Scala analysis: xen17-erlich-alternate-pentachordal-minor
Decatonic mode: Alternate Pentachordal 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: 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: 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: 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: 1 545.45455 cents 5: 8 600.00000 cents 5: 1 654.54545 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 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1090.9 1200.0 109.1 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 218.2 : 109.1 218.2 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 327.3 : 109.1 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 436.4 : 163.6 272.7 381.8 490.9 654.5 763.6 872.7 981.8 1090.9 1200.0 600.0 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1036.4 1200.0 709.1 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 818.2 : 109.1 272.7 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 927.3 : 163.6 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 1090.9: 109.1 218.2 327.3 436.4 545.5 709.1 818.2 927.3 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 54.54545 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: 545.4545 .. 654.5455 cents 109.09091 cents 54.54545 cents 6: 709.0909 .. 763.6364 cents 54.54545 cents 54.54545 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 : 118.15821 cents, oct.: 1181.58205 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 6 8 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: 15 = 5 more = 150.000% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 22-tone equal temperament Step pattern alph. order: AAAABAAABA Step pattern size order : SSSSLSSSLS 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 Formal octave complements present : 4 = 40.0000% Limited inverse transpositions : 3 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: 23.1417 c. M:-43.6364 c. 12: 1 1 1 1 2 1 1 1 2 1 P D3 SD: 19.2847 c. M: 36.3636 c. 18: 2 1 2 2 2 2 1 2 2 2 SP B ME S SD: 18.4824 c. M:-30.3030 c. 19: 2 1 2 2 2 2 2 2 2 2 SP M ME SD: 17.8822 c. M: 31.5789 c. 20: 2 2 1 2 3 2 2 1 3 2 P T3 SD: 17.5056 c. M: 27.2727 c. 21: 2 2 2 2 2 2 2 2 3 2 SP M ME SD: 16.4274 c. M: 28.5714 c. 22: 2 2 2 2 3 2 2 2 3 2 SP D3 SD: 0.0000 c. M:-0.0000 c. Alternate Pentachordal 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: 15.2789 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 16.4940 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 6.6290 cents 8 x 9 x 10:11:12:13:14:15:16 S SD: 10.7256 cents 9 x 10:11:12:13 x 14:15:17:18 SD: 13.4702 cents 10 x 11:12:13:14:15:16:17:19:20 SD: 7.1535 cents 11:12 x 13:14:16:17:18:19:21:22 SD: 11.2449 cents 12:13:14 x 15:17:18:19:21:23:24 SD: 10.7135 cents 13:14:15:16:17:18:20:21:22:24:26 S SD: 8.3911 cents 14:15:16:17:18:20:21:22:24:26:28 S SD: 4.8885 cents 24:26:27:29:31:34:36:39:41:45:48 SD: 4.1041 cents 28:30:32:34:36:40:42:45:48:53:56 SD: 3.0774 cents 31:33:35:37:40:44:47:50:53:58:62 SD: 2.8795 cents 38:40:43:46:49:54:57:61:65:71:76 SD: 2.5652 cents 43:46:49:52:55:61:65:69:73:81:86 SD: 2.1169 cents 45:48:51:54:58:64:68:72:77:85:90 SD: 2.0268 cents 48:51:54:58:62:68:72:77:82:90:96 SD: 1.8247 cents 58:62:66:70:75:82:87:93:99:109:116 SD: 1.4309 cents 63:67:71:76:81:89:95:101:108:118:126 SD: 1.4248 cents 73:78:83:88:94:103:110:117:125:137:146 SD: 0.9942 cents 91:97:103:110:117:129:137:146:155:171:182 SD: 0.8098 cents 106:113:120:128:136:150:160:170:181:199:212 SD: 0.7439 cents 111:118:126:134:143:157:167:178:190:208:222 SD: 0.6829 cents 121:129:137:146:156:171:182:194:207:227:242 SD: 0.6764 cents 126:134:143:152:162:178:190:202:215:237:252 SD: 0.6041 cents 140:149:159:169:180:198:211:225:239:263:280 SD: 0.4838 cents 154:164:175:186:198:218:232:247:263:289:308 SD: 0.4057 cents 164:175:186:198:211:232:247:263:280:308:328 SD: 0.3771 cents 202:215:229:244:260:286:304:324:345:379:404 SD: 0.3364 cents 230:245:261:278:296:325:346:369:393:432:460 SD: 0.2879 cents 261:278:296:315:336:369:393:419:446:490:522 SD: 0.2535 cents 275:293:312:332:354:389:414:441:470:516:550 SD: 0.2470 cents 328:349:372:396:422:464:494:526:560:616:656 SD: 0.2463 cents 336:358:381:406:432:475:506:539:574:631:672 SD: 0.1769 cents 432:460:490:522:556:611:651:693:738:811:864 SD: 0.1251 cents 596:635:676:720:767:843:898:956:1018:1119:1192 SD: 0.1135 cents