19th-octave temperaments: Difference between revisions
Move graywood and 5-limit enneadecal to the equivalence continuum |
m Units & misc. cleanup |
||
| Line 10: | Line 10: | ||
{{Mapping|legend=1| 19 30 44 0 | 0 0 0 1 }} | {{Mapping|legend=1| 19 30 44 0 | 0 0 0 1 }} | ||
: mapping generators: ~25/24, ~7 | : mapping generators: ~25/24, ~7 | ||
[[Optimal tuning]] ([[POTE]]): ~25/24 = | [[Optimal tuning]] ([[POTE]]): ~25/24 = 63.1579{{c}}, ~8/7 = 238.396{{c}} | ||
{{Optimal ET sequence|legend=1| 19, 38, 57, 76, 95bc }} | {{Optimal ET sequence|legend=1| 19, 38, 57, 76, 95bc }} | ||
[[Badness]]: 0.077023 | [[Badness]] (Smith): 0.077023 | ||
=== 11-limit === | === 11-limit === | ||
| Line 26: | Line 25: | ||
Mapping: {{mapping| 19 30 44 0 119 | 0 0 0 1 -1 }} | Mapping: {{mapping| 19 30 44 0 119 | 0 0 0 1 -1 }} | ||
Optimal tuning (POTE): ~25/24 = | Optimal tuning (POTE): ~25/24 = 63.1579{{c}}, ~8/7 = 233.486{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 38, 57, 76 }} | ||
Badness: 0.066829 | Badness (Smith): 0.066829 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 39: | Line 38: | ||
Mapping: {{mapping| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }} | Mapping: {{mapping| 19 30 44 0 119 17 | 0 0 0 1 -1 1 }} | ||
Optimal tuning (POTE): ~25/24 = | Optimal tuning (POTE): ~25/24 = 63.1579{{c}}, ~8/7 = 234.890{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 38, 57, 76 }} | ||
Badness: 0.045844 | Badness (Smith): 0.045844 | ||
== Undevigintone == | == Undevigintone == | ||
| Line 51: | Line 50: | ||
{{Mapping|legend=1| 19 30 44 53 0 | 0 0 0 0 1 }} | {{Mapping|legend=1| 19 30 44 53 0 | 0 0 0 0 1 }} | ||
: mapping generators: ~28/27, ~11 | : mapping generators: ~28/27, ~11 | ||
[[Optimal tuning]] ([[POTE]]): ~28/27 = | [[Optimal tuning]] ([[POTE]]): ~28/27 = 63.1579{{c}}, ~11/8 = 538.047{{c}} | ||
{{Optimal ET sequence|legend=1| 19, 38d }} | {{Optimal ET sequence|legend=1| 19, 38d }} | ||
[[Badness]]: 0.036387 | [[Badness]] (Smith): 0.036387 | ||
=== 13-limit === | === 13-limit === | ||
| Line 67: | Line 65: | ||
Mapping: {{mapping| 19 30 44 53 0 70 | 0 0 0 0 1 0 }} | Mapping: {{mapping| 19 30 44 53 0 70 | 0 0 0 0 1 0 }} | ||
Optimal tuning (POTE): ~28/27 = | Optimal tuning (POTE): ~28/27 = 63.1579{{c}}, ~11/8 = 537.061{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 19, 38df }} | ||
Badness: 0.022933 | Badness (Smith): 0.022933 | ||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||