Scala analysis: xen17-erlich-standard-pentachordal-minor
Decatonic mode: Standard 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: 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: 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: 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: 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: 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 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 927.3 1036.4 1200.0 109.1 : 109.1 218.2 381.8 490.9 600.0 709.1 818.2 927.3 1090.9 1200.0 218.2 : 109.1 272.7 381.8 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 327.3 : 163.6 272.7 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 490.9 : 109.1 218.2 327.3 436.4 545.5 709.1 818.2 927.3 1036.4 1200.0 600.0 : 109.1 218.2 327.3 436.4 600.0 709.1 818.2 927.3 1090.9 1200.0 709.1 : 109.1 218.2 327.3 490.9 600.0 709.1 818.2 981.8 1090.9 1200.0 818.2 : 109.1 218.2 381.8 490.9 600.0 709.1 872.7 981.8 1090.9 1200.0 927.3 : 109.1 272.7 381.8 490.9 600.0 763.6 872.7 981.8 1090.9 1200.0 1036.4: 163.6 272.7 381.8 490.9 654.5 763.6 872.7 981.8 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 54.54546 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: 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 54.54546 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 : 117.44982 cents, oct.: 1174.49823 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 9 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: 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: AAABAAAAAB Step pattern size order : SSSLSSSSSL 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 Scale contains two identical disjunct pentachords 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 2 1 1 1 1 1 2 P D3 SD: 19.2847 c. M: 36.3636 c. Raga Gambhir Basant 17: 2 1 2 2 2 1 2 1 2 2 P D3 SD: 21.0399 c. M:-35.2941 c. 18: 2 1 2 2 2 2 1 2 2 2 SP B ME S SD: 18.4824 c. M:-30.3030 c. 20: 2 2 1 3 2 2 2 1 2 3 P T3 SD: 17.5056 c. M: 27.2727 c. 22: 2 2 2 3 2 2 2 2 2 3 SP D3 SD: 0.0000 c. M:-0.0000 c. Standard 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: 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: 5.7045 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 11.1593 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.2012 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 13.1283 cents 9 x 10:11:12:13 x 14:15:16:18 S SD: 12.1051 cents 10 x 11:12:13:14:15:16:17:18:20 S SD: 7.9453 cents 11:12 x 13:15:16:17:18:19:20:22 SD: 11.7552 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 9.6146 cents 13:14:15:16:17:18:20:21:22:24:26 S SD: 8.1937 cents 14:15:16:17:19:20:21:22:24:25:28 SD: 6.7132 cents 15:16:17:18:20:21:23:24:26:27:30 SD: 4.9535 cents 24:26:27:29:32:34:36:39:41:44:48 SD: 4.3037 cents 27:29:31:33:36:38:41:43:46:49:54 SD: 3.9762 cents 28:30:32:34:37:40:42:45:48:51:56 SD: 2.8795 cents 30:32:34:36:40:42:45:48:51:55:60 SD: 2.8563 cents 34:36:39:41:45:48:51:55:58:62:68 SD: 2.8455 cents 43:46:49:52:57:61:65:69:73:78:86 SD: 1.8758 cents 58:62:66:70:77:82:87:93:99:106:116 SD: 1.3624 cents 61:65:69:74:81:86:92:98:104:111:122 SD: 1.1391 cents 73:78:83:88:97:103:110:117:125:133:146 SD: 1.0105 cents 89:95:101:108:118:126:134:143:152:162:178 SD: 0.9706 cents 91:97:103:110:121:129:137:146:155:166:182 SD: 0.9326 cents 104:111:118:126:138:147:157:167:178:189:208 SD: 0.8555 cents 106:113:120:128:141:150:160:170:181:193:212 SD: 0.6438 cents 126:134:143:152:167:178:190:202:215:229:252 SD: 0.6420 cents 134:143:152:162:178:190:202:215:229:244:268 SD: 0.6182 cents 140:149:159:169:186:198:211:225:239:255:280 SD: 0.5019 cents 164:175:186:198:218:232:247:263:280:298:328 SD: 0.4845 cents 172:183:195:208:228:243:259:276:294:313:344 SD: 0.4462 cents 186:198:211:225:247:263:280:298:318:338:372 SD: 0.4282 cents 201:214:228:243:267:284:303:322:343:366:402 SD: 0.4254 cents 202:215:229:244:268:286:304:324:345:368:404 SD: 0.3877 cents 217:231:246:262:288:307:327:348:371:395:434 SD: 0.2601 cents 275:293:312:332:365:389:414:441:470:500:550 SD: 0.2441 cents 326:347:370:394:433:461:491:523:557:593:652 SD: 0.1777 cents 336:358:381:406:446:475:506:539:574:611:672 SD: 0.1757 cents 432:460:490:522:574:611:651:693:738:786:864 SD: 0.1526 cents 476:507:540:575:632:673:717:764:813:866:952 SD: 0.1250 cents 543:578:616:656:721:768:818:871:928:988:1086 SD: 0.1169 cents