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Semicomma family: Difference between revisions

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Note the ploidacot. Misc. cleanup
m Spell 1\1 in decimal; note the badness metric being used; misc. cleanup
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: mapping generators: ~2, ~75/64
: mapping generators: ~2, ~75/64


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/64 = 271.627
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~75/64 = 271.627


[[Tuning ranges]]:
[[Tuning ranges]]:
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{{Optimal ET sequence|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
{{Optimal ET sequence|legend=1| 22, 31, 53, 190, 243, 296, 645c }}


[[Badness]]: 0.040807
[[Badness]] (Smith): 0.040807


=== Overview to extensions ===
=== Overview to extensions ===
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{{Multival|legend=1| 7 -3 8 -21 -7 27 }}
{{Multival|legend=1| 7 -3 8 -21 -7 27 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 271.509
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/6 = 271.509


[[Minimax tuning]]:
[[Minimax tuning]]:
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{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137, 221d, 358d }}
{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137, 221d, 358d }}


[[Badness]]: 0.020735
[[Badness]] (Smith): 0.020735


=== 11-limit ===
=== 11-limit ===
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{{Multival|legend=1| 7 -3 8 2 -21 -7 -21 27 15 -22 }}
{{Multival|legend=1| 7 -3 8 2 -21 -7 -21 27 15 -22 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 271.426
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.426


Minimax tuning:
Minimax tuning:
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* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]
* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]


{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84e }}
{{Optimal ET sequence|legend=0| 9, 22, 31, 53, 84e }}


Badness: 0.015231
Badness (Smith): 0.015231


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 3 1 3 8 | 0 7 -3 8 2 -19 }}
Mapping: {{mapping| 1 0 3 1 3 8 | 0 7 -3 8 2 -19 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 271.546
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.546


Tuning ranges:
Tuning ranges:
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* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]


{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 137e }}
{{Optimal ET sequence|legend=0| 22, 31, 53, 84e, 137e }}


Badness: 0.019718
Badness (Smith): 0.019718


==== Blair ====
==== Blair ====
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Mapping: {{mapping| 1 0 3 1 3 3 | 0 7 -3 8 2 3 }}
Mapping: {{mapping| 1 0 3 1 3 3 | 0 7 -3 8 2 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 271.301
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.301


{{Optimal ET sequence|legend=1| 9, 22, 31f }}
{{Optimal ET sequence|legend=0| 9, 22, 31f }}


Badness: 0.023086
Badness (Smith): 0.023086


==== Winston ====
==== Winston ====
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Mapping: {{mapping| 1 0 3 1 3 1 | 0 7 -3 8 2 12 }}
Mapping: {{mapping| 1 0 3 1 3 1 | 0 7 -3 8 2 12 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 271.088
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.088


Tuning ranges:
Tuning ranges:
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* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 281.691]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 281.691]


{{Optimal ET sequence|legend=1| 22f, 31 }}
{{Optimal ET sequence|legend=0| 22f, 31 }}


Badness: 0.019931
Badness (Smith): 0.019931


==== Doublethink ====
==== Doublethink ====
Doublethink is a weak extension of orwell to the 13-limit because it splits the generator of ~7/6 into two ~[[13/12]]~[[14/13]]'s (by tempering their difference, [[169/168]]).
Doublethink is a weak extension of orwell to the 13-limit. It splits the generator of ~7/6 into two [[13/12]]~[[14/13]]'s by tempering out their difference, [[169/168]].


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Mapping: {{mapping| 1 0 3 1 3 2 | 0 14 -6 16 4 15 }}
Mapping: {{mapping| 1 0 3 1 3 2 | 0 14 -6 16 4 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 135.723
Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 135.723


Tuning ranges:
Tuning ranges:
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* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]
* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]


{{Optimal ET sequence|legend=1| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
{{Optimal ET sequence|legend=0| 9, 35bd, 44, 53, 62, 115ef, 168eef }}


Badness: 0.027120
Badness (Smith): 0.027120


=== Newspeak ===
=== Newspeak ===
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Mapping: {{mapping| 1 0 3 1 -4 | 0 7 -3 8 33 }}
Mapping: {{mapping| 1 0 3 1 -4 | 0 7 -3 8 33 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 271.288
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.288


Tuning ranges:
Tuning ranges:
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* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 272.514]
* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 272.514]


{{Optimal ET sequence|legend=1| 31, 84, 115, 376b, 491bd, 606bde }}
{{Optimal ET sequence|legend=0| 31, 84, 115, 376b, 491bd, 606bde }}


Badness: 0.031438
Badness (Smith): 0.031438


=== Borwell ===
=== Borwell ===
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Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }}
Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }}


Optimal tuning (POTE): ~2 = 1\1, ~55/36 = 735.752
Optimal tuning (POTE): ~2 = 1200.000, ~55/36 = 735.752


{{Optimal ET sequence|legend=1| 31, 106, 137, 442bd }}
{{Optimal ET sequence|legend=0| 31, 106, 137, 442bd }}


Badness: 0.038377
Badness (Smith): 0.038377


== Sabric ==
== Sabric ==
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{{Multival|legend=1| 7 -3 61 -21 77 150 }}
{{Multival|legend=1| 7 -3 61 -21 77 150 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/64 = 271.607
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~75/64 = 271.607


{{Optimal ET sequence|legend=1| 53, 137d, 190, 243 }}
{{Optimal ET sequence|legend=1| 53, 137d, 190, 243 }}


[[Badness]]: 0.088355
[[Badness]] (Smith): 0.088355


== Triwell ==
== Triwell ==
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{{Multival|legend=1| 21 -9 -7 -63 -70 9 }}
{{Multival|legend=1| 21 -9 -7 -63 -70 9 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~448/375 = 309.472
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~448/375 = 309.472


{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}
{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}


[[Badness]]: 0.080575
[[Badness]] (Smith): 0.080575


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 7 0 1 13 | 0 -21 9 7 -37 }}
Mapping: {{mapping| 1 7 0 1 13 | 0 -21 9 7 -37 }}


Optimal tuning (POTE): ~2 = 1\1, ~448/375 = 309.471
Optimal tuning (POTE): ~2 = 1200.000, ~448/375 = 309.471


{{Optimal ET sequence|legend=1| 31, 97, 128, 159, 190 }}
{{Optimal ET sequence|legend=0| 31, 97, 128, 159, 190 }}


Badness: 0.029807
Badness (Smith): 0.029807


== Quadrawell ==
== Quadrawell ==
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{{Multival|legend=1| 28 -12 1 -84 -77 36 }}
{{Multival|legend=1| 28 -12 1 -84 -77 36 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 232.094
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 232.094


{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }}
{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }}


[[Badness]]: 0.075754
[[Badness]] (Smith): 0.075754


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 7 0 3 11 | 0 -28 12 -1 -39 }}
Mapping: {{mapping| 1 7 0 3 11 | 0 -28 12 -1 -39 }}


Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.083
Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.083


{{Optimal ET sequence|legend=1| 31, 119, 150, 181, 212, 455ee, 667cdee }}
{{Optimal ET sequence|legend=0| 31, 119, 150, 181, 212, 455ee, 667cdee }}


Badness: 0.036493
Badness (Smith): 0.036493


== Rainwell ==
== Rainwell ==
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{{Multival|legend=1| 35 -15 9 -105 -84 63 }}
{{Multival|legend=1| 35 -15 9 -105 -84 63 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~2625/2048 = 425.673
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~2625/2048 = 425.673


{{Optimal ET sequence|legend=1| 31, 172, 203, 234, 265, 296 }}
{{Optimal ET sequence|legend=1| 31, 172, 203, 234, 265, 296 }}


[[Badness]]: 0.143488
[[Badness]] (Smith): 0.143488


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 14 -3 6 29 | 0 -35 15 -9 -72 }}
Mapping: {{mapping| 1 14 -3 6 29 | 0 -35 15 -9 -72 }}


Optimal tuning (POTE): ~2 = 1\1, ~2625/2048 = 425.679
Optimal tuning (POTE): ~2 = 1200.000, ~2625/2048 = 425.679


{{Optimal ET sequence|legend=1| 31, 172e, 203e, 234, 265, 296, 919bc, 1215bcc, 1511bcc }}
{{Optimal ET sequence|legend=0| 31, 172e, 203e, 234, 265, 296, 919bc, 1215bcc, 1511bcc }}


Badness: 0.052774
Badness (Smith): 0.052774


== Quinwell ==
== Quinwell ==
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{{Multival|legend=1| 35 -15 62 -105 0 186 }}
{{Multival|legend=1| 35 -15 62 -105 0 186 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~405/392 = 54.324
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~405/392 = 54.324


{{Optimal ET sequence|legend=1| 22, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}
{{Optimal ET sequence|legend=1| 22, 221, 243, 751c, 994cd, 1237bccd, 1480bccd }}


[[Badness]]: 0.168897
[[Badness]] (Smith): 0.168897


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 3 0 5 | 0 35 -15 62 -34 }}
Mapping: {{mapping| 1 0 3 0 5 | 0 35 -15 62 -34 }}


Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 54.334
Optimal tuning (POTE): ~2 = 1200.000, ~33/32 = 54.334


{{Optimal ET sequence|legend=1| 22, 221, 243, 265, 773ce, 1038ccee, 1303ccee }}
{{Optimal ET sequence|legend=0| 22, 221, 243, 265, 773ce, 1038ccee, 1303ccee }}


Badness: 0.097202
Badness (Smith): 0.097202


=== Quinbetter ===
=== Quinbetter ===
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Mapping: {{mapping| 1 0 3 0 4 | 0 35 -15 62 -12 }}
Mapping: {{mapping| 1 0 3 0 4 | 0 35 -15 62 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~405/392 = 54.316
Optimal tuning (POTE): ~2 = 1200.000, ~405/392 = 54.316


{{Optimal ET sequence|legend=1| 22, 199d, 221e, 243e }}
{{Optimal ET sequence|legend=0| 22, 199d, 221e, 243e }}


Badness: 0.078657
Badness (Smith): 0.078657


[[Category:Temperament families]]
[[Category:Temperament families]]
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