Scala analysis: orwellian13
A distributionally even scale in orwellian temperament, abacbacabcabc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 43.330 cents 43.330000 2: 160.850 cents 160.850000 3: 270.470 cents 270.470000 4: 387.990 cents 387.990000 5: 431.320 cents 431.320000 6: 540.940 cents 540.940000 7: 658.460 cents 658.460000 8: 701.790 cents 701.790000 9: 819.310 cents 819.310000 10: 928.930 cents 928.930000 11: 972.260 cents 972.260000 12: 1089.780 cents 1089.780000 13: 1199.400 cents 1199.400000
SHOW/INTERVAL
0: 109.6200 cents 109.6200 1: 43.3300 cents 43.3300 2: 117.5200 cents 117.5200 3: 109.6200 cents 109.6200 4: 117.5200 cents 117.5200 5: 43.3300 cents 43.3300 6: 109.6200 cents 109.6200 7: 117.5200 cents 117.5200 8: 43.3300 cents 43.3300 9: 117.5200 cents 117.5200 10: 109.6200 cents 109.6200 11: 43.3300 cents 43.3300 12: 117.5200 cents 117.5200 13: 109.6200 cents 109.6200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 43.33000 cents 1: 4 109.62000 cents 1: 5 117.52000 cents 2: 3 152.95000 cents 2: 5 160.85000 cents 2: 5 227.14000 cents 3: 11 270.47000 cents 3: 1 278.37000 cents 3: 1 344.66000 cents 4: 3 313.80000 cents 4: 3 380.09000 cents 4: 7 387.99000 cents 5: 1 423.42000 cents 5: 6 431.32000 cents 5: 6 497.61000 cents 6: 9 540.94000 cents 6: 2 548.84000 cents 6: 2 615.13000 cents 7: 2 584.27000 cents 7: 2 650.56000 cents 7: 9 658.46000 cents 8: 6 701.79000 cents 8: 6 768.08000 cents 8: 1 775.98000 cents 9: 7 811.41000 cents 9: 3 819.31000 cents 9: 3 885.60000 cents 10: 1 854.74000 cents 10: 1 921.03000 cents 10: 11 928.93000 cents 11: 5 972.26000 cents 11: 5 1038.55000 cents 11: 3 1046.45000 cents 12: 5 1081.88000 cents 12: 4 1089.78000 cents 12: 4 1156.07000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 43.3 160.8 270.5 388.0 431.3 540.9 658.5 701.8 819.3 928.9 972.3 1089.8 1199.4 43.3 : 117.5 227.1 344.7 388.0 497.6 615.1 658.5 776.0 885.6 928.9 1046.5 1156.1 1199.4 160.8 : 109.6 227.1 270.5 380.1 497.6 540.9 658.5 768.1 811.4 928.9 1038.6 1081.9 1199.4 270.5 : 117.5 160.8 270.5 388.0 431.3 548.8 658.5 701.8 819.3 928.9 972.3 1089.8 1199.4 388.0 : 43.3 153.0 270.5 313.8 431.3 540.9 584.3 701.8 811.4 854.7 972.3 1081.9 1199.4 431.3 : 109.6 227.1 270.5 388.0 497.6 540.9 658.5 768.1 811.4 928.9 1038.6 1156.1 1199.4 540.9 : 117.5 160.8 278.4 388.0 431.3 548.8 658.5 701.8 819.3 928.9 1046.5 1089.8 1199.4 658.5 : 43.3 160.8 270.5 313.8 431.3 540.9 584.3 701.8 811.4 928.9 972.3 1081.9 1199.4 701.8 : 117.5 227.1 270.5 388.0 497.6 540.9 658.5 768.1 885.6 928.9 1038.6 1156.1 1199.4 819.3 : 109.6 153.0 270.5 380.1 423.4 540.9 650.6 768.1 811.4 921.0 1038.6 1081.9 1199.4 928.9 : 43.3 160.8 270.5 313.8 431.3 540.9 658.5 701.8 811.4 928.9 972.3 1089.8 1199.4 972.3 : 117.5 227.1 270.5 388.0 497.6 615.1 658.5 768.1 885.6 928.9 1046.5 1156.1 1199.4 1089.8: 109.6 153.0 270.5 380.1 497.6 540.9 650.6 768.1 811.4 928.9 1038.6 1081.9 1199.4 1199.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.3300 .. 117.5200 cents 74.19000 cents 43.33000 cents 2: 152.9500 .. 227.1400 cents 74.19000 cents 35.43000 cents 3: 270.4700 .. 344.6600 cents 74.19000 cents 43.33000 cents 4: 313.8000 .. 387.9900 cents 74.19000 cents -30.86000 cents 5: 423.4200 .. 497.6100 cents 74.19000 cents 35.43000 cents 6: 540.9400 .. 615.1300 cents 74.19000 cents 43.33000 cents 7: 584.2700 .. 658.4600 cents 74.19000 cents -30.86000 cents 8: 701.7900 .. 775.9800 cents 74.19000 cents 43.33000 cents 9: 811.4100 .. 885.6000 cents 74.19000 cents 35.43000 cents 10: 854.7400 .. 928.9300 cents 74.19000 cents -30.86000 cents 11: 972.2600 .. 1046.4500 cents 74.19000 cents 43.33000 cents 12: 1081.8800 .. 1156.0700 cents 74.19000 cents 35.43000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 43.33000 cents, class 1 Average step (divided formal octave): 92.2615 cents Largest one step interval : 117.52000 cents Average / Smallest step : 2.129276 Largest / Average step : 1.273770 Largest / Smallest step : 2.712209 Median interval of one step : 109.62000 cents, amount: 4 Most common interval of one step : 117.52000 cents, amount: 5 Least squares average step : 90.82013 cents, oct.: 1180.66175 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACBABCABC Step pattern size order : SLMLSMLSLMSLM Scale is a Constant Structure, by a margin of 30.86000 cents Scale diversity : 1.281613 Lumma stability : 0.334917 Lumma impropriety factor : 0.077189 Number of different interval sizes : 36 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 7.90000 cents Most common intervals : 270.47000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 497.610 928.930 cents Most common triad is 0.0 270.470 928.930 cents, amount: 9 Number of recognisable fifths : 6, average 701.7900 cents Number of recognisable fourths : 6, average 497.6100 cents Formal octave complements present : 5 = 38.4615% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 74.1900 cents: 5 -- Rational properties --
FIT/MODE
13: 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 25.0675 c. M:-48.9315 c. 16: 1 1 2 1 1 1 2 0 2 1 1 2 1 N D3 SD: 21.2233 c. M:-34.6575 c. 18: 1 1 2 2 0 2 2 1 1 2 1 1 2 P D3 S SD: 20.1026 c. M: 31.5200 c. 22: 1 2 2 2 1 2 2 1 2 2 1 2 2 P M ME S SD: 5.3667 c. M:-11.1882 c. 31: 1 3 3 3 1 3 3 1 3 3 1 3 3 N M DE S SD: 4.2581 c. M: 6.8132 c. 53: 2 5 5 5 2 5 5 2 5 5 2 5 5 N M DE S SD: 2.2999 c. M: 4.6232 c. 89: 3 9 8 9 3 8 9 3 9 8 3 9 8 N T3 SD: 1.7918 c. M: 2.9008 c. 111: 4 11 10 11 4 10 11 4 11 10 4 11 10 N T3 SD: 0.9154 c. M:-1.9008 c. 133: 5 13 12 13 5 12 13 5 13 12 5 13 12 N T3 SD: 1.1427 c. M:-1.7602 c. 142: 5 14 13 14 5 13 14 5 14 13 5 14 13 N T3 SD: 0.5322 c. M: 1.0976 c. 164: 6 16 15 16 6 15 16 6 16 15 6 16 15 N T3 SD: 0.2712 c. M:-0.5505 c. 306: 11 30 28 30 11 28 30 11 30 28 11 30 28 N T3 SD: 0.1240 c. M: 0.2143 c. 470: 17 46 43 46 17 43 46 17 46 43 17 46 43 N T3 SD: 0.0713 c. M: 0.1453 c. 776: 28 76 71 76 28 71 76 28 76 71 28 76 71 N T3 SD: 0.0723 c. M: 0.1322 c. 887: 32 87 81 87 32 81 87 32 87 81 32 87 81 N T3 SD: 0.0620 c. M:-0.1222 c. 1051: 38 103 96 103 38 96 103 38 103 96 38 103 96 N T3 SD: 0.0406 c. M:-0.0708 c. 1357: 49 133 124 133 49 124 133 49 133 124 49 133 124 N T3 SD: 0.0163 c. M:-0.0296 c. 1827: 66 179 167 179 66 167 179 66 179 167 66 179 167 N T3 SD: 0.0077 c. M: 0.0154 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.6000 cents 2 x x x x x x x 3 x x x x 4 S SD: 0.3111 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 20.6208 cents 4 x x x 5 x x x 6 x x 7 x 8 S SD: 0.9679 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 15.3050 cents 6 x x 7 x x 8 x 9 x 10 x 11:12 S SD: 12.3305 cents 7 x x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.0381 cents 8 x 9 x 10 x 11 x 12:13 x 14:15:16 S SD: 6.1610 cents 9 x 10 x 11 x 12:13 x 14:15:16:17:18 S SD: 11.1494 cents 10 x 11:12 x 13:14 x 15:16:17:18:19:20 S SD: 8.3439 cents 11 x 12:13 x 14:15:16:17:18:19 x 21:22 SD: 7.5718 cents 12 x 13:14:15 x 16 x 18:19 x 21:23:24 SD: 7.2550 cents 13 x 14:15:16:17:18:19:20:21:22:23:24:26 S SD: 7.1783 cents 14 x 15:16 x 18:19:20:21:22:24:25:26:28 S SD: 8.0273 cents 15 x 16:18:19 x 21:22:23:24 x 26:28:30 SD: 9.2907 cents 16 x 18:19:20:21:22:23:24:26:27:28:30:32 S SD: 6.5410 cents 17:18:19:20:21:22:23:25:26:27:29:30:32:34 SD: 6.4264 cents 18:19:20:21 x 23:25:26:27:29:31:32:34:36 SD: 6.0013 cents 19:20:21:22:24 x 26:28:29:31:32:33:36:38 SD: 6.4010 cents 20:21:22:23:25:26:27:29:30:32:34:35:38:40 SD: 5.0712 cents 22:23:24:26 x 28:30:32:33:35:38:39:41:44 SD: 4.5101 cents 24:25:26:28:30:31:33:35:36:39:41:42:45:48 SD: 3.4414 cents 25:26:27:29:31:32:34:37 x 40:43:44:47:50 SD: 4.1449 cents 26:27:29:30 x 33:36:38:39:42:44:46:49:52 SD: 4.8519 cents 27:28:30:32:34:35:37:39:40:43:46:47:51:54 SD: 4.4351 cents 28:29:31:33:35:36:38:41:42:45:48:49:53:56 SD: 2.6212 cents 30:31:33:35:38 x 41:44:45:48:51:53:56:60 SD: 2.7321 cents 32:33:35:37:40:41:44:47:48:51:55:56:60:64 SD: 2.3160 cents 40:41:44:47:50:51:55:59:60:64:68:70:75:80 SD: 2.0036 cents 41:42:45:48:51:53:56:60:61:66:70:72:77:82 SD: 1.7567 cents 48:49:53:56:60:62:66:70:72:77:82:84:90:96 SD: 1.6877 cents 52:53:57:61:65:67:71:76:78:83:89:91:98:104 SD: 1.4861 cents 60:62:66:70:75:77:82:88:90:96:103:105:113:120 SD: 1.4603 cents 70:72:77:82:88:90:96:102:105:112:120:123:131:140 SD: 1.3437 cents 71:73:78:83:89:91:97:104:106:114:121:124:133:142 SD: 1.0973 cents 82:84:90:96:103:105:112:120:123:132:140:144:154:164 SD: 0.7986 cents 106:109:116:124:133:136:145:155:159:170:181:186:199:212 SD: 0.7148 cents 112:115:123:131:140:144:153:164:168:180:192:196:210:224 SD: 0.6239 cents 114:117:125:133:143:146:156:167:171:183:195:200:214:228 SD: 0.5860 cents 142:146:156:166:178:182:194:208:213:228:243:249:266:284 SD: 0.5825 cents 152:156:167:178:190:195:208:222:228:244:260:267:285:304 SD: 0.4979 cents 155:159:170:181:194:199:212:227:232:249:265:272:291:310 SD: 0.4249 cents 194:199:213:227:243:249:265:284:291:311:332:340:364:388 SD: 0.3315 cents 236:242:259:276:295:303:323:345:354:379:404:414:443:472 SD: 0.3125 cents 238:244:261:278:298:305:325:348:357:382:407:417:447:476 SD: 0.3075 cents 248:254:272:290:310:318:339:363:372:398:424:435:465:496 SD: 0.2772 cents 276:283:303:323:345:354:377:404:414:443:472:484:518:552 SD: 0.2383 cents 318:326:349:372:398:408:435:465:477:510:544:558:597:636 SD: 0.2313 cents 350:359:384:409:438:449:478:512:525:562:599:614:657:700 SD: 0.1933 cents 390:400:428:456:488:500:533:570:585:626:667:684:732:780 SD: 0.1633 cents 438:449:481:512:548:562:599:641:657:703:749:768:822:876 SD: 0.1542 cents 474:486:520:554:593:608:648:693:711:761:811:831:890:948 SD: 0.1481 cents 502:515:551:587:628:644:686:734:753:806:858:880:942:1004 SD: 0.1469 cents 545:559:598:637:682:699:745:797:817:875:932:956:1023:1090 SD: 0.1321 cents 562:576:617:657:703:721:768:822:843:902:961:985:1055:1124 SD: 0.1306 cents 586:601:643:685:733:752:801:857:879:941:1002:1028:1100:1172 SD: 0.1234 cents 597:612:655:698:747:766:816:873:895:958:1021:1047:1120:1194 SD: 0.1175 cents