Smate family: Difference between revisions
Update keys |
m Spell 1\1 in decimal; note the badness metric being used; misc. cleanup |
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{{Mapping|legend=1| 1 3 2 | 0 -4 1 }} | {{Mapping|legend=1| 1 3 2 | 0 -4 1 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | : mapping generators: ~2, ~5/4 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 420.855 | |||
{{Optimal ET sequence|legend=1| 3, 11, 14, 17c, 20c, 37c }} | {{Optimal ET sequence|legend=1| 3, 11, 14, 17c, 20c, 37c }} | ||
[[Badness]]: 0.178624 | [[Badness]] (Smith): 0.178624 | ||
== Septimal smate == | == Septimal smate == | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 25: | Line 25: | ||
{{Multival|legend=1| 4 -1 9 -11 3 24 }} | {{Multival|legend=1| 4 -1 9 -11 3 24 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 422.275 | ||
{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }} | {{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }} | ||
[[Badness]]: 0.077871 | [[Badness]] (Smith): 0.077871 | ||
=== 11-limit === | === 11-limit === | ||
| Line 38: | Line 38: | ||
Mapping: {{mapping| 1 3 2 6 7 | 0 -4 1 -9 -10 }} | Mapping: {{mapping| 1 3 2 6 7 | 0 -4 1 -9 -10 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 422.217 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 3de, 14, 17c, 37ccddee }} | ||
Badness: 0.042518 | Badness (Smith): 0.042518 | ||
=== 13-limit === | === 13-limit === | ||
| Line 51: | Line 51: | ||
Mapping: {{mapping| 1 3 2 6 7 3 | 0 -4 1 -9 -10 2 }} | Mapping: {{mapping| 1 3 2 6 7 3 | 0 -4 1 -9 -10 2 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 423.020 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 3de, 14, 17c }} | ||
Badness: 0.036836 | Badness (Smith): 0.036836 | ||
== Hemismate == | == Hemismate == | ||
| Line 66: | Line 66: | ||
{{Multival|legend=1| 8 -2 1 -22 -21 8 }} | {{Multival|legend=1| 8 -2 1 -22 -21 8 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 210.452 | ||
{{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcd }} | {{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcd }} | ||
[[Badness]]: 0.154301 | [[Badness]] (Smith): 0.154301 | ||
=== 11-limit === | === 11-limit === | ||
| Line 79: | Line 79: | ||
Mapping: {{mapping| 1 3 2 3 4 | 0 -8 2 -1 -3 }} | Mapping: {{mapping| 1 3 2 3 4 | 0 -8 2 -1 -3 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 210.481 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 6, 11, 17c, 40bcde }} | ||
Badness: 0.065528 | Badness (Smith): 0.065528 | ||
=== 13-limit === | === 13-limit === | ||
| Line 92: | Line 92: | ||
Mapping: {{mapping| 1 3 2 3 4 3 | 0 -8 2 -1 -3 4 }} | Mapping: {{mapping| 1 3 2 3 4 3 | 0 -8 2 -1 -3 4 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 210.974 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 6, 11, 17c }} | ||
Badness: 0.050472 | Badness (Smith): 0.050472 | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Smate family| ]] <!-- main article --> | [[Category:Smate family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||