Scala analysis: xen14-mclaren-nonoctave-12-3
Enrique Moreno's 12th root of 3 non-octave scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 158.496 cents 158.496250 2: 316.993 cents 316.992500 3: 475.489 cents 475.488750 4: 633.985 cents 633.985000 5: 792.481 cents 792.481250 6: 950.977 cents 950.977500 7: 1109.474 cents 1109.473751 8: 1267.970 cents 1267.970001 9: 1426.466 cents 1426.466251 10: 1584.963 cents 1584.962501 11: 1743.459 cents 1743.458751 12: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 158.4962 cents 158.4962 1: 158.4962 cents 158.4962 2: 158.4963 cents 158.4963 3: 158.4962 cents 158.4962 4: 158.4962 cents 158.4962 5: 158.4962 cents 158.4962 6: 158.4962 cents 158.4962 7: 158.4963 cents 158.4963 8: 158.4962 cents 158.4962 9: 158.4963 cents 158.4963 10: 158.4962 cents 158.4962 11: 158.4962 cents 158.4962 12: 158.4962 cents 158.4962
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 158.49625 cents 2: 12 316.99250 cents 3: 12 475.48875 cents 4: 12 633.98500 cents 5: 12 792.48125 cents 6: 12 950.97750 cents 7: 12 1109.47375 cents 8: 12 1267.97000 cents 9: 12 1426.46625 cents 10: 12 1584.96250 cents 11: 12 1743.45875 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 158.5 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 317.0 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 475.5 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 634.0 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 792.5 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 951.0 : 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 1109.5: 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 1268.0: 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 1426.5: 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 1585.0: 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 1743.5: 158.5 317.0 475.5 634.0 792.5 951.0 1109.5 1268.0 1426.5 1585.0 1743.5 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 158.4962 .. 158.4962 cents 1/1, 0.0000 cents 158.49625 cents 2: 316.9925 .. 316.9925 cents 1/1, 0.0000 cents 158.49625 cents 3: 475.4887 .. 475.4887 cents 1/1, 0.0000 cents 158.49625 cents 4: 633.9850 .. 633.9850 cents 1/1, 0.0000 cents 158.49625 cents 5: 792.4812 .. 792.4812 cents 1/1, 0.0000 cents 158.49625 cents 6: 950.9775 .. 950.9775 cents 1/1, 0.0000 cents 158.49625 cents 7: 1109.4738 .. 1109.4738 cents 1/1, 0.0000 cents 158.49625 cents 8: 1267.9700 .. 1267.9700 cents 1/1, 0.0000 cents 158.49625 cents 9: 1426.4663 .. 1426.4663 cents 1/1, 0.0000 cents 158.49625 cents 10: 1584.9625 .. 1584.9625 cents 1/1, 0.0000 cents 158.49625 cents 11: 1743.4588 .. 1743.4588 cents 1/1, 0.0000 cents 158.49625 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 158.49625 cents, class 1 Average step (divided formal octave): 158.4963 cents Largest one step interval : 158.49625 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 158.49625 cents, amount: 12 Most common interval of one step : 158.49625 cents, amount: 12 Least squares average step : 158.49625 cents, oct.: 1901.95500 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 158.49625 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.083333 redundancy: 0.916667 Efficiency x scale size : 1.000000 Number of different interval sizes : 11 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct tetrachords Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c. Twelve-tone Chromatic (1/11-comma)
FIT/HARMONIC
1 x x x x x x x 2 x x x 3 S SD: 33.9850 cents 2 x x x 3 x x x 4 x 5 x 6 S SD: 24.0334 cents 3 x x 4 x x 5 x 6:7 x 8:9 S SD: 19.1933 cents 4 x 5 x 6 x 7 x 8:9:10:11:12 S SD: 15.2767 cents 5 x 6 x 7:8:9 x 10:11:13:14:15 SD: 16.5766 cents 6 x 7:8:9 x 10:11:12:14:15:16:18 S SD: 15.4948 cents 7:8 x 9:10:11:12:13:15:16:17:19:21 SD: 10.8735 cents 9:10:11:12:13:14:16:17:19:21:22:25:27 SD: 8.0001 cents 10:11:12:13:14:16:17:19:21:23:25:27:30 SD: 6.3081 cents 12:13:14:16:17:19:21:23:25:27:30:33:36 SD: 6.2191 cents 14:15:17:18:20:22:24:27:29:32:35:38:42 SD: 6.0488 cents 16:18:19:21:23:25:28:30:33:36:40:44:48 SD: 5.5574 cents 18:20:22:24:26:28:31:34:37:41:45:49:54 SD: 4.9018 cents 19:21:23:25:27:30:33:36:40:43:47:52:57 SD: 3.7059 cents 20:22:24:26:29:32:35:38:42:46:50:55:60 SD: 3.6609 cents 22:24:26:29:32:35:38:42:46:50:55:60:66 SD: 3.1843 cents 29:32:35:38:42:46:50:55:60:66:72:79:87 SD: 2.2163 cents 34:37:41:45:49:54:59:65:71:78:85:93:102 SD: 2.2082 cents 38:42:46:50:55:60:66:72:79:87:95:104:114 SD: 1.9380 cents 40:44:48:53:58:63:69:76:83:91:100:110:120 SD: 1.7679 cents 41:45:49:54:59:65:71:78:85:93:102:112:123 SD: 1.4639 cents 50:55:60:66:72:79:87:95:104:114:125:137:150 SD: 1.0159 cents 64:70:77:84:92:101:111:121:133:146:160:175:192 SD: 1.0044 cents 74:81:89:97:107:117:128:140:154:169:185:203:222 SD: 0.9942 cents 75:82:90:99:108:119:130:142:156:171:187:205:225 SD: 0.9703 cents 79:87:95:104:114:125:137:150:164:180:197:216:237 SD: 0.8875 cents 85:93:102:112:123:134:147:161:177:194:212:233:255 SD: 0.8658 cents 86:94:103:113:124:136:149:163:179:196:215:235:258 SD: 0.7027 cents 95:104:114:125:137:150:165:180:198:217:237:260:285 SD: 0.6998 cents 104:114:125:137:150:164:180:197:216:237:260:285:312 SD: 0.5703 cents 115:126:138:151:166:182:199:218:239:262:287:315:345 SD: 0.5262 cents 124:136:149:163:179:196:215:235:258:283:310:339:372 SD: 0.4712 cents 136:149:163:179:196:215:236:258:283:310:340:372:408 SD: 0.4550 cents 145:159:174:191:209:229:251:275:302:331:362:397:435 SD: 0.4032 cents 165:181:198:217:238:261:286:313:343:376:412:452:495 SD: 0.3170 cents 219:240:263:288:316:346:379:416:456:499:547:600:657 SD: 0.2918 cents 228:250:274:300:329:360:395:433:474:520:570:624:684 SD: 0.2763 cents 253:277:304:333:365:400:438:480:526:577:632:693:759 SD: 0.2330 cents 269:295:323:354:388:425:466:511:560:613:672:736:807 SD: 0.2243 cents 294:322:353:387:424:465:509:558:612:670:734:805:882 SD: 0.2097 cents 303:332:364:399:437:479:525:575:630:691:757:829:909 SD: 0.1707 cents 373:409:448:491:538:590:646:708:776:850:932:1021:1119 SD: 0.1597 cents 418:458:502:550:603:661:724:793:869:953:1044:1144:1254 SD: 0.1504 cents 439:481:527:578:633:694:760:833:913:1001:1097:1202:1317 SD: 0.1493 cents 448:491:538:590:646:708:776:850:932:1021:1119:1226:1344 SD: 0.1358 cents 462:506:555:608:666:730:800:877:961:1053:1154:1265:1386 SD: 0.1347 cents 488:535:586:642:704:771:845:926:1015:1112:1219:1336:1464 SD: 0.1321 cents 512:561:615:674:738:809:887:972:1065:1167:1279:1402:1536 SD: 0.1211 cents 522:572:627:687:753:825:904:991:1086:1190:1304:1429:1566 SD: 0.0600 cents