Scala analysis: xen18-erlich-hanson-15
4L 11s MOS for Hanson, L=113.10, s=67.99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.990 cents 67.990000 2: 181.090 cents 181.090000 3: 249.080 cents 249.080000 4: 317.070 cents 317.070000 5: 385.060 cents 385.060000 6: 498.160 cents 498.160000 7: 566.150 cents 566.150000 8: 634.140 cents 634.140000 9: 702.130 cents 702.130000 10: 815.230 cents 815.230000 11: 883.220 cents 883.220000 12: 951.210 cents 951.210000 13: 1019.200 cents 1019.200000 14: 1132.300 cents 1132.300000 15: 1200.290 cents 1200.290000
SHOW/INTERVAL
0: 67.9900 cents 67.9900 1: 67.9900 cents 67.9900 2: 113.1000 cents 113.1000 3: 67.9900 cents 67.9900 4: 67.9900 cents 67.9900 5: 67.9900 cents 67.9900 6: 113.1000 cents 113.1000 7: 67.9900 cents 67.9900 8: 67.9900 cents 67.9900 9: 67.9900 cents 67.9900 10: 113.1000 cents 113.1000 11: 67.9900 cents 67.9900 12: 67.9900 cents 67.9900 13: 67.9900 cents 67.9900 14: 113.1000 cents 113.1000 15: 67.9900 cents 67.9900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 67.99000 cents 1: 4 113.10000 cents 2: 7 135.98000 cents 2: 8 181.09000 cents 3: 3 203.97000 cents 3: 12 249.08000 cents 4: 14 317.07000 cents 4: 1 362.18000 cents 5: 10 385.06000 cents 5: 5 430.17000 cents 6: 6 453.05000 cents 6: 9 498.16000 cents 7: 2 521.04000 cents 7: 13 566.15000 cents 8: 13 634.14000 cents 8: 2 679.25000 cents 9: 9 702.13000 cents 9: 6 747.24000 cents 10: 5 770.12000 cents 10: 10 815.23000 cents 11: 1 838.11000 cents 11: 14 883.22000 cents 12: 12 951.21000 cents 12: 3 996.32000 cents 13: 8 1019.20000 cents 13: 7 1064.31000 cents 14: 4 1087.19000 cents 14: 11 1132.30000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 68.0 181.1 249.1 317.1 385.1 498.2 566.1 634.1 702.1 815.2 883.2 951.2 1019.2 1132.3 1200.3 68.0 : 113.1 181.1 249.1 317.1 430.2 498.2 566.1 634.1 747.2 815.2 883.2 951.2 1064.3 1132.3 1200.3 181.1 : 68.0 136.0 204.0 317.1 385.1 453.0 521.0 634.1 702.1 770.1 838.1 951.2 1019.2 1087.2 1200.3 249.1 : 68.0 136.0 249.1 317.1 385.1 453.1 566.1 634.1 702.1 770.1 883.2 951.2 1019.2 1132.3 1200.3 317.1 : 68.0 181.1 249.1 317.1 385.1 498.2 566.1 634.1 702.1 815.2 883.2 951.2 1064.3 1132.3 1200.3 385.1 : 113.1 181.1 249.1 317.1 430.2 498.2 566.1 634.1 747.2 815.2 883.2 996.3 1064.3 1132.3 1200.3 498.2 : 68.0 136.0 204.0 317.1 385.1 453.0 521.0 634.1 702.1 770.1 883.2 951.2 1019.2 1087.2 1200.3 566.1 : 68.0 136.0 249.1 317.1 385.1 453.1 566.1 634.1 702.1 815.2 883.2 951.2 1019.2 1132.3 1200.3 634.1 : 68.0 181.1 249.1 317.1 385.1 498.2 566.1 634.1 747.2 815.2 883.2 951.2 1064.3 1132.3 1200.3 702.1 : 113.1 181.1 249.1 317.1 430.2 498.2 566.1 679.3 747.2 815.2 883.2 996.3 1064.3 1132.3 1200.3 815.2 : 68.0 136.0 204.0 317.1 385.1 453.0 566.1 634.1 702.1 770.1 883.2 951.2 1019.2 1087.2 1200.3 883.2 : 68.0 136.0 249.1 317.1 385.1 498.2 566.2 634.1 702.1 815.2 883.2 951.2 1019.2 1132.3 1200.3 951.2 : 68.0 181.1 249.1 317.1 430.2 498.2 566.1 634.1 747.2 815.2 883.2 951.2 1064.3 1132.3 1200.3 1019.2: 113.1 181.1 249.1 362.2 430.2 498.2 566.1 679.3 747.2 815.2 883.2 996.3 1064.3 1132.3 1200.3 1132.3: 68.0 136.0 249.1 317.1 385.1 453.0 566.2 634.1 702.1 770.1 883.2 951.2 1019.2 1087.2 1200.3 1200.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9900 .. 113.1000 cents 45.11000 cents 67.99000 cents 2: 135.9800 .. 181.0900 cents 45.11000 cents 22.88000 cents 3: 203.9700 .. 249.0800 cents 45.11000 cents 22.88000 cents 4: 317.0700 .. 362.1800 cents 45.11000 cents 67.99000 cents 5: 385.0600 .. 430.1700 cents 45.11000 cents 22.88000 cents 6: 453.0500 .. 498.1600 cents 45.11000 cents 22.88000 cents 7: 521.0400 .. 566.1500 cents 45.11000 cents 22.88000 cents 8: 634.1400 .. 679.2500 cents 45.11000 cents 67.99000 cents 9: 702.1300 .. 747.2400 cents 45.11000 cents 22.88000 cents 10: 770.1200 .. 815.2300 cents 45.11000 cents 22.88000 cents 11: 838.1100 .. 883.2200 cents 45.11000 cents 22.88000 cents 12: 951.2100 .. 996.3200 cents 45.11000 cents 67.99000 cents 13: 1019.2000 .. 1064.3100 cents 45.11000 cents 22.88000 cents 14: 1087.1900 .. 1132.3000 cents 45.11000 cents 22.88000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 67.99000 cents, class 1 Average step (divided formal octave): 80.0193 cents Largest one step interval : 113.10000 cents Average / Smallest step : 1.176928 Largest / Average step : 1.413408 Largest / Smallest step : 1.663480 Median interval of one step : 67.99000 cents, amount: 11 Most common interval of one step : 67.99000 cents, amount: 11 Least squares average step : 79.92232 cents, oct.: 1198.83484 cents Scale is strictly proper Scale has Myhill's property chromas: 45.11000 cents and 22.88000 cents, ratio: 1.971591 generators: 4 of 317.07000 cents and 11 of 883.22000 cents ET pair of linear temperament : 15&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1730-tone equal temperament with octave 1200.290 cents degrees: 98 261 359 457 555 718 816 914 1012 1175 1273 1371 1469 1632 1730 generators: 457 and 1273 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAABAAABA Step pattern size order : SLSSSLSSSLSSSLS Scale is a Constant Structure, by a margin of 22.88000 cents Scale diversity : 1.193479 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.473844 Rothenberg efficiency : 0.711111 redundancy: 0.288889 Efficiency x scale size : 10.666667 Number of different interval sizes : 28 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 22.88000 cents Most common intervals : 317.07000 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 317.070 634.140 cents Most common triad is 0.0 317.070 883.220 cents, amount: 13 Number of recognisable fifths : 9, average 702.1300 cents Number of recognisable fourths : 9, average 498.1600 cents Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.9932 c. M: 21.0513 c. 19: 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 P M ME I SD: 5.2028 c. M: 8.4295 c. 34: 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 SP M ME I SD: 2.8248 c. M: 4.5768 c. 53: 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 SP M DE I SD: 0.0530 c. M: 0.0858 c. 935: 53 88 53 53 53 88 53 53 53 88 53 53 53 88 53 SP M DE I SD: 0.0517 c. M: 0.0837 c. 988: 56 93 56 56 56 93 56 56 56 93 56 56 56 93 56 SP M DE I SD: 0.0460 c. M: 0.0746 c. 1041: 59 98 59 59 59 98 59 59 59 98 59 59 59 98 59 SP M DE I SD: 0.0410 c. M: 0.0664 c. 1094: 62 103 62 62 62 103 62 62 62 103 62 62 62 103 62 SP M DE I SD: 0.0365 c. M: 0.0591 c. 1147: 65 108 65 65 65 108 65 65 65 108 65 65 65 108 65 SP M DE I SD: 0.0323 c. M: 0.0524 c. 1200: 68 113 68 68 68 113 68 68 68 113 68 68 68 113 68 SP M DE I SD: 0.0286 c. M: 0.0463 c. 1253: 71 118 71 71 71 118 71 71 71 118 71 71 71 118 71 SP M DE I SD: 0.0251 c. M: 0.0407 c. 1306: 74 123 74 74 74 123 74 74 74 123 74 74 74 123 74 SP M DE I SD: 0.0219 c. M: 0.0355 c. 1359: 77 128 77 77 77 128 77 77 77 128 77 77 77 128 77 SP M DE I SD: 0.0190 c. M: 0.0308 c. 1412: 80 133 80 80 80 133 80 80 80 133 80 80 80 133 80 SP M DE I SD: 0.0163 c. M: 0.0264 c. 1465: 83 138 83 83 83 138 83 83 83 138 83 83 83 138 83 SP M DE I SD: 0.0138 c. M: 0.0224 c. 1518: 86 143 86 86 86 143 86 86 86 143 86 86 86 143 86 SP M DE I SD: 0.0115 c. M: 0.0186 c. 1571: 89 148 89 89 89 148 89 89 89 148 89 89 89 148 89 SP M DE I SD: 0.0093 c. M: 0.0151 c. 1624: 92 153 92 92 92 153 92 92 92 153 92 92 92 153 92 SP M DE I SD: 0.0073 c. M: 0.0118 c. 1677: 95 158 95 95 95 158 95 95 95 158 95 95 95 158 95 SP M DE I SD: 0.0054 c. M: 0.0087 c. 1730: 98 163 98 98 98 163 98 98 98 163 98 98 98 163 98 SP M DE I SD: 0.0036 c. M: 0.0058 c. 1783: 101 168 101 101 101 168 101 101 101 168 101 101 101 168 101 SP M DE I SD: 0.0019 c. M: 0.0031 c. 1836: 104 173 104 104 104 173 104 104 104 173 104 104 104 173 104 SP M DE I SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.2900 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 0.1694 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 0.3936 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 4.4159 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 3.3154 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 5.8399 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 12.1685 cents 8 x 9 x x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.5327 cents 9 x 10 x 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.8348 cents 10 x 11 x 12 x 13:14 x 15:16 x 17:18:19:20 S SD: 6.3014 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.0551 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 5.7372 cents 13 x 14:15 x 16:17:18:19:20:21:22 x 23:25:26 SD: 7.9022 cents 14:15 x 16:17 x 19 x 20:21:22:23:24:25:27:28 SD: 6.8536 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.6135 cents 16:17:18 x 19:20:21:22:23:24:26:27:28:29:31:32 SD: 5.0550 cents 17:18:19:20 x 21:23:24:25:26:27:28:29:31:33:34 SD: 6.5108 cents 18:19:20:21:22 x 24:25:26:27:29:30:31:32:35:36 SD: 3.9200 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 3.2783 cents 24:25:27:28:29:30:32:33:35:36:38:40:42:43:46:48 SD: 3.2438 cents 25:26:28:29:30:31:33:35:36:38:40:42:43:45:48:50 SD: 2.9374 cents 30:31:33:35:36:37:40:42:43:45:48:50:52:54:58:60 SD: 2.7175 cents 36:37:40:42:43:45:48:50:52:54:58:60:62:65:69:72 SD: 2.2175 cents 44:46:49:51:53:55:59:61:63:66:70:73:76:79:85:88 SD: 1.8006 cents 45:47:50:52:54:56:60:62:65:68:72:75:78:81:87:90 SD: 1.4640 cents 52:54:58:60:62:65:69:72:75:78:83:87:90:94:100:104 SD: 1.3981 cents 56:58:62:65:67:70:75:78:81:84:90:93:97:101:108:112 SD: 1.3795 cents 60:62:67:69:72:75:80:83:87:90:96:100:104:108:115:120 SD: 1.3741 cents 64:67:71:74:77:80:85:89:92:96:102:107:111:115:123:128 SD: 1.3162 cents 65:68:72:75:78:81:87:90:94:98:104:108:113:117:125:130 SD: 1.2400 cents 70:73:78:81:84:87:93:97:101:105:112:117:121:126:135:140 SD: 1.0980 cents 72:75:80:83:86:90:96:100:104:108:115:120:125:130:138:144 SD: 0.9611 cents 80:83:89:92:96:100:107:111:115:120:128:133:139:144:154:160 SD: 0.9244 cents 90:94:100:104:108:112:120:125:130:135:144:150:156:162:173:180 SD: 0.7343 cents 108:112:120:125:130:135:144:150:156:162:173:180:187:195:208:216 SD: 0.6475 cents 116:121:129:134:139:145:155:161:167:174:186:193:201:209:223:232 SD: 0.6172 cents 120:125:133:139:144:150:160:166:173:180:192:200:208:216:231:240 SD: 0.5908 cents 129:134:143:149:155:161:172:179:186:194:207:215:223:232:248:258 SD: 0.5629 cents 144:150:160:166:173:180:192:200:208:216:231:240:249:259:277:288 SD: 0.5200 cents 153:159:170:177:184:191:204:212:221:230:245:255:265:276:294:306 SD: 0.4724 cents 156:162:173:180:187:195:208:216:225:234:250:260:270:281:300:312 SD: 0.4126 cents 174:181:193:201:209:217:232:241:251:261:279:290:301:313:335:348 SD: 0.4123 cents 180:187:200:208:216:225:240:250:260:270:288:300:312:324:346:360 SD: 0.3757 cents 201:209:223:232:241:251:268:279:290:302:322:335:348:362:387:402 SD: 0.3477 cents 220:229:244:254:264:275:293:305:317:330:352:366:381:396:423:440 SD: 0.3431 cents 224:233:249:259:269:280:299:311:323:336:359:373:388:404:431:448 SD: 0.3297 cents 228:237:253:263:274:285:304:316:329:342:365:380:395:411:439:456 SD: 0.2676 cents 246:256:273:284:295:307:328:341:355:369:394:410:426:443:473:492 SD: 0.2591 cents 272:283:302:314:327:340:363:377:392:408:436:453:471:490:523:544 SD: 0.2499 cents 273:284:303:315:328:341:364:379:394:410:437:455:473:492:525:546 SD: 0.2419 cents 298:310:331:344:358:372:397:413:430:447:477:496:516:537:573:596 SD: 0.2075 cents 318:331:353:367:382:397:424:441:459:477:509:530:551:573:612:636 SD: 0.2006 cents 328:341:364:379:394:410:437:455:473:492:525:546:568:591:631:656 SD: 0.1984 cents 344:358:382:397:413:430:459:477:496:516:551:573:596:620:662:688 SD: 0.1846 cents 354:368:393:409:425:442:472:491:511:531:567:590:613:638:681:708 SD: 0.1733 cents 418:435:464:483:502:522:557:580:603:627:669:696:724:753:804:836 SD: 0.1688 cents 434:451:482:501:521:542:579:602:626:651:695:723:752:782:835:868 SD: 0.1509 cents 452:470:502:522:543:565:603:627:652:678:724:753:783:814:869:904 SD: 0.1428 cents 497:517:552:574:597:621:663:689:717:746:796:828:861:895:956:994 SD: 0.1349 cents 574:597:637:663:689:717:765:796:828:861:919:956:994:1034:1104:1148 SD: 0.1193 cents