Scala analysis: xen18-erlich-miracle-08
1L 7s MOS for Miracle, L=383.59, s=116.72
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.720 cents 116.720000 2: 233.440 cents 233.440000 3: 350.160 cents 350.160000 4: 733.750 cents 733.750000 5: 850.470 cents 850.470000 6: 967.190 cents 967.190000 7: 1083.910 cents 1083.910000 8: 1200.630 cents 1200.630000
SHOW/INTERVAL
0: 116.7200 cents 116.7200 1: 116.7200 cents 116.7200 2: 116.7200 cents 116.7200 3: 116.7200 cents 116.7200 4: 383.5900 cents 383.5900 5: 116.7200 cents 116.7200 6: 116.7200 cents 116.7200 7: 116.7200 cents 116.7200 8: 116.7200 cents 116.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 116.72000 cents 1: 1 383.59000 cents 2: 6 233.44000 cents 2: 2 500.31000 cents 3: 5 350.16000 cents 3: 3 617.03000 cents 4: 4 466.88000 cents 4: 4 733.75000 cents 5: 3 583.60000 cents 5: 5 850.47000 cents 6: 2 700.32000 cents 6: 6 967.19000 cents 7: 1 817.04000 cents 7: 7 1083.91000 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 0.0 : 116.7 233.4 350.2 733.7 850.5 967.2 1083.9 1200.6 116.7 : 116.7 233.4 617.0 733.7 850.5 967.2 1083.9 1200.6 233.4 : 116.7 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 350.2 : 383.6 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 733.7 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 1200.6 850.5 : 116.7 233.4 350.2 466.9 583.6 700.3 1083.9 1200.6 967.2 : 116.7 233.4 350.2 466.9 583.6 967.2 1083.9 1200.6 1083.9: 116.7 233.4 350.2 466.9 850.5 967.2 1083.9 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.7200 .. 383.5900 cents 266.87000 cents 116.72000 cents 2: 233.4400 .. 500.3100 cents 266.87000 cents -150.15000 cents 3: 350.1600 .. 617.0300 cents 266.87000 cents -150.15000 cents 4: 466.8800 .. 733.7500 cents 266.87000 cents -150.15000 cents 5: 583.6000 .. 850.4700 cents 266.87000 cents -150.15000 cents 6: 700.3200 .. 967.1900 cents 266.87000 cents -150.15000 cents 7: 817.0400 .. 1083.9100 cents 266.87000 cents -150.15000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 116.72000 cents, class 1 Average step (divided formal octave): 150.0787 cents Largest one step interval : 383.59000 cents Average / Smallest step : 1.285801 Largest / Average step : 2.555925 Largest / Smallest step : 3.286412 Median interval of one step : 116.72000 cents, amount: 7 Most common interval of one step : 116.72000 cents, amount: 7 Least squares average step : 155.96559 cents, oct.: 1247.72471 cents Scale is not proper Scale has Myhill's property chromas: 266.87000 cents and 150.15000 cents, ratio: 1.777356 generators: 1 of 116.72000 cents and 7 of 1083.91000 cents ET pair of linear temperament : 10&31 Scale is distributional even Scale is a mode of a 1831-tone equal temperament with octave 1200.630 cents degrees: 178 356 534 1119 1297 1475 1653 1831 generators: 178 and 1653 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAA Step pattern size order : SSSLSSSS Scale is a Constant Structure, by a margin of 33.43000 cents Scale diversity : 1.215017 Lumma stability : 0.194431 Lumma impropriety factor : 0.611137 Rothenberg efficiency : 0.750000 redundancy: 0.250000 Efficiency x scale size : 6.000000 Number of different interval sizes : 14 = 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 : 33.43000 cents Most common intervals : 116.72000 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 350.160 1083.910 cents Number of recognisable fifths : 2, average 700.3200 cents Number of recognisable fourths : 2, average 500.3100 cents Scale contains two identical disjunct tetrachords Formal octave complements present : 7 = 87.5000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties --
FIT/MODE
8: 0 1 1 2 1 1 1 1 N T3 SD: 84.0068 c. M: 133.4350 c. 9: 0 1 1 3 1 1 1 1 N SD: 69.7573 c. M: 116.7200 c. 10: 1 1 1 3 1 1 1 1 N M DE SD: 7.8400 c. M: 13.3720 c. 21: 2 2 2 7 2 2 2 2 N M DE SD: 5.5682 c. M:-9.4971 c. 31: 3 3 3 10 3 3 3 3 N M DE SD: 1.2430 c. M:-2.1200 c. 41: 4 4 4 13 4 4 4 4 N M DE SD: 0.9724 c. M: 1.6585 c. 72: 7 7 7 23 7 7 7 7 N M DE SD: 0.0186 c. M: 0.0317 c. 1111: 108 108 108 355 108 108 108 108 N M DE SD: 0.0166 c. M:-0.0284 c. 1183: 115 115 115 378 115 115 115 115 N M DE SD: 0.0145 c. M:-0.0247 c. 1255: 122 122 122 401 122 122 122 122 N M DE SD: 0.0126 c. M:-0.0215 c. 1327: 129 129 129 424 129 129 129 129 N M DE SD: 0.0109 c. M:-0.0186 c. 1399: 136 136 136 447 136 136 136 136 N M DE SD: 0.0094 c. M:-0.0160 c. 1471: 143 143 143 470 143 143 143 143 N M DE SD: 0.0080 c. M:-0.0137 c. 1543: 150 150 150 493 150 150 150 150 N M DE SD: 0.0068 c. M:-0.0116 c. 1615: 157 157 157 516 157 157 157 157 N M DE SD: 0.0056 c. M:-0.0096 c. 1687: 164 164 164 539 164 164 164 164 N M DE SD: 0.0046 c. M:-0.0079 c. 1759: 171 171 171 562 171 171 171 171 N M DE SD: 0.0037 c. M:-0.0063 c. 1831: 178 178 178 585 178 178 178 178 N M DE SD: 0.0028 c. M:-0.0048 c. 1903: 185 185 185 608 185 185 185 185 N M DE SD: 0.0020 c. M:-0.0034 c. 1975: 192 192 192 631 192 192 192 192 N M DE SD: 0.0012 c. M:-0.0021 c. 2047: 199 199 199 654 199 199 199 199 N M DE SD: 0.0005 c. M:-0.0009 c. 2119: 206 206 206 677 206 206 206 206 N M DE SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.6300 cents 2 x x x 3 x x x 4 S SD: 15.9006 cents 3 x x 4 x 5 x x 6 S SD: 50.5732 cents 4 x x 5:6 x 7 x 8 S SD: 12.0444 cents 5 x x 6 x 8:9 x 10 S SD: 17.8287 cents 6 x 7 x 9:10 x 11:12 SD: 13.3729 cents 7 x 8:9:11 x 12:13:14 SD: 17.4026 cents 8 x 9:10:12:13:14:15:16 S SD: 8.2201 cents 9 x 10:11:14:15:16:17:18 SD: 10.9370 cents 10:11 x 12:15:16:17:19:20 SD: 13.5443 cents 11:12:13 x 17:18:19:21:22 SD: 11.3980 cents 12:13:14:15:18:20:21:22:24 S SD: 9.8886 cents 13:14:15:16:20:21:23:24:26 SD: 5.4591 cents 23:25:26:28:35:38:40:43:46 SD: 5.2871 cents 25:27:29:31:38:41:44:47:50 SD: 5.0741 cents 26:28:30:32:40:42:45:49:52 SD: 4.7761 cents 27:29:31:33:41:44:47:51:54 SD: 3.0022 cents 28:30:32:34:43:46:49:52:56 SD: 2.8561 cents 40:43:46:49:61:65:70:75:80 SD: 2.0804 cents 44:47:50:54:67:72:77:82:88 SD: 1.9827 cents 55:59:63:67:84:90:96:103:110 SD: 1.3496 cents 68:73:78:83:104:111:119:127:136 SD: 1.2289 cents 76:81:87:93:116:124:133:142:152 SD: 0.9643 cents 84:90:96:103:128:137:147:157:168 SD: 0.9576 cents 85:91:97:104:130:139:149:159:170 SD: 0.8950 cents 98:105:112:120:150:160:171:183:196 SD: 0.8444 cents 112:120:128:137:171:183:196:209:224 SD: 0.7312 cents 131:140:150:160:200:214:229:245:262 SD: 0.5889 cents 159:170:182:195:243:260:278:297:318 SD: 0.5224 cents 174:186:199:213:266:284:304:325:348 SD: 0.5025 cents 186:199:213:228:284:304:325:348:372 SD: 0.3925 cents 214:229:245:262:327:350:374:400:428 SD: 0.2636 cents 271:290:310:332:414:443:474:507:542 SD: 0.2451 cents 326:349:373:399:498:533:570:610:652 SD: 0.2318 cents 347:371:397:425:530:567:607:649:694 SD: 0.2313 cents 375:401:429:459:573:613:656:701:750 SD: 0.2190 cents 388:415:444:475:593:634:678:726:776 SD: 0.1952 cents 402:430:460:492:614:657:703:752:804 SD: 0.1324 cents