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}}. For other families that are defined by the tempering of this comma see [[the Nexus]]~~. However, most of the members of this rank-4 family have yet to be found~~.

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 ==

This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.

~~Period~~: ~~~121/96 = 1\~~3

Subgroup: 2.3.5.7.11

~~Optimal (POTE) generators~~: ~~950.9518, 386.2068, 968.6966~~

[[Comma list]]: [[1771561/1769472]]

~~Comma list~~: ~~1771561/1769472~~

[[Mapping]]: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]

Mapping: [~~{{val| 3 0 0 0 8}}~~, {{~~val~~| ~~0 2 0 0~~ 1}}, {{~~val~~| ~~0 0 1 0 0}}, {{val~~| ~~0 0 0 1 0~~}}]

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

{{Optimal ET sequence|legend=1| 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }}

[[Badness]]: 0.588 × 10<sup>-6</sup>

=== 13-limit ===

{{todo|review|inline=yes|comment=Add optimal ET sequence & badness}}

~~Mapping generators~~: ~~~121~~/96, ~~~1331~~/~~768~~, ~~~5/~~1, ~~~7/~~1

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: <<<<6 0 0 3 -16]~~]]]

[[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]

~~EDOs: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566~~

Badness: ~~0.588×10<sup>-6</sup>~~

[[Badness]]:

[[Category:Nexus]]

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Nexus family| ]]

[[Category:Rank 4]]

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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}}.  For other families that are defined by the tempering of this comma see [[the Nexus]].  However, most of the members of this rank-4 family have yet to be found.
+{{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 ==
-This is the parent temperament of the nexus family.  In this temperament, the 5-limit and 7-limit parts are represented by independent generators.
+This is the parent temperament of the nexus family. In this temperament, the 5-limit and 7-limit parts are represented by independent generators.
-Period: ~121/96 = 1\3
+Subgroup: 2.3.5.7.11
-Optimal (POTE) generators: 950.9518, 386.2068, 968.6966
+[[Comma list]]: [[1771561/1769472]]
-Comma list: 1771561/1769472
+[[Mapping]]: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]
-Mapping: [{{val| 3 0 0 0 8}}, {{val| 0 2 0 0 1}}, {{val| 0 0 1 0 0}}, {{val| 0 0 0 1 0}}]
+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
+{{Optimal ET sequence|legend=1| 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }}
+[[Badness]]: 0.588 × 10<sup>-6</sup>
+=== 13-limit ===
+{{todo|review|inline=yes|comment=Add optimal ET sequence & badness}}
-Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1
+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: <<<<6 0 0 3 -16]]]]
+[[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230]
-EDOs: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
+{{Optimal ET sequence|legend=1| }}
-Badness: 0.588×10<sup>-6</sup>
+[[Badness]]:
-[[Category:Nexus]]
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Nexus family| ]] <!-- main article -->
+[[Category:Rank 4]]