Semaphoresmic family: Difference between revisions
+ obvious no-11 13-limit extension |
Units |
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| Line 16: | Line 16: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1202.8324, ~7/4 = 951.8567, ~5/4 = 386.2644 | * [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = 386.2644{{c}} | ||
: [[error map]]: {{val| +2.832 +1.758 -0.049 -11.304 }} | : [[error map]]: {{val| +2.832 +1.758 -0.049 -11.304 }} | ||
* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522 | * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}, ~5/4 = 382.3522{{c}} | ||
: error map: {{val| 0.000 -0.577 -3.962 -18.137 }} | : error map: {{val| 0.000 -0.577 -3.962 -18.137 }} | ||
| Line 33: | Line 33: | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1202.7771, ~7/4 = 951.9629, ~5/4 = 381.0131 | * WE: ~2 = 1202.7771{{c}}, ~7/4 = 951.9629{{c}}, ~5/4 = 381.0131{{c}} | ||
* CWE: ~2 = 1200.0000, ~7/4 = 950.6703, ~5/4 = 382.2972 | * CWE: ~2 = 1200.0000{{c}}, ~7/4 = 950.6703{{c}}, ~5/4 = 382.2972{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }} | {{Optimal ET sequence|legend=0| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }} | ||
| Line 48: | Line 48: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0412, ~7/4 = 951.7616, ~5/4 = 390.7445 | * [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.7445{{c}} | ||
: [[error map]]: {{val| +0.041 +1.568 +4.431 -16.982 +9.905 }} | : [[error map]]: {{val| +0.041 +1.568 +4.431 -16.982 +9.905 }} | ||
* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582 | * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 951.7409{{c}}, ~5/4 = 390.6582{{c}} | ||
: error map: {{val| 0.000 +1.527 +4.344 -17.085 +9.765 }} | : error map: {{val| 0.000 +1.527 +4.344 -17.085 +9.765 }} | ||
| Line 65: | Line 65: | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1200.0790, ~7/4 = 951.3067, ~5/4 = 389.7793 | * WE: ~2 = 1200.0790{{c}}, ~7/4 = 951.3067{{c}}, ~5/4 = 389.7793{{c}} | ||
* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120 | * CWE: ~2 = 1200.0000{{c}}, ~7/4 = 951.2662{{c}}, ~5/4 = 389.6120{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 9, 10, 15, 19, 24, 34 }} | {{Optimal ET sequence|legend=0| 5, 9, 10, 15, 19, 24, 34 }} | ||
| Line 80: | Line 80: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1203.4810, ~15/14 = 125.9724, ~11/8 = 540.7985 | * [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}, ~11/8 = 540.7985{{c}} | ||
: [[error map]]: {{val| +3.481 +1.118 -1.435 -10.328 -0.076 }} | : [[error map]]: {{val| +3.481 +1.118 -1.435 -10.328 -0.076 }} | ||
* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688 | * [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}, ~11/8 = 541.8688{{c}} | ||
: error map: {{val| 0.000 -3.694 -10.009 -19.695 -9.449 }} | : error map: {{val| 0.000 -3.694 -10.009 -19.695 -9.449 }} | ||
| Line 97: | Line 97: | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1203.6981, ~14/13 = 125.9545, ~11/8 = 540.1440 | * WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}, ~11/8 = 540.1440{{c}} | ||
* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490 | * CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}, ~11/8 = 540.9490{{c}} | ||
{{Optimal ET sequence|legend=0| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }} | {{Optimal ET sequence|legend=0| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }} | ||
Revision as of 10:01, 14 July 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The semaphoresmic family of rank-3 temperaments tempers out 49/48 in the full 7-limit, 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-subgroup {49/48} temperament semaphore, and the 7-limit {49/48, 81/80} temperament godzilla.
Semaphoresmic a.k.a. 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
- WE: ~2 = 1202.8324 ¢, ~7/4 = 951.8567 ¢, ~5/4 = 386.2644 ¢
- error map: ⟨+2.832 +1.758 -0.049 -11.304]
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 950.6890 ¢, ~5/4 = 382.3522 ¢
- error map: ⟨0.000 -0.577 -3.962 -18.137]
Optimal ET sequence: 4, 5, 9, 10, 14c, 15, 19, 48d, 53d, 67cdd, 86cdd
Badness (Sintel): 0.510
2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 49/48, 91/90
Sval mapping: [⟨1 0 0 2 -1], ⟨0 2 0 1 3], ⟨0 0 1 0 1]]
Optimal tunings:
- WE: ~2 = 1202.7771 ¢, ~7/4 = 951.9629 ¢, ~5/4 = 381.0131 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 950.6703 ¢, ~5/4 = 382.2972 ¢
Optimal ET sequence: 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd
Badness (Sintel): 0.380
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]]
- WE: ~2 = 1200.0412 ¢, ~7/4 = 951.7616 ¢, ~5/4 = 390.7445 ¢
- error map: ⟨+0.041 +1.568 +4.431 -16.982 +9.905]
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 951.7409 ¢, ~5/4 = 390.6582 ¢
- error map: ⟨0.000 +1.527 +4.344 -17.085 +9.765]
Optimal ET sequence: 4, 5, 9, 10, 15, 19, 24, 34
Badness (Sintel): 0.800
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]]
Optimal tunings:
- WE: ~2 = 1200.0790 ¢, ~7/4 = 951.3067 ¢, ~5/4 = 389.7793 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/4 = 951.2662 ¢, ~5/4 = 389.6120 ¢
Optimal ET sequence: 5, 9, 10, 15, 19, 24, 34
Badness (Sintel): 0.736
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]]
- WE: ~2 = 1203.4810 ¢, ~15/14 = 125.9724 ¢, ~11/8 = 540.7985 ¢
- error map: ⟨+3.481 +1.118 -1.435 -10.328 -0.076]
- CWE: ~2 = 1200.0000 ¢, ~15/14 = 125.4347 ¢, ~11/8 = 541.8688 ¢
- error map: ⟨0.000 -3.694 -10.009 -19.695 -9.449]
Optimal ET sequence: 9, 10, 19, 29, 38d, 67cdde, 105cdddee
Badness (Sintel): 1.31
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]]
Optimal tunings:
- WE: ~2 = 1203.6981 ¢, ~14/13 = 125.9545 ¢, ~11/8 = 540.1440 ¢
- CWE: ~2 = 1200.0000 ¢, ~14/13 = 125.3543 ¢, ~11/8 = 540.9490 ¢
Optimal ET sequence: 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff
Badness (Sintel): 0.755