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| '''The Nexus''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[nexus comma]]- the unnoticeable comma with the ratio 1771561/1769472, and a monzo of {{monzo|-16 -3 0 0 6}}. Among the known branches of this collection are Nexus, Binexus, Nexiquart, Nexal and Tribilo, with "Dinexus" and "Trinexus" as proposed names for other branches. | | {{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]]. |
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| == 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. |
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| The 11-limit parent comma for the Nexus family is the the nexus comma with a ratio of 1771561/1769472 and a monzo of {{monzo|-16 -3 0 0 6}}. This is a rank-4 temperament in which the 5-limit and 7-limit parts are represented by independent generators.
| | Subgroup: 2.3.5.7.11 |
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| Period: ~121/96 = 1\3
| | [[Comma list]]: [[1771561/1769472]] |
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| Optimal (POTE) generators: 950.9518, 386.2068, 968.6966
| | [[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}}] |
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| Comma list: 1771561/1769472
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| 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}}] | |
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| Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1 | | Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1 |
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| Wedgie: <<<<6 0 0 3 -16]]]]
| | [[POTE generator]]s: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966 |
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| EDOs: 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566
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| Badness: 0.588×10<sup>-6</sup>
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| == Binexus ==
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| This temperament adds the [[schisma]] to the list of tempered out commas on account of the schisma being the unnoticeable comma adding the 5-limit to the mix. This is a rank-3 temperament.
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| Commas: 1771561/1769472, 32805/32768
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| POTE generators: ⟨400.0000, 950.8701, 3368.5689]
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| Map:
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| Wedgie:
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| EDOs: 24p, 135p, 159, 183, 207, 342, 525, 684, 867
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| Badness:
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| == Nexiquart ==
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| This temperament can be seen as adding the [[quartisma]] to the list of tempered out commas on account of the quartisma being the unnoticeable comma adding the 7-limit to the mix. This is a rank-3 temperament.
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| Commas: 1771561/1769472, 117440512/117406179
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| POTE generators:
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| Map:
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| Wedgie:
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| EDOs:
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| Badness:
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| == Nexal == | |
| {{main| Nexal family }}
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| This temperament can be seen as either adding the quartisma to Binexus, or adding the schisma to Nexiquart. Either way, you end up with a full 11-limit rank-2 temperament.
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| Commas: 1771561/1769472, 32805/32768, 117440512/117406179
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| POTE generators:
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| Map:
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| Wedgie:
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| EDOs:
| | {{Optimal ET sequence|legend=1| 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }} |
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| Badness: | | [[Badness]]: 0.588 × 10<sup>-6</sup> |
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| == Tribilo == | | === 13-limit === |
| {{main| Tribilo family }}
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| Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma- it's name comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]].
| | {{todo|review|inline=yes|comment=Add optimal ET sequence & badness}} |
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| Commas: 1771561/1769472
| | Subgroup: 2.3.5.7.11.13 |
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| POTE generators:
| | [[Comma list]]: [[1771561/1769472]], [[676/675]] |
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| Map:
| | [[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]⟩ |
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| Wedgie:
| | Mapping generators: ⟨1200.000, 1902.167, 2786.583, 3368.823, 4151.084, 4439.834] |
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| EDOs:
| | [[POTE generator]]s: ⟨400.0000, 951.0837, 2786.5829, 3368.8230] |
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| Badness:
| | {{Optimal ET sequence|legend=1| }} |
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| [[Category:Nexus]] | | [[Badness]]: |
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| {{todo|improve readability|discuss title|expand}}
| | [[Category:Temperament families]] |
| | [[Category:Pages with mostly numerical content]] |
| | [[Category:Nexus family| ]] <!-- main article --> |
| | [[Category:Rank 4]] |