Scala analysis: xen18-erlich-lemba-06
4L 2s MOS for Lemba, L=230.87, s=139.96
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 230.870 cents 230.870000 2: 370.830 cents 370.830000 3: 601.700 cents 601.700000 4: 832.570 cents 832.570000 5: 972.530 cents 972.530000 6: 1203.400 cents 1203.400000
SHOW/INTERVAL
0: 230.8700 cents 230.8700 1: 230.8700 cents 230.8700 2: 139.9600 cents 139.9600 3: 230.8700 cents 230.8700 4: 230.8700 cents 230.8700 5: 139.9600 cents 139.9600 6: 230.8700 cents 230.8700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 139.96000 cents 1: 4 230.87000 cents 2: 4 370.83000 cents 2: 2 461.74000 cents 3: 6 601.70000 cents 4: 2 741.66000 cents 4: 4 832.57000 cents 5: 4 972.53000 cents 5: 2 1063.44000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.80000 = 9/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 230.9 370.8 601.7 832.6 972.5 1203.4 230.9 : 140.0 370.8 601.7 741.7 972.5 1203.4 370.8 : 230.9 461.7 601.7 832.6 1063.4 1203.4 601.7 : 230.9 370.8 601.7 832.6 972.5 1203.4 832.6 : 140.0 370.8 601.7 741.7 972.5 1203.4 972.5 : 230.9 461.7 601.7 832.6 1063.4 1203.4 1203.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 139.9600 .. 230.8700 cents 90.91000 cents 139.96000 cents 2: 370.8300 .. 461.7400 cents 90.91000 cents 139.96000 cents 3: 601.7000 .. 601.7000 cents 1/1, 0.0000 cents 139.96000 cents 4: 741.6600 .. 832.5700 cents 90.91000 cents 139.96000 cents 5: 972.5300 .. 1063.4400 cents 90.91000 cents 139.96000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 139.96000 cents, class 1 Average step (divided formal octave): 200.5667 cents Largest one step interval : 230.87000 cents Average / Smallest step : 1.433028 Largest / Average step : 1.151089 Largest / Smallest step : 1.649543 Median interval of one step : 230.87000 cents, amount: 4 Most common interval of one step : 230.87000 cents, amount: 4 Least squares average step : 199.90066 cents, oct.: 1199.40396 cents Scale is strictly proper Scale has 2 repeating blocks of 3 notes Blocks have Myhill's property chromas: 90.91000 cents and 49.05000 cents, ratio: 1.853415 generators: 1 of 230.87000 cents and 2 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: 160 257 417 577 674 834 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: 420 = 414 more = 7000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABA Step pattern size order : LSLLSL Scale is a Constant Structure, by a margin of 139.96000 cents Scale diversity : 1.259707 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.697823 Rothenberg efficiency (ambiguous key): 0.544444 redundancy: 0.455556 Efficiency x scale size : 3.266667 Number of different interval sizes : 9 = 1.80000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.80000 = 9/5 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 90.91000 cents Most common intervals : 601.70000 cents & inv., amount: 6 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 6 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 Limited inverse transpositions : 3 Inversional symmetry on degrees : 0 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 24.7426 c. M:-30.3033 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 10: 2 1 2 2 1 2 SP B ME I SD: 8.0098 c. M:-9.8100 c. Lemba-6 16: 3 2 3 3 2 3 SP B ME I SD: 4.2723 c. M:-5.2325 c. Astrology-6, Lemba-6 26: 5 3 5 5 3 5 SP B DE I SD: 0.4516 c. M:-0.5531 c. Lemba-6 94: 18 11 18 18 11 18 SP B DE I SD: 0.3525 c. M:-0.4317 c. Lemba-6 120: 23 14 23 23 14 23 SP B DE I SD: 0.1783 c. M:-0.2183 c. 146: 28 17 28 28 17 28 SP B DE I SD: 0.0661 c. M:-0.0810 c. 172: 33 20 33 33 20 33 SP B DE I SD: 0.0122 c. M:-0.0149 c. 490: 94 57 94 94 57 94 SP B DE I SD: 0.0112 c. M:-0.0137 c. 662: 127 77 127 127 77 127 SP B DE I SD: 0.0051 c. M:-0.0063 c. 834: 160 97 160 160 97 160 SP B DE I SD: 0.0015 c. M:-0.0019 c. 1006: 193 117 193 193 117 193 SP B DE I SD: 0.0008 c. M:-0.0010 c. 1840: 353 214 353 353 214 353 SP B DE I SD: 0.0003 c. M:-0.0003 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 3.4000 cents 2 x x 3 x x 4 S SD: 50.1563 cents 3 x x 4:5 x 6 S SD: 38.6408 cents 4 x 5:6 x 7:8 S SD: 25.3920 cents 5 x 6:7:8:9:10 S SD: 15.2487 cents 6:7 x 9:10:11:12 SD: 28.2447 cents 7:8:9:10:11:12:14 S SD: 15.3204 cents 8:9:10:11:13:14:16 SD: 9.9910 cents 12:14:15:17:19:21:24 SD: 9.0257 cents 13:15:16:18:21:23:26 SD: 7.6926 cents 16:18:20:23:26:28:32 SD: 6.9948 cents 20:23:25:28:32:35:40 SD: 5.5598 cents 21:24:26:30:34:37:42 SD: 3.0239 cents 29:33:36:41:47:51:58 SD: 1.7839 cents 50:57:62:71:81:88:100 SD: 1.6992 cents 63:72:78:89:102:110:126 SD: 1.5485 cents 70:80:87:99:113:123:140 SD: 1.3806 cents 84:96:104:119:136:147:168 SD: 0.9251 cents 113:129:140:160:183:198:226 SD: 0.7610 cents 142:162:176:201:230:249:285 SD: 0.7608 cents 146:167:181:207:236:256:293 SD: 0.7404 cents 147:168:182:208:238:258:295 SD: 0.5863 cents 154:176:191:218:249:270:309 SD: 0.5138 cents 175:200:217:248:283:307:351 SD: 0.4990 cents 183:209:227:259:296:321:367 SD: 0.4587 cents 188:215:233:266:304:330:377 SD: 0.4563 cents 217:248:269:307:351:381:435 SD: 0.4283 cents 231:264:286:327:374:405:463 SD: 0.3417 cents 238:272:295:337:385:417:477 SD: 0.3235 cents 267:305:331:378:432:468:535 SD: 0.2751 cents 272:311:337:385:440:477:545 SD: 0.1924 cents 301:344:373:426:487:528:603 SD: 0.1728 cents 491:561:608:695:794:861:984 SD: 0.1642 cents 520:594:644:736:841:912:1042 SD: 0.1451 cents