Scala analysis: sonic13
A distributionally even scale in sonic temperament, ababababababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.020 cents 96.020000 2: 311.620 cents 311.620000 3: 379.720 cents 379.720000 4: 475.740 cents 475.740000 5: 543.840 cents 543.840000 6: 639.860 cents 639.860000 7: 707.960 cents 707.960000 8: 803.980 cents 803.980000 9: 872.080 cents 872.080000 10: 968.100 cents 968.100000 11: 1036.200 cents 1036.200000 12: 1132.220 cents 1132.220000 13: 1200.320 cents 1200.320000
SHOW/INTERVAL
0: 68.1000 cents 68.1000 1: 96.0200 cents 96.0200 2: 215.6000 cents 215.6000 3: 68.1000 cents 68.1000 4: 96.0200 cents 96.0200 5: 68.1000 cents 68.1000 6: 96.0200 cents 96.0200 7: 68.1000 cents 68.1000 8: 96.0200 cents 96.0200 9: 68.1000 cents 68.1000 10: 96.0200 cents 96.0200 11: 68.1000 cents 68.1000 12: 96.0200 cents 96.0200 13: 68.1000 cents 68.1000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 68.10000 cents 1: 6 96.02000 cents 1: 1 215.60000 cents 2: 11 164.12000 cents 2: 1 283.70000 cents 2: 1 311.62000 cents 3: 5 232.22000 cents 3: 5 260.14000 cents 3: 3 379.72000 cents 4: 9 328.24000 cents 4: 2 447.82000 cents 4: 2 475.74000 cents 5: 4 396.34000 cents 5: 4 424.26000 cents 5: 5 543.84000 cents 6: 7 492.36000 cents 6: 3 611.94000 cents 6: 3 639.86000 cents 7: 3 560.46000 cents 7: 3 588.38000 cents 7: 7 707.96000 cents 8: 5 656.48000 cents 8: 4 776.06000 cents 8: 4 803.98000 cents 9: 2 724.58000 cents 9: 2 752.50000 cents 9: 9 872.08000 cents 10: 3 820.60000 cents 10: 5 940.18000 cents 10: 5 968.10000 cents 11: 1 888.70000 cents 11: 1 916.62000 cents 11: 11 1036.20000 cents 12: 1 984.72000 cents 12: 6 1104.30000 cents 12: 6 1132.22000 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 : 96.0 311.6 379.7 475.7 543.8 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 96.0 : 215.6 283.7 379.7 447.8 543.8 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 311.6 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 656.5 724.6 820.6 888.7 984.7 1200.3 379.7 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 656.5 752.5 820.6 916.6 1132.2 1200.3 475.7 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 656.5 724.6 820.6 1036.2 1104.3 1200.3 543.8 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 656.5 752.5 968.1 1036.2 1132.2 1200.3 639.9 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 656.5 872.1 940.2 1036.2 1104.3 1200.3 708.0 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 804.0 872.1 968.1 1036.2 1132.2 1200.3 804.0 : 68.1 164.1 232.2 328.2 396.3 492.4 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 872.1 : 96.0 164.1 260.1 328.2 424.3 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 968.1 : 68.1 164.1 232.2 328.2 543.8 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 1036.2: 96.0 164.1 260.1 475.7 543.8 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 1132.2: 68.1 164.1 379.7 447.8 543.8 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 1200.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.1000 .. 215.6000 cents 147.50000 cents 68.10000 cents 2: 164.1200 .. 311.6200 cents 147.50000 cents -51.48000 cents 3: 232.2200 .. 379.7200 cents 147.50000 cents -79.40000 cents 4: 328.2400 .. 475.7400 cents 147.50000 cents -51.48000 cents 5: 396.3400 .. 543.8400 cents 147.50000 cents -79.40000 cents 6: 492.3600 .. 639.8600 cents 147.50000 cents -51.48000 cents 7: 560.4600 .. 707.9600 cents 147.50000 cents -79.40000 cents 8: 656.4800 .. 803.9800 cents 147.50000 cents -51.48000 cents 9: 724.5800 .. 872.0800 cents 147.50000 cents -79.40000 cents 10: 820.6000 .. 968.1000 cents 147.50000 cents -51.48000 cents 11: 888.7000 .. 1036.2000 cents 147.50000 cents -79.40000 cents 12: 984.7200 .. 1132.2200 cents 147.50000 cents -51.48000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 68.10000 cents, class 1 Average step (divided formal octave): 92.3323 cents Largest one step interval : 215.60000 cents Average / Smallest step : 1.355834 Largest / Average step : 2.335044 Largest / Smallest step : 3.165932 Median interval of one step : 96.02000 cents, amount: 6 Least squares average step : 97.46767 cents, oct.: 1267.07968 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCACACACACAC Step pattern size order : MLSMSMSMSMSMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 16.62000 cents Scale diversity : 1.315129 Lumma stability : 0.113470 Lumma impropriety factor : 0.588077 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 : 16.62000 cents Most common intervals : 164.12000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 68.100 164.120 cents Most common triad is 0.0 164.120 1036.200 cents, amount: 9 Number of recognisable fifths : 7, average 707.9600 cents Number of recognisable fourths : 7, average 492.3600 cents Formal octave complements present : 1 = 7.6923% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
13: 1 2 1 1 1 1 1 1 0 1 1 1 1 N T3 SD: 24.8658 c. M: 44.7769 c. 15: 1 3 1 1 1 1 1 1 1 1 1 1 1 N M DE S SD: 10.6668 c. M:-20.3867 c. 22: 2 4 1 2 1 2 1 2 1 2 1 2 1 N T3 SD: 10.6396 c. M:-15.7400 c. 30: 2 6 1 3 2 2 2 2 2 2 2 2 2 N SD: 10.5562 c. M: 19.6240 c. 34: 3 6 2 2 2 3 2 3 2 2 2 3 2 N SD: 9.9038 c. M: 16.7941 c. 35: 3 6 2 3 2 3 2 2 2 3 2 3 2 N SD: 8.5745 c. M: 15.1983 c. 36: 3 6 2 3 2 3 2 3 2 3 2 3 2 N T3 SD: 7.1067 c. M: 12.9556 c. 37: 3 7 2 3 2 3 2 3 2 3 2 3 2 N T3 SD: 7.0813 c. M:-12.7908 c. 46: 4 8 3 3 3 4 2 4 2 4 3 3 3 N SD: 7.5581 c. M:-12.4878 c. 47: 4 8 3 4 2 4 3 3 3 4 3 3 3 N SD: 6.9982 c. M: 12.2796 c. 48: 4 8 3 4 3 4 2 4 3 4 2 4 3 N SD: 6.9070 c. M: 11.5400 c. 51: 4 9 3 4 3 4 3 4 3 4 3 4 3 N T3 SD: 3.1894 c. M: 5.6561 c. 66: 5 12 4 5 4 5 4 5 4 5 4 5 4 N T3 SD: 2.9792 c. M: 5.0867 c. 73: 6 13 4 6 4 6 4 6 4 6 4 6 4 N T3 SD: 1.4784 c. M:-2.6364 c. 88: 7 16 5 7 5 7 5 7 5 7 5 7 5 N T3 SD: 1.2505 c. M:-2.2000 c. 124: 10 22 7 10 7 10 7 10 7 10 7 10 7 N T3 SD: 1.1803 c. M: 2.2000 c. 139: 11 25 8 11 8 11 8 11 8 11 8 11 8 N T3 SD: 0.6627 c. M: 1.0306 c. 212: 17 38 12 17 12 17 12 17 12 17 12 17 12 N T3 SD: 0.1889 c. M: 0.3736 c. 439: 35 79 25 35 25 35 25 35 25 35 25 35 25 N T3 SD: 0.1915 c. M:-0.3358 c. 512: 41 92 29 41 29 41 29 41 29 41 29 41 29 N T3 SD: 0.1089 c. M:-0.1819 c. 651: 52 117 37 52 37 52 37 52 37 52 37 52 37 N T3 SD: 0.0785 c. M: 0.1419 c. 724: 58 130 41 58 41 58 41 58 41 58 41 58 41 N T3 SD: 0.0807 c. M:-0.1382 c. 863: 69 155 49 69 49 69 49 69 49 69 49 69 49 N T3 SD: 0.0428 c. M: 0.0653 c. 1375: 110 247 78 110 78 110 78 110 78 110 78 110 78 N T3 SD: 0.0148 c. M:-0.0267 c. 2238: 179 402 127 179 127 179 127 179 127 179 127 179 127 N T3 SD: 0.0095 c. M: 0.0159 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.3200 cents 2 x x x x x x 3 x x x x x 4 S SD: 3.0068 cents 3 x x x 4 x x x x 5 x x x 6 S SD: 8.4878 cents 4 x x 5 x x x 6 x x 7 x x 8 S SD: 2.2384 cents 5 x 6 x x 7 x x 8 x x 9 x 10 S SD: 8.8366 cents 6 x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 8.9135 cents 7 x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 15.3664 cents 8 x x 10 x 11 x 12 x 13:14 x 15:16 S SD: 7.9068 cents 9:10 x 11:12 x 13 x 14:15:16 x 17:18 S SD: 12.3959 cents 10:11:12 x 13:14 x 15:16:17 x 18:19:20 S SD: 9.9097 cents 11:12:13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.2064 cents 12:13:14:15:16 x 17:18:19:20:21:22:23:24 S SD: 6.5507 cents 13:14 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 6.9207 cents 14:15:17 x 18:19:20:21:22:23:24:25:27:28 SD: 6.7111 cents 15:16:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.7652 cents 16:17:19:20:21:22:23:24:25:26:28:29:31:32 SD: 4.0415 cents 18:19 x 22:24:25:26:27:29:30:31:33:35:36 SD: 5.3336 cents 19:20:23:24:25:26:28:29:30:31:33:35:37:38 SD: 5.1357 cents 20:21:24:25:26:27:29:30:32:33:35:36:38:40 SD: 3.6106 cents 24:25:29:30:32:33:35:36:38:40:42:44:46:48 SD: 3.5580 cents 29:31:35:36:38:40:42:44:46:48:51:53:56:58 SD: 2.7117 cents 32:34:38:40:42:44:46:48:51:53:56:58:62:64 SD: 2.1655 cents 40:42:48:50:53:55:58:60:64:66:70:73:77:80 SD: 1.8514 cents 41:43:49:51:54:56:59:62:65:68:72:75:79:82 SD: 1.8362 cents 49:52:59:61:64:67:71:74:78:81:86:89:94:98 SD: 1.5999 cents 51:54:61:64:67:70:74:77:81:84:89:93:98:102 SD: 1.5004 cents 54:57:65:67:71:74:78:81:86:89:94:98:104:108 SD: 1.4090 cents 56:59:67:70:74:77:81:84:89:93:98:102:108:112 SD: 1.2958 cents 66:70:79:82:87:90:96:99:105:109:115:120:127:132 SD: 1.2835 cents 67:71:80:83:88:92:97:101:107:111:117:122:129:134 SD: 1.1630 cents 73:77:87:91:96:100:106:110:116:121:128:133:140:146 SD: 1.0288 cents 76:80:91:95:100:104:110:114:121:126:133:138:146:152 SD: 0.9747 cents 81:86:97:101:107:111:117:122:129:134:142:147:156:162 SD: 0.9740 cents 85:90:102:106:112:116:123:128:135:141:149:155:163:170 SD: 0.9278 cents 89:94:107:111:117:122:129:134:142:147:156:162:171:178 SD: 0.8752 cents 101:107:121:126:133:138:146:152:161:167:177:184:194:202 SD: 0.6686 cents 105:111:126:131:138:144:152:158:167:174:184:191:202:210 SD: 0.5921 cents 127:134:152:158:167:174:184:191:202:210:222:231:244:254 SD: 0.4255 cents 176:186:211:219:232:241:255:265:280:291:308:320:338:352 SD: 0.4146 cents 192:203:230:239:253:263:278:289:305:318:336:349:369:384 SD: 0.3542 cents 208:220:249:259:274:285:301:313:331:344:364:378:400:416 SD: 0.2595 cents 228:241:273:284:300:312:330:343:363:377:399:415:438:456 SD: 0.2508 cents 244:258:292:304:321:334:353:367:388:404:427:444:469:488 SD: 0.2151 cents 315:333:377:392:415:431:456:474:501:521:551:573:606:630 SD: 0.2119 cents 350:370:419:436:461:479:507:527:557:579:612:637:673:700 SD: 0.2025 cents 354:374:424:441:466:485:512:533:563:586:619:644:681:708 SD: 0.1920 cents 366:387:438:456:482:501:530:551:582:606:640:666:704:732 SD: 0.1915 cents 382:404:457:476:503:523:553:575:608:632:668:695:735:764 SD: 0.1913 cents 404:427:484:503:532:553:585:608:643:669:707:735:777:808 SD: 0.1801 cents 420:444:503:523:553:575:608:632:668:695:735:764:808:840 SD: 0.1267 cents 563:595:674:701:741:771:815:847:896:932:985:1024:1083:1126 SD: 0.1251 cents 582:615:697:725:766:797:842:876:926:963:1018:1059:1119:1164 SD: 0.1057 cents