Scala analysis: xen18-erlich-srutal-10
2L 8s MOS for Srutal, L=180.76, s=104.70
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: 390.160 cents 390.160000 4: 494.860 cents 494.860000 5: 599.560 cents 599.560000 6: 704.260 cents 704.260000 7: 808.960 cents 808.960000 8: 989.720 cents 989.720000 9: 1094.420 cents 1094.420000 10: 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: 180.7600 cents 180.7600 4: 104.7000 cents 104.7000 5: 104.7000 cents 104.7000 6: 104.7000 cents 104.7000 7: 104.7000 cents 104.7000 8: 180.7600 cents 180.7600 9: 104.7000 cents 104.7000 10: 104.7000 cents 104.7000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 104.70000 cents 1: 2 180.76000 cents 2: 6 209.40000 cents 2: 4 285.46000 cents 3: 4 314.10000 cents 3: 6 390.16000 cents 4: 2 418.80000 cents 4: 8 494.86000 cents 5: 10 599.56000 cents 6: 8 704.26000 cents 6: 2 780.32000 cents 7: 6 808.96000 cents 7: 4 885.02000 cents 8: 4 913.66000 cents 8: 6 989.72000 cents 9: 2 1018.36000 cents 9: 8 1094.42000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.88889 = 17/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 104.7 209.4 390.2 494.9 599.6 704.3 809.0 989.7 1094.4 1199.1 104.7 : 104.7 285.5 390.2 494.9 599.6 704.3 885.0 989.7 1094.4 1199.1 209.4 : 180.8 285.5 390.2 494.9 599.6 780.3 885.0 989.7 1094.4 1199.1 390.2 : 104.7 209.4 314.1 418.8 599.6 704.3 809.0 913.7 1018.4 1199.1 494.9 : 104.7 209.4 314.1 494.9 599.6 704.3 809.0 913.7 1094.4 1199.1 599.6 : 104.7 209.4 390.2 494.9 599.6 704.3 809.0 989.7 1094.4 1199.1 704.3 : 104.7 285.5 390.2 494.9 599.6 704.3 885.0 989.7 1094.4 1199.1 809.0 : 180.8 285.5 390.2 494.9 599.6 780.3 885.0 989.7 1094.4 1199.1 989.7 : 104.7 209.4 314.1 418.8 599.6 704.3 809.0 913.7 1018.4 1199.1 1094.4: 104.7 209.4 314.1 494.9 599.6 704.3 809.0 913.7 1094.4 1199.1 1199.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.7000 .. 180.7600 cents 76.06000 cents 104.70000 cents 2: 209.4000 .. 285.4600 cents 76.06000 cents 28.64000 cents 3: 314.1000 .. 390.1600 cents 76.06000 cents 28.64000 cents 4: 418.8000 .. 494.8600 cents 76.06000 cents 28.64000 cents 5: 599.5600 .. 599.5600 cents 1/1, 0.0000 cents 104.70000 cents 6: 704.2600 .. 780.3200 cents 76.06000 cents 104.70000 cents 7: 808.9600 .. 885.0200 cents 76.06000 cents 28.64000 cents 8: 913.6600 .. 989.7200 cents 76.06000 cents 28.64000 cents 9: 1018.3600 .. 1094.4200 cents 76.06000 cents 28.64000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 104.70000 cents, class 1 Average step (divided formal octave): 119.9120 cents Largest one step interval : 180.76000 cents Average / Smallest step : 1.145291 Largest / Average step : 1.507439 Largest / Smallest step : 1.726457 Median interval of one step : 104.70000 cents, amount: 8 Most common interval of one step : 104.70000 cents, amount: 8 Least squares average step : 120.30712 cents, oct.: 1203.07117 cents Scale is strictly proper Scale has 2 repeating blocks of 5 notes Blocks have Myhill's property chromas: 76.06000 cents and 28.64000 cents, ratio: 2.655726 generators: 1 of 104.70000 cents and 4 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 1088-tone equal temperament with octave 1199.120 cents degrees: 95 190 354 449 544 639 734 898 993 1088 Least number of segments generator : 545 of 600.662 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 639 of 704.263 cents and inv. generated superset size: 549 = 539 more = 5490.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAA Step pattern size order : SSLSSSSLSS Scale is a Constant Structure, by a margin of 28.64000 cents Scale diversity : 1.180608 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.492561 Rothenberg efficiency (ambiguous key): 0.513333 redundancy: 0.486667 Efficiency x scale size : 5.133333 Number of different interval sizes : 17 = 1.88889 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.88889 = 17/9 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 28.64000 cents Most common intervals : 599.56000 cents & inv., amount: 10 Number of recognisable fifths : 8, average 704.2600 cents Number of recognisable fourths : 8, average 494.8600 cents Scale contains two identical disjunct pentachords Formal octave complements present : 10 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 5 Limited inverse transpositions : 5 Inversional symmetry on degrees : 0 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.5130 c. M: 30.4240 c. 12: 1 1 2 1 1 1 1 2 1 1 P B ME I SD: 6.7505 c. M: 9.5467 c. Symmetrical Decatonic 22: 2 2 3 2 2 2 2 3 2 2 SP B ME I SD: 6.0965 c. M: 8.6218 c. Static Symmetrical Major 34: 3 3 5 3 3 3 3 5 3 3 SP B DE I SD: 1.5623 c. M: 2.2094 c. 46: 4 4 7 4 4 4 4 7 4 4 SP B DE I SD: 0.6063 c. M: 0.8574 c. Symmetrical Decatonic 80: 7 7 12 7 7 7 7 12 7 7 SP B DE I SD: 0.3154 c. M: 0.4460 c. 126: 11 11 19 11 11 11 11 19 11 11 SP B DE I SD: 0.0211 c. M: 0.0298 c. 710: 62 62 107 62 62 62 62 107 62 62 SP B DE I SD: 0.0168 c. M: 0.0238 c. 836: 73 73 126 73 73 73 73 126 73 73 SP B DE I SD: 0.0111 c. M: 0.0157 c. 962: 84 84 145 84 84 84 84 145 84 84 SP B DE I SD: 0.0069 c. M: 0.0097 c. 1088: 95 95 164 95 95 95 95 164 95 95 SP B DE I SD: 0.0036 c. M: 0.0051 c. 1214: 106 106 183 106 106 106 106 183 106 106 SP B DE I SD: 0.0011 c. M: 0.0015 c. 1340: 117 117 202 117 117 117 117 202 117 117 SP B DE I SD: 0.0010 c. M: 0.0014 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.8800 cents 2 x x x x x 3 x x x 4 S SD: 1.2336 cents 3 x x x 4 x x 5 x x 6 S SD: 25.1570 cents 4 x x 5 x x 6 x 7 x 8 S SD: 5.3470 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 16.3020 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 17.5073 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 12.1501 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.7553 cents 9 x 10:11:12:13 x 14:16:17:18 S SD: 9.6542 cents 10 x 11 x 13:14:15:16:18:19:20 SD: 8.8395 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 13.1031 cents 12:13:14:15:16:17:18:19:21:23:24 SD: 7.8274 cents 14:15:16:18:19:20:21:22:25:26:28 SD: 7.4809 cents 15:16:17:19:20:21:23:24:27:28:30 SD: 5.5115 cents 16:17:18:20:21:23:24:26:28:30:32 SD: 5.4095 cents 17:18:19:21:23:24:26:27:30:32:34 SD: 5.3036 cents 22:23:25:28:29:31:33:35:39:41:44 SD: 4.7768 cents 24:26:27:30:32:34:36:38:43:45:48 SD: 4.2797 cents 27:29:30:34:36:38:41:43:48:51:54 SD: 4.1202 cents 28:30:32:35:37:40:42:45:50:53:56 SD: 4.0550 cents 30:32:34:38:40:42:45:48:53:56:60 SD: 3.1753 cents 31:33:35:39:41:44:47:49:55:58:62 SD: 2.9414 cents 32:34:36:40:43:45:48:51:57:60:64 SD: 2.3512 cents 44:47:50:55:59:62:66:70:78:83:88 SD: 2.2423 cents 46:49:52:58:61:65:69:73:81:87:92 SD: 2.1706 cents 48:51:54:60:64:68:72:77:85:90:96 SD: 1.4009 cents 60:64:68:75:80:85:90:96:106:113:120 SD: 1.3790 cents 70:74:79:88:93:99:105:112:124:132:140 SD: 1.2648 cents 78:83:88:98:104:110:117:124:138:147:156 SD: 1.1026 cents 79:84:89:99:105:112:119:126:140:149:158 SD: 0.9111 cents 94:100:106:118:125:133:141:150:166:177:188 SD: 0.7624 cents 109:116:123:137:145:154:164:174:193:205:218 SD: 0.7407 cents 111:118:125:139:148:157:167:177:197:209:222 SD: 0.7080 cents 118:125:133:148:157:167:177:188:209:222:236 SD: 0.7042 cents 126:134:142:158:168:178:189:201:223:237:252 SD: 0.5736 cents 161:171:182:202:214:228:242:257:285:303:322 SD: 0.5637 cents 163:173:184:204:217:230:245:260:289:307:326 SD: 0.5111 cents 178:189:201:223:237:252:267:284:315:335:356 SD: 0.4026 cents 193:205:218:242:257:273:290:308:342:363:386 SD: 0.2928 cents 257:273:290:322:342:363:386:410:455:484:514 SD: 0.2607 cents 305:324:344:382:406:431:458:487:540:574:610 SD: 0.2293 cents 336:357:379:421:447:475:505:536:595:632:672 SD: 0.2079 cents 420:446:474:526:559:594:631:670:744:790:840 SD: 0.1653 cents 450:478:508:564:599:636:676:718:797:847:900 SD: 0.1573 cents 498:529:562:624:663:704:748:795:882:937:995 SD: 0.1402 cents