Semaphoresmic family: Difference between revisions
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The '''semaphoresmic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|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 [[Semaphoresmic clan #Semaphore|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla|godzilla]]. | The '''semaphoresmic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|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 [[Semaphoresmic clan #Semaphore|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla|godzilla]]. | ||
== | == Semaphoresmic a.k.a. semiphore == | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 18: | Line 16: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1202.8324, ~7/4 = 951.8567, ~5/4 = | * [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = 380.5997{{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 }} | ||
{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19 }} | {{Optimal ET sequence|legend=1| 4, 5, 9, 10, 14c, 15, 19, 48d, 53d, 67cdd, 86cdd }} | ||
[[Badness]] (Sintel): 0.510 | [[Badness]] (Sintel): 0.510 | ||
=== 2.3.5.7.13 subgroup === | |||
Subgroup: 2.3.5.7.13 | |||
Comma list: 49/48, 91/90 | |||
Sval mapping: {{mapping| 1 0 0 2 -1 | 0 2 0 1 3 | 0 0 1 0 1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1202.7771{{c}}, ~7/4 = 951.9629{{c}}, ~5/4 = 381.0131{{c}} | |||
* 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 }} | |||
Badness (Sintel): 0.380 | |||
== Selenium == | == Selenium == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0412, ~7/4 = 951.7616, ~5/4 = 390. | * [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.6621{{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 52: | Line 65: | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1200.0790, ~7/4 = 951.3067, ~5/4 = 389. | * WE: ~2 = 1200.0790{{c}}, ~7/4 = 951.3067{{c}}, ~5/4 = 389.6213{{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 67: | 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 84: | 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 }} | ||
| Line 91: | Line 104: | ||
Badness (Sintel): 0.755 | Badness (Sintel): 0.755 | ||
[[Category:Semaphoresmic family| ]] <!-- main article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Catalogs of rank-3 temperaments]] | ||