Scala analysis: xen18-erlich-lemba-10
6L 4s MOS for Lemba, L=139.96, s=90.91
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 139.960 cents 139.960000 2: 230.870 cents 230.870000 3: 370.830 cents 370.830000 4: 461.740 cents 461.740000 5: 601.700 cents 601.700000 6: 741.660 cents 741.660000 7: 832.570 cents 832.570000 8: 972.530 cents 972.530000 9: 1063.440 cents 1063.440000 10: 1203.400 cents 1203.400000
SHOW/INTERVAL
0: 139.9600 cents 139.9600 1: 139.9600 cents 139.9600 2: 90.9100 cents 90.9100 3: 139.9600 cents 139.9600 4: 90.9100 cents 90.9100 5: 139.9600 cents 139.9600 6: 139.9600 cents 139.9600 7: 90.9100 cents 90.9100 8: 139.9600 cents 139.9600 9: 90.9100 cents 90.9100 10: 139.9600 cents 139.9600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 90.91000 cents 1: 6 139.96000 cents 2: 8 230.87000 cents 2: 2 279.92000 cents 3: 2 321.78000 cents 3: 8 370.83000 cents 4: 6 461.74000 cents 4: 4 510.79000 cents 5: 10 601.70000 cents 6: 4 692.61000 cents 6: 6 741.66000 cents 7: 8 832.57000 cents 7: 2 881.62000 cents 8: 2 923.48000 cents 8: 8 972.53000 cents 9: 6 1063.44000 cents 9: 4 1112.49000 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 : 140.0 230.9 370.8 461.7 601.7 741.7 832.6 972.5 1063.4 1203.4 140.0 : 90.9 230.9 321.8 461.7 601.7 692.6 832.6 923.5 1063.4 1203.4 230.9 : 140.0 230.9 370.8 510.8 601.7 741.7 832.6 972.5 1112.5 1203.4 370.8 : 90.9 230.9 370.8 461.7 601.7 692.6 832.6 972.5 1063.4 1203.4 461.7 : 140.0 279.9 370.8 510.8 601.7 741.7 881.6 972.5 1112.5 1203.4 601.7 : 140.0 230.9 370.8 461.7 601.7 741.7 832.6 972.5 1063.4 1203.4 741.7 : 90.9 230.9 321.8 461.7 601.7 692.6 832.6 923.5 1063.4 1203.4 832.6 : 140.0 230.9 370.8 510.8 601.7 741.7 832.6 972.5 1112.5 1203.4 972.5 : 90.9 230.9 370.8 461.7 601.7 692.6 832.6 972.5 1063.4 1203.4 1063.4: 140.0 279.9 370.8 510.8 601.7 741.7 881.6 972.5 1112.5 1203.4 1203.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.9100 .. 139.9600 cents 49.05000 cents 90.91000 cents 2: 230.8700 .. 279.9200 cents 49.05000 cents 90.91000 cents 3: 321.7800 .. 370.8300 cents 49.05000 cents 41.86000 cents 4: 461.7400 .. 510.7900 cents 49.05000 cents 90.91000 cents 5: 601.7000 .. 601.7000 cents 1/1, 0.0000 cents 90.91000 cents 6: 692.6100 .. 741.6600 cents 49.05000 cents 90.91000 cents 7: 832.5700 .. 881.6200 cents 49.05000 cents 90.91000 cents 8: 923.4800 .. 972.5300 cents 49.05000 cents 41.86000 cents 9: 1063.4400 .. 1112.4900 cents 49.05000 cents 90.91000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 90.91000 cents, class 1 Average step (divided formal octave): 120.3400 cents Largest one step interval : 139.96000 cents Average / Smallest step : 1.323727 Largest / Average step : 1.163038 Largest / Smallest step : 1.539545 Median interval of one step : 139.96000 cents, amount: 6 Most common interval of one step : 139.96000 cents, amount: 6 Least squares average step : 120.08519 cents, oct.: 1200.85195 cents Scale is strictly proper Scale has 2 repeating blocks of 5 notes Blocks have Myhill's property chromas: 49.05000 cents and 41.86000 cents, ratio: 1.171763 generators: 2 of 230.87000 cents and 3 of 370.83000 cents ET pair of linear temperament : 26&146 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 834-tone equal temperament with octave 1203.400 cents degrees: 97 160 257 320 417 514 577 674 737 834 Least number of segments generator : 419 of 604.586 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 577 of 832.568 cents and inv. generated superset size: 422 = 412 more = 4220.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABA Step pattern size order : LSLSLLSLSL Scale is a Constant Structure, by a margin of 41.86000 cents Scale diversity : 1.208995 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.673924 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 : 41.86000 cents Most common intervals : 601.70000 cents & inv., amount: 10 Number of recognisable fifths : 4, average 692.6100 cents Number of recognisable fourths : 4, average 510.7900 cents Scale contains two identical disjunct pentachords Best major thirds form a closed circle Formal octave complements present : 10 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 5 Limited inverse transpositions : 5 Inversional symmetry on degrees : 0 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.8734 c. M:-19.6200 c. 16: 2 1 2 1 2 2 1 2 1 2 P B ME I SD: 7.3999 c. M:-10.4650 c. Lemba-10 26: 3 2 3 2 3 3 2 3 2 3 SP B ME I SD: 0.7822 c. M:-1.1062 c. Lemba-10 94: 11 7 11 7 11 11 7 11 7 11 SP B DE I SD: 0.6105 c. M: 0.8634 c. Lemba-10 120: 14 9 14 9 14 14 9 14 9 14 SP B DE I SD: 0.3088 c. M:-0.4367 c. 146: 17 11 17 11 17 17 11 17 11 17 SP B DE I SD: 0.1145 c. M: 0.1619 c. 172: 20 13 20 13 20 20 13 20 13 20 SP B DE I SD: 0.0210 c. M:-0.0298 c. 490: 57 37 57 37 57 57 37 57 37 57 SP B DE I SD: 0.0193 c. M:-0.0273 c. 662: 77 50 77 50 77 77 50 77 50 77 SP B DE I SD: 0.0088 c. M: 0.0125 c. 834: 97 63 97 63 97 97 63 97 63 97 SP B DE I SD: 0.0027 c. M: 0.0038 c. 1006: 117 76 117 76 117 117 76 117 76 117 SP B DE I SD: 0.0014 c. M:-0.0019 c. 1840: 214 139 214 139 214 214 139 214 139 214 SP B DE I SD: 0.0005 c. M: 0.0007 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 3.4000 cents 2 x x x x x 3 x x x 4 S SD: 19.9252 cents 3 x x x 4 x x 5 x x 6 S SD: 21.1126 cents 4 x x 5 x x 6 x 7 x 8 S SD: 10.7282 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 15.2487 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 14.0262 cents 7 x 8 x 9:10:11 x 12:13:14 S SD: 9.3234 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 9.5086 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 11.1616 cents 10:11 x 12:13:14:15:16:18 x 20 S SD: 11.2315 cents 11:12:13 x 14:16:17:18:19:20:22 S SD: 10.9656 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 7.7636 cents 13:14:15:16:17:18:20:21:23:24:26 SD: 4.7902 cents 20:22:23:25:26:28:31:32:35:37:40 SD: 4.5720 cents 21:23:24:26:27:30:32:34:37:39:42 SD: 3.9625 cents 26:28:30:32:34:37:40:42:46:48:52 SD: 3.0158 cents 33:36:38:41:43:47:51:53:58:61:66 SD: 2.7605 cents 34:37:39:42:44:48:52:55:60:63:68 SD: 2.3516 cents 45:49:51:56:59:64:69:73:79:83:90 SD: 2.2137 cents 46:50:53:57:60:65:71:74:81:85:92 SD: 2.2024 cents 48:52:55:59:63:68:74:78:84:89:96 SD: 2.1730 cents 49:53:56:61:64:69:75:79:86:91:98 SD: 1.7534 cents 50:54:57:62:65:71:77:81:88:92:100 SD: 1.7344 cents 58:63:66:72:76:82:89:94:102:107:116 SD: 1.3188 cents 79:86:90:98:103:112:121:128:139:146:158 SD: 1.2606 cents 82:89:94:102:107:116:126:133:144:152:164 SD: 1.2430 cents 84:91:96:104:110:119:129:136:147:155:168 SD: 0.8256 cents 105:114:120:130:137:149:161:170:184:194:210 SD: 0.6733 cents 118:128:135:146:154:167:181:191:207:218:236 SD: 0.5081 cents 154:167:176:191:201:218:236:249:270:285:309 SD: 0.4665 cents 176:191:201:218:230:249:270:285:309:325:353 SD: 0.4442 cents 202:219:231:250:264:286:310:327:354:373:405 SD: 0.3846 cents 226:245:258:280:295:320:347:366:396:418:453 SD: 0.3402 cents 238:258:272:295:311:337:365:385:417:440:477 SD: 0.2787 cents 272:295:311:337:355:385:417:440:477:503:545 SD: 0.2583 cents 288:312:329:357:376:408:442:466:505:532:577 SD: 0.2527 cents 301:326:344:373:393:426:462:487:528:556:603 SD: 0.2355 cents 344:373:393:426:449:487:528:556:603:636:689 SD: 0.2130 cents 402:436:459:498:525:569:617:650:705:743:806 SD: 0.1891 cents 426:462:487:528:556:603:654:689:747:787:854 SD: 0.1844 cents 428:464:489:530:559:606:657:692:751:791:858 SD: 0.1739 cents 462:501:528:572:603:654:709:747:810:854:926 SD: 0.1644 cents 510:553:583:632:666:722:783:825:894:943:1022 SD: 0.1517 cents 520:564:594:644:679:736:798:841:912:961:1042 SD: 0.1140 cents