No-threes subgroup temperaments: Difference between revisions
Switch to Sintel's badness, WE & CWE tunings (4/4) |
→No-threes no-fives subgroup temperaments: + missing entries |
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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 | [[Subgroup]]: 2.7.11 | ||
[[Comma list]]: | [[Comma list]]: 214358881/210827008 | ||
{{Mapping|legend=2| 1 0 1 | {{Mapping|legend=2| 1 0 1 | 0 8 7 }} | ||
{{Mapping|legend=3| 1 0 0 0 1 | {{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 = | * [[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= | {{Optimal ET sequence|legend=0| 17, 20, 37, 57, 94, 225 }} | ||
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 | ||