Semaphoresmic family: Difference between revisions
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Mapping: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}] | Mapping: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}] | ||
Mapping: | Mapping generators: ~2, ~7/4, ~5 | ||
Lattice basis: | Lattice basis: | ||
| Line 15: | Line 15: | ||
{{Val list|legend=1| 4, 5, 9, 10, 15, 19 }} | {{Val list|legend=1| 4, 5, 9, 10, 15, 19 }} | ||
Badness: 0. | Badness: 0.116 × 10<sup>-3</sup> | ||
= Selenium = | = Selenium = | ||
| Line 24: | Line 24: | ||
{{Val list|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }} | {{Val list|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }} | ||
Badness: 0. | Badness: 0.665 × 10<sup>-3</sup> | ||
== 13-limit == | == 13-limit == | ||
| Line 33: | Line 33: | ||
{{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }} | {{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }} | ||
Badness: 0. | Badness: 0.787 × 10<sup>-3</sup> | ||
= Negric = | = Negric = | ||
| Line 42: | Line 42: | ||
{{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }} | {{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }} | ||
Badness: | Badness: 1.087 × 10<sup>-3</sup> | ||
== 13-limit == | == 13-limit == | ||
| Line 51: | Line 51: | ||
{{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }} | {{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }} | ||
Badness: | Badness: 0.8076 × 10<sup>-3</sup> | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 07:57, 19 February 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
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
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]]
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]]
Badness: 0.787 × 10-3
Negric
Comma list: 49/48, 225/224
Mapping: [⟨1 2 2 3 0], ⟨0 -4 3 -2 0], ⟨0 0 0 0 1]]
Badness: 1.087 × 10-3
13-limit
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]]
Badness: 0.8076 × 10-3