The Nexus: Difference between revisions
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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. | 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 = | == Rank-4 temperaments == | ||
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 a rank-4 temperament. However, there are other rank-4 extensions which have yet to be explored. | ||
{{main| Nexus family }} | |||
== Nexus == | === 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. | 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. | ||
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[[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. | ||
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* ''[[Tyr]]'', {3025/3024, 102487/102400} → [[Lehmerismic temperaments #Tyr]] | * ''[[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. | ||
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[[Badness]]: 5.155 × 10<sup>-3</sup> | [[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. | ||
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[[Badness]]: 6.275 × 10<sup>-3</sup> | [[Badness]]: 6.275 × 10<sup>-3</sup> | ||
= Rank-2 temperaments = | == 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]]. | 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. | Considered below is the 2.3.11 subgroup temperament tribilo. | ||
== Tribilo == | === Tribilo === | ||
{{Main| Nexus clan }} | {{Main| Nexus clan }} | ||