mapping: [⟨1 -1 11 63], ⟨0 14 -47 -326]]

POTE generator: ~8388608/7381125 = 221.568031

Optimal GPV sequence: 612, 1901, 2513, 3125, 6862, 9987

Badness: 0.023704

See also