The Nexus: Difference between revisions
→Rank-2 temperaments: +links to other rank-2 temperaments |
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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 = | ||
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[[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~5/4 = 386.2068, ~7/4 = 968.6966 | [[POTE generator]]s: ~1331/768 = 950.9518 or ~12/11 = 150.9518, ~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 }} | {{Val list|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> | ||
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= 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 == | ||
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{{Multival|legend=1|rank=3| 0 6 0 -48 0 -3 -90 0 16 -173 }} | {{Multival|legend=1|rank=3| 0 6 0 -48 0 -3 -90 0 16 -173 }} | ||
[[POTE generator]]s: ~1331/768 = 950 | [[POTE generator]]s: ~1331/768 = 950.8701, ~7/4 = 968.5689 | ||
{{Val list|legend=1| 24, | {{Val list|legend=1| 24, 48c, 111cd, 135, 159, 183, 342, 1209, 1551e, 1893e, 2235ce }} | ||
[[Badness]]: 5.155 × 10<sup>-3</sup> | [[Badness]]: 5.155 × 10<sup>-3</sup> | ||
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{{Multival|legend=1|rank=3| 6 0 0 -51 -3 0 -64 16 0 -168 }} | {{Multival|legend=1|rank=3| 6 0 0 -51 -3 0 -64 16 0 -168 }} | ||
[[POTE generator]]s: ~1331/768 = 951 | [[POTE generator]]s: ~1331/768 = 951.1077, ~5/4 = 386.3748 | ||
{{Val list|legend=1| 24, | {{Val list|legend=1| 24, 48d, 87d, 111, 159, 246, 270, 1215, 1485, 1755, 2025, 2295b }} | ||
[[Badness]]: 6.275 × 10<sup>-3</sup> | [[Badness]]: 6.275 × 10<sup>-3</sup> | ||