Scala analysis: xen18-erlich-miracle-09
1L 8s MOS for Miracle, L=266.87, 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: 466.880 cents 466.880000 5: 733.750 cents 733.750000 6: 850.470 cents 850.470000 7: 967.190 cents 967.190000 8: 1083.910 cents 1083.910000 9: 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: 266.8700 cents 266.8700 6: 116.7200 cents 116.7200 7: 116.7200 cents 116.7200 8: 116.7200 cents 116.7200 9: 116.7200 cents 116.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 116.72000 cents 1: 1 266.87000 cents 2: 7 233.44000 cents 2: 2 383.59000 cents 3: 6 350.16000 cents 3: 3 500.31000 cents 4: 5 466.88000 cents 4: 4 617.03000 cents 5: 4 583.60000 cents 5: 5 733.75000 cents 6: 3 700.32000 cents 6: 6 850.47000 cents 7: 2 817.04000 cents 7: 7 967.19000 cents 8: 1 933.76000 cents 8: 8 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 9 0.0 : 116.7 233.4 350.2 466.9 733.7 850.5 967.2 1083.9 1200.6 116.7 : 116.7 233.4 350.2 617.0 733.7 850.5 967.2 1083.9 1200.6 233.4 : 116.7 233.4 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 350.2 : 116.7 383.6 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 466.9 : 266.9 383.6 500.3 617.0 733.7 850.5 967.2 1083.9 1200.6 733.7 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 933.8 1200.6 850.5 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 1083.9 1200.6 967.2 : 116.7 233.4 350.2 466.9 583.6 700.3 967.2 1083.9 1200.6 1083.9: 116.7 233.4 350.2 466.9 583.6 850.5 967.2 1083.9 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.7200 .. 266.8700 cents 150.15000 cents 116.72000 cents 2: 233.4400 .. 383.5900 cents 150.15000 cents -33.43000 cents 3: 350.1600 .. 500.3100 cents 150.15000 cents -33.43000 cents 4: 466.8800 .. 617.0300 cents 150.15000 cents -33.43000 cents 5: 583.6000 .. 733.7500 cents 150.15000 cents -33.43000 cents 6: 700.3200 .. 850.4700 cents 150.15000 cents -33.43000 cents 7: 817.0400 .. 967.1900 cents 150.15000 cents -33.43000 cents 8: 933.7600 .. 1083.9100 cents 150.15000 cents -33.43000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 116.72000 cents, class 1 Average step (divided formal octave): 133.4033 cents Largest one step interval : 266.87000 cents Average / Smallest step : 1.142935 Largest / Average step : 2.000475 Largest / Smallest step : 2.286412 Median interval of one step : 116.72000 cents, amount: 8 Most common interval of one step : 116.72000 cents, amount: 8 Least squares average step : 135.15947 cents, oct.: 1216.43526 cents Scale is not proper Scale has Myhill's property chromas: 150.15000 cents and 33.43000 cents, ratio: 4.491475 generators: 1 of 116.72000 cents and 8 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 1119 1297 1475 1653 1831 generators: 178 and 1653 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAA Step pattern size order : SSSSLSSSS Scale is a Constant Structure, by a margin of 33.43000 cents Scale diversity : 1.196150 Lumma stability : 0.194431 Lumma impropriety factor : 0.194906 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 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: 8 Scale is a chain of 4 triads 0.0 466.880 1083.910 cents Number of recognisable fifths : 3, average 700.3200 cents Number of recognisable fourths : 3, average 500.3100 cents Scale contains two identical disjunct pentachords Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
9: 1 1 0 1 2 1 1 1 1 N T3 SD: 48.4589 c. M: 83.3533 c. 10: 1 1 1 1 2 1 1 1 1 P M ME I SD: 8.6316 c. M: 13.3720 c. Yoyo & Latrizo-9 21: 2 2 2 2 5 2 2 2 2 N M DE I SD: 6.1304 c. M: 9.4971 c. 31: 3 3 3 3 7 3 3 3 3 N M DE I SD: 1.3685 c. M: 2.1200 c. 41: 4 4 4 4 9 4 4 4 4 N M DE I SD: 1.0706 c. M: 1.6585 c. 72: 7 7 7 7 16 7 7 7 7 N M DE I SD: 0.0204 c. M: 0.0317 c. 1111: 108 108 108 108 247 108 108 108 108 N M DE I SD: 0.0183 c. M: 0.0284 c. 1183: 115 115 115 115 263 115 115 115 115 N M DE I SD: 0.0160 c. M: 0.0247 c. 1255: 122 122 122 122 279 122 122 122 122 N M DE I SD: 0.0139 c. M: 0.0215 c. 1327: 129 129 129 129 295 129 129 129 129 N M DE I SD: 0.0120 c. M: 0.0186 c. 1399: 136 136 136 136 311 136 136 136 136 N M DE I SD: 0.0103 c. M: 0.0160 c. 1471: 143 143 143 143 327 143 143 143 143 N M DE I SD: 0.0088 c. M: 0.0137 c. 1543: 150 150 150 150 343 150 150 150 150 N M DE I SD: 0.0075 c. M: 0.0116 c. 1615: 157 157 157 157 359 157 157 157 157 N M DE I SD: 0.0062 c. M: 0.0096 c. 1687: 164 164 164 164 375 164 164 164 164 N M DE I SD: 0.0051 c. M:-0.0079 c. 1759: 171 171 171 171 391 171 171 171 171 N M DE I SD: 0.0040 c. M: 0.0063 c. 1831: 178 178 178 178 407 178 178 178 178 N M DE I SD: 0.0031 c. M: 0.0048 c. 1903: 185 185 185 185 423 185 185 185 185 N M DE I SD: 0.0022 c. M: 0.0034 c. 1975: 192 192 192 192 439 192 192 192 192 N M DE I SD: 0.0014 c. M:-0.0021 c. 2047: 199 199 199 199 455 199 199 199 199 N M DE I SD: 0.0006 c. M: 0.0009 c. 2119: 206 206 206 206 471 206 206 206 206 N M DE I SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.6300 cents 2 x x x x 3 x x x 4 S SD: 15.9006 cents 3 x x x 4 x 5 x x 6 S SD: 15.3482 cents 4 x x 5 x 6 x 7 x 8 S SD: 12.0444 cents 5 x x 6:7 x 8:9 x 10 S SD: 27.1710 cents 6 x 7 x 8:9:10 x 11:12 S SD: 12.2951 cents 7 x 8 x 9:11 x 12:13:14 SD: 11.4279 cents 8 x 9:10 x 12:13:14:15:16 S SD: 8.2201 cents 9 x 10:11:12:14:15:16:17:18 S SD: 10.3324 cents 10:11 x 12:13:15:16:17:19:20 SD: 11.9565 cents 11:12:13 x 14:17:18:19:21:22 SD: 11.7283 cents 12:13:14:15:16:18:20:21:22:24 S SD: 9.4474 cents 13:14:15:16:17:20:21:23:24:26 SD: 4.8602 cents 23:25:26:28:30:35:38:40:43:46 SD: 4.7615 cents 26:28:30:32:34:40:42:45:49:52 SD: 4.2542 cents 27:29:31:33:35:41:44:47:51:54 SD: 3.3088 cents 28:30:32:34:37:43:46:49:52:56 SD: 3.0765 cents 32:34:37:39:42:49:52:56:60:64 SD: 2.8745 cents 39:42:45:48:51:60:64:68:73:78 SD: 2.8337 cents 40:43:46:49:52:61:65:70:75:80 SD: 2.3239 cents 41:44:47:50:54:63:67:72:77:82 SD: 2.1960 cents 44:47:50:54:58:67:72:77:82:88 SD: 2.1690 cents 49:52:56:60:64:75:80:86:92:98 SD: 1.9906 cents 55:59:63:67:72:84:90:96:103:110 SD: 1.2015 cents 68:73:78:83:89:104:111:119:127:136 SD: 1.0975 cents 84:90:96:103:110:128:137:147:157:168 SD: 0.8512 cents 103:110:118:126:135:157:168:180:193:206 SD: 0.8278 cents 112:120:128:137:147:171:183:196:209:224 SD: 0.7813 cents 116:124:133:142:152:177:190:203:217:232 SD: 0.6674 cents 139:149:159:170:182:212:227:243:260:278 SD: 0.5765 cents 146:156:167:179:191:223:239:255:273:292 SD: 0.5697 cents 159:170:182:195:208:243:260:278:297:318 SD: 0.5061 cents 174:186:199:213:228:266:284:304:325:348 SD: 0.4618 cents 187:200:214:229:245:286:306:327:350:374 SD: 0.3702 cents 214:229:245:262:280:327:350:374:400:428 SD: 0.2876 cents 271:290:310:332:355:414:443:474:507:542 SD: 0.2263 cents 326:349:373:399:427:498:533:570:610:652 SD: 0.2098 cents 375:401:429:459:491:573:613:656:701:750 SD: 0.1971 cents 388:415:444:475:508:593:634:678:726:776 SD: 0.1779 cents 472:505:540:578:618:721:771:825:883:944 SD: 0.1742 cents 485:519:555:594:635:741:793:848:907:970 SD: 0.1610 cents 500:535:572:612:655:764:817:874:935:1000 SD: 0.1428 cents 588:629:673:720:770:898:961:1028:1100:1176 SD: 0.1285 cents