Scala analysis: xen17-erlich-dynamic-symmetrical-major
Decatonic mode: Dynamic 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: 272.727 cents 272.727273 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: 163.6364 cents 163.6364 3: 109.0909 cents 109.0909 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: 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 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 109.1 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 272.7 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 381.8 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 490.9 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 600.0 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 709.1 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 872.7 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 981.8 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 1090.9: 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 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 54.54546 cents 109.09091 cents 2: 218.1818 .. 272.7273 cents 54.54546 cents 54.54545 cents 3: 327.2727 .. 381.8182 cents 54.54546 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 54.54545 cents 54.54545 cents 8: 927.2727 .. 981.8182 cents 54.54545 cents 54.54545 cents 9: 1036.3636 .. 1090.9091 cents 54.54546 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 : 121.55844 cents, oct.: 1215.58442 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: 54.54546 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 5 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: 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: ABAAAABAAA Step pattern size order : SLSSSSLSSS 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 : 6 = 60.0000% Limited transpositions : 5 Limited inverse transpositions : 3 8 Inversional symmetry on degrees : 4 9 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.8951 c. M: 32.7273 c. 12: 1 2 1 1 1 1 2 1 1 1 P B ME S SD: 15.7459 c. M:-27.2727 c. 18: 2 2 2 1 2 2 2 2 1 2 SP B ME S SD: 17.5653 c. M:-24.2424 c. Supersharp-10 20: 2 3 1 2 2 2 3 1 2 2 P B D3 SD: 17.0754 c. M:-27.2727 c. 21: 2 3 2 2 1 2 3 2 2 2 P D3 SD: 16.7729 c. M: 28.5714 c. 22: 2 3 2 2 2 2 3 2 2 2 SP B ME S SD: 0.0000 c. M: 0.0000 c. Dynamic 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: 4.5486 cents 4 x x 5 x x 6 x 7 x 8 S SD: 3.8724 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 16.6293 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 7.4489 cents 7 x 8:9 x 10:11 x 12:13:14 S SD: 16.2864 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 11.4493 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 11.9199 cents 10:11:12 x 13:14:15:17:18:19:20 SD: 11.3698 cents 11:12:13:14:15:16:17:18:19:21:22 SD: 11.0614 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 5.0917 cents 17:18:20:21:23:24:26:28:30:32:34 SD: 4.7869 cents 24:26:28:30:32:34:36:40:42:45:48 S SD: 3.6682 cents 28:30:33:35:37:40:42:46:49:53:56 SD: 3.5023 cents 29:31:34:36:39:41:44:48:51:54:58 SD: 3.1333 cents 31:33:36:39:41:44:47:51:55:58:62 SD: 3.0458 cents 33:35:39:41:44:47:50:55:58:62:66 SD: 2.8854 cents 34:36:40:42:45:48:51:56:60:64:68 SD: 2.4951 cents 41:44:48:51:54:58:62:68:72:77:82 SD: 2.2234 cents 43:46:50:54:57:61:65:71:76:81:86 SD: 2.2234 cents 46:49:54:57:61:65:69:76:81:86:92 SD: 1.6461 cents 58:62:68:72:77:82:87:96:102:109:116 SD: 1.3301 cents 65:69:76:81:86:92:98:108:115:122:130 SD: 1.2524 cents 73:78:85:91:97:103:110:121:129:137:146 SD: 1.2467 cents 76:81:89:95:101:107:114:126:134:143:152 SD: 1.2374 cents 77:82:90:96:102:109:116:127:136:145:154 SD: 1.0054 cents 89:95:104:111:118:126:134:147:157:167:178 SD: 0.7347 cents 122:130:143:152:162:173:184:202:215:229:244 SD: 0.5968 cents 140:149:164:175:186:198:211:232:247:263:280 SD: 0.5455 cents 170:181:199:212:226:240:256:281:300:319:340 SD: 0.4984 cents 174:185:204:217:231:246:262:288:307:327:348 SD: 0.4471 cents 183:195:214:228:243:259:276:303:323:344:366 SD: 0.4353 cents 186:198:218:232:247:263:280:308:328:349:372 SD: 0.2990 cents 198:211:232:247:263:280:298:328:349:372:396 SD: 0.2989 cents 247:263:289:308:328:349:372:409:436:464:494 SD: 0.2792 cents 263:280:308:328:349:372:396:435:464:494:526 SD: 0.2584 cents 275:293:322:343:365:389:414:455:485:516:550 SD: 0.2391 cents 304:324:356:379:404:430:458:503:536:571:608 SD: 0.2298 cents 352:375:412:439:467:498:530:583:621:661:704 SD: 0.2294 cents 357:380:418:445:474:505:538:591:629:670:714 SD: 0.2228 cents 369:393:432:460:490:522:556:611:651:693:738 SD: 0.1406 cents 522:556:611:651:693:738:786:864:920:980:1044 SD: 0.1337 cents 555:591:650:692:737:785:836:919:979:1042:1110 SD: 0.1302 cents 567:604:664:707:753:802:854:939:1000:1065:1134 SD: 0.1241 cents