Nexus clan: Difference between revisions
m Moving from Category:Regular temperament theory to Category:Temperament families using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]: ~1331/768 = 950.9518 (or ~12/11 = 150.9518) | [[POTE generator]]: ~1331/768 = 950.9518 (or ~12/11 = 150.9518) | ||
{{ | {{Optimal ET sequence|legend=1| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }} | ||
[[Badness]]: 2.44 × 10<sup>-3</sup> | [[Badness]]: 2.44 × 10<sup>-3</sup> | ||
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POTE generator: ~1331/768 = 951.4814 | POTE generator: ~1331/768 = 951.4814 | ||
Optimal | {{Optimal ET sequence|legend=1| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }} | ||
Badness: 2.70 × 10<sup>-3</sup> | Badness: 2.70 × 10<sup>-3</sup> | ||
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POTE generator: ~1331/768 = 950.7810 | POTE generator: ~1331/768 = 950.7810 | ||
Optimal | {{Optimal ET sequence|legend=1| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }} | ||
Badness: 1.65 × 10<sup>-3</sup> | Badness: 1.65 × 10<sup>-3</sup> | ||
Revision as of 16:29, 7 May 2023
The tribilo family is a family of rank-2 temperaments in the 2.3.11 subgroup that temper out the nexus comma, the unnoticeable comma with the ratio 1771561/1769472, and a monzo of [-16 -3 0 0 6⟩, however, most of the members of this rank-2 family currently have yet to be explored. For other families that are defined by the tempering of the nexus comma, see the Nexus. This family's name comes from the nexus comma being referred to as the "tribilo comma" in color notation.
Tribilo
This is the parent temperament of the tribilo family.
Subgroup: 2.3.11
Comma list: 1771561/1769472
Sval mapping: [⟨3 0 8], ⟨0 2 1]]
Sval mapping generators: ~121/96, ~1331/768
POTE generator: ~1331/768 = 950.9518 (or ~12/11 = 150.9518)
Optimal ET sequence: 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e
Badness: 2.44 × 10-3
Triblet
Subgroup: 2.3.11.13
Comma list: 352/351, 1771561/1769472
Sval mapping: [⟨3 0 8 23], ⟨0 2 1 -5]]
POTE generator: ~1331/768 = 951.4814
Optimal ET sequence: 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f
Badness: 2.70 × 10-3
Trilobite
Subgroup: 2.3.11.13
Comma list: 85293/85184, 1771561/1769472
Sval mapping: [⟨3 0 8 42], ⟨0 2 1 -13]]
POTE generator: ~1331/768 = 950.7810
Optimal ET sequence: 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef
Badness: 1.65 × 10-3