12L 1s: Difference between revisions

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autopatrolled, Sysops
523 edits
m formatting, category
Line 1: Line 1:
This MOS, the Grumpy tridecatonic, apparently belongs to no particularly important temperament. However, it becomes a compressed 12ed scale when you ignore the octave (this obviously does not work when the generator is very near 12edo <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">(within -7/24¢ of it)</span><span style="font-size: 13px; line-height: 1.5;">, for the 13th degree of the scale registers as identical to the octave for human listeners, and it becomes indistinct from 13edo or the Happy dodecatonic ([[1L_11s|1L 11s]]) in the 1.75¢ above 1/13edo because the large and small steps register as identical to one another for human listeners).</span>
This MOS, the grumpy tridecatonic, apparently belongs to no particularly important temperament. However, it becomes a compressed 12ed scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24¢ of it), for the 13th degree of the scale registers as identical to the octave for human listeners, and it becomes indistinct from 13edo or the Happy dodecatonic ([[1L 11s]]) in the 1.75¢ above 1/13edo because the large and small steps register as identical to one another for human listeners).


{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="3" | Generator
! colspan="3" | Generator
! | <span style="font-size: 12.8000001907349px;">Cents</span>
! | Cents
! | <span style="font-size: 12.8000001907349px;">12g</span>
! | 12g
|-
|-
| | 1/13
| | 1/13
Line 11: Line 11:
| |  
| |  
| | 92.308
| | 92.308
| | <span style="font-size: 12.8000001907349px;">1107.692</span>
| | 1107.692
|-
|-
| | 5/64
| | 5/64
Line 17: Line 17:
| |  
| |  
| | 93.75
| | 93.75
| | <span style="font-size: 12.8000001907349px;">1125</span>
| | 1125
|-
|-
| |  
| |  
Line 23: Line 23:
| |  
| |  
| | 93.913
| | 93.913
| | <span style="font-size: 12.8000001907349px;">1126.9565</span>
| | 1126.9565
|-
|-
| |  
| |  
Line 29: Line 29:
| |  
| |  
| | 93.976
| | 93.976
| | <span style="font-size: 12.8000001907349px;">1127.711</span>
| | 1127.711
|-
|-
| |  
| |  
Line 35: Line 35:
| |  
| |  
| | 94.009
| | 94.009
| | <span style="font-size: 12.8000001907349px;">1128.111</span>
| | 1128.111
|-
|-
| | 4/51
| | 4/51
Line 41: Line 41:
| |  
| |  
| | 94.118
| | 94.118
| | <span style="font-size: 12.8000001907349px;">1129.412</span>
| | 1129.412
|-
|-
| |  
| |  
Line 47: Line 47:
| |  
| |  
| | 94.241
| | 94.241
| | <span style="font-size: 12.8000001907349px;">1130.89</span>
| | 1130.89
|-
|-
| |  
| |  
Line 53: Line 53:
| |  
| |  
| | 94.296
| | 94.296
| | <span style="font-size: 12.8000001907349px;">1131 3/7</span>
| | 1131 3/7
|-
|-
| |  
| |  
Line 59: Line 59:
| |  
| |  
| | 94.382
| | 94.382
| | <span style="font-size: 12.8000001907349px;">1132.584</span>
| | 1132.584
|-
|-
| |  
| |  
Line 65: Line 65:
| |  
| |  
| | 94.448
| | 94.448
| | <span style="font-size: 12.8000001907349px;">1133.858</span>
| | 1133.858
|-
|-
| |  
| |  
Line 71: Line 71:
| |  
| |  
| | 94.5455
| | 94.5455
| | <span style="font-size: 12.8000001907349px;">1134.5455</span>
| | 1134.5455
|-
|-
| |  
| |  
Line 77: Line 77:
| |  
| |  
| | 94.581
| | 94.581
| | <span style="font-size: 12.8000001907349px;">1134.975</span>
| | 1134.975
|-
|-
| |  
| |  
Line 83: Line 83:
| |  
| |  
| | 94.606
| | 94.606
| | <span style="font-size: 12.8000001907349px;">1135.27</span>
| | 1135.27
|-
|-
| | 3/38
| | 3/38
Line 89: Line 89:
| |  
| |  
| | 94.737
| | 94.737
| | <span style="font-size: 12.8000001907349px;">1136.842</span>
| | 1136.842
|-
|-
| |  
| |  
Line 95: Line 95:
| |  
| |  
| | 94.8875
| | 94.8875
| | <span style="font-size: 12.8000001907349px;">1137.6505</span>
| | 1137.6505
|-
|-
| |  
| |  
Line 101: Line 101:
| |  
| |  
| | 94.845
| | 94.845
| | <span style="font-size: 12.8000001907349px;">1138.1443</span>
| | 1138.1443
|-
|-
| |  
| |  
Line 107: Line 107:
| |  
| |  
| | 94.862
| | 94.862
| | <span style="font-size: 12.8000001907349px;">1138.34</span>
| | 1138.34
|-
|-
| |  
| |  
Line 113: Line 113:
| |  
| |  
| | 94.884
| | 94.884
| | <span style="font-size: 12.8000001907349px;">1138.605</span>
| | 1138.605
|-
|-
| |  
| |  
Line 119: Line 119:
| |  
| |  
| | 94.915
| | 94.915
| | <span style="font-size: 12.8000001907349px;">1138.983</span>
| | 1138.983
|-
|-
| |  
| |  
Line 131: Line 131:
| |  
| |  
| | 94.964
| | 94.964
| | <span style="font-size: 12.8000001907349px;">1139.568</span>
| | 1139.568
|-
|-
| |  
| |  
Line 137: Line 137:
| |  
| |  
| | 95.0495
| | 95.0495
| | <span style="font-size: 12.8000001907349px;">1140.594</span>
| | 1140.594
|-
|-
| |  
| |  
Line 149: Line 149:
| | 13/164
| | 13/164
| | 95.122
| | 95.122
| | <span style="font-size: 12.8000001907349px;">1141.463</span>
| | 1141.463
|-
|-
| |  
| |  
Line 155: Line 155:
| |  
| |  
| | 95.238
| | 95.238
| | <span style="font-size: 12.8000001907349px;">1142.714</span>
| | 1142.714
|-
|-
| |  
| |  
Line 161: Line 161:
| | 17/214
| | 17/214
| | 95.374
| | 95.374
| | <span style="font-size: 12.8000001907349px;">1143.486</span>
| | 1143.486
|-
|-
| |  
| |  
Line 167: Line 167:
| | 12/151
| | 12/151
| | 95.362
| | 95.362
| | <span style="font-size: 12.8000001907349px;">1144.371</span>
| | 1144.371
|-
|-
| |  
| |  
Line 179: Line 179:
| |  
| |  
| | 95,4545
| | 95,4545
| | <span style="font-size: 12.8000001907349px;">1145.4545</span>
| | 1145.4545
|-
|-
| |  
| |  
Line 185: Line 185:
| |  
| |  
| | 95.575
| | 95.575
| | <span style="font-size: 12.8000001907349px;">1146.903</span>
| | 1146.903
|-
|-
| |  
| |  
Line 191: Line 191:
| |  
| |  
| | 95.652
| | 95.652
| | <span style="font-size: 12.8000001907349px;">1147.826</span>
| | 1147.826
|-
|-
| |  
| |  
Line 197: Line 197:
| |  
| |  
| | 95.7055
| | 95.7055
| | <span style="font-size: 12.8000001907349px;">1148.466</span>
| | 1148.466
|-
|-
| |  
| |  
Line 203: Line 203:
| |  
| |  
| | 95.745
| | 95.745
| | <span style="font-size: 12.8000001907349px;">1148.936</span>
| | 1148.936
|-
|-
| |  
| |  
Line 209: Line 209:
| |  
| |  
| | 95.775
| | 95.775
| | <span style="font-size: 12.8000001907349px;">1149.296</span>
| | 1149.296
|-
|-
| |  
| |  
Line 215: Line 215:
| |  
| |  
| | 95.798
| | 95.798
| | <span style="font-size: 12.8000001907349px;">1149.58</span>
| | 1149.58
|-
|-
| |  
| |  
Line 221: Line 221:
| |  
| |  
| | 95.8175
| | 95.8175
| | <span style="font-size: 12.8000001907349px;">1149.81</span>
| | 1149.81
|-
|-
| |  
| |  
Line 227: Line 227:
| |  
| |  
| | 95.833
| | 95.833
| | <span style="font-size: 12.8000001907349px;">1150</span>
| | 1150
|-
|-
| |  
| |  
Line 233: Line 233:
| |  
| |  
| | 95.847
| | 95.847
| | <span style="font-size: 12.8000001907349px;">1150.16</span>
| | 1150.16
|-
|-
| |  
| |  
Line 239: Line 239:
| |  
| |  
| | 95.858
| | 95.858
| | <span style="font-size: 12.8000001907349px;">1150.296</span>
| | 1150.296
|-
|-
| |  
| |  
Line 245: Line 245:
| |  
| |  
| | 95.868
| | 95.868
| | <span style="font-size: 12.8000001907349px;">1150.467</span>
| | 1150.467
|-
|-
| |  
| |  
Line 251: Line 251:
| |  
| |  
| | 95.876
| | 95.876
| | <span style="font-size: 12.8000001907349px;">1150.5155</span>
| | 1150.5155
|-
|-
| |  
| |  
Line 257: Line 257:
| |  
| |  
| | 95.884
| | 95.884
| | <span style="font-size: 12.8000001907349px;">1150.605</span>
| | 1150.605
|-
|-
| |  
| |  
Line 263: Line 263:
| |  
| |  
| | 95.89
| | 95.89
| | <span style="font-size: 12.8000001907349px;">1150.685</span>
| | 1150.685
|-
|-
| |  
| |  
Line 269: Line 269:
| |  
| |  
| | 95.896
| | 95.896
| | <span style="font-size: 12.8000001907349px;">1150.75</span>
| | 1150.75
|-
|-
| |  
| |  
Line 275: Line 275:
| |  
| |  
| | 95.902
| | 95.902
| | <span style="font-size: 12.8000001907349px;">1150.82</span>
| | 1150.82
|-
|-
| |  
| |  
Line 281: Line 281:
| |  
| |  
| | 95.906
| | 95.906
| | <span style="font-size: 12.8000001907349px;">1150.877</span>
| | 1150.877
|-
|-
| |  
| |  
Line 287: Line 287:
| |  
| |  
| | 95.911
| | 95.911
| | <span style="font-size: 12.8000001907349px;">1150.929</span>
| | 1150.929
|-
|-
| |  
| |  
Line 293: Line 293:
| |  
| |  
| | 95.915
| | 95.915
| | <span style="font-size: 12.8000001907349px;">1150.977</span>
| | 1150.977
|-
|-
| |  
| |  
Line 299: Line 299:
| |  
| |  
| | 95.918
| | 95.918
| | <span style="font-size: 12.8000001907349px;">1151.02</span>
| | 1151.02
|-
|-
| | 2/25
| | 2/25
Line 305: Line 305:
| |  
| |  
| | 96
| | 96
| | <span style="font-size: 12.8000001907349px;">1152</span>
| | 1152
|-
|-
| |  
| |  
Line 311: Line 311:
| |  
| |  
| | 96.154
| | 96.154
| | <span style="font-size: 12.8000001907349px;">1153.846</span>
| | 1153.846
|-
|-
| |  
| |  
Line 317: Line 317:
| |  
| |  
| | 96.167
| | 96.167
| | <span style="font-size: 12.8000001907349px;">1154.007</span>
| | 1154.007
|-
|-
| |  
| |  
Line 323: Line 323:
| |  
| |  
| | 96.183
| | 96.183
| | <span style="font-size: 12.8000001907349px;">1154.1985</span>
| | 1154.1985
|-
|-
| |  
| |  
Line 329: Line 329:
| |  
| |  
| | 96.2025
| | 96.2025
| | <span style="font-size: 12.8000001907349px;">1154,43</span>
| | 1154,43
|-
|-
| |  
| |  
Line 335: Line 335:
| |  
| |  
| | 96.226
| | 96.226
| | <span style="font-size: 12.8000001907349px;">1154.717</span>
| | 1154.717
|-
|-
| |  
| |  
Line 341: Line 341:
| |  
| |  
| | 96.257
| | 96.257
| | <span style="font-size: 12.8000001907349px;">1155.08</span>
| | 1155.08
|-
|-
| |  
| |  
Line 347: Line 347:
| |  
| |  
| | 96.296
| | 96.296
| | <span style="font-size: 12.8000001907349px;">1155.556</span>
| | 1155.556
|-
|-
| |  
| |  
Line 353: Line 353:
| |  
| |  
| | 96.35
| | 96.35
| | <span style="font-size: 12.8000001907349px;">1156.204</span>
| | 1156.204
|-
|-
| |  
| |  
Line 359: Line 359:
| |  
| |  
| | 96.429
| | 96.429
| | <span style="font-size: 12.8000001907349px;">1157.143</span>
| | 1157.143
|-
|-
| |  
| |  
Line 365: Line 365:
| |  
| |  
| | 96.552
| | 96.552
| | <span style="font-size: 12.8000001907349px;">1158.621</span>
| | 1158.621
|-
|-
| |  
| |  
Line 371: Line 371:
| | 12/149
| | 12/149
| | 96.644
| | 96.644
| | <span style="font-size: 12.8000001907349px;">1159.7315</span>
| | 1159.7315
|-
|-
| |  
| |  
Line 377: Line 377:
| | 17/211
| | 17/211
| | 96.6825
| | 96.6825
| | <span style="font-size: 12.8000001907349px;">1160.278</span>
| | 1160.278
|-
|-
| |  
| |  
Line 383: Line 383:
| |  
| |  
| | 96.774
| | 96.774
| | <span style="font-size: 12.8000001907349px;">1161.29</span>
| | 1161.29
|-
|-
| |  
| |  
Line 389: Line 389:
| | 13/161
| | 13/161
| | 96.894
| | 96.894
| | <span style="font-size: 12.8000001907349px;">1162.733</span>
| | 1162.733
|-
|-
| |  
| |  
Line 401: Line 401:
| |  
| |  
| | 96.97
| | 96.97
| | <span style="font-size: 12.8000001907349px;">1163.636</span>
| | 1163.636
|-
|-
| |  
| |  
Line 407: Line 407:
| |  
| |  
| | 97.059
| | 97.059
| | <span style="font-size: 12.8000001907349px;">1164.706</span>
| | 1164.706
|-
|-
| |  
| |  
Line 413: Line 413:
| |  
| |  
| | 97.0255
| | 97.0255
| | <span style="font-size: 12.8000001907349px;">1164.306</span>
| | 1164.306
|-
|-
| |  
| |  
Line 419: Line 419:
| |  
| |  
| | 97.11
| | 97.11
| | <span style="font-size: 12.8000001907349px;">116</span><span style="font-size: 12.8000001907349px; line-height: 1.5;">5.318</span>
| | 1165.318
|-
|-
| |  
| |  
Line 425: Line 425:
| |  
| |  
| | 97.143
| | 97.143
| | <span style="font-size: 12.8000001907349px;">116</span><span style="font-size: 12.8000001907349px; line-height: 1.5;">5.714</span>
| | 1165.714
|-
|-
| |  
| |  
Line 431: Line 431:
| |  
| |  
| | 97.166
| | 97.166
| | <span style="font-size: 12.8000001907349px;">116</span><span style="font-size: 12.8000001907349px; line-height: 1.5;">5.992</span>
| | 1165.992
|-
|-
| |  
| |  
| | 23/284
| | 23/284
| |  
| |  
| | 97.<span style="line-height: 1.5;">183</span>
| | 97.183
| | 116<span style="font-size: 12.8000001907349px; line-height: 1.5;">6.197</span>
| | 1166.197
|-
|-
| | 3/37
| | 3/37
Line 443: Line 443:
| |  
| |  
| | 97.297
| | 97.297
| | <span style="font-size: 12.8000001907349px;">1167.568</span>
| | 1167.568
|-
|-
| |  
| |  
Line 449: Line 449:
| |  
| |  
| | 97.403
| | 97.403
| | 1168<span style="font-size: 12.8000001907349px; line-height: 1.5;">.831</span>
| | 1168.831
|-
|-
| |  
| |  
Line 455: Line 455:
| |  
| |  
| | 97.416
| | 97.416
| | <span style="font-size: 12.8000001907349px;">1168.9915</span>
| | 1168.9915
|-
|-
| |  
| |  
Line 461: Line 461:
| |  
| |  
| | 97.417
| | 97.417
| | <span style="font-size: 12.8000001907349px;">1169.004</span>
| | 1169.004
|-
|-
| |  
| |  
Line 467: Line 467:
| |  
| |  
| | 97.436
| | 97.436
| | <span style="font-size: 12.8000001907349px;">1169.231</span>
| | 1169.231
|-
|-
| |  
| |  
Line 473: Line 473:
| |  
| |  
| | 97.462
| | 97.462
| | <span style="font-size: 12.8000001907349px;">1169.543</span>
| | 1169.543
|-
|-
| |  
| |  
Line 479: Line 479:
| |  
| |  
| | 97.5
| | 97.5
| | <span style="font-size: 12.8000001907349px;">1170</span>
| | 1170
|-
|-
| |  
| |  
Line 485: Line 485:
| |  
| |  
| | 97.561
| | 97.561
| | <span style="font-size: 12.8000001907349px;">1170.731</span>
| | 1170.731
|-
|-
| |  
| |  
Line 491: Line 491:
| | 17/209
| | 17/209
| | 97.608
| | 97.608
| | <span style="font-size: 12.8000001907349px;">1171.292</span>
| | 1171.292
|-
|-
| |  
| |  
Line 497: Line 497:
| |  
| |  
| | 97.674
| | 97.674
| | <span style="font-size: 12.8000001907349px;">1172.093</span>
| | 1172.093
|-
|-
| |  
| |  
Line 503: Line 503:
| |  
| |  
| | 97,778
| | 97,778
| | <span style="font-size: 12.8000001907349px;">1173.333</span>
| | 1173.333
|-
|-
| |  
| |  
Line 509: Line 509:
| |  
| |  
| | 97.826
| | 97.826
| | <span style="font-size: 12.8000001907349px;">1173.913</span>
| | 1173.913
|-
|-
| |  
| |  
Line 515: Line 515:
| |  
| |  
| | 97.854
| | 97.854
| | <span style="font-size: 12.8000001907349px;">1174.249</span>
| | 1174.249
|-
|-
| | 4/49
| | 4/49
Line 521: Line 521:
| |  
| |  
| | 97.959
| | 97.959
| | <span style="font-size: 12.8000001907349px;">1175.51</span>
| | 1175.51
|-
|-
| |  
| |  
Line 527: Line 527:
| |  
| |  
| | 98.077
| | 98.077
| | <span style="font-size: 12.8000001907349px;">1176.923</span>
| | 1176.923
|-
|-
| |  
| |  
Line 533: Line 533:
| |  
| |  
| | 98.113
| | 98.113
| | <span style="font-size: 12.8000001907349px;">1177.3585</span>
| | 1177.3585
|-
|-
| |  
| |  
Line 539: Line 539:
| |  
| |  
| | 98.182
| | 98.182
| | <span style="font-size: 12.8000001907349px;">1178.182</span>
| | 1178.182
|-
|-
| |  
| |  
Line 545: Line 545:
| |  
| |  
| | 98.246
| | 98.246
| | <span style="font-size: 12.8000001907349px;">1178.947</span>
| | 1178.947
|-
|-
| |  
| |  
Line 551: Line 551:
| |  
| |  
| | 98.276
| | 98.276
| | <span style="font-size: 12.8000001907349px;">1179.31</span>
| | 1179.31
|-
|-
| | 5/61
| | 5/61
Line 557: Line 557:
| |  
| |  
| | 98.361
| | 98.361
| | <span style="font-size: 12.8000001907349px;">1180.323</span>
| | 1180.323
|-
|-
| | 1/12
| | 1/12
Line 565: Line 565:
| | 1200
| | 1200
|}
|}
[[category:todo:unify precision]]

Revision as of 01:25, 6 December 2018

This MOS, the grumpy tridecatonic, apparently belongs to no particularly important temperament. However, it becomes a compressed 12ed scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24¢ of it), for the 13th degree of the scale registers as identical to the octave for human listeners, and it becomes indistinct from 13edo or the Happy dodecatonic (1L 11s) in the 1.75¢ above 1/13edo because the large and small steps register as identical to one another for human listeners).

Generator Cents 12g
1/13 92.308 1107.692
5/64 93.75 1125
9/115 93.913 1126.9565
13/166 93.976 1127.711
17/217 94.009 1128.111
4/51 94.118 1129.412
15/191 94.241 1130.89
11/140 94.296 1131 3/7
7/89 94.382 1132.584
10/127 94.448 1133.858
13/165 94.5455 1134.5455
16/203 94.581 1134.975
19/241 94.606 1135.27
3/38 94.737 1136.842
26/329 94.8875 1137.6505
23/291 94.845 1138.1443
20/253 94.862 1138.34
17/215 94.884 1138.605
14/177 94.915 1138.983
94.962 1139.545
11/139 94.964 1139.568
8/101 95.0495 1140.594
95.102 1141.224
13/164 95.122 1141.463
5/63 95.238 1142.714
17/214 95.374 1143.486
12/151 95.362 1144.371
95.41 1144.915
7/88 95,4545 1145.4545
9/113 95.575 1146.903
11/138 95.652 1147.826
13/163 95.7055 1148.466
15/188 95.745 1148.936
17/213 95.775 1149.296
19/238 95.798 1149.58
21/263 95.8175 1149.81
23/288 95.833 1150
25/313 95.847 1150.16
27/338 95.858 1150.296
29/363 95.868 1150.467
31/388 95.876 1150.5155
33/413 95.884 1150.605
35/438 95.89 1150.685
37/463 95.896 1150.75
39/488 95.902 1150.82
41/513 95.906 1150.877
43/538 95.911 1150.929
45/563 95.915 1150.977
47/588 95.918 1151.02
2/25 96 1152
25/312 96.154 1153.846
23/287 96.167 1154.007
21/262 96.183 1154.1985
19/237 96.2025 1154,43
17/212 96.226 1154.717
15/187 96.257 1155.08
13/162 96.296 1155.556
11/137 96.35 1156.204
9/112 96.429 1157.143
7/87 96.552 1158.621
12/149 96.644 1159.7315
17/211 96.6825 1160.278
5/62 96.774 1161.29
13/161 96.894 1162.733
96.915 1162.982
8/99 96.97 1163.636
11/136 97.059 1164.706
97.0255 1164.306
14/173 97.11 1165.318
17/210 97.143 1165.714
20/247 97.166 1165.992
23/284 97.183 1166.197
3/37 97.297 1167.568
25/308 97.403 1168.831
97.416 1168.9915
22/271 97.417 1169.004
19/234 97.436 1169.231
16/197 97.462 1169.543
13/160 97.5 1170
10/123 97.561 1170.731
17/209 97.608 1171.292
7/86 97.674 1172.093
11/135 97,778 1173.333
15/184 97.826 1173.913
19/233 97.854 1174.249
4/49 97.959 1175.51
17/208 98.077 1176.923
13/159 98.113 1177.3585
9/110 98.182 1178.182
14/171 98.246 1178.947
19/232 98.276 1179.31
5/61 98.361 1180.323
1/12 100 1200
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