Scala analysis: xen18-erlich-miracle-11
10L 1s MOS for Miracle, L=116.72, s=33.43
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: 466.880 cents 466.880000 5: 583.600 cents 583.600000 6: 617.030 cents 617.030000 7: 733.750 cents 733.750000 8: 850.470 cents 850.470000 9: 967.190 cents 967.190000 10: 1083.910 cents 1083.910000 11: 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: 116.7200 cents 116.7200 5: 116.7200 cents 116.7200 6: 33.4300 cents 33.4300 7: 116.7200 cents 116.7200 8: 116.7200 cents 116.7200 9: 116.7200 cents 116.7200 10: 116.7200 cents 116.7200 11: 116.7200 cents 116.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.43000 cents 1: 10 116.72000 cents 2: 2 150.15000 cents 2: 9 233.44000 cents 3: 3 266.87000 cents 3: 8 350.16000 cents 4: 4 383.59000 cents 4: 7 466.88000 cents 5: 5 500.31000 cents 5: 6 583.60000 cents 6: 6 617.03000 cents 6: 5 700.32000 cents 7: 7 733.75000 cents 7: 4 817.04000 cents 8: 8 850.47000 cents 8: 3 933.76000 cents 9: 9 967.19000 cents 9: 2 1050.48000 cents 10: 10 1083.91000 cents 10: 1 1167.20000 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 0.0 : 116.7 233.4 350.2 466.9 583.6 617.0 733.7 850.5 967.2 1083.9 1200.6 116.7 : 116.7 233.4 350.2 466.9 500.3 617.0 733.7 850.5 967.2 1083.9 1200.6 233.4 : 116.7 233.4 350.2 383.6 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 350.2 : 116.7 233.4 266.9 383.6 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 466.9 : 116.7 150.1 266.9 383.6 500.3 617.0 733.7 850.5 967.2 1083.9 1200.6 583.6 : 33.4 150.1 266.9 383.6 500.3 617.0 733.7 850.5 967.2 1083.9 1200.6 617.0 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 933.8 1050.5 1167.2 1200.6 733.7 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 933.8 1050.5 1083.9 1200.6 850.5 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 933.8 967.2 1083.9 1200.6 967.2 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 850.5 967.2 1083.9 1200.6 1083.9: 116.7 233.4 350.2 466.9 583.6 700.3 733.7 850.5 967.2 1083.9 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.4300 .. 116.7200 cents 83.29000 cents 33.43000 cents 2: 150.1500 .. 233.4400 cents 83.29000 cents 33.43000 cents 3: 266.8700 .. 350.1600 cents 83.29000 cents 33.43000 cents 4: 383.5900 .. 466.8800 cents 83.29000 cents 33.43000 cents 5: 500.3100 .. 583.6000 cents 83.29000 cents 33.43000 cents 6: 617.0300 .. 700.3200 cents 83.29000 cents 33.43000 cents 7: 733.7500 .. 817.0400 cents 83.29000 cents 33.43000 cents 8: 850.4700 .. 933.7600 cents 83.29000 cents 33.43000 cents 9: 967.1900 .. 1050.4800 cents 83.29000 cents 33.43000 cents 10: 1083.9100 .. 1167.2000 cents 83.29000 cents 33.43000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 33.43000 cents, class 1 Average step (divided formal octave): 109.1482 cents Largest one step interval : 116.72000 cents Average / Smallest step : 3.264977 Largest / Average step : 1.069372 Largest / Smallest step : 3.491475 Median interval of one step : 116.72000 cents, amount: 10 Most common interval of one step : 116.72000 cents, amount: 10 Least squares average step : 108.32516 cents, oct.: 1191.57674 cents Scale is strictly proper Scale has Myhill's property chromas: 83.29000 cents and 49.86000 cents, ratio: 1.670477 generators: 1 of 116.72000 cents and 10 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: 178 356 534 712 890 941 1119 1297 1475 1653 1831 generators: 178 and 1653 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAABAAAAA Step pattern size order : LLLLLSLLLLL Scale is a Constant Structure, by a margin of 33.43000 cents Scale diversity : 1.197007 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.306281 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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: 10 Scale is a chain of 5 triads 0.0 583.600 1083.910 cents Most common triad is 0.0 116.720 1083.910 cents, amount: 9 Number of recognisable fifths : 5, average 700.3200 cents Number of recognisable fourths : 5, average 500.3100 cents Scale contains two identical disjunct pentachords Best minor thirds form a closed circle Formal octave complements present : 11 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 23.9442 c. M: 37.8591 c. 15: 1 2 1 2 1 1 1 2 1 2 1 P D3 I SD: 23.3996 c. M: 36.6780 c. 16: 2 1 2 1 2 0 2 1 2 1 2 N T3 I SD: 20.7378 c. M: 33.3588 c. 17: 2 1 2 2 1 1 1 2 2 1 2 N D3 I SD: 19.8976 c. M: 27.4971 c. 18: 2 1 2 2 2 0 2 2 1 2 2 N T3 SD: 18.8163 c. M: 33.3667 c. 20: 2 2 2 2 2 0 2 2 2 2 2 P M DE I SD: 10.5715 c. M: 16.7150 c. 21: 2 2 2 2 2 1 2 2 2 2 2 SP M ME I SD: 7.5082 c. M: 11.8714 c. 31: 3 3 3 3 3 1 3 3 3 3 3 SP M DE I SD: 1.6760 c. M: 2.6500 c. 41: 4 4 4 4 4 1 4 4 4 4 4 SP M DE I SD: 1.3112 c. M: 2.0732 c. 72: 7 7 7 7 7 2 7 7 7 7 7 SP M DE I SD: 0.0250 c. M: 0.0396 c. 1111: 108 108 108 108 108 31 108 108 108 108 108 SP M DE I SD: 0.0224 c. M: 0.0355 c. 1183: 115 115 115 115 115 33 115 115 115 115 115 SP M DE I SD: 0.0195 c. M: 0.0309 c. 1255: 122 122 122 122 122 35 122 122 122 122 122 SP M DE I SD: 0.0170 c. M: 0.0269 c. 1327: 129 129 129 129 129 37 129 129 129 129 129 SP M DE I SD: 0.0147 c. M: 0.0232 c. 1399: 136 136 136 136 136 39 136 136 136 136 136 SP M DE I SD: 0.0127 c. M: 0.0200 c. 1471: 143 143 143 143 143 41 143 143 143 143 143 SP M DE I SD: 0.0108 c. M: 0.0171 c. 1543: 150 150 150 150 150 43 150 150 150 150 150 SP M DE I SD: 0.0091 c. M: 0.0145 c. 1615: 157 157 157 157 157 45 157 157 157 157 157 SP M DE I SD: 0.0076 c. M: 0.0120 c. 1687: 164 164 164 164 164 47 164 164 164 164 164 SP M DE I SD: 0.0062 c. M:-0.0098 c. 1759: 171 171 171 171 171 49 171 171 171 171 171 SP M DE I SD: 0.0049 c. M: 0.0078 c. 1831: 178 178 178 178 178 51 178 178 178 178 178 SP M DE I SD: 0.0038 c. M: 0.0060 c. 1903: 185 185 185 185 185 53 185 185 185 185 185 SP M DE I SD: 0.0027 c. M: 0.0042 c. 1975: 192 192 192 192 192 55 192 192 192 192 192 SP M DE I SD: 0.0017 c. M:-0.0026 c. 2047: 199 199 199 199 199 57 199 199 199 199 199 SP M DE I SD: 0.0007 c. M: 0.0011 c. 2119: 206 206 206 206 206 59 206 206 206 206 206 SP M DE I SD: 0.0001 c. M:-0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.6300 cents 2 x x x x x x 3 x x x 4 S SD: 15.9006 cents 3 x x x 4 x x x 5 x x 6 S SD: 15.3482 cents 4 x x 5 x x x 6 x 7 x 8 S SD: 12.0444 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 14.2646 cents 6 x 7 x 8 x x 9:10 x 11:12 S SD: 12.2951 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 9.7956 cents 8 x 9:10 x 11 x 12:13:14:15:16 S SD: 8.2472 cents 9 x 10:11:12 x 13:14:15:16:17:18 S SD: 9.4387 cents 10:11 x 12:13:14 x 15:16:17:19:20 SD: 10.6287 cents 11:12:13 x 14:15:16:17:18:19:21:22 SD: 10.9460 cents 12:13:14:15:16 x 17:18:20:21:22:24 S SD: 8.6176 cents 13:14:15:16:17:18:19:20:21:23:24:26 SD: 5.6907 cents 14:15:16:17:18 x 20:21:23:24:26:28 SD: 6.0181 cents 15:16:17:18:20:21 x 23:25:26:28:30 SD: 6.2383 cents 16:17:18:20:21:22:23:24:26:28:30:32 S SD: 6.1879 cents 17:18:19:21:22:24 x 26:28:30:32:34 SD: 5.8311 cents 19:20:22:23:25 x 27:29:31:33:36:38 SD: 4.8599 cents 22:24:25:27:29:31 x 34:36:38:41:44 SD: 4.9273 cents 23:25:26:28:30:32:33:35:38:40:43:46 SD: 4.1070 cents 24:26:27:29:31 x 34:37:39:42:45:48 SD: 5.4647 cents 25:27:29:31:33:35:36:38:41:44:47:50 SD: 4.1076 cents 26:28:30:32:34:36:37:40:42:45:49:52 SD: 3.9765 cents 27:29:31:33:35:38:39:41:44:47:51:54 SD: 3.3219 cents 28:30:32:34:37:39:40:43:46:49:52:56 SD: 2.6748 cents 29:31:33:36:38:41 x 44:47:51:54:58 SD: 3.8097 cents 30:32:34:37:39:42:43:46:49:52:56:60 SD: 2.7984 cents 32:34:37:39:42:45:46:49:52:56:60:64 SD: 2.6341 cents 40:43:46:49:52:56:57:61:65:70:75:80 SD: 1.9362 cents 49:52:56:60:64:69:70:75:80:86:92:98 SD: 1.8222 cents 54:58:62:66:71:76:77:83:88:94:101:108 SD: 1.8213 cents 55:59:63:67:72:77:79:84:90:96:103:110 SD: 1.3350 cents 68:73:78:83:89:95:97:104:111:119:127:136 SD: 1.0135 cents 84:90:96:103:110:118:120:128:137:147:157:168 SD: 0.8225 cents 98:105:112:120:128:137:140:150:160:171:183:196 SD: 0.8103 cents 103:110:118:126:135:144:147:157:168:180:193:206 SD: 0.7562 cents 110:118:126:135:144:154:157:168:180:192:206:220 SD: 0.7420 cents 112:120:128:137:147:157:160:171:183:196:209:224 SD: 0.6486 cents 117:125:134:143:153:164:167:179:191:205:219:234 SD: 0.6346 cents 140:150:160:171:183:196:200:214:229:245:262:280 SD: 0.6172 cents 152:163:174:186:199:213:217:232:248:266:284:304 SD: 0.5554 cents 159:170:182:195:208:223:227:243:260:278:297:318 SD: 0.4566 cents 175:187:200:214:229:245:250:267:286:306:327:350 SD: 0.4436 cents 187:200:214:229:245:262:267:286:306:327:350:374 SD: 0.3066 cents 255:273:292:312:334:357:364:390:417:446:477:510 SD: 0.3052 cents 262:280:300:321:343:367:374:400:428:458:490:524 SD: 0.2830 cents 271:290:310:332:355:380:387:414:443:474:507:542 SD: 0.2387 cents 317:339:363:388:415:444:453:484:518:554:593:634 SD: 0.2120 cents 339:363:388:415:444:475:484:518:554:593:634:678 SD: 0.1992 cents 362:387:414:443:474:507:517:553:592:633:677:724 SD: 0.1941 cents 401:429:459:491:525:562:573:613:655:701:750:802 SD: 0.1891 cents 402:430:460:492:526:563:574:614:657:703:752:804 SD: 0.1720 cents 472:505:540:578:618:661:674:721:771:825:883:944 SD: 0.1535 cents 504:539:577:617:660:706:720:770:824:881:943:1008 SD: 0.1391 cents 561:600:642:687:735:786:801:857:917:981:1049:1122 SD: 0.1341 cents 588:629:673:720:770:824:840:898:961:1028:1100:1176 SD: 0.1253 cents