Schismatic family: Difference between revisions
| Line 2,404: | Line 2,404: | ||
Badness: 0.127820 | Badness: 0.127820 | ||
== Taylor == | == Subgroup extensions == | ||
=== Taylor (2.3.5.13) === | |||
This is a 2.3.5.13 subgroup restriction of 13-limit hemischis. | This is a 2.3.5.13 subgroup restriction of 13-limit hemischis. | ||
| Line 2,422: | Line 2,423: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1485 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1485 cents | ||
=== Photia (2.3.5.17) === | |||
: <small>''See also: [[No-elevens subgroup temperaments #Garibaldia]]''</small> | |||
Subgroup: 2.3.5.17 | |||
[[Comma list]]: 256/255, 1458/1445 | |||
[[Gencom]]: [2 4/3; 256/255 1458/1445] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 0 0 0 7}}, {{val|0 -1 8 0 0 0 -7}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 7}}, {{val|0 -1 8 -7}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 701.491 | |||
{{Optimal ET sequence|legend=1| 12, 41, 53, 65 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.4842 cents | |||
==== 2.3.5.17.19 ==== | |||
Subgroup: 2.3.5.17.19 | |||
[[Comma list]]: 171/170, 256/255, 324/323 | |||
[[Gencom]]: [2 4/3; 171/170 256/255 324/323] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 0 0 0 7 3}}, {{val|0 -1 8 0 0 0 -7 3}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 7 3}}, {{val|0 -1 8 -7 3}}] | |||
[[Tp tuning|POL2 generator]]: ~3/2 = 701.470 | |||
{{Optimal ET sequence|legend=1| 12, 41, 53, 65 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.5374 cents | |||
=== Quintilischis (2.3.5.17) === | |||
: <small>''For full 17- and 19-limit extensions, see [[Schismatic family#Quintilipyth|Quintilipyth]] or [[Schismatic family#Quintaschis|Quintaschis]].''</small> | |||
Subgroup: 2.3.5.17 | |||
[[Comma list]]: 32805/32768, 1419857/1417176 | |||
[[Gencom]]: [2 18/17; 32805/32768 1419857/1417176] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 0 0 0 5}}, {{val|0 -5 40 0 0 0 -11}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 5}}, {{val|0 -5 40 -11}}] | |||
[[Tp tuning|POL2 generator]]: ~18/17 = 99.649 | |||
{{Optimal ET sequence|legend=1| 12, 253, 265, 277, 289 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.0719 cents | |||
==== 2.3.5.17.19 ==== | |||
Subgroup: 2.3.5.17.19 | |||
[[Comma list]]: 4624/4617, 6144/6137, 6885/6859 | |||
[[Gencom]]: [2 18/17; 4624/4617 6144/6137 6885/6859] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 0 0 0 5 4}}, {{val|0 -5 40 0 0 0 -11 3}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 -1 5 4}}, {{val|0 -5 40 -11 3}}] | |||
[[Tp tuning|POL2 generator]]: ~18/17 = 99.652 | |||
{{Optimal ET sequence|legend=1| 12, 253, 265, 277, 289 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.1636 cents | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||