Kleismic family: Difference between revisions

Godtone (talk | contribs)
+reduced generators
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{{Multival|legend=1| 18 15 -6 -18 -60 -56 }}
{{Multival|legend=1| 18 15 -6 -18 -60 -56 }}


[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~6/5 = 316.872
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~6/5 = 316.872 (~21/20 = 83.128)


[[Minimax tuning]]:
[[Minimax tuning]]:
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Mapping: {{mapping| 3 0 3 10 8 | 0 6 5 -2 3 }}
Mapping: {{mapping| 3 0 3 10 8 | 0 6 5 -2 3 }}


Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.881
Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.881 (~21/20 = 83.119)


Minimax tuning:
Minimax tuning:
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Mapping: {{mapping| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}
Mapping: {{mapping| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}


Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.9585
Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.9585 (~21/20 = 83.0415)


{{Optimal ET sequence|legend=1| 72, 87, 159 }}
{{Optimal ET sequence|legend=1| 72, 87, 159 }}
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Mapping: {{mapping| 3 0 3 10 8 0 -2 | 0 6 5 -2 3 14 18 }}
Mapping: {{mapping| 3 0 3 10 8 0 -2 | 0 6 5 -2 3 14 18 }}


Optimal tuning (POTE): ~34/27 = 1\3, ~6/5 = 316.9082
Optimal tuning (POTE): ~34/27 = 1\3, ~6/5 = 316.9082 (~21/20 = 83.0918)


{{Optimal ET sequence|legend=1| 72, 159, 231f }}
{{Optimal ET sequence|legend=1| 72, 159, 231f }}
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{{Multival|legend=1| 24 20 16 -24 -42 -19 }}
{{Multival|legend=1| 24 20 16 -24 -42 -19 }}


[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~6/5 = 316.9999
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~6/5 = 316.9999 (~126/125 = 16.9999)


{{Optimal ET sequence|legend=1| 68, 72, 140, 212, 776cd, 988ccd, 1200ccd }}
{{Optimal ET sequence|legend=1| 68, 72, 140, 212, 776cd, 988ccd, 1200ccd }}
Line 719: Line 719:
Mapping: {{mapping| 4 0 4 7 17 | 0 6 5 4 -3 }}
Mapping: {{mapping| 4 0 4 7 17 | 0 6 5 4 -3 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9247
Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9247 (~100/99 = 16.9247)


{{Optimal ET sequence|legend=1| 68, 72, 140, 212, 284, 496ce, 780ccdee }}
{{Optimal ET sequence|legend=1| 68, 72, 140, 212, 284, 496ce, 780ccdee }}
Line 732: Line 732:
Mapping: {{mapping| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}
Mapping: {{mapping| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9887
Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9887 (~100/99 = 16.9887)


{{Optimal ET sequence|legend=1| 68, 72, 140, 212 }}
{{Optimal ET sequence|legend=1| 68, 72, 140, 212 }}
Line 745: Line 745:
Mapping: {{mapping| 4 0 4 7 17 0 10 | 0 6 5 4 -3 14 6 }}
Mapping: {{mapping| 4 0 4 7 17 0 10 | 0 6 5 4 -3 14 6 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9846
Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9846 (~100/99 = 16.9846)


{{Optimal ET sequence|legend=1| 68, 72, 140, 212g }}
{{Optimal ET sequence|legend=1| 68, 72, 140, 212g }}
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{{Multival|legend=1| 54 45 54 -54 -66 -1 }}
{{Multival|legend=1| 54 45 54 -54 -66 -1 }}


[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~6/5 = 317.005
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~6/5 = 317.005 (~36/35 = 50.338)


{{Optimal ET sequence|legend=1| 72, 261, 333, 405, 477c, 882c }}
{{Optimal ET sequence|legend=1| 72, 261, 333, 405, 477c, 882c }}
Line 1,007: Line 1,007:
Mapping: {{mapping| 9 0 9 11 24 | 0 6 5 6 3 }}
Mapping: {{mapping| 9 0 9 11 24 | 0 6 5 6 3 }}


Optimal tuning (POTE): ~250/231 = 1\9, ~6/5 = 317.010
Optimal tuning (POTE): ~250/231 = 1\9, ~6/5 = 317.010 (~36/35 = 50.343)


{{Optimal ET sequence|legend=1| 72, 261, 333, 405, 882c }}
{{Optimal ET sequence|legend=1| 72, 261, 333, 405, 882c }}
Line 1,020: Line 1,020:
Mapping: {{mapping| 9 0 9 11 24 0 | 0 6 5 6 3 14 }}
Mapping: {{mapping| 9 0 9 11 24 0 | 0 6 5 6 3 14 }}


Optimal tuning (POTE): ~250/231 = 1\9, ~6/5 = 317.086
Optimal tuning (POTE): ~250/231 = 1\9, ~6/5 = 317.086 (~36/35 = 50.419)


{{Optimal ET sequence|legend=1| 72, 189f, 261, 333, 738cf }}
{{Optimal ET sequence|legend=1| 72, 189f, 261, 333, 738cf }}