Scala analysis: lemba12
Lemba[12] in 270-et (poptimal)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.333 cents 93.333333 2: 137.778 cents 137.777778 3: 231.111 cents 231.111111 4: 368.889 cents 368.888889 5: 462.222 cents 462.222222 6: 600.000 cents 600.000000 7: 693.333 cents 693.333333 8: 737.778 cents 737.777778 9: 831.111 cents 831.111111 10: 968.889 cents 968.888889 11: 1062.222 cents 1062.222222 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 137.7778 cents 137.7778 1: 93.3333 cents 93.3333 2: 44.4444 cents 44.4444 3: 93.3333 cents 93.3333 4: 137.7778 cents 137.7778 5: 93.3333 cents 93.3333 6: 137.7778 cents 137.7778 7: 93.3333 cents 93.3333 8: 44.4444 cents 44.4444 9: 93.3333 cents 93.3333 10: 137.7778 cents 137.7778 11: 93.3333 cents 93.3333 12: 137.7778 cents 137.7778
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 44.44445 cents 1: 6 93.33333 cents 1: 4 137.77778 cents 2: 4 137.77778 cents 2: 8 231.11111 cents 3: 2 231.11111 cents 3: 4 275.55556 cents 3: 4 324.44444 cents 3: 2 368.88889 cents 4: 8 368.88889 cents 4: 4 462.22222 cents 5: 4 462.22222 cents 5: 6 506.66667 cents 5: 2 555.55555 cents 6: 12 600.00000 cents 7: 2 644.44444 cents 7: 6 693.33333 cents 7: 4 737.77778 cents 8: 4 737.77778 cents 8: 8 831.11111 cents 9: 2 831.11111 cents 9: 4 875.55556 cents 9: 4 924.44444 cents 9: 2 968.88889 cents 10: 8 968.88889 cents 10: 4 1062.22222 cents 11: 4 1062.22222 cents 11: 6 1106.66667 cents 11: 2 1155.55555 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.63636 = 29/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.3 137.8 231.1 368.9 462.2 600.0 693.3 737.8 831.1 968.9 1062.2 1200.0 93.3 : 44.4 137.8 275.6 368.9 506.7 600.0 644.4 737.8 875.6 968.9 1106.7 1200.0 137.8 : 93.3 231.1 324.4 462.2 555.6 600.0 693.3 831.1 924.4 1062.2 1155.6 1200.0 231.1 : 137.8 231.1 368.9 462.2 506.7 600.0 737.8 831.1 968.9 1062.2 1106.7 1200.0 368.9 : 93.3 231.1 324.4 368.9 462.2 600.0 693.3 831.1 924.4 968.9 1062.2 1200.0 462.2 : 137.8 231.1 275.6 368.9 506.7 600.0 737.8 831.1 875.6 968.9 1106.7 1200.0 600.0 : 93.3 137.8 231.1 368.9 462.2 600.0 693.3 737.8 831.1 968.9 1062.2 1200.0 693.3 : 44.4 137.8 275.6 368.9 506.7 600.0 644.4 737.8 875.6 968.9 1106.7 1200.0 737.8 : 93.3 231.1 324.4 462.2 555.6 600.0 693.3 831.1 924.4 1062.2 1155.6 1200.0 831.1 : 137.8 231.1 368.9 462.2 506.7 600.0 737.8 831.1 968.9 1062.2 1106.7 1200.0 968.9 : 93.3 231.1 324.4 368.9 462.2 600.0 693.3 831.1 924.4 968.9 1062.2 1200.0 1062.2: 137.8 231.1 275.6 368.9 506.7 600.0 737.8 831.1 875.6 968.9 1106.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 137.7778 cents 93.33333 cents 44.44445 cents 2: 137.7778 .. 231.1111 cents 93.33333 cents 1/1, 0.0000 cents 3: 231.1111 .. 368.8889 cents 137.77778 cents 1/1, 0.0000 cents 4: 368.8889 .. 462.2222 cents 93.33333 cents 1/1, 0.0000 cents 5: 462.2222 .. 555.5556 cents 93.33333 cents 1/1, 0.0000 cents 6: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 44.44444 cents 7: 644.4444 .. 737.7778 cents 93.33333 cents 44.44444 cents 8: 737.7778 .. 831.1111 cents 93.33333 cents 1/1, 0.0000 cents 9: 831.1111 .. 968.8889 cents 137.77778 cents 1/1, 0.0000 cents 10: 968.8889 .. 1062.2222 cents 93.33333 cents 1/1, 0.0000 cents 11: 1062.2222 .. 1155.5556 cents 93.33333 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 137.77778 cents Average / Smallest step : 2.250000 Largest / Average step : 1.377778 Largest / Smallest step : 3.100000 Median interval of one step : 93.33333 cents, amount: 6 Most common interval of one step : 93.33333 cents, amount: 6 Least squares average step : 96.08889 cents, oct.: 1153.06667 cents Scale is proper Scale has 2 repeating blocks of 6 notes Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 21 31 52 83 104 135 156 166 187 218 239 270 Least number of segments generator : 137 of 608.889 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 187 of 831.111 cents and inv. generated superset size: 141 = 129 more = 1175.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACACABACAC Step pattern size order : MSMLMLMSMLML Scale is not a Constant Structure Scale diversity : 1.200634 Rothenberg stability : 0.454545 = 5/11 Lumma stability : 0.148148 Rothenberg efficiency (ambiguous key): 0.505556 redundancy: 0.494444 Efficiency x scale size : 6.066667 Number of different interval sizes : 21 = 1.90909 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.63636 = 29/11 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 44.44444 cents Most common intervals : 600.00000 cents & inv., amount: 12 Number of recognisable fifths : 6, average 693.3333 cents Scale contains two identical disjunct hexachords Formal octave complements present : 10 = 83.3333% Limited transpositions : 6 Limited inverse transpositions : 3 9 Inversional symmetry on intervals : 1-2 4-5 7-8 10-11 -- Rational properties --
FIT/MODE
12: 1 0 1 2 1 1 1 0 1 2 1 1 N B D3 SD: 28.3859 c. M: 37.7778 c. 16: 1 1 1 2 1 2 1 1 1 2 1 2 P B D3 SD: 10.8748 c. M: 18.3333 c. 26: 2 1 2 3 2 3 2 1 2 3 2 3 P B SD: 0.6084 c. M: 1.0256 c. 140: 11 5 11 16 11 16 11 5 11 16 11 16 P B SD: 0.5649 c. M:-0.9524 c. 166: 13 6 13 19 13 19 13 6 13 19 13 19 P B SD: 0.3812 c. M:-0.6426 c. 192: 15 7 15 22 15 22 15 7 15 22 15 22 P B SD: 0.2472 c. M:-0.4167 c. 218: 17 8 17 25 17 25 17 8 17 25 17 25 P B SD: 0.1451 c. M:-0.2446 c. 244: 19 9 19 28 19 28 19 9 19 28 19 28 P B SD: 0.0648 c. M:-0.1093 c. 270: 21 10 21 31 21 31 21 10 21 31 21 31 P B SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 4.3108 cents 3 x x x x 4 x x x 5 x x 6 S SD: 21.3921 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 4.8603 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 14.7462 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.5134 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 9.4871 cents 8 x x 9:10 x 11:12 x 13:14:15:16 S SD: 8.1537 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 11.5982 cents 10 x 11 x 12:13:14:15 x 16 x 18:20 S SD: 9.9341 cents 11 x 12:13 x 14 x 16:17:18:19:20:22 S SD: 10.8316 cents 12 x 13:14:15:16:17:18 x 19:21:22:24 SD: 6.6174 cents 13 x 14:15:16:17:18:19:20:21:23:24:26 SD: 5.4113 cents 14 x 15:16:17:18:20:21 x 23:25:26:28 SD: 6.8101 cents 15:16 x 17:19:20:21:22:23:24:26:28:30 SD: 6.8046 cents 16:17 x 18:20:21:23:24:25:26:28:30:32 SD: 5.8261 cents 17:18 x 19:21:22:24:25:26:27:30:31:34 SD: 5.7938 cents 18:19 x 21:22:24:25:27:28:29:32:33:36 SD: 6.8922 cents 19:20:21:22:24:25:27:28:29:31:33:35:38 SD: 5.4489 cents 20:21:22:23:25:26:28:30:31:32:35:37:40 SD: 4.1127 cents 21:22:23:24:26:27:30:31:32:34:37:39:42 SD: 3.9689 cents 26:27:28:30:32:34:37:39:40:42:46:48:52 SD: 3.5903 cents 28 x 30:32:35:37:40:42:43:45:49:52:56 SD: 3.6818 cents 29:31 x 33:36:38:41:43:44:47:51:54:58 SD: 3.2606 cents 30:32 x 34:37:39:42:45:46:48:53:55:60 SD: 3.8201 cents 32:34:35:37:40:42:45:48:49:52:56:59:64 SD: 3.2174 cents 33:35:36:38:41:43:47:49:51:53:58:61:66 SD: 2.8021 cents 34:36:37:39:42:44:48:51:52:55:60:63:68 SD: 2.2630 cents 36:38:39:41:45:47:51:54:55:58:63:66:72 SD: 2.1000 cents 49:52:53:56:61:64:69:73:75:79:86:91:98 SD: 1.6673 cents 55:58:60:63:68:72:78:82:84:89:96:102:110 SD: 1.5044 cents 68:72:74:78:84:89:96:101:104:110:119:126:136 SD: 1.4151 cents 71:75:77:81:88:93:100:106:109:115:124:131:142 SD: 1.0237 cents 75:79:81:86:93:98:106:112:115:121:131:139:150 SD: 0.9922 cents 84:89:91:96:104:110:119:125:129:136:147:155:168 SD: 0.9881 cents 85:90:92:97:105:111:120:127:130:137:149:157:170 SD: 0.8146 cents 92:97:100:105:114:120:130:137:141:149:161:170:184 SD: 0.8129 cents 104:110:113:119:129:136:147:155:159:168:182:192:208 SD: 0.7979 cents 109:115:118:125:135:142:154:163:167:176:191:201:218 SD: 0.7791 cents 111:117:120:127:137:145:157:166:170:179:194:205:222 SD: 0.6937 cents 130:137:141:149:161:170:184:194:199:210:228:240:260 SD: 0.6702 cents 140:148:152:160:173:183:198:209:214:226:245:259:280 SD: 0.6445 cents 143:151:155:163:177:187:202:213:219:231:250:264:286 SD: 0.5888 cents 147:155:159:168:182:192:208:219:225:238:257:272:294 SD: 0.5335 cents 156:165:169:178:193:204:221:233:239:252:273:288:312 SD: 0.5250 cents 160:169:173:183:198:209:226:239:245:259:280:296:320 SD: 0.4736 cents 169:178:183:193:209:221:239:252:259:273:296:312:338 SD: 0.4389 cents 181:191:196:207:224:236:256:270:277:293:317:334:362 SD: 0.4085 cents 203:214:220:232:251:265:287:303:311:328:355:375:406 SD: 0.2824 cents 252:266:273:288:312:329:356:376:386:407:441:465:504 SD: 0.2626 cents 307:324:332:351:380:401:434:458:470:496:537:567:614 SD: 0.2394 cents 341:360:369:390:422:445:482:509:522:551:597:630:682 SD: 0.2258 cents 359:379:389:410:444:469:508:536:550:580:628:663:718 SD: 0.2222 cents 363:383:393:415:449:474:513:542:556:587:635:670:726 SD: 0.2111 cents 399:421:432:456:494:521:564:596:611:645:698:737:798 SD: 0.1725 cents 412:435:446:471:510:538:583:615:631:666:721:761:824 SD: 0.1374 cents 471:497:510:538:583:615:666:703:721:761:824:870:942 SD: 0.1258 cents 581:613:629:664:719:759:822:867:890:939:1017:1073:1162 SD: 0.1084 cents