Nexus family: Difference between revisions
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The '''nexus family''' is a family of rank-4 temperaments tempers 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-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Nexus]]. | {{Technical data page}} | ||
The '''nexus family''' is a family of [[rank-4]] temperaments tempers 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-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Nexus]]. | |||
== Nexus == | == Nexus == | ||
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Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1 | Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1 | ||
[[POTE generator]]s: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966 | [[POTE generator]]s: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966 | ||
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=== 13-limit === | === 13-limit === | ||
{{todo | {{todo|review|inline=yes|comment=Add optimal ET sequence & badness}} | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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[[Comma list]]: [[1771561/1769472]], [[676/675]] | [[Comma list]]: [[1771561/1769472]], [[676/675]] | ||
[[Mapping]]: [ | [[Mapping]]: [⟨3 0 0 0 8 -3], ⟨0 2 0 0 1 3], ⟨0 0 1 0 0 1], ⟨0 0 0 1 0 0]⟩ | ||
Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834] | Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834] | ||
[[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230] | [[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230] | ||
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[[Badness]]: | [[Badness]]: | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Nexus family| ]] <!-- main article --> | [[Category:Nexus family| ]] <!-- main article --> | ||
[[Category:Rank 4]] | [[Category:Rank 4]] | ||
Latest revision as of 00:25, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The nexus family is a family of rank-4 temperaments tempers 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-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see the Nexus.
Nexus
This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.
Subgroup: 2.3.5.7.11
Mapping: [⟨3 0 0 0 8], ⟨0 2 0 0 1], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1
POTE generators: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966
Optimal ET sequence: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
Badness: 0.588 × 10-6
13-limit
|
Todo: review Add optimal ET sequence & badness |
Subgroup: 2.3.5.7.11.13
Comma list: 1771561/1769472, 676/675
Mapping: [⟨3 0 0 0 8 -3], ⟨0 2 0 0 1 3], ⟨0 0 1 0 0 1], ⟨0 0 0 1 0 0]⟩
Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834]
POTE generators: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]