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Alphatricot family: Difference between revisions

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Post-move cleanup
m Spell the periods in cents. Note the badness metric being used. Misc. cleanup
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{{Multival|legend=1| 3 29 39 }}
{{Multival|legend=1| 3 29 39 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~59049/40960 = 634.012
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~59049/40960 = 634.012


{{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
{{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}


[[Badness]]: 0.046093
[[Badness]] (Smith): 0.046093


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
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Subgroup: 2.3.5.13
Subgroup: 2.3.5.13


[[Comma list]]: 2197/2187, 41067/40960
Comma list: 2197/2187, 41067/40960


[[Gencom]]: [2 13/9; 2197/2187, 41067/40960]
[[Sval]] [[mapping]]: {{mapping| 1 0 -13 0 | 0 3 29 7 }}


[[Gencom|Gencom mapping]]: [{{val|1 0 -13 0 0 0}}, {{val|0 3 29 0 0 7}}]
[[Gencom]] [[mapping]]: {{mapping| 1 0 -13 0 0 0 | 0 3 29 0 0 7 }}


[[Mapping|Sval mapping]]: [{{val|1 0 -13 0}}, {{val|0 3 29 7}}]
: gencom: [2 13/9; 2197/2187, 41067/40960]


[[Tp tuning|POL2 generator]]: ~13/9 = 633.997
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~13/9 = 633.997


{{Optimal ET sequence|legend=1| 17c, 36c, 53 }}
{{Optimal ET sequence|legend=0| 17c, 36c, 53 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.2342 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2342 cents
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{{Multival|legend=1| 3 29 11 39 9 -56 }}
{{Multival|legend=1| 3 29 11 39 9 -56 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~81/56 = 634.0259
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~81/56 = 634.0259


{{Optimal ET sequence|legend=1| 17c, 36c, 53, 70, 229dd, 282dd }}
{{Optimal ET sequence|legend=1| 17c, 36c, 53, 70, 229dd, 282dd }}


[[Badness]]: 0.100127
[[Badness]] (Smith): 0.100127


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -13 -3 -5 | 0 3 29 11 16 }}
Mapping: {{mapping| 1 0 -13 -3 -5 | 0 3 29 11 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~63/44 = 634.0273
Optimal tuning (POTE): ~2 = 1200.0000, ~63/44 = 634.0273


{{Optimal ET sequence|legend=1| 17c, 36ce, 53, 70, 123de }}
{{Optimal ET sequence|legend=0| 17c, 36ce, 53, 70, 123de }}


Badness: 0.056134
Badness (Smith): 0.056134


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 -13 -3 -5 0 | 0 3 29 11 16 7 }}
Mapping: {{mapping| 1 0 -13 -3 -5 0 | 0 3 29 11 16 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0115
Optimal tuning (POTE): ~2 = 1200.0000, ~13/9 = 634.0115


{{Optimal ET sequence|legend=1| 17c, 36ce, 53, 70, 123de }}
{{Optimal ET sequence|legend=0| 17c, 36ce, 53, 70, 123de }}


Badness: 0.032102
Badness (Smith): 0.032102


== Alphatrident ==
== Alphatrident ==
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{{Multival|legend=1| 3 29 -42 39 -75 -179 }}
{{Multival|legend=1| 3 29 -42 39 -75 -179 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~4096/2835 = 634.0480
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~4096/2835 = 634.0480


{{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511 }}
{{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511 }}


[[Badness]]: 0.101694
[[Badness]] (Smith): 0.101694


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -13 25 -33 | 0 3 29 -42 69 }}
Mapping: {{mapping| 1 0 -13 25 -33 | 0 3 29 -42 69 }}


Optimal tuning (POTE): ~2 = 1\1, ~231/160 = 634.0669
Optimal tuning (POTE): ~2 = 1200.0000, ~231/160 = 634.0669


{{Optimal ET sequence|legend=1| 53, 176, 229 }}
{{Optimal ET sequence|legend=0| 53, 176, 229 }}


Badness: 0.074272
Badness (Smith): 0.074272


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 -13 25 -33 0 | 0 3 29 -42 69 7 }}
Mapping: {{mapping| 1 0 -13 25 -33 0 | 0 3 29 -42 69 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0652
Optimal tuning (POTE): ~2 = 1200.0000, ~13/9 = 634.0652


{{Optimal ET sequence|legend=1| 53, 176, 229 }}
{{Optimal ET sequence|legend=0| 53, 176, 229 }}


Badness: 0.046593
Badness (Smith): 0.046593


== Alphatrillium ==
== Alphatrillium ==
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{{Multival|legend=1| 3 29 -95 39 -159 -302 }}
{{Multival|legend=1| 3 29 -95 39 -159 -302 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~23625/16384 = 634.0118
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~23625/16384 = 634.0118


{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}
{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}


[[Badness]]: 0.030852
[[Badness]] (Smith): 0.030852


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 -13 53 -89 | 0 3 29 -95 175 }}
Mapping: {{mapping| 1 0 -13 53 -89 | 0 3 29 -95 175 }}


Optimal tuning (POTE): ~2 = 1\1, ~3888/2695 = 634.0094
Optimal tuning (POTE): ~2 = 1200.0000, ~3888/2695 = 634.0094


{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
{{Optimal ET sequence|legend=0| 53, 441, 494, 935, 1429 }}


Badness: 0.046758
Badness (Smith): 0.046758


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 -13 53 -89 -28 | 0 3 29 -95 175 60 }}
Mapping: {{mapping| 1 0 -13 53 -89 -28 | 0 3 29 -95 175 60 }}


Optimal tuning (POTE): ~2 = 1\1, ~75/52 = 634.0095
Optimal tuning (POTE): ~2 = 1200.0000, ~75/52 = 634.0095


{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
{{Optimal ET sequence|legend=0| 53, 441, 494, 935, 1429 }}


Badness: 0.019393
Badness (Smith): 0.019393


=== Pseudotrillium ===
=== Pseudotrillium ===
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Mapping: {{mapping| 1 0 -13 53 -61 | 0 3 29 -95 122 }}
Mapping: {{mapping| 1 0 -13 53 -61 | 0 3 29 -95 122 }}


Optimal tuning (POTE): ~2 = 1\1, ~231/160 = 634.0190
Optimal tuning (POTE): ~2 = 1200.0000, ~231/160 = 634.0190


{{Optimal ET sequence|legend=1| 53, 335, 388 }}
{{Optimal ET sequence|legend=0| 53, 335, 388 }}


Badness: 0.111931
Badness (Smith): 0.111931


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 -13 53 -61 -28 | 0 3 29 -95 122 60 }}
Mapping: {{mapping| 1 0 -13 53 -61 -28 | 0 3 29 -95 122 60 }}


Optimal tuning (POTE): ~2 = 1\1, ~75/52 = 634.0181
Optimal tuning (POTE): ~2 = 1200.0000, ~75/52 = 634.0181


{{Optimal ET sequence|legend=1| 53, 335, 388 }}
{{Optimal ET sequence|legend=0| 53, 335, 388 }}


Badness: 0.054837
Badness (Smith): 0.054837


== Tritricot ==
== Tritricot ==
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{{Multival|legend=1| 9 87 156 117 222 118 }}
{{Multival|legend=1| 9 87 156 117 222 118 }}


[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~100352/91125 = 165.9837
[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.0000, ~100352/91125 = 165.9837


{{Optimal ET sequence|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
{{Optimal ET sequence|legend=1| 159, 282, 441, 2487, 2928, 3369 }}


[[Badness]]: 0.086081
[[Badness]] (Smith): 0.086081


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 3 6 19 30 22 | 0 -3 -29 -52 -28 }}
Mapping: {{mapping| 3 6 19 30 22 | 0 -3 -29 -52 -28 }}


Optimal tuning (POTE): ~63/50 = 1\3, ~11/10 = 165.9835
Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9835


{{Optimal ET sequence|legend=1| 159, 282, 441 }}
{{Optimal ET sequence|legend=0| 159, 282, 441 }}


Badness: 0.074002
Badness (Smith): 0.074002


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 3 6 19 30 22 36 | 0 -3 -29 -52 -28 -60 }}
Mapping: {{mapping| 3 6 19 30 22 36 | 0 -3 -29 -52 -28 -60 }}


Optimal tuning (POTE): ~63/50 = 1\3, ~11/10 = 165.9842
Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9842


{{Optimal ET sequence|legend=1| 159, 282, 441 }}
{{Optimal ET sequence|legend=0| 159, 282, 441 }}


Badness: 0.035641
Badness (Smith): 0.035641


==== 17-limit ====
==== 17-limit ====
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Mapping: {{mapping| 3 6 19 30 22 36 16 | 0 -3 -29 -52 -28 -60 -9 }}
Mapping: {{mapping| 3 6 19 30 22 36 16 | 0 -3 -29 -52 -28 -60 -9 }}


Optimal tuning (POTE): ~34/27 = 1\3, ~11/10 = 165.9805
Optimal tuning (POTE): ~34/27 = 400.0000, ~11/10 = 165.9805


{{Optimal ET sequence|legend=1| 159, 282, 441 }}
{{Optimal ET sequence|legend=0| 159, 282, 441 }}


Badness: 0.025972
Badness (Smith): 0.025972


=== Noletaland ===
=== Noletaland ===
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: mappin generators: ~63/50, ~1936/1875
: mappin generators: ~63/50, ~1936/1875


Optimal tuning (CTE): ~63/50 = 1\3, ~1936/1875 = 55.3290
Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3290


{{Optimal ET sequence|legend=1| 282, 759de, 1041, 1323, 4251e }}
{{Optimal ET sequence|legend=0| 282, 759de, 1041, 1323, 4251e }}


Badness: 0.158
Badness (Smith): 0.158


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 3 6 19 30 35 36 | 0 -9 -87 -156 -178 -180 }}
Mapping: {{mapping| 3 6 19 30 35 36 | 0 -9 -87 -156 -178 -180 }}


Optimal tuning (CTE): ~63/50 = 1\3, ~1936/1875 = 55.3294
Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3294


{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness: 0.0725
Badness (Smith): 0.0725


==== 17-limit ====
==== 17-limit ====
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Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}


Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.3295
Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3295


{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness: 0.0380
Badness (Smith): 0.0380


==== 19-limit ====
==== 19-limit ====
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Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}


Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.3295
Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3295


{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness: 0.0269
Badness (Smith): 0.0269


==== 23-limit ====
==== 23-limit ====
Line 319: Line 319:
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}


Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.3296
Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3296


{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness: 0.0194
Badness (Smith): 0.0194


==== 29-limit ====
==== 29-limit ====
Line 332: Line 332:
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}


Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.3296
Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3296


{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness: 0.0168
Badness (Smith): 0.0168


== Notes ==
== Notes ==
Retrieved from "https://en.xen.wiki/w/Alphatricot_family"