Scala analysis: rainbow
Circulating 1/4-comma meantone
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.049 cents 76.048999 2: 193.157 cents 193.156857 3: 296.578 cents 296.578429 4: 386.314 cents 386.313713 5: 503.422 cents 503.421572 6: 579.471 cents 579.470571 7: 696.578 cents 696.578429 8: 786.314 cents 786.313713 9: 889.735 cents 889.735285 10: 1006.843 cents 1006.843143 11: 1082.892 cents 1082.892142 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 117.1079 cents 117.1079 1: 76.0490 cents 76.0490 2: 117.1079 cents 117.1079 3: 103.4216 cents 103.4216 4: 89.7353 cents 89.7353 5: 117.1079 cents 117.1079 6: 76.0490 cents 76.0490 7: 117.1079 cents 117.1079 8: 89.7353 cents 89.7353 9: 103.4216 cents 103.4216 10: 117.1079 cents 117.1079 11: 76.0490 cents 76.0490 12: 117.1079 cents 117.1079
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 76.04900 cents 1: 2 89.73528 cents 1: 2 103.42157 cents 1: 5 117.10786 cents 2: 8 193.15686 cents 2: 2 206.84314 cents 2: 2 220.52943 cents 3: 1 269.20586 cents 3: 2 282.89214 cents 3: 2 296.57843 cents 3: 7 310.26471 cents 4: 6 386.31371 cents 4: 2 400.00000 cents 4: 2 413.68629 cents 4: 2 427.37257 cents 5: 3 489.73528 cents 5: 9 503.42157 cents 6: 4 579.47057 cents 6: 2 593.15686 cents 6: 2 606.84314 cents 6: 4 620.52943 cents 7: 9 696.57843 cents 7: 3 710.26471 cents 8: 2 772.62743 cents 8: 2 786.31371 cents 8: 2 800.00000 cents 8: 6 813.68629 cents 9: 7 889.73528 cents 9: 2 903.42157 cents 9: 2 917.10786 cents 9: 1 930.79414 cents 10: 2 979.47057 cents 10: 2 993.15686 cents 10: 8 1006.84314 cents 11: 5 1082.89214 cents 11: 2 1096.57843 cents 11: 2 1110.26472 cents 11: 3 1123.95100 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 76.0 193.2 296.6 386.3 503.4 579.5 696.6 786.3 889.7 1006.8 1082.9 1200.0 76.0 : 117.1 220.5 310.3 427.4 503.4 620.5 710.3 813.7 930.8 1006.8 1124.0 1200.0 193.2 : 103.4 193.2 310.3 386.3 503.4 593.2 696.6 813.7 889.7 1006.8 1082.9 1200.0 296.6 : 89.7 206.8 282.9 400.0 489.7 593.2 710.3 786.3 903.4 979.5 1096.6 1200.0 386.3 : 117.1 193.2 310.3 400.0 503.4 620.5 696.6 813.7 889.7 1006.8 1110.3 1200.0 503.4 : 76.0 193.2 282.9 386.3 503.4 579.5 696.6 772.6 889.7 993.2 1082.9 1200.0 579.5 : 117.1 206.8 310.3 427.4 503.4 620.5 696.6 813.7 917.1 1006.8 1124.0 1200.0 696.6 : 89.7 193.2 310.3 386.3 503.4 579.5 696.6 800.0 889.7 1006.8 1082.9 1200.0 786.3 : 103.4 220.5 296.6 413.7 489.7 606.8 710.3 800.0 917.1 993.2 1110.3 1200.0 889.7 : 117.1 193.2 310.3 386.3 503.4 606.8 696.6 813.7 889.7 1006.8 1096.6 1200.0 1006.8: 76.0 193.2 269.2 386.3 489.7 579.5 696.6 772.6 889.7 979.5 1082.9 1200.0 1082.9: 117.1 193.2 310.3 413.7 503.4 620.5 696.6 813.7 903.4 1006.8 1124.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0490 .. 117.1079 cents 41.05886 cents 76.04900 cents 2: 193.1569 .. 220.5294 cents 27.37257 cents 76.04900 cents 3: 269.2059 .. 310.2647 cents 41.05886 cents 48.67643 cents 4: 386.3137 .. 427.3726 cents 41.05886 cents 76.04900 cents 5: 489.7353 .. 503.4216 cents 13.68629 cents 62.36271 cents 6: 579.4706 .. 620.5294 cents 41.05886 cents 76.04900 cents 7: 696.5784 .. 710.2647 cents 13.68628 cents 76.04900 cents 8: 772.6274 .. 813.6863 cents 41.05886 cents 62.36271 cents 9: 889.7353 .. 930.7941 cents 41.05886 cents 76.04900 cents 10: 979.4706 .. 1006.8431 cents 27.37257 cents 48.67643 cents 11: 1082.8921 .. 1123.9510 cents 41.05886 cents 76.04900 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 76.04900 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 117.10786 cents Average / Smallest step : 1.314942 Largest / Average step : 1.171079 Largest / Smallest step : 1.539900 Median interval of one step : 103.42157 cents, amount: 2 Most common interval of one step : 117.10786 cents, amount: 5 Least squares average step : 99.14724 cents, oct.: 1189.76687 cents Scale is strictly proper Scale is a mode of a 789-tone equal temperament with octave 1200.000 cents degrees: 50 127 195 254 331 381 458 517 585 662 712 789 Least number of segments generator : 395 of 600.760 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 760 of 1155.894 cents and inv. generated superset size: 398 = 386 more = 3316.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDBABDCBAB Step pattern size order : ADCBDADBCDAD Scale is a Constant Structure, by a margin of 48.67643 cents Scale diversity : 1.253965 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.692059 Rothenberg efficiency : 0.366162 redundancy: 0.633838 Efficiency x scale size : 4.393939 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 13.68628 cents Most common intervals : 503.42157 cents & inv., amount: 9 Most common triad is 0.0 503.422 696.578 cents, amount: 8 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 5 = 41.6667% Limited transpositions with margin 41.0589 cents: 5 7 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.5717 c. M:-23.9510 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 11.7915 c. M: 28.4190 c. Meantone Chromatic (1/3-comma) 23: 1 3 2 1 3 1 2 2 2 2 2 2 P D3 SD: 14.8753 c. M: 23.8751 c. 27: 2 2 3 2 2 2 3 2 2 3 1 3 SP D3 SD: 12.6259 c. M: 16.2255 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 10.1610 c. M: 20.7698 c. Schismic-12 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 5.1965 c. M:-13.0990 c. Meantone Chromatic (53/220-comma) 38: 2 4 3 3 4 2 4 3 3 4 2 4 SP D3 SD: 7.3864 c. M: 12.8911 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 7.7328 c. M:-11.7559 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 5.0538 c. M:-10.3983 c. Meantone Chromatic (1/5-comma) 50: 3 5 4 4 5 3 5 4 4 5 3 5 SP D3 SD: 3.5874 c. M: 8.5784 c. 58: 4 5 5 5 5 4 6 4 5 6 3 6 SP SD: 5.6237 c. M: 7.0301 c. 60: 4 6 5 4 6 4 6 4 5 6 4 6 SP D3 SD: 5.2244 c. M: 9.7353 c. 61: 4 6 5 5 6 3 6 5 5 6 4 6 SP SD: 5.1407 c. M: 8.9788 c. 62: 4 6 5 5 6 4 6 5 5 6 4 6 SP D3 SD: 2.8436 c. M:-7.2347 c. 69: 4 7 6 5 7 4 7 5 6 7 4 7 SP SD: 3.4033 c. M: 6.4838 c. 81: 5 8 7 6 8 5 8 6 7 8 5 8 SP SD: 1.0366 c. M: 1.9749 c. 93: 6 9 8 7 9 6 9 7 8 9 6 9 SP SD: 0.7193 c. M:-1.3704 c. 174: 11 17 15 13 17 11 17 13 15 17 11 17 SP SD: 0.0981 c. M: 0.1869 c. 441: 28 43 38 33 43 28 43 33 38 43 28 43 SP SD: 0.0743 c. M:-0.1415 c. 615: 39 60 53 46 60 39 60 46 53 60 39 60 SP SD: 0.0255 c. M:-0.0486 c. 789: 50 77 68 59 77 50 77 59 68 77 50 77 SP SD: 0.0018 c. M: 0.0034 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 2.6883 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.5345 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.5989 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.0357 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.6257 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.1990 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.6897 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.5027 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.8213 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.4072 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.6910 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.9974 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.5188 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.7601 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.1587 cents 20:21:22:24:25:27:28:30:32:33:36:37:40 SD: 4.7345 cents 21:22:23:25:26:28:29:31:33:35:38:39:42 SD: 4.6497 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.8732 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.5249 cents 27:28:30:32:34:36:38:40:43:45:48:50:54 SD: 3.4077 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 3.0793 cents 33:34:37:39:41:44:46:49:52:55:59:62:66 SD: 2.7513 cents 36:38:40:43:45:48:50:54:57:60:64:67:72 SD: 2.6419 cents 40:42:45:47:50:54:56:60:63:67:72:75:80 SD: 2.5580 cents 41:43:46:49:51:55:57:61:65:69:73:77:82 SD: 2.4637 cents 42:44:47:50:53:56:59:63:66:70:75:79:84 SD: 2.0880 cents 43:45:48:51:54:58:60:64:68:72:77:80:86 SD: 1.8525 cents 48:50:54:57:60:64:67:72:76:80:86:90:96 SD: 1.5776 cents 60:63:67:71:75:80:84:90:94:100:107:112:120 SD: 1.4774 cents 65:68:73:77:81:87:91:97:102:109:116:121:130 SD: 1.3468 cents 68:71:76:81:85:91:95:102:107:114:122:127:136 SD: 0.9310 cents 85:89:95:101:106:114:119:127:134:142:152:159:170 SD: 0.7195 cents 113:118:126:134:141:151:158:169:178:189:202:211:226 SD: 0.5453 cents 151:158:169:179:189:202:211:226:238:252:270:282:302 SD: 0.4967 cents 160:167:179:190:200:214:224:239:252:267:286:299:320 SD: 0.4616 cents 176:184:197:209:220:235:246:263:277:294:315:329:352 SD: 0.3712 cents 204:213:228:242:255:273:285:305:321:341:365:381:408 SD: 0.2460 cents 289:302:323:343:361:387:404:432:455:483:517:540:578 SD: 0.2338 cents 332:347:371:394:415:444:464:496:523:555:594:621:664 SD: 0.1919 cents 380:397:425:451:475:508:531:568:598:635:680:710:760 SD: 0.1865 cents 397:415:444:471:496:531:555:594:625:664:710:742:794 SD: 0.1768 cents 400:418:447:475:500:535:559:598:630:669:716:748:800 SD: 0.1668 cents 465:486:520:552:581:622:650:695:732:777:832:869:930 SD: 0.1579 cents 491:513:549:583:614:657:686:734:773:821:878:918:982 SD: 0.1507 cents 492:514:550:584:615:658:688:736:775:823:880:920:984 SD: 0.1500 cents 515:538:576:611:644:689:720:770:811:861:921:963:1030 SD: 0.1413 cents 536:560:599:636:670:717:749:802:844:896:959:1002:1072 SD: 0.1274 cents 551:576:616:654:689:737:770:824:868:921:986:1030:1102 SD: 0.1107 cents