Scala analysis: xen18-erlich-miracle-07
1L 6s MOS for Miracle, L=500.31, 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: 850.470 cents 850.470000 5: 967.190 cents 967.190000 6: 1083.910 cents 1083.910000 7: 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: 500.3100 cents 500.3100 5: 116.7200 cents 116.7200 6: 116.7200 cents 116.7200 7: 116.7200 cents 116.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 116.72000 cents 1: 1 500.31000 cents 2: 5 233.44000 cents 2: 2 617.03000 cents 3: 4 350.16000 cents 3: 3 733.75000 cents 4: 3 466.88000 cents 4: 4 850.47000 cents 5: 2 583.60000 cents 5: 5 967.19000 cents 6: 1 700.32000 cents 6: 6 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 0.0 : 116.7 233.4 350.2 850.5 967.2 1083.9 1200.6 116.7 : 116.7 233.4 733.7 850.5 967.2 1083.9 1200.6 233.4 : 116.7 617.0 733.8 850.5 967.2 1083.9 1200.6 350.2 : 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 850.5 : 116.7 233.4 350.2 466.9 583.6 700.3 1200.6 967.2 : 116.7 233.4 350.2 466.9 583.6 1083.9 1200.6 1083.9: 116.7 233.4 350.2 466.9 967.2 1083.9 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.7200 .. 500.3100 cents 383.59000 cents 116.72000 cents 2: 233.4400 .. 617.0300 cents 383.59000 cents -266.87000 cents 3: 350.1600 .. 733.7500 cents 383.59000 cents -266.87000 cents 4: 466.8800 .. 850.4700 cents 383.59000 cents -266.87000 cents 5: 583.6000 .. 967.1900 cents 383.59000 cents -266.87000 cents 6: 700.3200 .. 1083.9100 cents 383.59000 cents -266.87000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 116.72000 cents, class 1 Average step (divided formal octave): 171.5186 cents Largest one step interval : 500.31000 cents Average / Smallest step : 1.469487 Largest / Average step : 2.916944 Largest / Smallest step : 4.286412 Median interval of one step : 116.72000 cents, amount: 6 Most common interval of one step : 116.72000 cents, amount: 6 Least squares average step : 176.99843 cents, oct.: 1238.98900 cents Scale is not proper Scale has Myhill's property chromas: 383.59000 cents and 266.87000 cents, ratio: 1.437367 generators: 1 of 116.72000 cents and 6 of 1083.91000 cents ET pair of linear temperament : 10&31 Scale is distributional even Scale is a mode of a 1687-tone equal temperament with octave 1200.630 cents degrees: 164 328 492 1195 1359 1523 1687 generators: 164 and 1523 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAA Step pattern size order : SSSLSSS Scale is a Constant Structure, by a margin of 33.43000 cents Scale diversity : 1.250977 Lumma stability : 0.194431 Lumma impropriety factor : 0.611137 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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: 6 Scale is a chain of 3 triads 0.0 350.160 1083.910 cents Number of recognisable fifths : 1, average 700.3200 cents Number of recognisable fourths : 1, average 500.3100 cents Scale contains two identical disjunct tetrachords Formal octave complements present : 7 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 0 1 3 1 0 1 N T3 I SD: 44.3618 c. M:-61.9214 c. 9: 1 1 1 3 1 1 1 N M DE I SD: 33.3667 c. M: 50.0500 c. 10: 1 1 1 4 1 1 1 N M DE I SD: 6.6860 c. M: 10.0290 c. 21: 2 2 2 9 2 2 2 N M DE I SD: 4.7486 c. M: 7.1229 c. 31: 3 3 3 13 3 3 3 N M DE I SD: 1.0600 c. M: 1.5900 c. 41: 4 4 4 17 4 4 4 N M DE I SD: 0.8293 c. M: 1.2439 c. 72: 7 7 7 30 7 7 7 N M DE I SD: 0.0158 c. M: 0.0238 c. 1111: 108 108 108 463 108 108 108 N M DE I SD: 0.0142 c. M: 0.0213 c. 1183: 115 115 115 493 115 115 115 N M DE I SD: 0.0124 c. M: 0.0185 c. 1255: 122 122 122 523 122 122 122 N M DE I SD: 0.0107 c. M: 0.0161 c. 1327: 129 129 129 553 129 129 129 N M DE I SD: 0.0093 c. M: 0.0139 c. 1399: 136 136 136 583 136 136 136 N M DE I SD: 0.0080 c. M: 0.0120 c. 1471: 143 143 143 613 143 143 143 N M DE I SD: 0.0068 c. M: 0.0103 c. 1543: 150 150 150 643 150 150 150 N M DE I SD: 0.0058 c. M: 0.0087 c. 1615: 157 157 157 673 157 157 157 N M DE I SD: 0.0048 c. M: 0.0072 c. 1687: 164 164 164 703 164 164 164 N M DE I SD: 0.0039 c. M: 0.0059 c. 1759: 171 171 171 733 171 171 171 N M DE I SD: 0.0031 c. M: 0.0047 c. 1831: 178 178 178 763 178 178 178 N M DE I SD: 0.0024 c. M: 0.0036 c. 1903: 185 185 185 793 185 185 185 N M DE I SD: 0.0017 c. M: 0.0025 c. 1975: 192 192 192 823 192 192 192 N M DE I SD: 0.0011 c. M: 0.0016 c. 2047: 199 199 199 853 199 199 199 N M DE I SD: 0.0005 c. M: 0.0007 c. 2119: 206 206 206 883 206 206 206 N M DE I SD: 0.0001 c. M: 0.0001 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.6300 cents 2 x x x 3 x x 4 S SD: 74.2582 cents 3 x x 4:5 x x 6 S SD: 50.5732 cents 4 x x 5 x 7 x 8 SD: 12.0654 cents 5 x x 6:8:9 x 10 S SD: 17.8287 cents 6 x 7 x 10 x 11:12 SD: 14.7054 cents 7 x 8:9:11:12:13:14 SD: 19.1107 cents 8 x 9:10:13:14:15:16 SD: 7.9931 cents 9 x 10:11:15:16:17:18 SD: 11.6547 cents 10:11 x 12:16:17:19:20 SD: 14.8866 cents 11:12:13 x 18:19:21:22 SD: 12.8780 cents 12:13:14:15:20:21:22:24 S SD: 10.3483 cents 13:14:15:16:21:23:24:26 SD: 5.9974 cents 14:15:16:17:23:24:26:28 SD: 5.7136 cents 25:27:29:31:41:44:47:50 SD: 5.6590 cents 26:28:30:32:42:45:49:52 SD: 5.1805 cents 27:29:31:33:44:47:51:54 SD: 3.0821 cents 28:30:32:34:46:49:52:56 SD: 3.0038 cents 40:43:46:49:65:70:75:80 SD: 2.3338 cents 41:44:47:50:67:72:77:82 SD: 1.9881 cents 54:58:62:66:88:94:101:108 SD: 1.8728 cents 55:59:63:67:90:96:103:110 SD: 1.5400 cents 68:73:78:83:111:119:127:136 SD: 1.3802 cents 71:76:81:87:116:124:133:142 SD: 0.9467 cents 84:90:96:103:137:147:157:168 SD: 0.8825 cents 98:105:112:120:160:171:183:196 SD: 0.8514 cents 112:120:128:137:183:196:209:224 SD: 0.8193 cents 116:124:133:142:190:203:217:232 SD: 0.7841 cents 131:140:150:160:214:229:245:262 SD: 0.6497 cents 139:149:159:170:227:243:260:278 SD: 0.6062 cents 147:157:168:180:240:257:275:294 SD: 0.5879 cents 174:186:199:213:284:304:325:348 SD: 0.5541 cents 186:199:213:228:304:325:348:372 SD: 0.4230 cents 187:200:214:229:306:327:350:374 SD: 0.3812 cents 200:214:229:245:327:350:374:400 SD: 0.3533 cents 214:229:245:262:350:374:400:428 SD: 0.2989 cents 271:290:310:332:443:474:507:542 SD: 0.2793 cents 285:305:326:349:466:498:533:570 SD: 0.2595 cents 317:339:363:388:518:554:593:634 SD: 0.2392 cents 361:386:413:442:590:631:675:722 SD: 0.1871 cents 402:430:460:492:657:703:752:804 SD: 0.1335 cents