The Nexus: Difference between revisions
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{{Technical data page}} | |||
'''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, altinex, and tribilo. | '''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, altinex, and tribilo. | ||
Because the nexus comma is the difference between (121/96)<sup>3</sup> and 2/1, all nexus temperaments divide 2/1 into three equal parts of (approximately) 400 cents. | |||
== Rank-4 temperaments == | |||
{{main| Nexus family }} | |||
The parent temperament of this whole collection is a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored. | |||
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 === | ||
The parent temperament for the Nexus is Nexus temperament itself. | 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 | Subgroup: 2.3.5.7.11 | ||
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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 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966 | |||
{{Optimal ET sequence|legend=1| 9, 15, 24, 33cd, 39d, 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }} | |||
{{ | |||
[[Badness]]: 0.588 × 10<sup>-6</sup> | [[Badness]]: 0.588 × 10<sup>-6</sup> | ||
= Rank-3 temperaments = | == Rank-3 temperaments == | ||
From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived. | From the rank-4 parent temperament, there are several rank-3 temperaments that can be derived. | ||
{ | Temperaments not discussed here include: | ||
* ''[[Tyr]]'', {3025/3024, 102487/102400} → [[Lehmerismic temperaments #Tyr]] | |||
== 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 | Subgroup: 2.3.5.7.11 | ||
Comma list: 32805/32768, 1771561/1769472 | [[Comma list]]: 32805/32768, 1771561/1769472 | ||
[[Mapping]]: [{{val| 3 0 45 0 8 }}, {{val| 0 2 -16 0 1 }}, {{val| 0 0 0 1 0 }}] | |||
POTE | [[POTE generator]]s: ~1331/768 = 950.8701, ~7/4 = 968.5689 | ||
{{ | {{Optimal ET sequence|legend=1| 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce }} | ||
Badness: | [[Badness]]: 5.155 × 10<sup>-3</sup> | ||
== Nexiquart == | === 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. | 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 | Subgroup: 2.3.5.7.11 | ||
Comma list: 19712/19683, 1771561/1769472 | [[Comma list]]: 19712/19683, 1771561/1769472 | ||
Mapping: | [[Mapping]]: [{{val| 3 0 0 -32 8 }}, {{val| 0 2 0 17 1 }}, {{val| 0 0 1 0 0 }}] | ||
[[POTE generator]]s: ~1331/768 = 951.1077, ~5/4 = 386.3748 | |||
{{Optimal ET sequence|legend=1| 24, 48d, 87d, 111, 159, 246, 270, 1215, 1485, 1755, 2025, 2295b }} | |||
[[Badness]]: 6.275 × 10<sup>-3</sup> | |||
== Rank-2 temperaments == | |||
Rank-2 temperaments in the Nexus include [[Ragismic microtemperaments #Hemiennealimmal|hemiennealimmal]], [[Misty family #Hemimist|hemimist]], [[Schismatic family #Hemiterm|hemiterm]], [[Schismatic family #Altinex|altinex]], [[Mirkwai clan #Mirkat|mirkat]], [[Kleismic family #Tritikleismic|tritikleismic]], [[Landscape microtemperaments #Terture|terture]], and [[Landscape microtemperaments #Avicenna|avicenna]]. | |||
Considered below is the 2.3.11 subgroup temperament tribilo. | |||
== Tribilo == | === Tribilo === | ||
{{Main| Nexus clan }} | |||
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]]. | 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]]. | ||
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Subgroup: 2.3.11 | Subgroup: 2.3.11 | ||
Comma list: 1771561/1769472 | [[Comma list]]: 1771561/1769472 | ||
[[Sval]] [[mapping]]: [{{val| 3 0 8 }}, {{val| 0 2 1 }}] | |||
Sval mapping generators: ~121/96, ~1331/768 | |||
POTE generator: | [[POTE generator]]: ~1331/768 = 950.9518 | ||
{{Optimal ET sequence|legend=1| 9, 15, 24, 87, 111, 135, 159, 1407, 1566, 1725e, 1884e, 2043e, 2202e, 2361e, 2520e, 2679e }} | |||
Badness: | Badness: | ||
[[Category: | [[Category:Commatic realms]] | ||
[[Category: | [[Category:The Nexus| ]] <!-- main article --> | ||
[[Category:Nexus]] | [[Category:Nexus]] | ||