Scala analysis: 13-53a
53-tET Orwell[13]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45.283 cents 45.283019 2: 158.491 cents 158.490566 3: 271.698 cents 271.698113 4: 316.981 cents 316.981132 5: 430.189 cents 430.188679 6: 543.396 cents 543.396226 7: 588.679 cents 588.679245 8: 701.887 cents 701.886792 9: 815.094 cents 815.094340 10: 860.377 cents 860.377358 11: 973.585 cents 973.584906 12: 1086.792 cents 1086.792453 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 113.2075 cents 113.2075 1: 45.2830 cents 45.2830 2: 113.2075 cents 113.2075 3: 113.2075 cents 113.2075 4: 45.2830 cents 45.2830 5: 113.2075 cents 113.2075 6: 113.2075 cents 113.2075 7: 45.2830 cents 45.2830 8: 113.2075 cents 113.2075 9: 113.2075 cents 113.2075 10: 45.2830 cents 45.2830 11: 113.2075 cents 113.2075 12: 113.2075 cents 113.2075 13: 113.2075 cents 113.2075
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 45.28302 cents 1: 9 113.20755 cents 2: 8 158.49057 cents 2: 5 226.41509 cents 3: 12 271.69811 cents 3: 1 339.62264 cents 4: 3 316.98113 cents 4: 10 384.90566 cents 5: 7 430.18868 cents 5: 6 498.11321 cents 6: 11 543.39623 cents 6: 2 611.32075 cents 7: 2 588.67925 cents 7: 11 656.60377 cents 8: 6 701.88679 cents 8: 7 769.81132 cents 9: 10 815.09434 cents 9: 3 883.01887 cents 10: 1 860.37736 cents 10: 12 928.30189 cents 11: 5 973.58491 cents 11: 8 1041.50943 cents 12: 9 1086.79245 cents 12: 4 1154.71698 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 0.0 : 45.3 158.5 271.7 317.0 430.2 543.4 588.7 701.9 815.1 860.4 973.6 1086.8 1200.0 45.3 : 113.2 226.4 271.7 384.9 498.1 543.4 656.6 769.8 815.1 928.3 1041.5 1154.7 1200.0 158.5 : 113.2 158.5 271.7 384.9 430.2 543.4 656.6 701.9 815.1 928.3 1041.5 1086.8 1200.0 271.7 : 45.3 158.5 271.7 317.0 430.2 543.4 588.7 701.9 815.1 928.3 973.6 1086.8 1200.0 317.0 : 113.2 226.4 271.7 384.9 498.1 543.4 656.6 769.8 883.0 928.3 1041.5 1154.7 1200.0 430.2 : 113.2 158.5 271.7 384.9 430.2 543.4 656.6 769.8 815.1 928.3 1041.5 1086.8 1200.0 543.4 : 45.3 158.5 271.7 317.0 430.2 543.4 656.6 701.9 815.1 928.3 973.6 1086.8 1200.0 588.7 : 113.2 226.4 271.7 384.9 498.1 611.3 656.6 769.8 883.0 928.3 1041.5 1154.7 1200.0 701.9 : 113.2 158.5 271.7 384.9 498.1 543.4 656.6 769.8 815.1 928.3 1041.5 1086.8 1200.0 815.1 : 45.3 158.5 271.7 384.9 430.2 543.4 656.6 701.9 815.1 928.3 973.6 1086.8 1200.0 860.4 : 113.2 226.4 339.6 384.9 498.1 611.3 656.6 769.8 883.0 928.3 1041.5 1154.7 1200.0 973.6 : 113.2 226.4 271.7 384.9 498.1 543.4 656.6 769.8 815.1 928.3 1041.5 1086.8 1200.0 1086.8: 113.2 158.5 271.7 384.9 430.2 543.4 656.6 701.9 815.1 928.3 973.6 1086.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.2830 .. 113.2075 cents 67.92453 cents 45.28302 cents 2: 158.4906 .. 226.4151 cents 67.92453 cents 45.28302 cents 3: 271.6981 .. 339.6226 cents 67.92453 cents 45.28302 cents 4: 316.9811 .. 384.9057 cents 67.92453 cents -22.64151 cents 5: 430.1887 .. 498.1132 cents 67.92453 cents 45.28302 cents 6: 543.3962 .. 611.3208 cents 67.92453 cents 45.28302 cents 7: 588.6792 .. 656.6038 cents 67.92453 cents -22.64151 cents 8: 701.8868 .. 769.8113 cents 67.92453 cents 45.28302 cents 9: 815.0943 .. 883.0189 cents 67.92453 cents 45.28302 cents 10: 860.3774 .. 928.3019 cents 67.92453 cents -22.64151 cents 11: 973.5849 .. 1041.5094 cents 67.92453 cents 45.28302 cents 12: 1086.7925 .. 1154.7170 cents 67.92453 cents 45.28302 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 45.28302 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 113.20755 cents Average / Smallest step : 2.038462 Largest / Average step : 1.226415 Largest / Smallest step : 2.500000 Median interval of one step : 113.20755 cents, amount: 9 Most common interval of one step : 113.20755 cents, amount: 9 Least squares average step : 88.99026 cents, oct.: 1156.87332 cents Scale is not proper Scale has Myhill's property chromas: 67.92453 cents and 22.64151 cents, ratio: 3.000000 generators: 3 of 271.69811 cents and 928.30189 cents ET pair of linear temperament : 22&31 Scale is distributional even Scale is a mode of a 53-tone equal temperament with octave 2/1 degrees: 2 7 12 14 19 24 26 31 36 38 43 48 53 generators: 12 and 41 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABBABBB Step pattern size order : SLLSLLSLLSLLL Interval vector is [ 0 4 0 0 9 0 8 0 0 5 0 12 0 3 1 0 10 0 7 0 0 6 0 11 0 2 ] Scale is a Constant Structure, by a margin of 22.64151 cents Scale diversity : 1.226064 Lumma stability : 0.377358 Lumma impropriety factor : 0.056604 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 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 : 22.64151 cents Most common intervals : 271.69811 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 430.189 928.302 cents Most common triad is 0.0 271.698 928.302 cents, amount: 11 Number of recognisable fifths : 6, average 701.8868 cents Scale contains two identical conjunct heptachords Formal octave complements present : 1 = 7.6923% Limited inverse transpositions : 10 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
13: 0 1 1 1 1 1 1 1 1 1 1 1 2 N T3 SD: 58.6739 c. M: 87.0827 c. 14: 1 1 1 1 1 1 1 1 2 0 1 2 1 N D3 SD: 23.8616 c. M:-42.0485 c. 15: 1 1 1 1 1 2 0 2 1 1 1 2 1 N D3 SD: 22.2905 c. M:-34.7170 c. 17: 1 1 2 0 2 2 0 2 2 0 2 1 2 N T3 SD: 20.6396 c. M: 34.6282 c. 21: 1 2 2 1 2 2 0 2 2 1 2 2 2 N T3 SD: 16.3840 c. M:-28.0323 c. 22: 1 2 2 1 2 2 1 2 2 1 2 2 2 P M ME S SD: 7.2773 c. M:-12.3499 c. Orwell-13 31: 1 3 3 1 3 3 1 3 3 1 3 3 3 N M DE S SD: 5.1645 c. M: 8.7645 c. Orwell-13 53: 2 5 5 2 5 5 2 5 5 2 5 5 5 N M DE S SD: 0.0000 c. M:-0.0000 c. Orwell-13
FIT/HARMONIC
1 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 4 S SD: 0.0341 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 17.1005 cents 4 x x x x 5 x x 6 x x 7 x 8 S SD: 11.0331 cents 5 x x x 6 x x 7 x 8 x 9 x 10 S SD: 8.8968 cents 6 x x 7 x x 8 x 9 x 10 x 11:12 S SD: 10.6146 cents 7 x x 8 x 9 x 10 x 11 x 12:13:14 S SD: 10.5205 cents 8 x 9 x x 10:11 x 12 x 13:14:15:16 S SD: 8.3568 cents 9 x 10 x 11 x 12:13 x 14:15:16:17:18 S SD: 10.9178 cents 10 x 11 x 12:13 x 14:15:16 x 18:19:20 S SD: 6.2796 cents 11 x 12:13 x 14:15 x 17 x 18:19:21:22 SD: 7.9559 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:24 S SD: 7.5991 cents 13 x 14:15:16:17:18 x 20:21 x 23:24:26 SD: 8.8677 cents 14 x 15:16:17:18:19:20:21:22:23:25:26:28 SD: 6.8761 cents 15 x 16 x 18:19 x 21:23:24:25:26:28:30 SD: 7.2033 cents 16 x 18 x 19:21:22 x 24 x 26:28:30:32 SD: 7.5123 cents 17:18:19:20 x 22:23:24:26:27:28:30:32:34 S SD: 6.6559 cents 18:19:20:21:22:23 x 25:27:29:30:32:34:36 SD: 6.2831 cents 19:20:21:22:23:24:26:27:29:30:31:33:36:38 SD: 5.9796 cents 20:21:22:23:24:26:27:28:30:32:33:35:37:40 SD: 4.9788 cents 21:22:23 x 25:27:29:30:32:34:35:37:39:42 SD: 5.6067 cents 22:23:24:26 x 28:30:31:33:35:36:39:41:44 SD: 3.8890 cents 24:25:26:28:29:31:33:34:36:38:39:42:45:48 SD: 3.7782 cents 25:26:27:29:30:32:34:35:38:40:41:44:47:50 SD: 3.5640 cents 27:28:30:32 x 35:37:38:41:43:44:47:51:54 SD: 4.5098 cents 28:29:31:33:34:36:38:39:42:45:46:49:52:56 SD: 3.2991 cents 29:30:32:34:35:37:40:41:44:46:48:51:54:58 SD: 3.1776 cents 30:31:33:35:36:38:41:42:45:48:49:53:56:60 SD: 2.4085 cents 40:41:44:47:48:51:55:56:60:64:66:70:75:80 SD: 1.4791 cents 60:62:66:70:72:77:82:84:90:96:99:105:112:120 SD: 1.4471 cents 64:66:70:75:77:82:88:90:96:102:105:112:120:128 SD: 1.2460 cents 70:72:77:82:84:90:96:98:105:112:115:123:131:140 SD: 0.9309 cents 104:107:114:122:125:133:142:146:156:167:171:183:195:208 SD: 0.8657 cents 106:109:116:124:127:136:145:149:159:170:174:186:199:212 SD: 0.6002 cents 146:150:160:171:175:187:200:205:219:234:240:256:274:292 SD: 0.4671 cents 160:164:175:187:192:205:219:225:240:256:263:281:300:320 SD: 0.4371 cents 188:193:206:220:226:241:257:264:282:301:309:330:352:376 SD: 0.2438 cents 294:302:322:344:353:377:402:413:441:471:483:516:551:588 SD: 0.2158 cents 334:343:366:391:401:428:457:469:501:535:549:586:626:668 SD: 0.1733 cents 418:429:458:489:502:536:572:587:627:669:687:734:783:836 SD: 0.1403 cents 482:495:528:564:579:618:660:677:723:772:792:846:903:964 SD: 0.1304 cents 564:579:618:660:677:723:772:792:846:903:927:990:1057:1128 SD: 0.1238 cents