Scala analysis: xen18-erlich-keemun-15
4L 11s MOS for Keemun, L=113.33, s=68.17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.170 cents 68.170000 2: 181.500 cents 181.500000 3: 249.670 cents 249.670000 4: 317.840 cents 317.840000 5: 386.010 cents 386.010000 6: 499.340 cents 499.340000 7: 567.510 cents 567.510000 8: 635.680 cents 635.680000 9: 703.850 cents 703.850000 10: 817.180 cents 817.180000 11: 885.350 cents 885.350000 12: 953.520 cents 953.520000 13: 1021.690 cents 1021.690000 14: 1135.020 cents 1135.020000 15: 1203.190 cents 1203.190000
SHOW/INTERVAL
0: 68.1700 cents 68.1700 1: 68.1700 cents 68.1700 2: 113.3300 cents 113.3300 3: 68.1700 cents 68.1700 4: 68.1700 cents 68.1700 5: 68.1700 cents 68.1700 6: 113.3300 cents 113.3300 7: 68.1700 cents 68.1700 8: 68.1700 cents 68.1700 9: 68.1700 cents 68.1700 10: 113.3300 cents 113.3300 11: 68.1700 cents 68.1700 12: 68.1700 cents 68.1700 13: 68.1700 cents 68.1700 14: 113.3300 cents 113.3300 15: 68.1700 cents 68.1700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 68.17000 cents 1: 4 113.33000 cents 2: 7 136.34000 cents 2: 8 181.50000 cents 3: 3 204.51000 cents 3: 12 249.67000 cents 4: 14 317.84000 cents 4: 1 363.00000 cents 5: 10 386.01000 cents 5: 5 431.17000 cents 6: 6 454.18000 cents 6: 9 499.34000 cents 7: 2 522.35000 cents 7: 13 567.51000 cents 8: 13 635.68000 cents 8: 2 680.84000 cents 9: 9 703.85000 cents 9: 6 749.01000 cents 10: 5 772.02000 cents 10: 10 817.18000 cents 11: 1 840.19000 cents 11: 14 885.35000 cents 12: 12 953.52000 cents 12: 3 998.68000 cents 13: 8 1021.69000 cents 13: 7 1066.85000 cents 14: 4 1089.86000 cents 14: 11 1135.02000 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 : 68.2 181.5 249.7 317.8 386.0 499.3 567.5 635.7 703.8 817.2 885.3 953.5 1021.7 1135.0 1203.2 68.2 : 113.3 181.5 249.7 317.8 431.2 499.3 567.5 635.7 749.0 817.2 885.3 953.5 1066.8 1135.0 1203.2 181.5 : 68.2 136.3 204.5 317.8 386.0 454.2 522.4 635.7 703.8 772.0 840.2 953.5 1021.7 1089.9 1203.2 249.7 : 68.2 136.3 249.7 317.8 386.0 454.2 567.5 635.7 703.8 772.0 885.4 953.5 1021.7 1135.0 1203.2 317.8 : 68.2 181.5 249.7 317.8 386.0 499.3 567.5 635.7 703.8 817.2 885.3 953.5 1066.8 1135.0 1203.2 386.0 : 113.3 181.5 249.7 317.8 431.2 499.3 567.5 635.7 749.0 817.2 885.3 998.7 1066.8 1135.0 1203.2 499.3 : 68.2 136.3 204.5 317.8 386.0 454.2 522.4 635.7 703.8 772.0 885.3 953.5 1021.7 1089.9 1203.2 567.5 : 68.2 136.3 249.7 317.8 386.0 454.2 567.5 635.7 703.8 817.2 885.4 953.5 1021.7 1135.0 1203.2 635.7 : 68.2 181.5 249.7 317.8 386.0 499.3 567.5 635.7 749.0 817.2 885.3 953.5 1066.8 1135.0 1203.2 703.8 : 113.3 181.5 249.7 317.8 431.2 499.3 567.5 680.8 749.0 817.2 885.4 998.7 1066.8 1135.0 1203.2 817.2 : 68.2 136.3 204.5 317.8 386.0 454.2 567.5 635.7 703.8 772.0 885.3 953.5 1021.7 1089.9 1203.2 885.3 : 68.2 136.3 249.7 317.8 386.0 499.3 567.5 635.7 703.9 817.2 885.3 953.5 1021.7 1135.0 1203.2 953.5 : 68.2 181.5 249.7 317.8 431.2 499.3 567.5 635.7 749.0 817.2 885.4 953.5 1066.8 1135.0 1203.2 1021.7: 113.3 181.5 249.7 363.0 431.2 499.3 567.5 680.8 749.0 817.2 885.3 998.7 1066.8 1135.0 1203.2 1135.0: 68.2 136.3 249.7 317.8 386.0 454.2 567.5 635.7 703.8 772.0 885.3 953.5 1021.7 1089.9 1203.2 1203.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.1700 .. 113.3300 cents 45.16000 cents 68.17000 cents 2: 136.3400 .. 181.5000 cents 45.16000 cents 23.01000 cents 3: 204.5100 .. 249.6700 cents 45.16000 cents 23.01000 cents 4: 317.8400 .. 363.0000 cents 45.16000 cents 68.17000 cents 5: 386.0100 .. 431.1700 cents 45.16000 cents 23.01000 cents 6: 454.1800 .. 499.3400 cents 45.16000 cents 23.01000 cents 7: 522.3500 .. 567.5100 cents 45.16000 cents 23.01000 cents 8: 635.6800 .. 680.8400 cents 45.16000 cents 68.17000 cents 9: 703.8500 .. 749.0100 cents 45.16000 cents 23.01000 cents 10: 772.0200 .. 817.1800 cents 45.16000 cents 23.01000 cents 11: 840.1900 .. 885.3500 cents 45.16000 cents 23.01000 cents 12: 953.5200 .. 998.6800 cents 45.16000 cents 68.17000 cents 13: 1021.6900 .. 1066.8500 cents 45.16000 cents 23.01000 cents 14: 1089.8600 .. 1135.0200 cents 45.16000 cents 23.01000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 68.17000 cents, class 1 Average step (divided formal octave): 80.2127 cents Largest one step interval : 113.33000 cents Average / Smallest step : 1.176656 Largest / Average step : 1.412869 Largest / Smallest step : 1.662461 Median interval of one step : 68.17000 cents, amount: 11 Most common interval of one step : 68.17000 cents, amount: 11 Least squares average step : 80.11555 cents, oct.: 1201.73323 cents Scale is strictly proper Scale has Myhill's property chromas: 45.16000 cents and 23.01000 cents, ratio: 1.962625 generators: 4 of 317.84000 cents and 11 of 885.35000 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 1359-tone equal temperament with octave 1203.190 cents degrees: 77 205 282 359 436 564 641 718 795 923 1000 1077 1154 1282 1359 generators: 359 and 1000 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 23.01000 cents Scale diversity : 1.191051 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.474530 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 : 23.01000 cents Most common intervals : 317.84000 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 317.840 635.680 cents Most common triad is 0.0 317.840 885.350 cents, amount: 13 Number of recognisable fifths : 9, average 703.8500 cents Number of recognisable fourths : 9, average 499.3400 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: 13.0076 c. M: 21.0747 c. 19: 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 P M ME I SD: 5.2323 c. M: 8.4774 c. 34: 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 SP M ME I SD: 2.8147 c. M: 4.5603 c. 53: 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 SP M DE I SD: 0.0701 c. M: 0.1136 c. 723: 41 68 41 41 41 68 41 41 41 68 41 41 41 68 41 SP M DE I SD: 0.0656 c. M: 0.1062 c. 776: 44 73 44 44 44 73 44 44 44 73 44 44 44 73 44 SP M DE I SD: 0.0563 c. M: 0.0912 c. 829: 47 78 47 47 47 78 47 47 47 78 47 47 47 78 47 SP M DE I SD: 0.0482 c. M: 0.0781 c. 882: 50 83 50 50 50 83 50 50 50 83 50 50 50 83 50 SP M DE I SD: 0.0411 c. M: 0.0666 c. 935: 53 88 53 53 53 88 53 53 53 88 53 53 53 88 53 SP M DE I SD: 0.0348 c. M: 0.0564 c. 988: 56 93 56 56 56 93 56 56 56 93 56 56 56 93 56 SP M DE I SD: 0.0292 c. M: 0.0473 c. 1041: 59 98 59 59 59 98 59 59 59 98 59 59 59 98 59 SP M DE I SD: 0.0241 c. M: 0.0391 c. 1094: 62 103 62 62 62 103 62 62 62 103 62 62 62 103 62 SP M DE I SD: 0.0195 c. M: 0.0317 c. 1147: 65 108 65 65 65 108 65 65 65 108 65 65 65 108 65 SP M DE I SD: 0.0154 c. M: 0.0250 c. 1200: 68 113 68 68 68 113 68 68 68 113 68 68 68 113 68 SP M DE I SD: 0.0116 c. M: 0.0188 c. 1253: 71 118 71 71 71 118 71 71 71 118 71 71 71 118 71 SP M DE I SD: 0.0082 c. M: 0.0132 c. 1306: 74 123 74 74 74 123 74 74 74 123 74 74 74 123 74 SP M DE I SD: 0.0050 c. M: 0.0081 c. 1359: 77 128 77 77 77 128 77 77 77 128 77 77 77 128 77 SP M DE I SD: 0.0021 c. M: 0.0033 c. 1412: 80 133 80 80 80 133 80 80 80 133 80 80 80 133 80 SP M DE I SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 3.1900 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 1.8552 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 1.1942 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 3.9380 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 3.2805 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 5.4724 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 12.1317 cents 8 x 9 x x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.6478 cents 9 x 10 x 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 8.1876 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 6.5245 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.0812 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 5.7532 cents 13 x 14:15 x 16:17:18:19:20:21:22 x 23:25:26 SD: 7.8951 cents 14:15 x 16:17:18:19 x 20:21:22:23:24:25:27:28 SD: 7.5108 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.4840 cents 16:17:18 x 19:20:21:22:23:24:26:27:28:29:31:32 SD: 4.9373 cents 17:18:19:20 x 21:23:24:25:26:27:28:29:31:33:34 SD: 6.4057 cents 18:19:20:21:22:23:24:25:26:27:29:30:31:32:35:36 SD: 4.4479 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:39:40 SD: 3.2357 cents 25:26:28:29:30:31:33:35:36:38:40:42:43:45:48:50 SD: 2.9400 cents 30:31:33:35:36:37:40:42:43:45:48:50:52:54:58:60 SD: 2.7447 cents 36:37:40:42:43:45:48:50:52:54:58:60:62:65:69:72 SD: 2.2638 cents 43:45:48:50:52:54:57:60:62:65:69:72:75:78:83:86 SD: 2.2301 cents 44:46:49:51:53:55:59:61:64:66:71:73:76:79:85:88 SD: 1.8471 cents 45:47:50:52:54:56:60:62:65:68:72:75:78:81:87:90 SD: 1.4530 cents 56:58:62:65:67:70:75:78:81:84:90:93:97:101:108:112 SD: 1.3175 cents 65:68:72:75:78:81:87:90:94:98:104:108:113:117:125:130 SD: 1.2613 cents 70:73:78:81:84:87:93:97:101:105:112:117:121:126:135:140 SD: 1.1998 cents 72:75:80:83:87:90:96:100:104:108:115:120:125:130:139:144 SD: 0.9301 cents 90:94:100:104:108:112:120:125:130:135:144:150:156:162:173:180 SD: 0.8805 cents 96:100:107:111:115:120:128:133:139:144:154:160:167:173:185:192 SD: 0.8399 cents 99:103:110:114:119:124:132:137:143:149:159:165:172:179:191:198 SD: 0.7832 cents 108:112:120:125:130:135:144:150:156:162:173:180:187:195:208:216 SD: 0.6030 cents 124:129:138:143:149:155:165:172:179:186:199:207:215:224:239:248 SD: 0.5654 cents 129:134:143:149:155:161:172:179:186:194:207:215:224:233:248:258 SD: 0.5430 cents 144:150:160:166:173:180:192:200:208:216:231:240:250:260:277:289 SD: 0.4569 cents 173:180:192:200:208:216:231:240:250:260:277:288:300:312:333:347 SD: 0.3915 cents 180:187:200:208:216:225:240:250:260:270:289:300:312:325:347:361 SD: 0.3827 cents 199:207:221:230:239:249:266:276:287:299:319:332:345:359:383:399 SD: 0.3381 cents 219:228:243:253:263:274:292:304:316:329:351:365:380:395:422:439 SD: 0.2566 cents 245:255:272:283:294:306:327:340:354:368:393:409:425:442:472:491 SD: 0.2545 cents 297:309:330:343:357:371:396:412:429:446:476:495:515:536:572:595 SD: 0.1860 cents 343:357:381:396:412:429:458:476:495:515:550:572:595:619:661:687 SD: 0.1807 cents 353:367:392:408:424:441:471:490:510:530:566:589:612:637:680:707 SD: 0.1729 cents 433:450:481:500:520:541:578:601:625:650:694:722:751:781:834:868 SD: 0.1642 cents 446:464:495:515:536:557:595:619:644:670:715:744:774:805:859:894 SD: 0.1630 cents 451:469:501:521:542:564:602:626:651:677:723:752:782:814:869:904 SD: 0.1345 cents 496:516:551:573:596:620:662:688:716:745:795:827:860:895:955:994 SD: 0.1262 cents 541:563:601:625:650:676:722:751:781:812:867:902:938:976:1042:1084 SD: 0.1223 cents 572:595:635:661:687:715:763:794:826:859:917:954:992:1032:1102:1146 SD: 0.1001 cents