Scala analysis: xen17-erlich-static-symmetrical-major
Decatonic mode: Static Symmetrical 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: 818.182 cents 818.181818 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: 109.0909 cents 109.0909 8: 163.6364 cents 163.6364 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: 10 600.00000 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: 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 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 109.1 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 218.2 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 381.8 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 490.9 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 600.0 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 709.1 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 818.2 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 981.8 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 1090.9: 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 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: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 109.09091 cents 6: 709.0909 .. 763.6364 cents 54.54546 cents 109.09091 cents 7: 818.1818 .. 872.7273 cents 54.54546 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 : 120.28335 cents, oct.: 1202.83353 cents Scale is strictly proper Scale is maximally even in 22-tone equal temperament Scale has 2 repeating blocks of 5 notes Blocks have Myhill's property chromas: 54.54545 cents and 54.54545 cents, ratio: 1.000000 generators: 1 of 109.09091 cents and 4 of 490.90909 cents ET pair of linear temperament : 22&22 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 22-tone equal temperament with octave 1200.000 cents degrees: 2 4 7 9 11 13 15 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: 16 = 6 more = 160.000% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 22-tone equal temperament Step pattern alph. order: AABAAAABAA Step pattern size order : SSLSSSSLSS Interval vector is [ 0 8 2 6 4 4 6 2 8 0 5 ] Scale is a Constant Structure, by a margin of 54.54545 cents Scale diversity : 1.207724 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.636364 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 : 54.54545 cents Most common intervals : 600.00000 cents & inv., amount: 10 Number of recognisable fifths : 8, average 709.0909 cents Scale contains two identical disjunct pentachords Formal octave complements present : 10 = 100.0000% 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: 15.4278 c. M:-21.8182 c. 12: 1 1 2 1 1 1 1 2 1 1 P B ME I SD: 12.8565 c. M:-18.1818 c. Symmetrical Decatonic 22: 2 2 3 2 2 2 2 3 2 2 SP B ME I SD: 0.0000 c. M:-0.0000 c. Static Symmetrical 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: 22.1868 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: 15.4732 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 15.4362 cents 7 x 8:9 x 10 x 11:12:13:14 S SD: 12.2268 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.2023 cents 9 x 10:11:12:13 x 14:16:17:18 S SD: 10.4580 cents 10 x 11:12:13:14:15:16:18:19:20 S SD: 11.4517 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 12.5425 cents 12:13:14:15:16:17:18:19:21:23:24 SD: 7.2838 cents 15:16:17:19:20:21:23:24:26:28:30 SD: 5.5453 cents 16:17:18:20:21:23:24:26:28:30:32 SD: 4.6601 cents 24:26:27:30:32:34:36:39:42:45:48 S SD: 4.3348 cents 25:27:28:31:33:35:38:40:44:47:50 SD: 4.3005 cents 27:29:31:34:36:38:41:43:48:51:54 SD: 4.1662 cents 28:30:32:35:37:40:42:45:49:53:56 SD: 3.3046 cents 30:32:34:37:40:42:45:48:53:56:60 SD: 3.0120 cents 31:33:35:39:41:44:47:50:55:58:62 SD: 2.7782 cents 36:38:41:45:48:51:54:58:63:68:72 SD: 2.7333 cents 43:46:49:54:57:61:65:69:76:81:86 SD: 2.0055 cents 45:48:51:56:60:64:68:72:79:85:90 SD: 1.9420 cents 46:49:52:57:61:65:69:74:81:86:92 SD: 1.7152 cents 58:62:66:72:77:82:87:93:102:109:116 SD: 1.4169 cents 60:64:68:75:80:85:90:96:106:113:120 SD: 1.4054 cents 61:65:69:76:81:86:92:98:108:115:122 SD: 1.2798 cents 73:78:83:91:97:103:110:117:129:137:146 SD: 0.9186 cents 89:95:101:111:118:126:134:143:157:167:178 SD: 0.6071 cents 126:134:143:157:167:178:190:202:222:237:252 SD: 0.6060 cents 150:160:170:187:199:212:226:241:264:282:300 SD: 0.5833 cents 164:175:186:204:218:232:247:263:289:308:328 SD: 0.5628 cents 170:181:193:212:226:240:256:273:300:319:340 SD: 0.4830 cents 186:198:211:232:247:263:280:298:328:349:372 SD: 0.3011 cents 263:280:298:328:349:372:396:422:464:494:526 SD: 0.2719 cents 275:293:312:343:365:389:414:441:485:516:550 SD: 0.2229 cents 336:358:381:419:446:475:506:539:592:631:672 SD: 0.1851 cents 401:427:455:500:532:567:604:643:707:753:802 SD: 0.1834 cents 417:444:473:520:554:590:628:669:735:783:834 SD: 0.1494 cents 478:509:542:596:635:676:720:767:843:898:956 SD: 0.1446 cents 490:522:556:611:651:693:738:786:864:920:980 SD: 0.1259 cents