The Nexus: Difference between revisions
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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 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, schisnex, nexiquart, and tribilo. | ||
= Rank-4 temperaments = | = Rank-4 temperaments = | ||
The parent temperament of this whole collection is rank-4 temperament | The parent temperament of this whole collection is rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored. | ||
== Nexus == | == Nexus == | ||
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The parent temperament for the Nexus is Nexus temperament itself. In this temperament, the 5-limit and 7-limit parts are represented by independent generators. | The parent temperament for the Nexus is Nexus temperament itself. In this temperament, the 5-limit and 7-limit parts are represented by independent generators. | ||
Subgroup: 2.3.5.7.11 | |||
[[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: | Mapping generators: ~121/96, ~1331/768, ~5/1, ~7/1 | ||
{{Multival|legend=1|rank=4| 6 0 0 3 -16 }} | |||
[[POTE generator]]s: ~1331/768 = 950.9518, ~5/4 = 386.2068, ~7/4 = 968.6966 | |||
{{Val list|legend=1| 9, 15, 24, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }} | |||
Badness: 0. | [[Badness]]: 0.588 × 10<sup>-6</sup> | ||
= Rank-3 temperaments = | = Rank-3 temperaments = | ||
From the | From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived. | ||
{{todo|inline=1| expand | comment = Fill the data chunks. }} | |||
== Schisnex == | == Schisnex == | ||
This temperament adds the [[schisma]] to the list of tempered out commas on account of the schisma being an unnoticeable comma for adding the 5-limit to the mix. | This temperament adds the [[schisma]] to the list of tempered out commas on account of the schisma being an unnoticeable comma for adding the 5-limit to the mix. | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 32805/32768, 1771561/1769472 | |||
Mapping: | |||
Wedgie: | Wedgie: | ||
POTE generators: ⟨400.0000, 950.8701, 3368.5689] | |||
{{Val list|legend=1| 24p, 135p, 159, 183, 207, 342, 525, 684, 867 }} | |||
Badness: | Badness: | ||
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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 an unnoticeable comma for adding the 7-limit to the mix. | This temperament can be seen as adding the [[quartisma]] to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix. | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 19712/19683, 1771561/1769472 | |||
Mapping: | |||
Wedgie: | Wedgie: | ||
POTE generators: | |||
Vals: | |||
Badness: | Badness: | ||
= Rank-2 temperaments = | = Rank-2 temperaments = | ||
So far, the only | So far, the only explored rank-2 temperament in the Nexus is the tribilo temperament. | ||
== | == Tribilo == | ||
Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma – its name comes from the nexus comma being referred to as the "tribilo comma" in [[color notation]]. | |||
Subgroup: 2.3.11 | |||
Comma list: 1771561/1769472 | |||
Mapping: | |||
Wedgie: | Wedgie: | ||
POTE generator: | |||
Vals: | |||
Badness: | Badness: | ||
[[Category:Regular temperament theory]] | |||
[[Category:Commatic realm]] | |||
[[Category:Nexus]] | [[Category:Nexus]] | ||
Revision as of 10:57, 8 June 2021
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 [-16 -3 0 0 6⟩. Among the known branches of this collection are nexus, schisnex, nexiquart, and tribilo.
Rank-4 temperaments
The parent temperament of this whole collection is rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored.
Nexus
The parent temperament for the Nexus is Nexus temperament itself. 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
Badness: 0.588 × 10-6
Rank-3 temperaments
From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived.
|
Todo: expand
Fill the data chunks. |
Schisnex
This temperament adds the schisma to the list of tempered out commas on account of the schisma being an unnoticeable comma for adding the 5-limit to the mix.
Subgroup: 2.3.5.7.11
Comma list: 32805/32768, 1771561/1769472
Mapping:
Wedgie:
POTE generators: ⟨400.0000, 950.8701, 3368.5689]
Badness:
Nexiquart
This temperament can be seen as adding the quartisma to the list of tempered out commas on account of the quartisma being an unnoticeable comma for adding the 7-limit to the mix.
Subgroup: 2.3.5.7.11
Comma list: 19712/19683, 1771561/1769472
Mapping:
Wedgie:
POTE generators:
Vals:
Badness:
Rank-2 temperaments
So far, the only explored rank-2 temperament in the Nexus is the tribilo temperament.
Tribilo
Tribilo is the pure Rank-2 2.3.11 temperament that tempers out the nexus comma – its name comes from the nexus comma being referred to as the "tribilo comma" in color notation.
Subgroup: 2.3.11
Comma list: 1771561/1769472
Mapping:
Wedgie:
POTE generator:
Vals:
Badness: