15th-octave temperaments: Difference between revisions
No edit summary |
m Cleanup |
||
| Line 2: | Line 2: | ||
[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps. | [[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps. | ||
Temperaments discussed elsewhere include [[Cloudy clan|pentadecal]]. | Temperaments discussed elsewhere include [[Cloudy clan #Pentadecal|pentadecal]]. | ||
== Pentadecoid == | == Pentadecoid == | ||
Subgroup: 2.3.7.11 | [[Subgroup]]: 2.3.7.11 | ||
[[Comma list]]: 1362944/1361367, 1771561/1769472 | [[Comma list]]: 1362944/1361367, 1771561/1769472 | ||
| Line 11: | Line 11: | ||
[[Mapping]]: {{mapping| 15 108 0 94 | 0 -2 1 -1 }} | [[Mapping]]: {{mapping| 15 108 0 94 | 0 -2 1 -1 }} | ||
: | : mapping generators: ~22/21, ~7 | ||
[[Optimal tuning]] ([[CTE]]): ~22/21 = | [[Optimal tuning]] ([[CTE]]): ~22/21 = 80.0000, ~8/7 = 231.0071 | ||
{{Optimal ET sequence|legend=1| 120, 135, 660, 795, 930, 1065, 1200 }} | {{Optimal ET sequence|legend=1| 120, 135, 660, 795, 930, 1065, 1200 }} | ||
| Line 20: | Line 20: | ||
== Phosphorus == | == Phosphorus == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 250047/250000, {{monzo|60 -96 1 32}} | [[Comma list]]: 250047/250000, {{monzo| 60 -96 1 32 }} | ||
[[Mapping]]: {{mapping| 15 8 -4 -4 | 0 13 32 38 }} | [[Mapping]]: {{mapping| 15 8 -4 -4 | 0 13 32 38 }} | ||
: | : mapping generators: ~{{monzo| -21 34 4 -15 }}, ~210827008/199290375 | ||
[[Optimal tuning]] ([[CTE]]): ~{{monzo|-21 34 4 -15}} = | [[Optimal tuning]] ([[CTE]]): ~{{monzo|-21 34 4 -15}} = 80.0000, ~28/27 = 62.9267 | ||
{{Optimal ET sequence|legend=1| 1125, 1335, 2460 }} | {{Optimal ET sequence|legend=1| 1125, 1335, 2460 }} | ||
| Line 43: | Line 43: | ||
[[Mapping]]: {{mapping| 15 24 35 42 52 0 | 0 0 0 0 0 1 }} | [[Mapping]]: {{mapping| 15 24 35 42 52 0 | 0 0 0 0 0 1 }} | ||
: | : mapping generators: ~22/21, ~13 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~22/21 = | * [[CTE]]: ~22/21 = 80.000, ~13/8 = 840.528 (~40/39 = 39.472) | ||
* [[POTE]]: ~22/21 = | * [[POTE]]: ~22/21 = 80.000, ~13/8 = 852.924 (~40/39 = 27.076) | ||
{{Optimal ET sequence|legend=1| 15, 30 }} | {{Optimal ET sequence|legend=1| 15, 30 }} | ||