Scala analysis: xen17-erlich-standard-pentachordal-major
Decatonic mode: Standard Pentachordal Major
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 109.091 cents 109.090909 2: 218.182 cents 218.181818 3: 381.818 cents 381.818182 4: 490.909 cents 490.909091 5: 600.000 cents 600.000000 6: 709.091 cents 709.090909 7: 872.727 cents 872.727273 8: 981.818 cents 981.818182 9: 1090.909 cents 1090.909091 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 109.0909 cents 109.0909 1: 109.0909 cents 109.0909 2: 109.0909 cents 109.0909 3: 163.6364 cents 163.6364 4: 109.0909 cents 109.0909 5: 109.0909 cents 109.0909 6: 109.0909 cents 109.0909 7: 163.6364 cents 163.6364 8: 109.0909 cents 109.0909 9: 109.0909 cents 109.0909 10: 109.0909 cents 109.0909
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 109.09091 cents 1: 2 163.63636 cents 2: 6 218.18182 cents 2: 4 272.72727 cents 3: 4 327.27273 cents 3: 6 381.81818 cents 4: 2 436.36364 cents 4: 8 490.90909 cents 5: 1 545.45454 cents 5: 8 600.00000 cents 5: 1 654.54546 cents 6: 8 709.09091 cents 6: 2 763.63636 cents 7: 6 818.18182 cents 7: 4 872.72727 cents 8: 4 927.27273 cents 8: 6 981.81818 cents 9: 2 1036.36364 cents 9: 8 1090.90909 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.11111 = 19/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 109.1 218.2 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 109.1 : 109.1 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 218.2 : 163.6 272.7 381.8 490.9 654.5 763.6 872.7 981.8 1090.9 1200.0 381.8 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1036.4 1200.0 490.9 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 600.0 : 109.1 272.7 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 709.1 : 163.6 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 872.7 : 109.1 218.2 327.3 436.4 545.5 709.1 818.2 927.3 1036.4 1200.0 981.8 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1090.9 1200.0 1090.9: 109.1 218.2 327.3 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 109.0909 .. 163.6364 cents 54.54545 cents 109.09091 cents 2: 218.1818 .. 272.7273 cents 54.54546 cents 54.54545 cents 3: 327.2727 .. 381.8182 cents 54.54545 cents 54.54545 cents 4: 436.3636 .. 490.9091 cents 54.54545 cents 54.54545 cents 5: 545.4545 .. 654.5455 cents 109.09091 cents 54.54545 cents 6: 709.0909 .. 763.6364 cents 54.54546 cents 54.54545 cents 7: 818.1818 .. 872.7273 cents 54.54545 cents 54.54545 cents 8: 927.2727 .. 981.8182 cents 54.54545 cents 54.54545 cents 9: 1036.3636 .. 1090.9091 cents 54.54545 cents 54.54545 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 109.09091 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 163.63636 cents Average / Smallest step : 1.100000 Largest / Average step : 1.363636 Largest / Smallest step : 1.500000 Median interval of one step : 109.09091 cents, amount: 8 Most common interval of one step : 109.09091 cents, amount: 8 Least squares average step : 121.27509 cents, oct.: 1212.75089 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 22-tone equal temperament with octave 1200.000 cents degrees: 2 4 7 9 11 13 16 18 20 22 Least number of segments generator : 13 of 709.091 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 13 of 709.091 cents and inv. generated superset size: 15 = 5 more = 150.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAA Step pattern size order : SSLSSSLSSS Interval vector is [ 0 8 2 6 4 4 6 2 8 1 4 ] Scale is a Constant Structure, by a margin of 54.54545 cents Scale diversity : 1.269872 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.545455 Rothenberg efficiency : 0.623333 redundancy: 0.376667 Efficiency x scale size : 6.233333 Number of different interval sizes : 19 = 2.11111 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.11111 = 19/9 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 54.54545 cents Number of recognisable fifths : 8, average 709.0909 cents Scale contains two identical conjunct pentachords Formal octave complements present : 8 = 80.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 9-10 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.2488 c. M: 32.7273 c. 12: 1 1 2 1 1 1 2 1 1 1 P D3 SD: 14.3740 c. M:-27.2727 c. 18: 2 1 3 1 2 2 2 2 1 2 P D3 SD: 18.3827 c. M:-24.2424 c. 20: 2 2 2 2 2 2 3 1 2 2 P T3 SD: 16.2725 c. M:-27.2727 c. 22: 2 2 3 2 2 2 3 2 2 2 SP D3 SD: 0.0000 c. M: 0.0000 c. Standard Pentachordal Major
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 3.5680 cents 3 x x x 4 x x 5 x x 6 S SD: 4.5486 cents 4 x x 5 x x 6 x 7 x 8 S SD: 3.8724 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 19.4434 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 10.9720 cents 7 x 8:9 x 10:11 x 12:13:14 S SD: 15.2791 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.7634 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 9.5672 cents 10 x 11:12:13:14:15:17:18:19:20 SD: 12.5267 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 12.1532 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 7.0206 cents 15:16:17:19:20:21:23:25:26:28:30 SD: 5.6481 cents 16:17:18:20:21:23:24:26:28:30:32 SD: 5.2049 cents 21:22:24:26:28:30:32:35:37:39:42 SD: 4.8964 cents 24:26:27:30:32:34:36:40:42:45:48 S SD: 3.8923 cents 28:30:32:35:37:40:42:46:49:53:56 SD: 3.5469 cents 29:31:33:36:39:41:44:48:51:54:58 SD: 3.1704 cents 31:33:35:39:41:44:47:51:55:58:62 SD: 2.8303 cents 37:39:42:46:49:52:56:61:65:69:74 SD: 2.8151 cents 43:46:49:54:57:61:65:71:76:81:86 SD: 2.0558 cents 46:49:52:57:61:65:69:76:81:86:92 SD: 1.6807 cents 58:62:66:72:77:82:87:96:102:109:116 SD: 1.4153 cents 61:65:69:76:81:86:92:101:108:115:122 SD: 1.2537 cents 73:78:83:91:97:103:110:121:129:137:146 SD: 0.9302 cents 89:95:101:111:118:126:134:147:157:167:178 SD: 0.6717 cents 125:133:142:156:166:177:188:207:220:235:250 SD: 0.6130 cents 140:149:159:175:186:198:211:232:247:263:280 SD: 0.5735 cents 150:160:170:187:199:212:226:248:264:282:300 SD: 0.5647 cents 170:181:193:212:226:240:256:281:300:319:340 SD: 0.5204 cents 171:182:194:213:227:242:258:283:302:321:342 SD: 0.4816 cents 186:198:211:232:247:263:280:308:328:349:372 SD: 0.2130 cents 336:358:381:419:446:475:506:556:592:631:672 SD: 0.2008 cents 372:396:422:464:494:526:560:616:656:699:744 SD: 0.1934 cents 401:427:455:500:532:567:604:664:707:753:802 SD: 0.1726 cents 417:444:473:520:554:590:628:690:735:783:834 SD: 0.1720 cents 418:445:474:521:555:591:630:692:737:785:836 SD: 0.1583 cents 461:491:523:575:612:652:694:763:813:866:922 SD: 0.1506 cents 490:522:556:611:651:693:738:811:864:920:980 SD: 0.1325 cents 507:540:575:632:673:717:764:839:894:952:1014 SD: 0.1299 cents 567:604:643:707:753:802:854:939:1000:1065:1134 SD: 0.1123 cents