Nexus family: Difference between revisions
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=== 13-limit === | === 13-limit === | ||
{{todo|expand|review|inline=yes|comment= | {{todo|expand|review|inline=yes|comment=Add multival, 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] | ||
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[[Badness]]: | [[Badness]]: | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Nexus family| ]] <!-- main article --> | [[Category:Nexus family| ]] <!-- main article --> | ||
[[Category:Rank 4]] | [[Category:Rank 4]] | ||
Revision as of 06:03, 24 February 2024
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
Wedgie: ⟨⟨⟨⟨ 6 0 0 3 -16 ]]]]
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
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Todo: expand , review Add multival, 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]
Wedgie: ⟨⟨⟨⟨ ]]]]
POTE generators: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]