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Catalog of rank-4 temperaments: Difference between revisions

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[[Comma list]]: [[100/99]]
[[Comma list]]: [[100/99]]


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 0 }}]
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}


[[Optimal tuning]] ([[POTE]]): ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803


{{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} <nowiki>*</nowiki>
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[[Comma list]]: [[121/120]]
[[Comma list]]: [[121/120]]


[[Mapping]]: [{{val| 1 0 1 0 2 }}, {{val| 0 1 1 0 1 }}, {{val| 0 0 -2 0 -1 }}, {{val| 0 0 0 1 0 }}]
{{Mapping|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }}


Mapping generators: ~2, ~3, ~11/10, ~7
: mapping generators: ~2, ~3, ~11/10, ~7


[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589


{{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}
{{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}
Line 36: Line 36:
[[Comma list]]: [[176/175]]
[[Comma list]]: [[176/175]]


[[Mapping]]: [{{val| 1 0 0 0 -4 }}, {{val| 0 1 0 0 0 }}, {{val| 0 0 1 0 2 }}, {{val| 0 0 0 1 1 }}]
{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }}


Mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.0449, ~5/4 = 389.7641, ~7/4 = 972.1113
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.0449, ~5/4 = 389.7641, ~7/4 = 972.1113


{{Optimal ET sequence|legend=1| 22, 31, 46, 53, 58, 80, 111 }}
{{Optimal ET sequence|legend=1| 22, 31, 46, 53, 58, 80, 111 }}
Line 51: Line 51:
[[Comma list]]: [[243/242]]
[[Comma list]]: [[243/242]]


[[Mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 0 0 5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0}}]
{{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0}}


[[Optimal tuning]] ([[POTE]]): ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464
: mapping generators: ~2, ~11/9, ~5, ~7
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464


{{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
Line 64: Line 66:
[[Comma list]]: 352/351, 847/845
[[Comma list]]: 352/351, 847/845


[[Mapping]]: [{{val| 1 0 0 10 0 5 }}, {{val| 0 1 0 -6 0 -3 }}, {{val| 0 0 1 1 0 0 }}, {{val| 0 0 0 0 1 1 }}]
{{Mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }}


Mapping generators: ~2, ~3, ~5, ~11
: mapping generators: ~2, ~3, ~5, ~11


[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538


{{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}
{{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}
Line 79: Line 81:
[[Comma list]]: [[441/440]]
[[Comma list]]: [[441/440]]


[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}]
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }}


Mapping generators:~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 10, 12, 15, 19e, 26, 27e, 31, 41, 58, 72, 118, 130, 190, 248, 289, 320, 609d }}
{{Optimal ET sequence|legend=1| 10, 12, 15, 19e, 26, 27e, 31, 41, 58, 72, 118, 130, 190, 248, 289, 320, 609d }}
Line 90: Line 92:
[[Comma list]]: 364/363, 441/440
[[Comma list]]: 364/363, 441/440


[[Mapping]]: [{{val| 1 0 0 0 -3 -8 }}, {{val| 0 1 0 0 2 5 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 2 3 }}]
{{Mapping|legend=1| 1 0 0 0 -3 -8 | 0 1 0 0 2 5 | 0 0 1 0 -1 -2 | 0 0 0 1 2 3 }}
 
Mapping generators: ~2, ~3, ~5, ~7


[[Mapping to lattice]]: [{{val| 0 1 1 -1 -1 0 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 1 1 1 1 }}]
[[Mapping to lattice]]: [{{val| 0 1 1 -1 -1 0 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 1 1 1 1 }}]
Line 114: Line 114:
[[Comma list]]: 351/350, 441/440
[[Comma list]]: 351/350, 441/440


[[Mapping]]: [{{val| 1 0 0 0 -3 1 }}, {{val| 0 1 0 0 2 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 2 1 }}]
{{Mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }}
 
Mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }}
{{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }}
Line 125: Line 123:
[[Comma list]]: 196/195, 352/351
[[Comma list]]: 196/195, 352/351


[[Mapping]]: [{{val| 1 0 0 0 -3 2 }}, {{val| 0 1 0 0 2 -1 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 2 2 }}]
{{Mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }}
 
Mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }}
{{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }}
Line 136: Line 132:
[[Comma list]]: 441/440, 1287/1280
[[Comma list]]: 441/440, 1287/1280


[[Mapping]]: [{{val| 1 0 0 0 -3 11 }}, {{val| 0 1 0 0 2 -4 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 2 -2 }}]
{{Mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }}
 
Mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}
{{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}
Line 147: Line 141:
[[Comma list]]: 273/272, 441/440, 561/560
[[Comma list]]: 273/272, 441/440, 561/560


[[Mapping]]: [{{val| 1 0 0 0 -3 11 7 }}, {{val| 0 1 0 0 2 -4 -3 }}, {{val| 0 0 1 0 -1 2 2 }}, {{val| 0 0 0 1 2 -2 -1 }}]
{{Mapping|legend=1| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}
 
Mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }}
{{Optimal ET sequence|legend=1| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }}
Line 158: Line 150:
[[Comma list]]: 441/440, 847/845
[[Comma list]]: 441/440, 847/845


[[Mapping]]: [{{val| 1 0 0 0 -3 -3 }}, {{val| 0 1 0 0 2 2 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 4 5 }}]
{{Mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }}


Mapping generators: ~2, ~3, ~5, ~13/11
: mapping generators: ~2, ~3, ~5, ~13/11


{{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }}
{{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }}
Line 273: Line 265:
[[Comma list]]: [[540/539]]
[[Comma list]]: [[540/539]]


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 -2 }}]
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }}


Mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }}
{{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }}
Line 284: Line 276:
[[Comma list]]: 540/539, 847/845
[[Comma list]]: 540/539, 847/845


[[Mapping]]: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 0 0 3 3 }}, {{val| 0 0 1 1 -1 -1 }}, {{val| 0 0 0 2 -4 -3 }}]
{{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }}


Mapping generators: ~2, ~3, ~5, ~13/11
: mapping generators: ~2, ~3, ~5, ~13/11


{{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }}
{{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }}
Line 295: Line 287:
[[Comma list]]: 540/539, 625/624
[[Comma list]]: 540/539, 625/624


[[Mapping]]: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 0 0 3 -1 }}, {{val| 0 0 1 0 1 4 }}, {{val| 0 0 0 1 -2 0 }}]
{{Mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }}
 
Mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }}
{{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }}
Line 306: Line 296:
[[Comma list]]: 540/539, 676/675
[[Comma list]]: 540/539, 676/675


[[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}]
{{Mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }}


Mapping generators: ~2, ~26/15, ~5, ~7
: mapping generators: ~2, ~26/15, ~5, ~7


{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}
{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}
Line 317: Line 307:
[[Comma list]]: 896/891
[[Comma list]]: 896/891


[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 1 }}]
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }}


[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.8345, ~5/4 = 387.7585, ~7/4 = 969.8722
: mapping generators: ~2, ~3, ~5, ~7
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.8345, ~5/4 = 387.7585, ~7/4 = 969.8722


{{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}
{{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}
Line 325: Line 317:
[[Badness]]: 0.0658 × 10<sup>-6</sup>
[[Badness]]: 0.0658 × 10<sup>-6</sup>


=== Commas 352/351, 364/363 ===
=== Tridecimal pentacircle ===
[[Subgroup]]: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11.13


[[Comma list]]: 352/351, 364/363
[[Comma list]]: 352/351, 364/363


[[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 -4 -7 }}, {{val| 0 0 1 0 0 0 }}, {{val| 0 0 0 1 1 1 }}]
{{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }}


{{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }}
{{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }}
Line 341: Line 333:
[[Comma list]]: 847/845, 1001/1000
[[Comma list]]: 847/845, 1001/1000


[[Mapping]]: [{{val| 1 0 0 2 0 1 }}, {{val| 0 1 0 0 0 0 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 4 -3 1 }}]
{{Mapping|legend=1| 1 0 0 2 0 1 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 1 }}


Mapping generators: ~2, ~3, ~5, ~13/10
: mapping generators: ~2, ~3, ~5, ~13/10


{{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }}
{{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }}
Line 352: Line 344:
[[Comma list]]: [[3025/3024]]
[[Comma list]]: [[3025/3024]]


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}]
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }}


Mapping generators: ~2, ~3, ~5, ~55/36
: mapping generators: ~2, ~3, ~5, ~55/36


{{Optimal ET sequence|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
{{Optimal ET sequence|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
Line 363: Line 355:
[[Comma list]]: [[8019/8000]]
[[Comma list]]: [[8019/8000]]


[[Mapping]]: [{{val| 1 0 0 0 6 }}, {{val| 0 1 0 0 -6 }}, {{val| 0 0 1 0 3 }}, {{val| 0 0 0 1 0 }}]
{{Mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }}


Mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }}
{{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }}
Line 374: Line 366:
[[Comma list]]: [[9801/9800]]
[[Comma list]]: [[9801/9800]]


[[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}]
{{Mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }}


Mapping generators: ~99/70, ~3, ~5, ~7
: mapping generators: ~99/70, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}
Line 385: Line 377:
[[Comma list]]: 1716/1715, 2080/2079
[[Comma list]]: 1716/1715, 2080/2079


[[Mapping]]: [{{val| 2 0 0 0 3 -7 }}, {{val| 0 1 0 0 -2 1 }}, {{val| 0 0 1 0 1 0 }}, {{val| 0 0 0 1 1 2 }}]
{{Mapping|legend=1| 2 0 0 0 3 -7 | 0 1 0 0 -2 1 | 0 0 1 0 1 0 | 0 0 0 1 1 2 }}
 
Mapping generators: ~99/70, ~3, ~5, ~7


Lattice basis:  
Lattice basis:  
Line 395: Line 385:
* [[13-odd-limit|13-]] and [[15-odd-limit]]
* [[13-odd-limit|13-]] and [[15-odd-limit]]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 7/10 4/5 0 -2/5 0 1/5 }}, {{monzo| 7/10 -1/5 1 -2/5 0 1/5 }}, {{monzo| 7/5 -2/5 0 1/5 0 2/5 }}, {{monzo| 11/5 -11/5 1 3/5 0 1/5 }}, {{monzo| 0 0 0 0 0 1 }}]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 7/10 4/5 0 -2/5 0 1/5 }}, {{monzo| 7/10 -1/5 1 -2/5 0 1/5 }}, {{monzo| 7/5 -2/5 0 1/5 0 2/5 }}, {{monzo| 11/5 -11/5 1 3/5 0 1/5 }}, {{monzo| 0 0 0 0 0 1 }}]
: [[Eigenmonzo]]s (unchanged-intervals): 2, 6/5, 16/13, 9/7
: [[Eigenmonzo basis|Eigenmonzo (unchanged-intervals) basis]]: 2, 6/5, 16/13, 9/7


{{Optimal ET sequence|legend=1| 10e, 12f, 14cf, 22f, 26, 36ce, 46, 58, 72, 130, 198, 224, 270, 494, 764, 1258, 1810d, 2304d, 2574d }}
{{Optimal ET sequence|legend=1| 10e, 12f, 14cf, 22f, 26, 36ce, 46, 58, 72, 130, 198, 224, 270, 494, 764, 1258, 1810d, 2304d, 2574d }}
Line 404: Line 394:
[[Comma list]]: [[14641/14580]]
[[Comma list]]: [[14641/14580]]


[[Mapping]]: [{{val| 1 0 2 0 1 }}, {{val| 0 1 2 0 2 }}, {{val| 0 0 -4 0 -1 }}, {{val| 0 0 0 1 0 }}]
{{Mapping|legend=1| 1 0 2 0 1 | 0 1 2 0 2 | 0 0 -4 0 -1 | 0 0 0 1 0 }}


Mapping generators: ~2, ~3, ~18/11, ~7
: mapping generators: ~2, ~3, ~18/11, ~7


[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866


{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}
{{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}
Line 419: Line 409:
Comma list: 2080/2079, 14641/14580
Comma list: 2080/2079, 14641/14580


Mapping: [{{val| 1 0 2 0 1 -6 }}, {{val| 0 1 2 0 2 3 }}, {{val| 0 0 -4 0 -1 3 }}, {{val| 0 0 0 1 0 1 }}]
Mapping: {{mapping| 1 0 2 0 1 -6 | 0 1 2 0 2 3 | 0 0 -4 0 -1 3 | 0 0 0 1 0 1 }}


Optimal tuning (POTE): ~3/2 = 702.4931, ~18/11 = 854.6400, ~7/4 = 969.0099
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.4931, ~18/11 = 854.6400, ~7/4 = 969.0099


{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 323, 410 }}
{{Optimal ET sequence|legend=1| 87, 111, 181, 198, 323, 410 }}
Line 432: Line 422:
Comma list: 715/714, 1089/1088, 14641/14580
Comma list: 715/714, 1089/1088, 14641/14580


Mapping: [{{val| 1 0 2 0 1 -6 -4 }}, {{val| 0 1 2 0 2 3 6 }}, {{val| 0 0 -4 0 -1 3 -2 }}, {{val| 0 0 0 1 0 1 0 }}]
Mapping: {{mapping| 1 0 2 0 1 -6 -4 | 0 1 2 0 2 3 6 | 0 0 -4 0 -1 3 -2 | 0 0 0 1 0 1 0 }}


Optimal tuning (POTE): ~3/2 = 702.4099, ~18/11 = 854.6338, ~7/4 = 969.0228
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.4099, ~18/11 = 854.6338, ~7/4 = 969.0228


{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}
{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}
Line 445: Line 435:
Comma list: 715/714, 1089/1088, 1216/1215, 1445/1444
Comma list: 715/714, 1089/1088, 1216/1215, 1445/1444


Mapping: [{{val| 1 0 2 0 1 -6 -4 -4 }}, {{val| 0 1 2 0 2 3 6 7 }}, {{val| 0 0 -4 0 -1 3 -2 -4 }}, {{val| 0 0 0 1 0 1 0 0 }}]
Mapping: {{mapping| 1 0 2 0 1 -6 -4 -4 | 0 1 2 0 2 3 6 7 | 0 0 -4 0 -1 3 -2 -4 | 0 0 0 1 0 1 0 0 }}


Optimal tuning (POTE): ~3/2 = 702.3413, ~18/11 = 854.6472, ~7/4 = 968.9734
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.3413, ~18/11 = 854.6472, ~7/4 = 968.9734


{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}
{{Optimal ET sequence|legend=1| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}
Line 459: Line 449:
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 19712/19683
[[Comma list]]: [[19712/19683]]


[[Mapping]]: [{{val| 1 0 0 0 -8 }}, {{val| 0 1 0 0 9 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 -1 }}]
{{Mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }}


Mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.2681, ~5/4 = 386.4785, ~7/4 = 968.9552
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2681, ~5/4 = 386.4785, ~7/4 = 968.9552


{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}
{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}
Line 476: Line 466:
[[Comma list]]: 2080/2079, 19712/19683
[[Comma list]]: 2080/2079, 19712/19683


[[Mapping]]: [{{val| 1 0 0 0 -8 -13 }}, {{val| 0 1 0 0 9 12 }}, {{val| 0 0 1 0 0 -1 }}, {{val| 0 0 0 1 -1 0 }}]
{{Mapping|legend=1| 1 0 0 0 -8 -13 | 0 1 0 0 9 12 | 0 0 1 0 0 -1 | 0 0 0 1 -1 0 }}


[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.2721, ~5/4 = 386.4790, ~7/4 = 968.9705
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2721, ~5/4 = 386.4790, ~7/4 = 968.9705


{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}
{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}
Line 489: Line 479:
[[Comma list]]: [[131072/130977]]
[[Comma list]]: [[131072/130977]]


[[Mapping]]: [{{val| 1 0 0 0 17 }}, {{val| 0 1 0 0 -5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 -2 }}]
{{Mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }}


Mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }}
{{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }}
Line 500: Line 490:
[[Comma list]]: 2080/2079, 4096/4095
[[Comma list]]: 2080/2079, 4096/4095


[[Mapping]]: [{{val| 1 0 0 0 17 12 }}, {{val| 0 1 0 0 -5 -2 }}, {{val| 0 0 1 0 0 -1 }}, {{val| 0 0 0 1 -2 -1 }}]
{{Mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }}
 
Mapping generators: ~2, ~3, ~5, ~7


{{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} *
{{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} *
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