Scala analysis: xen17-erlich-static-symmetrical-minor
Decatonic mode: Static Symmetrical Minor
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: 327.273 cents 327.272727 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: 927.273 cents 927.272727 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: 109.0909 cents 109.0909 4: 163.6364 cents 163.6364 5: 109.0909 cents 109.0909 6: 109.0909 cents 109.0909 7: 109.0909 cents 109.0909 8: 109.0909 cents 109.0909 9: 163.6364 cents 163.6364 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 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 109.1 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 218.2 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 327.3 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 490.9 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 600.0 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 709.1 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 818.2 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 927.3 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 1090.9: 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 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 54.54545 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 : 118.72491 cents, oct.: 1187.24911 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 6 9 11 13 15 17 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: AAABAAAABA Step pattern size order : SSSLSSSSLS 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 : 2 7 Inversional symmetry on degrees : 1 6 Inversional symmetry on intervals : 3-4 8-9 -- 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 1 1 2 1 1 1 1 2 1 P B ME S SD: 15.7459 c. M: 27.2727 c. 22: 2 2 2 3 2 2 2 2 3 2 SP B ME S SD: 0.0000 c. M:-0.0000 c. Static Symmetrical Minor, Pajara-10
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 x 5 x 6 S SD: 14.5011 cents 4 x x 5 x x 6 x 7 x 8 S SD: 18.1374 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 15.2789 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 12.9531 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 10.3687 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 11.4178 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 11.0813 cents 10 x 11:12:13:14:15:16:17:19:20 SD: 7.9914 cents 11:12 x 13:15:16:17:18:19:21:22 SD: 12.1749 cents 12:13:14:15:16:17:18:19:21:23:24 SD: 10.1631 cents 13:14:15:16:17:18:20:21:22:24:26 S SD: 8.3395 cents 14:15:16:17:19:20:21:22:24:26:28 SD: 6.1768 cents 15:16:17:18:20:21:23:24:26:28:30 SD: 4.6996 cents 24:26:27:29:32:34:36:39:41:45:48 SD: 4.1112 cents 27:29:31:33:36:38:41:43:46:51:54 SD: 4.0777 cents 28:30:32:34:37:40:42:45:48:53:56 SD: 3.1872 cents 30:32:34:36:40:42:45:48:51:56:60 SD: 2.7460 cents 42:45:48:51:56:59:63:67:72:79:84 SD: 2.6957 cents 43:46:49:52:57:61:65:69:73:81:86 SD: 1.8757 cents 48:51:54:58:64:68:72:77:82:90:96 SD: 1.8405 cents 58:62:66:70:77:82:87:93:99:109:116 SD: 1.1410 cents 73:78:83:88:97:103:110:117:125:137:146 SD: 0.9922 cents 89:95:101:108:118:126:134:143:152:167:178 SD: 0.9781 cents 91:97:103:110:121:129:137:146:155:171:182 SD: 0.8341 cents 106:113:120:128:141:150:160:170:181:199:212 SD: 0.6364 cents 140:149:159:169:186:198:211:225:239:263:280 SD: 0.4760 cents 164:175:186:198:218:232:247:263:280:308:328 SD: 0.4199 cents 186:198:211:225:247:263:280:298:318:349:372 SD: 0.3874 cents 202:215:229:244:268:286:304:324:345:379:404 SD: 0.3612 cents 217:231:246:262:288:307:327:348:371:407:434 SD: 0.3289 cents 247:263:280:298:328:349:372:396:422:464:494 SD: 0.3238 cents 260:277:295:314:345:368:392:417:444:488:520 SD: 0.2974 cents 275:293:312:332:365:389:414:441:470:516:550 SD: 0.2449 cents 326:347:370:394:433:461:491:523:557:612:652 SD: 0.1760 cents 336:358:381:406:446:475:506:539:574:631:672 SD: 0.1366 cents 476:507:540:575:632:673:717:764:813:894:952 SD: 0.1247 cents