Scala analysis: xen18-erlich-lemba-16
10L 6s MOS for Lemba, L=90.91, s=49.05
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90.910 cents 90.910000 2: 139.960 cents 139.960000 3: 230.870 cents 230.870000 4: 279.920 cents 279.920000 5: 370.830 cents 370.830000 6: 461.740 cents 461.740000 7: 510.790 cents 510.790000 8: 601.700 cents 601.700000 9: 692.610 cents 692.610000 10: 741.660 cents 741.660000 11: 832.570 cents 832.570000 12: 881.620 cents 881.620000 13: 972.530 cents 972.530000 14: 1063.440 cents 1063.440000 15: 1112.490 cents 1112.490000 16: 1203.400 cents 1203.400000
SHOW/INTERVAL
0: 90.9100 cents 90.9100 1: 90.9100 cents 90.9100 2: 49.0500 cents 49.0500 3: 90.9100 cents 90.9100 4: 49.0500 cents 49.0500 5: 90.9100 cents 90.9100 6: 90.9100 cents 90.9100 7: 49.0500 cents 49.0500 8: 90.9100 cents 90.9100 9: 90.9100 cents 90.9100 10: 49.0500 cents 49.0500 11: 90.9100 cents 90.9100 12: 49.0500 cents 49.0500 13: 90.9100 cents 90.9100 14: 90.9100 cents 90.9100 15: 49.0500 cents 49.0500 16: 90.9100 cents 90.9100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 49.05000 cents 1: 10 90.91000 cents 2: 12 139.96000 cents 2: 4 181.82000 cents 3: 2 189.01000 cents 3: 14 230.87000 cents 4: 8 279.92000 cents 4: 8 321.78000 cents 5: 14 370.83000 cents 5: 2 412.69000 cents 6: 4 419.88000 cents 6: 12 461.74000 cents 7: 10 510.79000 cents 7: 6 552.65000 cents 8: 16 601.70000 cents 9: 6 650.75000 cents 9: 10 692.61000 cents 10: 12 741.66000 cents 10: 4 783.52000 cents 11: 2 790.71000 cents 11: 14 832.57000 cents 12: 8 881.62000 cents 12: 8 923.48000 cents 13: 14 972.53000 cents 13: 2 1014.39000 cents 14: 4 1021.58000 cents 14: 12 1063.44000 cents 15: 10 1112.49000 cents 15: 6 1154.35000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.93333 = 29/15
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 90.9 140.0 230.9 279.9 370.8 461.7 510.8 601.7 692.6 741.7 832.6 881.6 972.5 1063.4 1112.5 1203.4 90.9 : 49.0 140.0 189.0 279.9 370.8 419.9 510.8 601.7 650.8 741.7 790.7 881.6 972.5 1021.6 1112.5 1203.4 140.0 : 90.9 140.0 230.9 321.8 370.8 461.7 552.6 601.7 692.6 741.7 832.6 923.5 972.5 1063.4 1154.3 1203.4 230.9 : 49.0 140.0 230.9 279.9 370.8 461.7 510.8 601.7 650.7 741.7 832.6 881.6 972.5 1063.4 1112.5 1203.4 279.9 : 90.9 181.8 230.9 321.8 412.7 461.7 552.6 601.7 692.6 783.5 832.6 923.5 1014.4 1063.4 1154.4 1203.4 370.8 : 90.9 140.0 230.9 321.8 370.8 461.7 510.8 601.7 692.6 741.7 832.6 923.5 972.5 1063.4 1112.5 1203.4 461.7 : 49.1 140.0 230.9 279.9 370.8 419.9 510.8 601.7 650.8 741.7 832.6 881.6 972.5 1021.6 1112.5 1203.4 510.8 : 90.9 181.8 230.9 321.8 370.8 461.7 552.7 601.7 692.6 783.5 832.6 923.5 972.5 1063.4 1154.3 1203.4 601.7 : 90.9 140.0 230.9 279.9 370.8 461.7 510.8 601.7 692.6 741.7 832.6 881.6 972.5 1063.4 1112.5 1203.4 692.6 : 49.1 140.0 189.0 279.9 370.8 419.9 510.8 601.7 650.8 741.7 790.7 881.6 972.5 1021.6 1112.5 1203.4 741.7 : 90.9 140.0 230.9 321.8 370.8 461.7 552.6 601.7 692.6 741.7 832.6 923.5 972.5 1063.4 1154.4 1203.4 832.6 : 49.0 140.0 230.9 279.9 370.8 461.7 510.8 601.7 650.8 741.7 832.6 881.6 972.5 1063.4 1112.5 1203.4 881.6 : 90.9 181.8 230.9 321.8 412.7 461.7 552.7 601.7 692.6 783.5 832.6 923.5 1014.4 1063.4 1154.4 1203.4 972.5 : 90.9 140.0 230.9 321.8 370.8 461.7 510.8 601.7 692.6 741.7 832.6 923.5 972.5 1063.4 1112.5 1203.4 1063.4: 49.0 140.0 230.9 279.9 370.8 419.9 510.8 601.7 650.8 741.7 832.6 881.6 972.5 1021.6 1112.5 1203.4 1112.5: 90.9 181.8 230.9 321.8 370.8 461.7 552.7 601.7 692.6 783.5 832.6 923.5 972.5 1063.4 1154.4 1203.4 1203.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.0500 .. 90.9100 cents 41.86000 cents 49.05000 cents 2: 139.9600 .. 181.8200 cents 41.86000 cents 49.05000 cents 3: 189.0100 .. 230.8700 cents 41.86000 cents 7.19000 cents 4: 279.9200 .. 321.7800 cents 41.86000 cents 49.05000 cents 5: 370.8300 .. 412.6900 cents 41.86000 cents 49.05000 cents 6: 419.8800 .. 461.7400 cents 41.86000 cents 7.19000 cents 7: 510.7900 .. 552.6500 cents 41.86000 cents 49.05000 cents 8: 601.7000 .. 601.7000 cents 1/1, 0.0000 cents 49.05000 cents 9: 650.7500 .. 692.6100 cents 41.86000 cents 49.05000 cents 10: 741.6600 .. 783.5200 cents 41.86000 cents 49.05000 cents 11: 790.7100 .. 832.5700 cents 41.86000 cents 7.19000 cents 12: 881.6200 .. 923.4800 cents 41.86000 cents 49.05000 cents 13: 972.5300 .. 1014.3900 cents 41.86000 cents 49.05000 cents 14: 1021.5800 .. 1063.4400 cents 41.86000 cents 7.19000 cents 15: 1112.4900 .. 1154.3500 cents 41.86000 cents 49.05000 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 49.05000 cents, class 1 Average step (divided formal octave): 75.2125 cents Largest one step interval : 90.91000 cents Average / Smallest step : 1.533384 Largest / Average step : 1.208709 Largest / Smallest step : 1.853415 Median interval of one step : 90.91000 cents, amount: 10 Most common interval of one step : 90.91000 cents, amount: 10 Least squares average step : 74.90471 cents, oct.: 1198.47529 cents Scale is strictly proper Scale has 2 repeating blocks of 8 notes Blocks have Myhill's property chromas: 41.86000 cents and 7.19000 cents, ratio: 5.821975 generators: 3 of 230.87000 cents and 5 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 1006-tone equal temperament with octave 1203.400 cents degrees: 76 117 193 234 310 386 427 503 579 620 696 737 813 889 930 1006 Least number of segments generator : 505 of 604.092 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 813 of 972.529 cents and inv. generated superset size: 511 = 495 more = 3193.750% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABAABABAABA Step pattern size order : LSLSLLSLLSLSLLSL Scale is a Constant Structure, by a margin of 7.19000 cents Scale diversity : 1.186581 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.513013 Number of different interval sizes : 29 = 1.93333 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.93333 = 29/15 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 7.19000 cents Most common intervals : 601.70000 cents & inv., amount: 16 Number of recognisable fifths : 10, average 692.6100 cents Number of recognisable fourths : 10, average 510.7900 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best major thirds form a closed circle Formal octave complements present : 14 = 87.5000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 8 Limited inverse transpositions : 5 13 Inversional symmetry on intervals : 2-3 6-7 10-11 14-15 -- Rational properties --
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.2713 c. M:-20.9300 c. 26: 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P B ME SD: 1.2971 c. M: 2.2123 c. 94: 7 4 7 4 7 7 4 7 7 4 7 4 7 7 4 7 SP B DE SD: 1.0124 c. M:-1.7268 c. 120: 9 5 9 5 9 9 5 9 9 5 9 5 9 9 5 9 SP B DE SD: 0.5120 c. M:-0.8733 c. 146: 11 6 11 6 11 11 6 11 11 6 11 6 11 11 6 11 SP B DE SD: 0.1899 c. M:-0.3238 c. 172: 13 7 13 7 13 13 7 13 13 7 13 7 13 13 7 13 SP B DE SD: 0.0349 c. M: 0.0595 c. 490: 37 20 37 20 37 37 20 37 37 20 37 20 37 37 20 37 SP B DE SD: 0.0321 c. M:-0.0547 c. 662: 50 27 50 27 50 50 27 50 50 27 50 27 50 50 27 50 SP B DE SD: 0.0147 c. M:-0.0250 c. 834: 63 34 63 34 63 63 34 63 63 34 63 34 63 63 34 63 SP B DE SD: 0.0044 c. M:-0.0076 c. 1006: 76 41 76 41 76 76 41 76 76 41 76 41 76 76 41 76 SP B DE SD: 0.0023 c. M: 0.0039 c. 1840: 139 75 139 75 139 139 75 139 139 75 139 75 139 139 75 139 SP B DE SD: 0.0008 c. M:-0.0013 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 3.4000 cents 2 .. 4 match: 2 H SD: 4.9721 cents 3 .. 6 match: 3 H SD: 4.4907 cents 4 .. 8 match: 4 H SD: 4.6928 cents 5 .. 10 match: 5 H SD: 12.7174 cents 6 .. 12 match: 6 H SD: 4.2074 cents 7 .. 14 match: 7 H SD: 9.3234 cents 8 .. 16 match: 8 H SD: 7.2583 cents 9 .. 18 match: 9 H SD: 7.8392 cents 10 .. 20 match: 10 H SD: 7.8656 cents 11 .. 22 match: 11 H SD: 7.5394 cents 12 .. 24 match: 12 H SD: 4.1294 cents 13 .. 26 match: 13 H SD: 5.3289 cents 14 .. 28 match: 12 SD: 5.9771 cents 15 .. 30 match: 14 S SD: 5.8483 cents 16 .. 32 match: 13 SD: 5.2005 cents 17 .. 34 match: 14 S SD: 4.4762 cents 18 .. 36 match: 14 SD: 5.2280 cents 19 .. 38 match: 15 SD: 4.9887 cents 20 .. 40 match: 16 SD: 3.8469 cents 21 .. 42 match: 16 SD: 3.2323 cents 25 .. 50 match: 15 SD: 4.1055 cents 26 .. 52 match: 16 SD: 3.1986 cents 28 .. 56 match: 15 SD: 3.1813 cents 29 .. 58 match: 15 SD: 2.6016 cents 33 .. 66 match: 16 SD: 2.2139 cents 34 .. 68 match: 16 SD: 2.0903 cents 39 .. 78 match: 16 SD: 1.9820 cents 41 .. 82 match: 16 SD: 1.8961 cents 47 .. 94 match: 16 SD: 1.8943 cents 49 .. 98 match: 16 SD: 1.6887 cents 50 .. 100 match: 16 SD: 1.4890 cents 56 .. 112 match: 16 SD: 1.4823 cents 58 .. 116 match: 16 SD: 1.2416 cents 69 .. 138 match: 16 SD: 1.1757 cents 71 .. 142 match: 16 SD: 1.1524 cents 72 .. 144 match: 16 SD: 1.1340 cents 73 .. 146 match: 16 SD: 1.0926 cents 75 .. 150 match: 16 SD: 0.9938 cents 79 .. 158 match: 16 SD: 0.9773 cents 84 .. 168 match: 16 SD: 0.9199 cents 91 .. 182 match: 16 SD: 0.8117 cents 92 .. 184 match: 16 SD: 0.7027 cents 108 .. 216 match: 16 SD: 0.6888 cents 118 .. 236 match: 16 SD: 0.6616 cents 125 .. 250 match: 16 SD: 0.6474 cents 130 .. 261 match: 16 SD: 0.6271 cents 131 .. 263 match: 16 SD: 0.5325 cents 146 .. 293 match: 16 SD: 0.5170 cents 154 .. 309 match: 16 SD: 0.4025 cents 183 .. 367 match: 16 SD: 0.3670 cents 204 .. 409 match: 16 SD: 0.3263 cents 222 .. 445 match: 16 SD: 0.3172 cents 238 .. 477 match: 16 SD: 0.2617 cents 262 .. 525 match: 16 SD: 0.2559 cents 295 .. 591 match: 16 SD: 0.2478 cents 297 .. 595 match: 16 SD: 0.2234 cents 301 .. 603 match: 16 SD: 0.2046 cents 370 .. 741 match: 16 SD: 0.1952 cents 393 .. 788 match: 16 SD: 0.1633 cents 426 .. 854 match: 16 SD: 0.1529 cents 428 .. 858 match: 16 SD: 0.1442 cents 484 .. 970 match: 16 SD: 0.1309 cents 520 .. 1042 match: 16 SD: 0.1232 cents 559 .. 1120 match: 16 SD: 0.1216 cents