Semaphoresmic family: Difference between revisions
m →Selenium: Add missing subgroup fields. |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]s: ~7/6 = 250.3846, ~5/4 = 379.7035 | [[POTE generator]]s: ~7/6 = 250.3846, ~5/4 = 379.7035 | ||
{{ | {{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19 }} | ||
[[Badness]]: 0.116 × 10<sup>-3</sup> | [[Badness]]: 0.116 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~7/6 = 248.2710, ~5/4 = 390.6487 | [[POTE generator]]s: ~7/6 = 248.2710, ~5/4 = 390.6487 | ||
{{ | {{Optimal ET sequence|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }} | ||
[[Badness]]: 0.665 × 10<sup>-3</sup> | [[Badness]]: 0.665 × 10<sup>-3</sup> | ||
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POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957 | POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957 | ||
{{ | {{Optimal ET sequence|legend=1| 5, 9, 10, 15, 19, 24, 34 }} | ||
Badness: 0.787 × 10<sup>-3</sup> | Badness: 0.787 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~15/14 = 125.6080, ~11/8 = 539.2342 | [[POTE generator]]s: ~15/14 = 125.6080, ~11/8 = 539.2342 | ||
{{ | {{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38d, 67cde }} | ||
[[Badness]]: 1.087 × 10<sup>-3</sup> | [[Badness]]: 1.087 × 10<sup>-3</sup> | ||
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POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845 | POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845 | ||
{{ | {{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38df, 67cdef }} | ||
Badness: 0.8076 × 10<sup>-3</sup> | Badness: 0.8076 × 10<sup>-3</sup> | ||
Revision as of 18:14, 7 May 2023
Semiphore family is a rank-3 temperament family of 2.3.5.7 that tempers out 49/48 and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament called "semaphore", and the 2.3.5.7 49/48 and 81/80 temperament called "godzilla".
Semiphore
Subgroup: 2.3.5.7
Comma list: 49/48
Mapping: [⟨1 0 2 2], ⟨0 2 0 1], ⟨0 0 1 0]]
Mapping generators: ~2, ~7/4, ~5
Lattice basis:
- 7/6 length = 0.7627, 5/4 length = 2.322
- Angle (7/6, 5/4) = 90 degrees
POTE generators: ~7/6 = 250.3846, ~5/4 = 379.7035
Optimal ET sequence: 4, 5, 9, 10, 14c, 15, 19
Badness: 0.116 × 10-3
Selenium
Subgroup: 2.3.5.7.11
Comma list: 49/48, 56/55
Mapping: [⟨1 0 2 2 5], ⟨0 2 0 1 1], ⟨0 0 1 0 -1]]
POTE generators: ~7/6 = 248.2710, ~5/4 = 390.6487
Optimal ET sequence: 4, 5, 9, 10, 15, 19, 24, 34
Badness: 0.665 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 56/55, 91/90
Mapping: [⟨1 0 2 2 5 -1], ⟨0 2 0 1 1 3], ⟨0 0 1 0 -1 1]]
POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957
Optimal ET sequence: 5, 9, 10, 15, 19, 24, 34
Badness: 0.787 × 10-3
Negric
Subgroup: 2.3.5.7.11
Comma list: 49/48, 225/224
Mapping: [⟨1 2 2 3 0], ⟨0 -4 3 -2 0], ⟨0 0 0 0 1]]
POTE generators: ~15/14 = 125.6080, ~11/8 = 539.2342
Optimal ET sequence: 9, 10, 19, 29, 38d, 67cde
Badness: 1.087 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 65/64, 91/90
Mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3], ⟨0 0 0 0 1 0]]
POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845
Optimal ET sequence: 9, 10, 19, 29, 38df, 67cdef
Badness: 0.8076 × 10-3