Scala analysis: lumma_synchtrinesplus2
The 12-tone equal temperament with 2:3:4 brats of +2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.783 cents 99.782870 2: 199.566 cents 199.565750 3: 299.349 cents 299.348620 4: 399.132 cents 399.131500 5: 498.914 cents 498.914370 6: 598.697 cents 598.697250 7: 698.480 cents 698.480120 8: 798.263 cents 798.263000 9: 898.046 cents 898.045870 10: 997.829 cents 997.828750 11: 1097.612 cents 1097.611620 12: 1197.395 cents 1197.394500
SHOW/INTERVAL
0: 99.7829 cents 99.7829 1: 99.7829 cents 99.7829 2: 99.7829 cents 99.7829 3: 99.7829 cents 99.7829 4: 99.7829 cents 99.7829 5: 99.7829 cents 99.7829 6: 99.7829 cents 99.7829 7: 99.7829 cents 99.7829 8: 99.7829 cents 99.7829 9: 99.7829 cents 99.7829 10: 99.7829 cents 99.7829 11: 99.7829 cents 99.7829 12: 99.7829 cents 99.7829
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 99.78287 cents 2: 12 199.56575 cents 3: 12 299.34862 cents 4: 12 399.13150 cents 5: 12 498.91437 cents 6: 12 598.69725 cents 7: 12 698.48012 cents 8: 12 798.26300 cents 9: 12 898.04587 cents 10: 12 997.82875 cents 11: 12 1097.61162 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 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 99.8 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 199.6 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 299.3 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 399.1 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 498.9 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 598.7 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 698.5 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 798.3 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 898.0 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 997.8 : 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 1097.6: 99.8 199.6 299.3 399.1 498.9 598.7 698.5 798.3 898.0 997.8 1097.6 1197.4 1197.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.7829 .. 99.7829 cents 1/1, 0.0000 cents 99.78287 cents 2: 199.5658 .. 199.5658 cents 1/1, 0.0000 cents 99.78288 cents 3: 299.3486 .. 299.3486 cents 1/1, 0.0000 cents 99.78287 cents 4: 399.1315 .. 399.1315 cents 1/1, 0.0000 cents 99.78288 cents 5: 498.9144 .. 498.9144 cents 1/1, 0.0000 cents 99.78287 cents 6: 598.6972 .. 598.6972 cents 1/1, 0.0000 cents 99.78288 cents 7: 698.4801 .. 698.4801 cents 1/1, 0.0000 cents 99.78287 cents 8: 798.2630 .. 798.2630 cents 1/1, 0.0000 cents 99.78288 cents 9: 898.0459 .. 898.0459 cents 1/1, 0.0000 cents 99.78287 cents 10: 997.8288 .. 997.8288 cents 1/1, 0.0000 cents 99.78288 cents 11: 1097.6116 .. 1097.6116 cents 1/1, 0.0000 cents 99.78287 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 99.78287 cents, class 1 Average step (divided formal octave): 99.7829 cents Largest one step interval : 99.78287 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 99.78287 cents, amount: 12 Most common interval of one step : 99.78287 cents, amount: 12 Least squares average step : 99.78287 cents, oct.: 1197.39450 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 99.78288 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 : 12, average 698.4801 cents Number of recognisable fourths : 12, average 498.9144 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
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 x x x x 2 S SD: 2.6055 cents 2 x x x x x x 3 x x x x 4 S SD: 2.1716 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.6533 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.0013 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.8201 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.9857 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8999 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9805 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1376 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0543 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.2624 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1804 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.6846 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.2053 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8843 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0642 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.9859 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.6389 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2633 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.6203 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1869 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.9779 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.8251 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6450 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5582 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.2530 cents 65:69:73:77:82:87:92:97:103:109:116:123:130 SD: 1.2258 cents 68:72:76:81:86:91:96:102:108:114:121:128:136 SD: 1.1646 cents 80:85:90:95:101:107:113:120:127:134:142:151:160 SD: 1.0601 cents 84:89:94:100:106:112:119:126:133:141:149:158:168 SD: 0.9729 cents 85:90:95:101:107:113:120:127:135:143:151:160:170 SD: 0.9727 cents 90:95:101:107:113:120:127:135:143:151:160:170:180 SD: 0.9181 cents 96:102:108:114:121:128:136:144:152:161:171:181:192 SD: 0.8661 cents 99:105:111:118:125:132:140:148:157:166:176:187:198 SD: 0.7840 cents 116:123:130:138:146:155:164:174:184:195:206:219:232 SD: 0.6419 cents 123:130:138:146:155:164:174:184:195:207:219:232:246 SD: 0.5768 cents 131:139:147:156:165:175:185:196:208:220:233:247:262 SD: 0.5144 cents 155:164:174:184:195:207:219:232:246:260:276:292:310 SD: 0.4929 cents 165:175:185:196:208:220:233:247:262:277:294:311:330 SD: 0.4707 cents 181:192:203:215:228:241:256:271:287:304:322:341:361 SD: 0.4399 cents 201:213:226:239:253:268:284:301:319:338:358:379:401 SD: 0.4088 cents 203:215:228:241:256:271:287:304:322:341:361:383:405 SD: 0.3973 cents 213:226:239:253:268:284:301:319:338:358:379:402:425 SD: 0.3866 cents 237:251:266:282:298:316:335:355:376:398:422:447:473 SD: 0.3283 cents 254:269:285:302:320:339:359:380:403:427:452:479:507 SD: 0.2078 cents 350:371:393:416:441:467:495:524:555:588:623:660:699 SD: 0.2025 cents 386:409:433:459:486:515:545:578:612:648:687:728:771 SD: 0.2015 cents 401:425:450:477:505:535:567:600:636:674:714:756:801 SD: 0.2006 cents 408:432:458:485:514:544:577:611:647:685:726:769:815 SD: 0.1998 cents 409:433:459:486:515:546:578:612:649:687:728:771:817 SD: 0.1939 cents 425:450:477:505:535:567:601:636:674:714:756:801:849 SD: 0.1780 cents 435:461:488:517:548:580:615:651:690:731:774:820:869 SD: 0.1662 cents 440:466:494:523:554:587:622:659:698:739:783:829:879 SD: 0.1646 cents 509:539:571:605:641:679:719:762:807:855:906:960:1016 SD: 0.1428 cents 540:572:606:642:680:720:763:808:856:907:961:1018:1078 SD: 0.1296 cents 572:606:642:680:720:763:808:856:907:961:1018:1078:1142 SD: 0.1179 cents