Quintaleap family: Difference between revisions
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=== Subgroup temperament === | === Subgroup temperament === | ||
The quintaleap temperament works well for the 2.3.5.17.19 subgroup, tempering out 256/255 (equating 16/15 with 17/16), 361/360 (equating 19/18 with 20/19), and 4624/4617. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and sixteen 18/17s with [[5/2]]. | The quintaleap temperament works well for the 2.3.5.17.19 subgroup, tempering out 256/255 (equating 16/15 with 17/16), 361/360 (equating 19/18 with 20/19), and 4624/4617. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and sixteen 18/17s with [[5/2]]. | ||
==== 2.3.5.17 ==== | |||
Subgroup: 2.3.5.17 | |||
[[Comma list]]: 256/255, 1419857/1417176 | |||
[[Gencom]]: [2 18/17; 256/255 1419857/1417176] | |||
[[Gencom|Gencom mapping]]: [{{val| 1 2 1 0 0 0 5 }}, {{val| 0 -5 16 0 0 0 -11 }}] | |||
[[Mapping|Sval mapping]]: [{{val| 1 2 1 5 }}, {{val| 0 -5 16 -11 }}] | |||
[[Tp tuning|POL2 generator]]: ~18/17 = 99.272 | |||
{{Optimal ET sequence|legend=1| 12, 109, 121, 133 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3051 cents | |||
==== 2.3.5.17.19 ==== | |||
Subgroup: 2.3.5.17.19 | Subgroup: 2.3.5.17.19 | ||
Comma list: 256/255, 361/360, 4624/4617 | [[Comma list]]: 256/255, 361/360, 4624/4617 | ||
[[Gencom]]: [2 18/17; 256/255 361/360 4624/4617] | |||
[[Gencom|Gencom mapping]]: [{{val| 1 2 1 0 0 0 5 4 }}, {{val| 0 -5 16 0 0 0 -11 3 }}] | |||
Sval mapping: [{{val| 1 2 1 5 4 }}, {{val| 0 -5 16 -11 3 }}] | [[Mapping|Sval mapping]]: [{{val| 1 2 1 5 4 }}, {{val| 0 -5 16 -11 3 }}] | ||
[[Tp tuning|POL2 generator]]: ~18/17 = 99.276 | |||
{{Optimal ET sequence|legend=1| 12, 109, 121, 133 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3427 cents | |||
Badness: 0.014623 | Badness: 0.014623 | ||