Nexus clan: Difference between revisions
m FloraC moved page Tribilo family to Nexus clan: Minimal subgroup is 2.3.11 so "nexus clan" should be fine |
Clarify that this is a clan; update keys |
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The '''tribilo family''' is a | The '''nexus clan''', a.k.a. '''tribilo family''', is a [[Temperament families and clans|clan]] of [[rank-2 temperament]]s 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 clan 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'' comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]]. | ||
== Tribilo == | == Tribilo == | ||
This is the parent temperament of the | This is the parent temperament of the nexus clan. | ||
Subgroup: 2.3.11 | [[Subgroup]]: 2.3.11 | ||
[[Comma list]]: 1771561/1769472 | [[Comma list]]: 1771561/1769472 | ||
{{Mapping|legend=2| 3 0 8 | 0 2 1 }} | |||
: sval mapping generators: ~121/96, ~1331/768 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~121/96 = 1\3, ~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 }} | {{Optimal ET sequence|legend=1| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }} | ||
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[[Badness]]: 2.44 × 10<sup>-3</sup> | [[Badness]]: 2.44 × 10<sup>-3</sup> | ||
== Triblet == | |||
Subgroup: 2.3.11.13 | [[Subgroup]]: 2.3.11.13 | ||
Comma list: 352/351, 1771561/1769472 | [[Comma list]]: 352/351, 1771561/1769472 | ||
{{Mapping|legend=2| 3 0 8 23 | 0 2 1 -5 }} | |||
POTE | [[Optimal tuning]] ([[POTE]]): ~121/96 = 1\3, ~1331/768 = 951.4814 | ||
{{Optimal ET sequence|legend=1| 9f, 15f, 24, 63, 87, 111, 198, 309f, 507f }} | {{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> | ||
== Trilobite == | |||
[[Subgroup]]: 2.3.11.13 | |||
[[Comma list]]: 85293/85184, 1771561/1769472 | |||
{{Mapping|legend=2| 3 0 8 42 | 0 2 1 -13 }} | |||
[[Optimal tuning]] ([[POTE]]): ~121/96 = 1\3, ~1331/768 = 950.7810 | |||
POTE | |||
{{Optimal ET sequence|legend=1| 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef }} | {{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> | ||
[[Category:Temperament | [[Category:Temperament clans]] | ||
[[Category:Nexus clan| ]] <!-- main article --> | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 07:02, 17 June 2023
The nexus clan, a.k.a. tribilo family, is a clan 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 clan 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 comes from the nexus comma being referred to as the "tribilo comma" in color notation.
Tribilo
This is the parent temperament of the nexus clan.
Subgroup: 2.3.11
Comma list: 1771561/1769472
Sval mapping: [⟨3 0 8], ⟨0 2 1]]
- sval mapping generators: ~121/96, ~1331/768
Optimal tuning (POTE): ~121/96 = 1\3, ~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]]
Optimal tuning (POTE): ~121/96 = 1\3, ~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]]
Optimal tuning (POTE): ~121/96 = 1\3, ~1331/768 = 950.7810
Optimal ET sequence: 24, 111f, 135f, 159, 183, 390, 573, 963f, 1536bef
Badness: 1.65 × 10-3