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Sensamagic clan: Difference between revisions

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Cmloegcmluin (talk | contribs)
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5,160 edits
add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 14: Line 14:
[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~9/7 = 440.4881
[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~9/7 = 440.4881


[[Optimal GPV sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]
[[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]


=== Overview to extensions ===
=== Overview to extensions ===
Line 60: Line 60:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 443.383
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 443.383


{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}


[[Badness]]: 0.025622
[[Badness]]: 0.025622
Line 77: Line 77:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.322
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.322


Optimal GPV sequence: {{Val list| 19, 27, 46, 111de, 157de }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111de, 157de }}


=== Sensor ===
=== Sensor ===
Line 88: Line 88:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.294
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.294


Optimal GPV sequence: {{Val list| 19, 27, 46, 111d, 157d, 268cdd }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111d, 157d, 268cdd }}


Badness: 0.037942
Badness: 0.037942
Line 101: Line 101:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.321
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.321


Optimal GPV sequence: {{Val list| 19, 27, 46, 111df, 157df }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 111df, 157df }}


Badness: 0.025575
Badness: 0.025575
Line 114: Line 114:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.365
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.365


Optimal GPV sequence: {{Val list| 19, 27, 46, 157df, 203cdff, 249cddff }}
{{Optimal ET sequence|legend=1| 19, 27, 46, 157df, 203cdff, 249cddff }}


Badness: 0.022908
Badness: 0.022908
Line 127: Line 127:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962


Optimal GPV sequence: {{Val list| 8d, 19, 27e, 73ee }}
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}


Badness: 0.028680
Badness: 0.028680
Line 140: Line 140:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945


Optimal GPV sequence: {{Val list| 19, 27e, 46e, 73ee }}
{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}


Badness: 0.020017
Badness: 0.020017
Line 153: Line 153:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.626
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.626


Optimal GPV sequence: {{Val list| 19e, 27e, 46, 119c, 165c }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 119c, 165c }}


Badness: 0.029486
Badness: 0.029486
Line 166: Line 166:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.559
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.559


Optimal GPV sequence: {{Val list| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
{{Optimal ET sequence|legend=1| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}


Badness: 0.020789
Badness: 0.020789
Line 179: Line 179:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.551
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.551


Optimal GPV sequence: {{Val list| 19eg, 27eg, 46 }}
{{Optimal ET sequence|legend=1| 19eg, 27eg, 46 }}


Badness: 0.016238
Badness: 0.016238
Line 192: Line 192:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.518
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.518


Optimal GPV sequence: {{Val list| 19e, 27, 46ee }}
{{Optimal ET sequence|legend=1| 19e, 27, 46ee }}


Badness: 0.036835
Badness: 0.036835
Line 205: Line 205:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.506
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.506


Optimal GPV sequence: {{Val list| 19e, 27, 46ee }}
{{Optimal ET sequence|legend=1| 19e, 27, 46ee }}


Badness: 0.023258
Badness: 0.023258
Line 218: Line 218:
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605


Optimal GPV sequence: {{Val list| 27e, 38d, 65, 157de, 222cde }}
{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}


Badness: 0.048714
Badness: 0.048714
Line 231: Line 231:
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.556
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.556


Optimal GPV sequence: {{Val list| 27e, 38df, 65f }}
{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}


Badness: 0.033016
Badness: 0.033016
Line 244: Line 244:
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 156.692
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 156.692


Optimal GPV sequence: {{Val list| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}


Badness: 0.041723
Badness: 0.041723
Line 257: Line 257:
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 156.725
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 156.725


Optimal GPV sequence: {{Val list| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}


Badness: 0.026339
Badness: 0.026339
Line 274: Line 274:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 549.944
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 549.944


{{Val list|legend=1| 11cd, 13cd, 24 }}
{{Optimal ET sequence|legend=1| 11cd, 13cd, 24 }}


[[Badness]]: 0.190208
[[Badness]]: 0.190208
Line 287: Line 287:
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945


Optimal GPV sequence: {{Val list| 11cdee, 13cdee, 24 }}
{{Optimal ET sequence|legend=1| 11cdee, 13cdee, 24 }}


Badness: 0.082716
Badness: 0.082716
Line 300: Line 300:
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958


Optimal GPV sequence: {{Val list| 11cdeef, 13cdeef, 24 }}
{{Optimal ET sequence|legend=1| 11cdeef, 13cdeef, 24 }}


Badness: 0.049933
Badness: 0.049933
Line 326: Line 326:
: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3
: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3


{{Val list|legend=1| 41, 131, 172, 213c }}
{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }}


[[Badness]]: 0.068237
[[Badness]]: 0.068237
Line 343: Line 343:
: Eigenmonzo basis (unchanged-interval basis): 2.11/9
: Eigenmonzo basis (unchanged-interval basis): 2.11/9


Optimal GPV sequence: {{Val list| 41, 90e, 131e }}
{{Optimal ET sequence|legend=1| 41, 90e, 131e }}


Badness: 0.033949
Badness: 0.033949
Line 360: Line 360:
: Eigenmonzo basis (unchanged-interval basis): 2.5
: Eigenmonzo basis (unchanged-interval basis): 2.5


Optimal GPV sequence: {{Val list| 41, 90ef, 131ef, 221bdeff }}
{{Optimal ET sequence|legend=1| 41, 90ef, 131ef, 221bdeff }}


Badness: 0.024864
Badness: 0.024864
Line 380: Line 380:
Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.828
Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.828


Optimal GPV sequence: {{Val list| 49, 123ce, 172 }}
{{Optimal ET sequence|legend=1| 49, 123ce, 172 }}


Badness: 0.162592
Badness: 0.162592
Line 393: Line 393:
Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.822
Optimal tuning (POTE): ~2 = 1\1, ~77/75 = 48.822


Optimal GPV sequence: {{Val list| 49f, 123ce, 172f, 295ce, 467bccef }}
{{Optimal ET sequence|legend=1| 49f, 123ce, 172f, 295ce, 467bccef }}


Badness: 0.082158
Badness: 0.082158
Line 410: Line 410:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 351.049
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 351.049


{{Val list|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}
{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}


[[Badness]]: 0.080152
[[Badness]]: 0.080152
Line 423: Line 423:
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014


Optimal GPV sequence: {{Val list| 17, 24, 41, 106d, 147d }}
{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d }}


Badness: 0.039444
Badness: 0.039444
Line 436: Line 436:
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.025
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.025


Optimal GPV sequence: {{Val list| 17, 24, 41, 106df, 147df }}
{{Optimal ET sequence|legend=1| 17, 24, 41, 106df, 147df }}


Badness: 0.030793
Badness: 0.030793
Line 455: Line 455:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~45/32 = 567.720
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~45/32 = 567.720


{{Val list|legend=1| 17, 19, 55c, 74cd, 93cdd }}
{{Optimal ET sequence|legend=1| 17, 19, 55c, 74cd, 93cdd }}


[[Badness]]: 0.073735
[[Badness]]: 0.073735
Line 472: Line 472:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 439.076
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 439.076


{{Val list|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}
{{Optimal ET sequence|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}


[[Badness]]: 0.139379
[[Badness]]: 0.139379
Line 485: Line 485:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.152
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.152


Optimal GPV sequence: {{Val list| 11cd, 30d, 41, 153be, 194be, 235bcee }}
{{Optimal ET sequence|legend=1| 11cd, 30d, 41, 153be, 194be, 235bcee }}


Badness: 0.070917
Badness: 0.070917
Line 498: Line 498:
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.119
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 439.119


Optimal GPV sequence: {{Val list| 11cdf, 30df, 41 }}
{{Optimal ET sequence|legend=1| 11cdf, 30df, 41 }}


Badness: 0.052835
Badness: 0.052835
Line 511: Line 511:
[[Mapping]]: [{{val| 19 0 14 -7 }}, {{val| 0 1 1 2 }}]
[[Mapping]]: [{{val| 19 0 14 -7 }}, {{val| 0 1 1 2 }}]


{{Val list|legend=1| 19, 76bcd, 95, 114, 133, 247b, 380bcd }}
{{Optimal ET sequence|legend=1| 19, 76bcd, 95, 114, 133, 247b, 380bcd }}


=== 11-limit ===
=== 11-limit ===
Line 520: Line 520:
Mapping: [{{val| 19 0 14 -7 96 }}, {{val| 0 1 1 2 -1 }}]
Mapping: [{{val| 19 0 14 -7 96 }}, {{val| 0 1 1 2 -1 }}]


{{Val list|legend=1| 19, 76bcd, 95, 114e }}
{{Optimal ET sequence|legend=1| 19, 76bcd, 95, 114e }}


=== 13-limit ===
=== 13-limit ===
Line 529: Line 529:
Mapping: [{{val| 19 0 14 -7 96 10 }}, {{val| 0 1 1 2 -1 2 }}]
Mapping: [{{val| 19 0 14 -7 96 10 }}, {{val| 0 1 1 2 -1 2 }}]


{{Val list|legend=1| 19, 76bcdf, 95, 114e }}
{{Optimal ET sequence|legend=1| 19, 76bcdf, 95, 114e }}


== Magus ==
== Magus ==
Line 546: Line 546:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 391.465
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 391.465


{{Val list|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}
{{Optimal ET sequence|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}


[[Badness]]: 0.108417
[[Badness]]: 0.108417
Line 559: Line 559:
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.503
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.503


Optimal GPV sequence: {{Val list| 46, 95, 141bc }}
{{Optimal ET sequence|legend=1| 46, 95, 141bc }}


Badness: 0.045108
Badness: 0.045108
Line 572: Line 572:
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.366
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.366


Optimal GPV sequence: {{Val list| 46, 233bcff, 279bccff }}
{{Optimal ET sequence|legend=1| 46, 233bcff, 279bccff }}


Badness: 0.043024
Badness: 0.043024
Line 589: Line 589:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.536
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.536


{{Val list|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}
{{Optimal ET sequence|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}


[[Badness]]: 0.140577
[[Badness]]: 0.140577
Line 602: Line 602:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.554
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.554


Optimal GPV sequence: {{Val list| 17, 29c, 46, 109, 264b, 373b, 637bbe }}
{{Optimal ET sequence|legend=1| 17, 29c, 46, 109, 264b, 373b, 637bbe }}


Badness: 0.050679
Badness: 0.050679
Line 615: Line 615:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.571
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.571


Optimal GPV sequence: {{Val list| 17, 29c, 46, 63, 109 }}
{{Optimal ET sequence|legend=1| 17, 29c, 46, 63, 109 }}


Badness: 0.032727
Badness: 0.032727
Line 628: Line 628:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.540
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.540


Optimal GPV sequence: {{Val list| 17g, 29cg, 46, 109, 155f, 264bfg }}
{{Optimal ET sequence|legend=1| 17g, 29cg, 46, 109, 155f, 264bfg }}


Badness: 0.026243
Badness: 0.026243
Line 641: Line 641:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.537
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.537


Optimal GPV sequence: {{Val list| 17, 29c, 46, 109g, 155fg, 264bfgg }}
{{Optimal ET sequence|legend=1| 17, 29c, 46, 109g, 155fg, 264bfgg }}


Badness: 0.026774
Badness: 0.026774
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