Scala analysis: circ5120
Circle of seven minor, six major, and one subminor thirds in 531-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24.859 cents 24.858757 2: 205.650 cents 205.649718 3: 230.508 cents 230.508475 4: 316.384 cents 316.384181 5: 411.299 cents 411.299435 6: 522.034 cents 522.033898 7: 616.949 cents 616.949153 8: 702.825 cents 702.824859 9: 727.684 cents 727.683616 10: 908.475 cents 908.474576 11: 933.333 cents 933.333333 12: 1019.209 cents 1019.209040 13: 1114.124 cents 1114.124294 14: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 85.8757 cents 85.8757 1: 24.8588 cents 24.8588 2: 180.7910 cents 180.7910 3: 24.8588 cents 24.8588 4: 85.8757 cents 85.8757 5: 94.9153 cents 94.9153 6: 110.7345 cents 110.7345 7: 94.9153 cents 94.9153 8: 85.8757 cents 85.8757 9: 24.8588 cents 24.8588 10: 180.7910 cents 180.7910 11: 24.8588 cents 24.8588 12: 85.8757 cents 85.8757 13: 94.9153 cents 94.9153 14: 85.8757 cents 85.8757
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 24.85876 cents 1: 4 85.87571 cents 1: 3 94.91525 cents 1: 1 110.73446 cents 1: 2 180.79096 cents 2: 4 110.73446 cents 2: 4 180.79096 cents 2: 6 205.64972 cents 3: 4 205.64972 cents 3: 2 230.50848 cents 3: 1 266.66667 cents 3: 6 291.52542 cents 3: 1 300.56497 cents 4: 2 291.52542 cents 4: 6 316.38418 cents 4: 6 386.44068 cents 5: 1 316.38418 cents 5: 2 402.25989 cents 5: 6 411.29944 cents 5: 3 472.31638 cents 5: 2 497.17514 cents 6: 10 497.17514 cents 6: 2 522.03390 cents 6: 2 592.09040 cents 7: 3 522.03390 cents 7: 2 583.05085 cents 7: 2 592.09040 cents 7: 2 607.90960 cents 7: 2 616.94915 cents 7: 3 677.96610 cents 8: 2 607.90960 cents 8: 2 677.96610 cents 8: 10 702.82486 cents 9: 2 702.82486 cents 9: 3 727.68362 cents 9: 6 788.70056 cents 9: 2 797.74011 cents 9: 1 883.61582 cents 10: 6 813.55932 cents 10: 6 883.61582 cents 10: 2 908.47458 cents 11: 1 899.43503 cents 11: 6 908.47458 cents 11: 1 933.33333 cents 11: 2 969.49152 cents 11: 4 994.35028 cents 12: 6 994.35028 cents 12: 4 1019.20904 cents 12: 4 1089.26554 cents 13: 2 1019.20904 cents 13: 1 1089.26554 cents 13: 3 1105.08475 cents 13: 4 1114.12429 cents 13: 4 1175.14124 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.15385 = 54/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 24.9 205.6 230.5 316.4 411.3 522.0 616.9 702.8 727.7 908.5 933.3 1019.2 1114.1 1200.0 24.9 : 180.8 205.6 291.5 386.4 497.2 592.1 678.0 702.8 883.6 908.5 994.4 1089.3 1175.1 1200.0 205.6 : 24.9 110.7 205.6 316.4 411.3 497.2 522.0 702.8 727.7 813.6 908.5 994.4 1019.2 1200.0 230.5 : 85.9 180.8 291.5 386.4 472.3 497.2 678.0 702.8 788.7 883.6 969.5 994.4 1175.1 1200.0 316.4 : 94.9 205.6 300.6 386.4 411.3 592.1 616.9 702.8 797.7 883.6 908.5 1089.3 1114.1 1200.0 411.3 : 110.7 205.6 291.5 316.4 497.2 522.0 607.9 702.8 788.7 813.6 994.4 1019.2 1105.1 1200.0 522.0 : 94.9 180.8 205.6 386.4 411.3 497.2 592.1 678.0 702.8 883.6 908.5 994.4 1089.3 1200.0 616.9 : 85.9 110.7 291.5 316.4 402.3 497.2 583.1 607.9 788.7 813.6 899.4 994.4 1105.1 1200.0 702.8 : 24.9 205.6 230.5 316.4 411.3 497.2 522.0 702.8 727.7 813.6 908.5 1019.2 1114.1 1200.0 727.7 : 180.8 205.6 291.5 386.4 472.3 497.2 678.0 702.8 788.7 883.6 994.4 1089.3 1175.1 1200.0 908.5 : 24.9 110.7 205.6 291.5 316.4 497.2 522.0 607.9 702.8 813.6 908.5 994.4 1019.2 1200.0 933.3 : 85.9 180.8 266.7 291.5 472.3 497.2 583.1 678.0 788.7 883.6 969.5 994.4 1175.1 1200.0 1019.2: 94.9 180.8 205.6 386.4 411.3 497.2 592.1 702.8 797.7 883.6 908.5 1089.3 1114.1 1200.0 1114.1: 85.9 110.7 291.5 316.4 402.3 497.2 607.9 702.8 788.7 813.6 994.4 1019.2 1105.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.8588 .. 180.7910 cents 155.93220 cents 24.85876 cents 2: 110.7345 .. 205.6497 cents 94.91525 cents -70.05650 cents 3: 205.6497 .. 300.5650 cents 94.91526 cents -0.00000 cents 4: 291.5254 .. 386.4407 cents 94.91525 cents -9.03955 cents 5: 316.3842 .. 497.1751 cents 180.79096 cents -70.05650 cents 6: 497.1751 .. 592.0904 cents 94.91526 cents 1/1, 0.0000 cents 7: 522.0339 .. 677.9661 cents 155.93220 cents -70.05650 cents 8: 607.9096 .. 702.8249 cents 94.91526 cents -70.05650 cents 9: 702.8249 .. 883.6158 cents 180.79096 cents 1/1, 0.0000 cents 10: 813.5593 .. 908.4746 cents 94.91525 cents -70.05650 cents 11: 899.4350 .. 994.3503 cents 94.91526 cents -9.03955 cents 12: 994.3503 .. 1089.2655 cents 94.91525 cents -0.00000 cents 13: 1019.2090 .. 1175.1412 cents 155.93220 cents -70.05650 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 24.85876 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 180.79096 cents Average / Smallest step : 3.448052 Largest / Average step : 2.109228 Largest / Smallest step : 7.272727 Median interval of one step : 85.87571 cents, amount: 4 Least squares average step : 85.65306 cents, oct.: 1199.14280 cents Scale is not proper Scale is a mode of a 531-tone equal temperament with octave 1200.000 cents degrees: 11 91 102 140 182 231 273 311 322 402 413 451 493 531 Least number of segments generator : 266 of 601.130 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 421 of 951.412 cents and inv. generated superset size: 60 = 46 more = 428.571% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 531-tone equal temperament Step pattern alph. order: ABACDEDCABACDC Step pattern size order : AEABCDCBAEABCB Scale is not a Constant Structure Scale diversity : 1.241325 Lumma stability : 0.041431 Lumma impropriety factor : 0.365348 Number of different interval sizes : 38 = 2.92308 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.15385 = 54/13 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 9.03955 cents Most common intervals : 497.17514 cents & inv., amount: 12 Most common triad is 0.0 497.175 702.825 cents, amount: 10 Number of recognisable fifths : 12, average 702.8249 cents Formal octave complements present : 1 = 7.1429% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 12-13 -- Rational properties --
FIT/MODE
14: 0 2 1 1 1 1 1 1 0 3 0 1 1 1 N SD: 22.7716 c. M: 41.9693 c. 15: 0 3 0 1 1 2 1 1 0 2 1 1 1 1 N SD: 21.2875 c. M:-37.9661 c. 17: 0 3 0 1 2 1 2 1 0 3 0 1 2 1 N SD: 19.7089 c. M: 34.0312 c. 18: 0 3 0 2 1 2 1 2 0 3 0 1 2 1 N SD: 18.3793 c. M: 30.5085 c. 20: 0 3 1 1 2 2 1 2 0 3 1 1 2 1 N SD: 17.1699 c. M:-26.6667 c. 23: 0 4 0 2 2 2 2 1 1 3 1 1 2 2 N SD: 15.7262 c. M: 27.9047 c. 26: 0 4 1 2 2 2 2 2 1 4 0 2 2 2 N SD: 12.5814 c. M: 24.8588 c. 27: 1 4 0 2 2 3 2 2 0 4 1 2 2 2 N SD: 11.2851 c. M:-19.5857 c. 29: 1 4 1 2 2 3 2 2 1 4 1 2 2 2 N SD: 11.8223 c. M:-18.3908 c. 30: 1 4 1 2 2 3 2 3 0 5 0 2 3 2 N SD: 11.5002 c. M: 19.2090 c. 31: 1 4 1 2 3 2 3 2 1 4 1 2 3 2 N SD: 10.8101 c. M: 18.8081 c. 32: 1 4 1 2 3 3 2 3 0 5 1 2 3 2 N SD: 10.8960 c. M: 18.1497 c. 33: 1 5 0 3 2 3 3 2 1 5 1 2 3 2 N SD: 9.7102 c. M:-13.1484 c. 37: 1 5 1 3 3 3 3 3 0 6 1 2 3 3 N SD: 8.6999 c. M: 14.1701 c. 40: 1 6 1 3 3 3 4 2 1 6 1 3 3 3 N SD: 8.6013 c. M:-13.6158 c. 41: 1 6 1 3 3 4 3 3 1 6 1 3 3 3 N SD: 3.3147 c. M:-5.5670 c. 53: 1 8 1 4 4 5 4 4 1 8 1 4 4 4 N SD: 3.1524 c. M: 5.6284 c. 87: 2 13 2 6 7 8 7 6 2 13 2 6 7 6 N SD: 2.6501 c. M:-4.5977 c. 94: 2 14 2 7 7 9 7 7 2 14 2 7 7 7 N SD: 2.0877 c. M: 4.1832 c. 99: 2 15 2 7 8 9 8 7 2 15 2 7 8 7 N SD: 0.7407 c. M: 1.2327 c. 140: 3 21 3 10 11 13 11 10 3 21 3 10 11 10 N SD: 0.6122 c. M:-0.9524 c. 239: 5 36 5 17 19 22 19 17 5 36 5 17 19 17 N SD: 0.3495 c. M:-0.6241 c. 292: 6 44 6 21 23 27 23 21 6 44 6 21 23 21 N SD: 0.2861 c. M: 0.5108 c. 391: 8 59 8 28 31 36 31 28 8 59 8 28 31 28 N SD: 0.2192 c. M: 0.3410 c. 432: 9 65 9 31 34 40 34 31 9 65 9 31 34 31 N SD: 0.1698 c. M: 0.2825 c. 531: 11 80 11 38 42 49 42 38 11 80 11 38 42 38 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x x 4 S SD: 0.4349 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 11.3384 cents 4 x x x x 5 x x 6 x x 7 x x 8 S SD: 10.8535 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 18.5316 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 9.7029 cents 7 x x 8 x 9 x 10 x 11 x 12 x 13:14 S SD: 10.4687 cents 8 x 9 x x 10:11 x 12 x x 14 x 15:16 S SD: 8.3469 cents 9 x 10 x 11 x 12:13 x 14:15 x 16:17:18 S SD: 7.9648 cents 10 x 11 x 12:13 x 14:15 x 17 x 18:19:20 SD: 7.6944 cents 11 x 12 x 13:14:15:16 x 17 x 19:20:21:22 SD: 7.8420 cents 12 x x 14 x 15:16:17:18 x 20:21:22:23:24 S SD: 7.4944 cents 13 x x 15:16 x 18:19 x 20:22 x 23:25:26 SD: 9.3704 cents 14 x x 16:17:18:19:20:21 x x 24:25:27:28 SD: 4.1998 cents 15:16:17 x 18:19:20:21 x 23:25:26:27:29:30 SD: 8.8459 cents 16:17:18 x 19:20:22:23:24 x 27 x 29:30:32 SD: 8.7047 cents 17:18:19 x 20:22:23:24 x 26 x 29:31:32:34 SD: 8.8398 cents 18:19:20:21:22:23:24:26:27 x 30:31:32:34:36 S SD: 7.7048 cents 19:20:21:22:23:24:26:27 x 29:32:33:34:36:38 SD: 6.5289 cents 20:21 x 23:24:25:27:29:30 x 34 x 36:38:40 SD: 6.5069 cents 21:22 x 24:25:27:28:30 x 32:35:36:38:40:42 SD: 5.9488 cents 22:23 x 25:26:28:30:31:33 x 37:38:40:42:44 SD: 5.8055 cents 23:24:26 x 28:29:31:33 x 35:39 x 41:44:46 SD: 5.4970 cents 24:25:27 x 29:30:32:34:36:37 x 41:43:46:48 SD: 5.5119 cents 25:26:28:29:30:32:34:36 x 38:42:43:45:48:50 SD: 4.6092 cents 26:27:29:30:31:33:35:37:39:40:44:45:47:49:52 SD: 4.1470 cents 27:28:30:31:32:34:37:39 x 41 x 46:49:51:54 SD: 5.3467 cents 28:29 x 32:34:36:38:40:42:43:47:48:50:53:56 SD: 4.1996 cents 29:30 x 33:35:37:39:41 x 44:49:50:52:55:58 SD: 3.7344 cents 30:31:34 x 36:38:41:43:45:46:51 x 54:57:60 SD: 3.5389 cents 31:32:35 x 37:39:42:44 x 47:52:53:56:59:62 SD: 3.3462 cents 33:34:37:38:40:42:45:47 x 50:56:57:59:63:66 SD: 3.4545 cents 34:35:38:39:41:43:46:49:51:52:57:58:61:65:68 SD: 2.8933 cents 35:36:39:40:42:44:47:50 x 53:59:60:63:67:70 SD: 2.9623 cents 36:37 x 41:43:46:49:51:54:55:61:62:65:69:72 SD: 2.8766 cents 37:38 x 42:44:47:50:53 x 56 x 63:67:70:74 SD: 3.2928 cents 38:39:43 x 46:48:51:54:57:58:64:65:68:72:76 SD: 2.6995 cents 39:40:44:45:47:49:53:56 x 59:66:67:70:74:78 SD: 2.8257 cents 40:41:45:46:48:51:54:57:60:61:68:69:72:76:80 SD: 2.0170 cents 41:42:46:47:49:52:55:59 x 62:69:70:74:78:82 SD: 2.4679 cents 42:43:47:48:50:53:57:60:63:64:71:72:76:80:84 SD: 1.9734 cents 43:44:48:49:52:55:58:61 x 65:73:74:77:82:86 SD: 2.8597 cents 44:45 x 50:53:56:59:63:66:67:74:75:79:84:88 SD: 2.1936 cents 45:46:51 x 54:57:61:64:68:69:76:77:81:86:90 SD: 2.0842 cents 46:47:52:53:55:58:62:66:69:70:78:79:83:88:92 SD: 2.0005 cents 48:49:54:55:58:61:65:69:72:73:81:82:86:91:96 SD: 1.7658 cents 49:50:55:56:59:62:66:70:74:75:83:84:88:93:98 SD: 1.5823 cents 52:53 x 59:62:66:70:74:78:79:88:89:94:99:104 SD: 1.7280 cents 54:55:61:62:65:68:73:77:81:82:91:93:97:103:108 SD: 1.5595 cents 55:56:62:63:66:70:74:79:83:84:93:94:99:105:110 SD: 1.5242 cents 56:57:63:64:67:71:76:80:84:85:95:96:101:107:112 SD: 1.0997 cents 70:71:79:80:84:89:95:100:105:107:118:120:126:133:140 SD: 0.9013 cents 71:72:80:81:85:90:96:101:107:108:120:122:128:135:142 SD: 0.8761 cents 86:87:97:98:103:109:116:123:129:131:145:147:155:164:172 SD: 0.8694 cents 94:95:106:107:113:119:127:134:141:143:159:161:169:179:188 SD: 0.8305 cents 105:107:118:120:126:133:142:150:158:160:177:180:189:200:210 SD: 0.8068 cents 119:121:134:136:143:151:161:170:179:181:201:204:214:226:238 SD: 0.5794 cents 126:128:142:144:151:160:170:180:189:192:213:216:227:240:252 SD: 0.4531 cents 168:170:189:192:202:213:227:240:252:256:284:288:303:320:336 SD: 0.4508 cents 190:193:214:217:228:241:257:271:285:289:321:326:342:362:380 SD: 0.3438 cents 213:216:240:243:256:270:288:304:320:324:360:365:384:405:426 SD: 0.3432 cents 216:219:243:247:259:274:292:308:324:329:365:370:389:411:432 SD: 0.3421 cents 224:227:252:256:269:284:303:320:336:341:379:384:404:426:448 SD: 0.3043 cents 268:272:302:306:322:340:362:383:402:408:453:459:483:510:536 SD: 0.2618 cents 287:291:323:328:345:364:388:410:431:437:485:492:517:546:574 SD: 0.2241 cents 339:344:382:387:407:430:458:484:509:516:573:581:611:645:678 SD: 0.1848 cents 343:348:386:392:412:435:464:490:515:522:580:588:618:653:686 SD: 0.1821 cents 358:363:403:409:430:454:484:511:537:545:605:614:645:681:716 SD: 0.1547 cents 413:419:465:472:496:524:558:590:620:629:698:708:744:786:826 SD: 0.1407 cents 469:476:528:536:563:595:634:670:704:714:793:804:845:893:938 SD: 0.1337 cents 477:484:537:545:573:605:645:681:716:726:806:818:859:908:954 SD: 0.1330 cents 484:491:545:553:581:614:654:691:726:737:818:830:872:921:968 SD: 0.1152 cents 549:557:618:627:659:696:742:784:824:836:928:941:989:1045:1098 SD: 0.1001 cents