Scala analysis: xen17-erlich-dynamic-symmetrical-minor
Decatonic mode: Dynamic 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: 436.364 cents 436.363636 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: 1036.364 cents 1036.363636 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 163.6364 cents 163.6364 1: 109.0909 cents 109.0909 2: 109.0909 cents 109.0909 3: 109.0909 cents 109.0909 4: 109.0909 cents 109.0909 5: 163.6364 cents 163.6364 6: 109.0909 cents 109.0909 7: 109.0909 cents 109.0909 8: 109.0909 cents 109.0909 9: 109.0909 cents 109.0909 10: 163.6364 cents 163.6364
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 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 109.1 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 218.2 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 327.3 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 436.4 : 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 600.0 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1036.4 1200.0 709.1 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 818.2 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 927.3 : 109.1 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 1036.4: 163.6 272.7 381.8 490.9 600.0 763.6 872.7 981.8 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 54.54545 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 54.54546 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 : 116.88312 cents, oct.: 1168.83117 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 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 8 11 13 15 17 19 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: AAAABAAAAB Step pattern size order : SSSSLSSSSL 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 : 2 = 20.0000% Limited transpositions : 5 Limited inverse transpositions : 4 9 Inversional symmetry on degrees : 2 7 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: 26.7217 c. M:-43.6364 c. 12: 1 1 1 1 2 1 1 1 1 2 P B ME S SD: 22.2681 c. M: 36.3636 c. Messiaen mode 7 14: 1 2 1 1 2 1 2 1 1 2 P B ME S SD: 21.7625 c. M:-38.9610 c. 16: 1 2 1 2 2 1 2 1 2 2 P B ME S SD: 20.6806 c. M: 34.0909 c. Decibel-10 18: 2 1 2 2 2 2 1 2 2 2 SP B ME S SD: 19.3560 c. M:-30.3030 c. 20: 2 2 1 2 3 2 2 1 2 3 P B D3 SD: 17.9255 c. M: 27.2727 c. 21: 2 2 2 2 3 1 2 2 2 3 P D3 SD: 16.5298 c. M:-28.5714 c. 22: 2 2 2 2 3 2 2 2 2 3 SP B ME S SD: 0.0000 c. M:-0.0000 c. Dynamic Symmetrical Minor
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: 25.0471 cents 4 x x x 5 x 6 x 7 x 8 S SD: 16.3604 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 5.7045 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 15.1261 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 7.8677 cents 8 x 9 x 10:11:12:13:14:15:16 S SD: 12.5310 cents 9 x 10:11:12:13 x 14:15:16:18 S SD: 14.3242 cents 10 x 11:12:13:14:15:16:17:18:20 S SD: 7.1019 cents 11:12 x 13:14:16:17:18:19:20:22 S SD: 10.7891 cents 12:13:14 x 15:17:18:19:21:22:24 SD: 10.0690 cents 13:14:15:16:17:18:20:21:22:24:26 S SD: 8.2462 cents 14:15:16:17:18:20:21:22:24:25:28 SD: 5.5508 cents 20:21:23:24:26:28:30:32:34:36:40 SD: 4.9288 cents 24:26:27:29:31:34:36:39:41:44:48 SD: 4.2969 cents 27:29:31:33:35:38:41:43:46:49:54 SD: 4.1192 cents 28:30:32:34:36:40:42:45:48:51:56 SD: 2.7575 cents 38:40:43:46:49:54:57:61:65:69:76 SD: 2.4396 cents 43:46:49:52:55:61:65:69:73:78:86 SD: 2.1170 cents 44:47:50:53:57:62:66:71:75:80:88 SD: 2.0319 cents 45:48:51:54:58:64:68:72:77:82:90 SD: 1.7725 cents 58:62:66:70:75:82:87:93:99:106:116 SD: 1.6130 cents 59:63:67:71:76:83:89:95:101:107:118 SD: 1.5819 cents 61:65:69:74:78:86:92:98:104:111:122 SD: 1.5673 cents 63:67:71:76:81:89:95:101:108:115:126 SD: 1.4599 cents 66:70:75:80:85:93:99:106:113:120:132 SD: 1.4416 cents 73:78:83:88:94:103:110:117:125:133:146 SD: 1.0124 cents 91:97:103:110:117:129:137:146:155:166:182 SD: 0.9109 cents 104:111:118:126:134:147:157:167:178:189:208 SD: 0.8807 cents 106:113:120:128:136:150:160:170:181:193:212 SD: 0.7503 cents 111:118:126:134:143:157:167:178:190:202:222 SD: 0.5756 cents 126:134:143:152:162:178:190:202:215:229:252 SD: 0.5711 cents 140:149:159:169:180:198:211:225:239:255:280 SD: 0.5093 cents 150:160:170:181:193:212:226:241:256:273:300 SD: 0.5070 cents 154:164:175:186:198:218:232:247:263:280:308 SD: 0.4126 cents 172:183:195:208:221:243:259:276:294:313:344 SD: 0.4112 cents 202:215:229:244:260:286:304:324:345:368:404 SD: 0.3647 cents 217:231:246:262:279:307:327:348:371:395:434 SD: 0.2768 cents 261:278:296:315:336:369:393:419:446:475:522 SD: 0.2514 cents 275:293:312:332:354:389:414:441:470:500:550 SD: 0.2462 cents 336:358:381:406:432:475:506:539:574:611:672 SD: 0.2086 cents 401:427:455:484:516:567:604:643:685:730:802 SD: 0.2062 cents 415:442:471:501:534:587:625:666:709:755:830 SD: 0.1787 cents 432:460:490:522:556:611:651:693:738:786:864 SD: 0.1157 cents