Nexus clan: Difference between revisions
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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 {{monzo|-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]]. | 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 {{monzo| -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 == | == Tribilo == | ||
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[[Comma list]]: 1771561/1769472 | [[Comma list]]: 1771561/1769472 | ||
[[Sval]] [[mapping]]: [{{val| 3 0 8}}, {{val| 0 2 1}}] | [[Sval]] [[mapping]]: [{{val| 3 0 8 }}, {{val| 0 2 1 }}] | ||
Sval mapping generators: ~121/96, ~1331/768 | Sval mapping generators: ~121/96, ~1331/768 | ||
[[POTE generator]]: ~1331/768 = 950.9518 or ~12/11 = 150.9518 | [[POTE generator]]: ~1331/768 = 950.9518 (or ~12/11 = 150.9518) | ||
{{Val list|legend=1| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }} | {{Val list|legend=1| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }} | ||
Badness: | [[Badness]]: 2.44 × 10<sup>-3</sup> | ||
=== Triblet === | === Triblet === | ||
Subgroup: 2.3.11.13 | Subgroup: 2.3.11.13 | ||
Comma list: 1771561/1769472 | Comma list: 352/351, 1771561/1769472 | ||
Sval mapping: [{{val| 3 0 8 23 }}, {{val| 0 2 1 -5 }}] | |||
POTE generator: ~1331/768 = 951.4814 | |||
Optimal GPV sequence: {{Val list| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }} | |||
Badness: 2.70 × 10<sup>-3</sup> | |||
Badness: | |||
=== Trilobite === | === Trilobite === | ||
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Subgroup: 2.3.11.13 | Subgroup: 2.3.11.13 | ||
Comma list: 1771561/1769472 | Comma list: 85293/85184, 1771561/1769472 | ||
Sval mapping: [{{val| 3 0 8 42 }}, {{val| 0 2 1 -13 }}] | |||
POTE generator: | POTE generator: ~1331/768 = 950.7810 | ||
Optimal GPV sequence: {{Val list| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }} | |||
Badness: | Badness: 1.65 × 10<sup>-3</sup> | ||
Revision as of 20:46, 26 February 2022
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)
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 GPV sequence: Template:Val list
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 GPV sequence: Template:Val list
Badness: 1.65 × 10-3