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Semaphoresmic family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
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-limit 49/48 temperament [[Semaphoresmic clan #Semaphore|semaphore]], and the 2.3.5.7 49/48 and 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]].
 
== Semiphore ==
This temperament is also known as '''semaphoresmic'''.  


== 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:  
* [[CTE]]: ~2 = 1200.0000, ~7/4 = 952.2948, ~5/4 = 386.3137
* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = 380.5997{{c}}
: [[error map]]: {{val| 0.000 +2.635 0.000 -16.531 }}
: [[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 }}
<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 949.6154, ~5/4 = 379.7035
: error map: {{val| 0.000 -2.724 -6.610 -19.211 }} -->


{{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:  
* [[CTE]]: ~2 = 1200.0000, ~7/4 = 951.8194, ~5/4 = 390.7202
* [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.6621{{c}}
: [[error map]]: {{val| 0.000 +1.684 +4.407 -17.007 +9.781 }}
: [[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 }}
<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 951.7290, ~5/4 = 390.6487
: error map: {{val| 0.000 +1.503 +4.335 -17.097 +9.762 }} -->


{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}
{{Optimal ET sequence|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}
Line 56: Line 65:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~7/4 = 951.3729, ~5/4 = 389.6907
* 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}}
<!-- * POTE: ~2 = 1200.0000, ~7/4 = 951.2441, ~5/4 = 389.5957 -->


{{Optimal ET sequence|legend=0| 5, 9, 10, 15, 19, 24, 34 }}
{{Optimal ET sequence|legend=0| 5, 9, 10, 15, 19, 24, 34 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000, ~15/14 = 124.8134, ~11/8 = 551.3179
* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}, ~11/8 = 540.7985{{c}}
: [[error map]]: {{val| 0.000 -1.209 -11.874 -18.453 0.000 }}
: [[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 }}
<!-- * [[POTE]]: ~2 = 1200.0000, ~15/14 = 125.6080, ~11/8 = 539.2342
: error map: {{val| 0.000 -4.387 -9.490 -20.042 -12.084 }} -->


{{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38d, 67cdde, 105cdddee }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 29, 38d, 67cdde, 105cdddee }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~14/13 = 124.4571, ~11/8 = 551.3179
* 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}}
<!-- * POTE: ~2 = 1200.0000, ~14/13 = 125.5675, ~11/8 = 538.4845 -->


{{Optimal ET sequence|legend=0| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}
{{Optimal ET sequence|legend=0| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}
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Badness (Sintel): 0.755
Badness (Sintel): 0.755


[[Category:Semaphoresmic family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Semaphoresmic family| ]] <!-- main article -->
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Rank 3]]
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