No-threes subgroup temperaments: Difference between revisions

Switch to Sintel's badness, WE & CWE tunings (4/4)
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=== Score ===
=== Score ===
{{See also| Chromatic pairs #Score }}
{{See also| Chromatic pairs #Score }}
Score is a low-accuracy [[extension]] of the unnamed 2.7.11-subgroup temperament tempering out 14641/14336.


[[Subgroup]]: 2.7.11.13
[[Subgroup]]: 2.7.11.13
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Bossier can be described as the 3 & 17 in the 2.7.11.13 subgroup, tempering out [[1573/1568]] and [[15488/15379]].  
Bossier can be described as the 3 & 17 in the 2.7.11.13 subgroup, tempering out [[1573/1568]] and [[15488/15379]].  


[[Subgroup]]: 2.7.11.13
[[Subgroup]]: 2.7.11


[[Comma list]]: 1573/1568, 15488/15379
[[Comma list]]: 214358881/210827008


{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}
{{Mapping|legend=2| 1 0 1 | 0 8 7 }}


{{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
{{Mapping|legend=3| 1 0 0 0 1 | 0 0 0 8 7 }}
: mapping generators: ~2, ~14/11
: mapping generators: ~2, ~14/11


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.8668{{c}}, ~14/11 = 421.2623{{c}}
* [[WE]]: ~2 = 1200.1886{{c}}, ~14/11 = 421.2661{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/11 = 421.2874{{c}}
: [[error map]]: {{val| +0.189 +1.303 -2.266 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/11 = 421.2365{{c}}
: error map: {{val| 0.000 +1.066 -2.662 }}
 
{{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 151 }}
 
[[Badness]] (Sintel): 1.73
 
==== 2.7.11.13 subgroup ====
Subgroup: 2.7.11.13
 
Comma list: 1573/1568, 15488/15379
 
Subgroup-val mapping: {{mapping| 1 0 1 3 | 0 8 7 2 }}
 
Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
 
Optimal tunings:
* WE: ~2 = 1199.8668{{c}}, ~14/11 = 421.2623{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/11 = 421.2874{{c}}


{{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 225 }}
{{Optimal ET sequence|legend=0| 17, 20, 37, 57, 94, 225 }}


[[Badness]] (Sintel): 0.307
Badness (Sintel): 0.307


=== Voltage ===
=== Voltage ===
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=== Yamablu ===
=== Yamablu ===
Yamablu, with a generator of ~26/17, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). The [[Kite's Genchain mode numbering|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]].
Yamablu, with a generator of ~26/17, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). It extends the 2.11.13-subgroup temperament tempering out 556573090931/549755813888. The [[Kite's Genchain mode numbering|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]].  


[[Subgroup]]: 2.11.13.17.19
[[Subgroup]]: 2.11.13.17.19