Semaphoresmic family: Difference between revisions
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'''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 "[[Slendro clan #Semaphore|semaphore]]", and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]". | '''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 "[[Slendro clan #Semaphore|semaphore]]", and the 2.3.5.7 49/48 and 81/80 temperament called "[[Meantone family #Godzilla|godzilla]]". | ||
= Semiphore = | == Semiphore == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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</div></div> | </div></div> | ||
= Selenium = | == Selenium == | ||
[[Comma list]]: 49/48, 56/55 | [[Comma list]]: 49/48, 56/55 | ||
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[[Badness]]: 0.665 × 10<sup>-3</sup> | [[Badness]]: 0.665 × 10<sup>-3</sup> | ||
== 13-limit == | === 13-limit === | ||
Comma list: 49/48, 56/55, 91/90 | Comma list: 49/48, 56/55, 91/90 | ||
| Line 47: | Line 47: | ||
Badness: 0.787 × 10<sup>-3</sup> | Badness: 0.787 × 10<sup>-3</sup> | ||
= Negric = | == Negric == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 1.087 × 10<sup>-3</sup> | [[Badness]]: 1.087 × 10<sup>-3</sup> | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Revision as of 21:51, 1 June 2021
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
Badness: 0.116 × 10-3
Selenium
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
Badness: 0.665 × 10-3
13-limit
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
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
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
Badness: 0.8076 × 10-3