Semaphoresmic family: Difference between revisions
Databoxified |
Revert databoxes |
||
| Line 4: | Line 4: | ||
= Semiphore = | = Semiphore = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 49/48 | |||
[[Mapping]]: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}] | |||
Mapping generators: ~2, ~7/4, ~5 | Mapping generators: ~2, ~7/4, ~5 | ||
| Line 25: | Line 15: | ||
: 7/6 length = 0.7627, 5/4 length = 2.322 | : 7/6 length = 0.7627, 5/4 length = 2.322 | ||
: Angle (7/6, 5/4) = 90 degrees | : Angle (7/6, 5/4) = 90 degrees | ||
[[POTE generator]]s: ~7/6 = 250.3846, ~5/4 = 379.7035 | |||
{{Val list|legend=1| 4, 5, 9, 10, 14c, 15, 19 }} | {{Val list|legend=1| 4, 5, 9, 10, 14c, 15, 19 }} | ||
Badness: 0.116 × 10<sup>-3</sup> | [[Badness]]: 0.116 × 10<sup>-3</sup> | ||
</div></div> | </div></div> | ||
| Line 34: | Line 26: | ||
= Selenium = | = Selenium = | ||
[[Comma list]]: 49/48, 56/55 | |||
[[Mapping]]: [{{val| 1 0 2 2 5 }}, {{val| 0 2 0 1 1 }}, {{val| 0 0 1 0 -1 }}] | |||
[[POTE generator]]s: ~7/6 = 248.2710, ~5/4 = 390.6487 | |||
{{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: 0.665 × 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 | ||
Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}] | Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}] | ||
POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957 | |||
{{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }} | {{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }} | ||
Badness: 0.787 × 10<sup>-3</sup> | Badness: 0.787 × 10<sup>-3</sup> | ||
= Negric = | = Negric = | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 49/48, 225/224 | |||
[[Mapping]]: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}] | |||
[[POTE generator]]s: ~15/14 = 125.6080, ~11/8 = 539.2342 | |||
{{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }} | {{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }} | ||
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 | |||
Comma list: 49/48, 65/64, 91/90 | Comma list: 49/48, 65/64, 91/90 | ||
Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}] | Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}] | ||
POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845 | |||
{{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }} | {{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }} | ||
Badness: 0.8076 × 10<sup>-3</sup> | Badness: 0.8076 × 10<sup>-3</sup> | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 10:30, 27 March 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