Scala analysis: xen18-erlich-srutal-12
10L 2s MOS for Srutal, L=104.70, s=76.06
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 104.700 cents 104.700000 2: 209.400 cents 209.400000 3: 314.100 cents 314.100000 4: 390.160 cents 390.160000 5: 494.860 cents 494.860000 6: 599.560 cents 599.560000 7: 704.260 cents 704.260000 8: 808.960 cents 808.960000 9: 913.660 cents 913.660000 10: 989.720 cents 989.720000 11: 1094.420 cents 1094.420000 12: 1199.120 cents 1199.120000
SHOW/INTERVAL
0: 104.7000 cents 104.7000 1: 104.7000 cents 104.7000 2: 104.7000 cents 104.7000 3: 104.7000 cents 104.7000 4: 76.0600 cents 76.0600 5: 104.7000 cents 104.7000 6: 104.7000 cents 104.7000 7: 104.7000 cents 104.7000 8: 104.7000 cents 104.7000 9: 104.7000 cents 104.7000 10: 76.0600 cents 76.0600 11: 104.7000 cents 104.7000 12: 104.7000 cents 104.7000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 76.06000 cents 1: 10 104.70000 cents 2: 4 180.76000 cents 2: 8 209.40000 cents 3: 6 285.46000 cents 3: 6 314.10000 cents 4: 8 390.16000 cents 4: 4 418.80000 cents 5: 10 494.86000 cents 5: 2 523.50000 cents 6: 12 599.56000 cents 7: 2 675.62000 cents 7: 10 704.26000 cents 8: 4 780.32000 cents 8: 8 808.96000 cents 9: 6 885.02000 cents 9: 6 913.66000 cents 10: 8 989.72000 cents 10: 4 1018.36000 cents 11: 10 1094.42000 cents 11: 2 1123.06000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.90909 = 21/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 104.7 209.4 314.1 390.2 494.9 599.6 704.3 809.0 913.7 989.7 1094.4 1199.1 104.7 : 104.7 209.4 285.5 390.2 494.9 599.6 704.3 809.0 885.0 989.7 1094.4 1199.1 209.4 : 104.7 180.8 285.5 390.2 494.9 599.6 704.3 780.3 885.0 989.7 1094.4 1199.1 314.1 : 76.1 180.8 285.5 390.2 494.9 599.6 675.6 780.3 885.0 989.7 1094.4 1199.1 390.2 : 104.7 209.4 314.1 418.8 523.5 599.6 704.3 809.0 913.7 1018.4 1123.1 1199.1 494.9 : 104.7 209.4 314.1 418.8 494.9 599.6 704.3 809.0 913.7 1018.4 1094.4 1199.1 599.6 : 104.7 209.4 314.1 390.2 494.9 599.6 704.3 809.0 913.7 989.7 1094.4 1199.1 704.3 : 104.7 209.4 285.5 390.2 494.9 599.6 704.3 809.0 885.0 989.7 1094.4 1199.1 809.0 : 104.7 180.8 285.5 390.2 494.9 599.6 704.3 780.3 885.0 989.7 1094.4 1199.1 913.7 : 76.1 180.8 285.5 390.2 494.9 599.6 675.6 780.3 885.0 989.7 1094.4 1199.1 989.7 : 104.7 209.4 314.1 418.8 523.5 599.6 704.3 809.0 913.7 1018.4 1123.1 1199.1 1094.4: 104.7 209.4 314.1 418.8 494.9 599.6 704.3 809.0 913.7 1018.4 1094.4 1199.1 1199.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0600 .. 104.7000 cents 28.64000 cents 76.06000 cents 2: 180.7600 .. 209.4000 cents 28.64000 cents 76.06000 cents 3: 285.4600 .. 314.1000 cents 28.64000 cents 76.06000 cents 4: 390.1600 .. 418.8000 cents 28.64000 cents 76.06000 cents 5: 494.8600 .. 523.5000 cents 28.64000 cents 76.06000 cents 6: 599.5600 .. 599.5600 cents 1/1, 0.0000 cents 76.06000 cents 7: 675.6200 .. 704.2600 cents 28.64000 cents 76.06000 cents 8: 780.3200 .. 808.9600 cents 28.64000 cents 76.06000 cents 9: 885.0200 .. 913.6600 cents 28.64000 cents 76.06000 cents 10: 989.7200 .. 1018.3600 cents 28.64000 cents 76.06000 cents 11: 1094.4200 .. 1123.0600 cents 28.64000 cents 76.06000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 76.06000 cents, class 1 Average step (divided formal octave): 99.9267 cents Largest one step interval : 104.70000 cents Average / Smallest step : 1.313787 Largest / Average step : 1.047768 Largest / Smallest step : 1.376545 Median interval of one step : 104.70000 cents, amount: 10 Most common interval of one step : 104.70000 cents, amount: 10 Least squares average step : 100.07354 cents, oct.: 1200.88246 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Blocks have Myhill's property chromas: 28.64000 cents and 47.42000 cents, ratio: 1.655726 generators: 1 of 104.70000 cents and 5 of 494.86000 cents ET pair of linear temperament : 34&46 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1214-tone equal temperament with octave 1199.120 cents degrees: 106 212 318 395 501 607 713 819 925 1002 1108 1214 Least number of segments generator : 609 of 601.535 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 713 of 704.261 cents and inv. generated superset size: 613 = 601 more = 5108.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAABAA Step pattern size order : LLLSLLLLLSLL Scale is a Constant Structure, by a margin of 76.06000 cents Scale diversity : 1.175404 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.761158 Rothenberg efficiency (ambiguous key): 0.505556 redundancy: 0.494444 Efficiency x scale size : 6.066667 Number of different interval sizes : 21 = 1.90909 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.90909 = 21/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 28.64000 cents Most common intervals : 599.56000 cents & inv., amount: 12 Number of recognisable fifths : 10, average 704.2600 cents Number of recognisable fourths : 10, average 494.8600 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 10 = 83.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 6 Limited inverse transpositions : 1 7 Inversional symmetry on intervals : 0-1 3-4 6-7 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.4942 c. M: 14.3200 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 7.6713 c. M:-12.9327 c. Pajara-12 34: 3 3 3 2 3 3 3 3 3 2 3 3 SP B ME SD: 1.9658 c. M:-3.3141 c. Diaschismic-12, Pajara-12 46: 4 4 4 3 4 4 4 4 4 3 4 4 SP B ME SD: 0.7629 c. M: 1.2861 c. Diaschismic-12, Pajara-12 80: 7 7 7 5 7 7 7 7 7 5 7 7 SP B DE SD: 0.3968 c. M:-0.6690 c. Diaschismic-12 126: 11 11 11 8 11 11 11 11 11 8 11 11 SP B DE SD: 0.0266 c. M: 0.0448 c. Diaschismic-12 710: 62 62 62 45 62 62 62 62 62 45 62 62 SP B DE SD: 0.0212 c. M:-0.0357 c. 836: 73 73 73 53 73 73 73 73 73 53 73 73 SP B DE SD: 0.0140 c. M:-0.0235 c. 962: 84 84 84 61 84 84 84 84 84 61 84 84 SP B DE SD: 0.0087 c. M:-0.0146 c. 1088: 95 95 95 69 95 95 95 95 95 69 95 95 SP B DE SD: 0.0046 c. M:-0.0077 c. 1214: 106 106 106 77 106 106 106 106 106 77 106 106 SP B DE SD: 0.0013 c. M:-0.0023 c. 1340: 117 117 117 85 117 117 117 117 117 85 117 117 SP B DE SD: 0.0013 c. M: 0.0021 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.8800 cents 2 x x x x x x 3 x x x x 4 S SD: 1.2336 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.8290 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 5.3470 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.6127 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.9438 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.4870 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.7553 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.6818 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0908 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 11.7007 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.9906 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.3729 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.6982 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.2032 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 4.7596 cents 20:21:23:24:25:27:28:30:32:34:35:38:40 SD: 4.6833 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.6302 cents 24:26:27:29:30:32:34:36:38:41:43:45:48 SD: 3.9044 cents 27:29:30:32:34:36:38:41:43:46:48:51:54 SD: 3.8844 cents 29:31:33:35:36:39:41:44:46:49:51:55:58 SD: 3.5452 cents 30:32:34:36:38:40:42:45:48:51:53:56:60 SD: 2.6815 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.4842 cents 36:38:41:43:45:48:51:54:57:61:64:68:72 SD: 2.2374 cents 44:47:50:53:55:59:62:66:70:75:78:83:88 SD: 2.1416 cents 45:48:51:54:56:60:64:68:72:76:80:85:90 S SD: 2.0596 cents 46:49:52:55:58:61:65:69:73:78:81:87:92 SD: 1.8521 cents 48:51:54:58:60:64:68:72:77:81:85:90:96 SD: 1.7477 cents 52:55:59:62:65:69:74:78:83:88:92:98:104 SD: 1.7262 cents 60:64:68:72:75:80:85:90:96:102:106:113:120 SD: 1.2286 cents 70:74:79:84:88:93:99:105:112:119:124:132:140 SD: 1.1401 cents 75:80:85:90:94:100:106:113:120:127:133:141:150 SD: 1.1114 cents 79:84:89:95:99:105:112:119:126:134:140:149:158 SD: 0.8787 cents 94:100:106:113:118:125:133:141:150:159:166:177:188 SD: 0.8041 cents 99:105:112:119:124:132:140:149:158:168:175:186:198 SD: 0.7992 cents 109:116:123:131:137:145:154:164:174:185:193:205:218 SD: 0.7319 cents 111:118:125:133:139:148:157:167:177:188:197:209:222 SD: 0.6087 cents 126:134:142:151:158:168:178:189:201:214:223:237:252 SD: 0.5577 cents 131:139:148:157:164:174:185:197:209:222:232:246:262 SD: 0.5480 cents 157:167:177:188:197:209:222:236:251:266:278:295:314 SD: 0.5373 cents 161:171:182:193:202:214:228:242:257:273:285:303:322 SD: 0.4724 cents 171:182:193:205:214:228:242:257:273:290:303:322:342 SD: 0.4723 cents 178:189:201:213:223:237:252:267:284:302:315:335:356 SD: 0.4540 cents 181:192:204:217:227:241:256:272:289:307:321:341:362 SD: 0.4533 cents 193:205:218:231:242:257:273:290:308:327:342:363:386 SD: 0.3532 cents 227:241:256:272:284:302:321:341:362:385:402:427:454 SD: 0.2981 cents 257:273:290:308:322:342:363:386:410:436:455:484:514 SD: 0.2539 cents 302:321:341:362:378:402:427:454:482:512:535:568:604 SD: 0.2402 cents 305:324:344:366:382:406:431:458:487:517:540:574:610 SD: 0.2302 cents 321:341:362:385:402:427:454:482:512:544:569:604:642 SD: 0.2196 cents 336:357:379:403:421:447:475:505:536:570:595:632:672 SD: 0.2139 cents 341:362:385:409:427:454:482:512:544:578:604:642:682 SD: 0.2032 cents 372:395:420:446:466:495:526:559:594:631:659:700:744 SD: 0.1978 cents 396:421:447:475:496:527:560:595:632:671:701:745:792 SD: 0.1966 cents 403:428:455:483:505:536:570:605:643:683:714:758:806 SD: 0.1933 cents 420:446:474:504:526:559:594:631:670:712:744:790:840 SD: 0.1886 cents 450:478:508:540:564:599:636:676:718:763:797:847:900 SD: 0.1873 cents 466:495:526:559:584:620:659:700:744:790:825:877:932 SD: 0.1746 cents 498:529:562:597:624:663:704:748:795:844:882:937:995 SD: 0.1214 cents