Scala analysis: xen18-erlich-lemba-26
16L 10s MOS for Lemba, L=49.05, s=41.86
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49.050 cents 49.050000 2: 90.910 cents 90.910000 3: 139.960 cents 139.960000 4: 181.820 cents 181.820000 5: 230.870 cents 230.870000 6: 279.920 cents 279.920000 7: 321.780 cents 321.780000 8: 370.830 cents 370.830000 9: 419.880 cents 419.880000 10: 461.740 cents 461.740000 11: 510.790 cents 510.790000 12: 552.650 cents 552.650000 13: 601.700 cents 601.700000 14: 650.750 cents 650.750000 15: 692.610 cents 692.610000 16: 741.660 cents 741.660000 17: 783.520 cents 783.520000 18: 832.570 cents 832.570000 19: 881.620 cents 881.620000 20: 923.480 cents 923.480000 21: 972.530 cents 972.530000 22: 1021.580 cents 1021.580000 23: 1063.440 cents 1063.440000 24: 1112.490 cents 1112.490000 25: 1154.350 cents 1154.350000 26: 1203.400 cents 1203.400000
SHOW/INTERVAL
0: 49.0500 cents 49.0500 1: 49.0500 cents 49.0500 2: 41.8600 cents 41.8600 3: 49.0500 cents 49.0500 4: 41.8600 cents 41.8600 5: 49.0500 cents 49.0500 6: 49.0500 cents 49.0500 7: 41.8600 cents 41.8600 8: 49.0500 cents 49.0500 9: 49.0500 cents 49.0500 10: 41.8600 cents 41.8600 11: 49.0500 cents 49.0500 12: 41.8600 cents 41.8600 13: 49.0500 cents 49.0500 14: 49.0500 cents 49.0500 15: 41.8600 cents 41.8600 16: 49.0500 cents 49.0500 17: 41.8600 cents 41.8600 18: 49.0500 cents 49.0500 19: 49.0500 cents 49.0500 20: 41.8600 cents 41.8600 21: 49.0500 cents 49.0500 22: 49.0500 cents 49.0500 23: 41.8600 cents 41.8600 24: 49.0500 cents 49.0500 25: 41.8600 cents 41.8600 26: 49.0500 cents 49.0500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 41.86000 cents 1: 16 49.05000 cents 2: 20 90.91000 cents 2: 6 98.10000 cents 3: 4 132.77000 cents 3: 22 139.96000 cents 4: 14 181.82000 cents 4: 12 189.01000 cents 5: 24 230.87000 cents 5: 2 238.06000 cents 6: 8 272.73000 cents 6: 18 279.92000 cents 7: 18 321.78000 cents 7: 8 328.97000 cents 8: 2 363.64000 cents 8: 24 370.83000 cents 9: 12 412.69000 cents 9: 14 419.88000 cents 10: 22 461.74000 cents 10: 4 468.93000 cents 11: 6 503.60000 cents 11: 20 510.79000 cents 12: 16 552.65000 cents 12: 10 559.84000 cents 13: 26 601.70000 cents 14: 10 643.56000 cents 14: 16 650.75000 cents 15: 20 692.61000 cents 15: 6 699.80000 cents 16: 4 734.47000 cents 16: 22 741.66000 cents 17: 14 783.52000 cents 17: 12 790.71000 cents 18: 24 832.57000 cents 18: 2 839.76000 cents 19: 8 874.43000 cents 19: 18 881.62000 cents 20: 18 923.48000 cents 20: 8 930.67000 cents 21: 2 965.34000 cents 21: 24 972.53000 cents 22: 12 1014.39000 cents 22: 14 1021.58000 cents 23: 22 1063.44000 cents 23: 4 1070.63000 cents 24: 6 1105.30000 cents 24: 20 1112.49000 cents 25: 16 1154.35000 cents 25: 10 1161.54000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.96000 = 49/25
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0.0 : 49.0 90.9 140.0 181.8 230.9 279.9 321.8 370.8 419.9 461.7 510.8 552.6 601.7 650.8 692.6 741.7 783.5 832.6 881.6 923.5 972.5 1021.6 1063.4 1112.5 1154.3 1203.4 49.0 : 41.9 90.9 132.8 181.8 230.9 272.7 321.8 370.8 412.7 461.7 503.6 552.7 601.7 643.6 692.6 734.5 783.5 832.6 874.4 923.5 972.5 1014.4 1063.4 1105.3 1154.4 1203.4 90.9 : 49.0 90.9 140.0 189.0 230.9 279.9 329.0 370.8 419.9 461.7 510.8 559.8 601.7 650.8 692.6 741.7 790.7 832.6 881.6 930.7 972.5 1021.6 1063.4 1112.5 1161.5 1203.4 140.0 : 41.9 90.9 140.0 181.8 230.9 279.9 321.8 370.8 412.7 461.7 510.8 552.6 601.7 643.6 692.6 741.7 783.5 832.6 881.6 923.5 972.5 1014.4 1063.4 1112.5 1154.3 1203.4 181.8 : 49.0 98.1 140.0 189.0 238.1 279.9 329.0 370.8 419.9 468.9 510.8 559.8 601.7 650.8 699.8 741.7 790.7 839.8 881.6 930.7 972.5 1021.6 1070.6 1112.5 1161.5 1203.4 230.9 : 49.0 90.9 140.0 189.0 230.9 279.9 321.8 370.8 419.9 461.7 510.8 552.7 601.7 650.7 692.6 741.7 790.7 832.6 881.6 923.5 972.5 1021.6 1063.4 1112.5 1154.4 1203.4 279.9 : 41.9 90.9 140.0 181.8 230.9 272.7 321.8 370.8 412.7 461.7 503.6 552.6 601.7 643.6 692.6 741.7 783.5 832.6 874.4 923.5 972.5 1014.4 1063.4 1105.3 1154.4 1203.4 321.8 : 49.0 98.1 140.0 189.0 230.9 279.9 329.0 370.8 419.9 461.7 510.8 559.8 601.7 650.8 699.8 741.7 790.7 832.6 881.6 930.7 972.5 1021.6 1063.4 1112.5 1161.5 1203.4 370.8 : 49.0 90.9 140.0 181.8 230.9 279.9 321.8 370.8 412.7 461.7 510.8 552.7 601.7 650.8 692.6 741.7 783.5 832.6 881.6 923.5 972.5 1014.4 1063.4 1112.5 1154.4 1203.4 419.9 : 41.9 90.9 132.8 181.8 230.9 272.7 321.8 363.6 412.7 461.7 503.6 552.7 601.7 643.6 692.6 734.5 783.5 832.6 874.4 923.5 965.3 1014.4 1063.4 1105.3 1154.4 1203.4 461.7 : 49.1 90.9 140.0 189.0 230.9 279.9 321.8 370.8 419.9 461.7 510.8 559.8 601.7 650.8 692.6 741.7 790.7 832.6 881.6 923.5 972.5 1021.6 1063.4 1112.5 1161.5 1203.4 510.8 : 41.9 90.9 140.0 181.8 230.9 272.7 321.8 370.8 412.7 461.7 510.8 552.7 601.7 643.6 692.6 741.7 783.5 832.6 874.4 923.5 972.5 1014.4 1063.4 1112.5 1154.3 1203.4 552.6 : 49.1 98.1 140.0 189.0 230.9 279.9 329.0 370.8 419.9 468.9 510.8 559.8 601.7 650.8 699.8 741.7 790.7 832.6 881.6 930.7 972.5 1021.6 1070.6 1112.5 1161.5 1203.4 601.7 : 49.0 90.9 140.0 181.8 230.9 279.9 321.8 370.8 419.9 461.7 510.8 552.6 601.7 650.7 692.6 741.7 783.5 832.6 881.6 923.5 972.5 1021.6 1063.4 1112.5 1154.3 1203.4 650.8 : 41.9 90.9 132.8 181.8 230.9 272.7 321.8 370.8 412.7 461.7 503.6 552.7 601.7 643.6 692.6 734.5 783.5 832.6 874.4 923.5 972.5 1014.4 1063.4 1105.3 1154.4 1203.4 692.6 : 49.1 90.9 140.0 189.0 230.9 279.9 329.0 370.8 419.9 461.7 510.8 559.8 601.7 650.8 692.6 741.7 790.7 832.6 881.6 930.7 972.5 1021.6 1063.4 1112.5 1161.5 1203.4 741.7 : 41.9 90.9 140.0 181.8 230.9 279.9 321.8 370.8 412.7 461.7 510.8 552.6 601.7 643.6 692.6 741.7 783.5 832.6 881.6 923.5 972.5 1014.4 1063.4 1112.5 1154.4 1203.4 783.5 : 49.0 98.1 140.0 189.0 238.1 279.9 329.0 370.8 419.9 468.9 510.8 559.8 601.7 650.8 699.8 741.7 790.7 839.8 881.6 930.7 972.5 1021.6 1070.6 1112.5 1161.5 1203.4 832.6 : 49.0 90.9 140.0 189.0 230.9 279.9 321.8 370.8 419.9 461.7 510.8 552.7 601.7 650.8 692.6 741.7 790.7 832.6 881.6 923.5 972.5 1021.6 1063.4 1112.5 1154.4 1203.4 881.6 : 41.9 90.9 140.0 181.8 230.9 272.7 321.8 370.8 412.7 461.7 503.6 552.7 601.7 643.6 692.6 741.7 783.5 832.6 874.4 923.5 972.5 1014.4 1063.4 1105.3 1154.4 1203.4 923.5 : 49.0 98.1 140.0 189.0 230.9 279.9 329.0 370.8 419.9 461.7 510.8 559.8 601.7 650.7 699.8 741.7 790.7 832.6 881.6 930.7 972.5 1021.6 1063.4 1112.5 1161.5 1203.4 972.5 : 49.1 90.9 140.0 181.8 230.9 279.9 321.8 370.8 412.7 461.7 510.8 552.7 601.7 650.8 692.6 741.7 783.5 832.6 881.6 923.5 972.5 1014.4 1063.4 1112.5 1154.4 1203.4 1021.6: 41.9 90.9 132.8 181.8 230.9 272.7 321.8 363.6 412.7 461.7 503.6 552.6 601.7 643.6 692.6 734.5 783.5 832.6 874.4 923.5 965.3 1014.4 1063.4 1105.3 1154.3 1203.4 1063.4: 49.0 90.9 140.0 189.0 230.9 279.9 321.8 370.8 419.9 461.7 510.8 559.8 601.7 650.8 692.6 741.7 790.7 832.6 881.6 923.5 972.5 1021.6 1063.4 1112.5 1161.5 1203.4 1112.5: 41.9 90.9 140.0 181.8 230.9 272.7 321.8 370.8 412.7 461.7 510.8 552.7 601.7 643.6 692.6 741.7 783.5 832.6 874.4 923.5 972.5 1014.4 1063.4 1112.5 1154.4 1203.4 1154.3: 49.1 98.1 140.0 189.0 230.9 279.9 329.0 370.8 419.9 468.9 510.8 559.8 601.7 650.8 699.8 741.7 790.7 832.6 881.6 930.7 972.5 1021.6 1070.6 1112.5 1161.5 1203.4 1203.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.8600 .. 49.0500 cents 7.19000 cents 41.86000 cents 2: 90.9100 .. 98.1000 cents 7.19000 cents 41.86000 cents 3: 132.7700 .. 139.9600 cents 7.19000 cents 34.67000 cents 4: 181.8200 .. 189.0100 cents 7.19000 cents 41.86000 cents 5: 230.8700 .. 238.0600 cents 7.19000 cents 41.86000 cents 6: 272.7300 .. 279.9200 cents 7.19000 cents 34.67000 cents 7: 321.7800 .. 328.9700 cents 7.19000 cents 41.86000 cents 8: 363.6400 .. 370.8300 cents 7.19000 cents 34.67000 cents 9: 412.6900 .. 419.8800 cents 7.19000 cents 41.86000 cents 10: 461.7400 .. 468.9300 cents 7.19000 cents 41.86000 cents 11: 503.6000 .. 510.7900 cents 7.19000 cents 34.67000 cents 12: 552.6500 .. 559.8400 cents 7.19000 cents 41.86000 cents 13: 601.7000 .. 601.7000 cents 1/1, 0.0000 cents 41.86000 cents 14: 643.5600 .. 650.7500 cents 7.19000 cents 41.86000 cents 15: 692.6100 .. 699.8000 cents 7.19000 cents 41.86000 cents 16: 734.4700 .. 741.6600 cents 7.19000 cents 34.67000 cents 17: 783.5200 .. 790.7100 cents 7.19000 cents 41.86000 cents 18: 832.5700 .. 839.7600 cents 7.19000 cents 41.86000 cents 19: 874.4300 .. 881.6200 cents 7.19000 cents 34.67000 cents 20: 923.4800 .. 930.6700 cents 7.19000 cents 41.86000 cents 21: 965.3400 .. 972.5300 cents 7.19000 cents 34.67000 cents 22: 1014.3900 .. 1021.5800 cents 7.19000 cents 41.86000 cents 23: 1063.4400 .. 1070.6300 cents 7.19000 cents 41.86000 cents 24: 1105.3000 .. 1112.4900 cents 7.19000 cents 34.67000 cents 25: 1154.3500 .. 1161.5400 cents 7.19000 cents 41.86000 cents
SHOW DATA
Number of notes : 26 -- Interval properties -- Smallest interval : 41.86000 cents, class 1 Average step (divided formal octave): 46.2846 cents Largest one step interval : 49.05000 cents Average / Smallest step : 1.105700 Largest / Average step : 1.059747 Largest / Smallest step : 1.171763 Median interval of one step : 49.05000 cents, amount: 16 Most common interval of one step : 49.05000 cents, amount: 16 Least squares average step : 46.28230 cents, oct.: 1203.33971 cents Scale is strictly proper Scale has 2 repeating blocks of 13 notes Blocks have Myhill's property chromas: 7.19000 cents and 34.67000 cents, ratio: 4.821975 generators: 5 of 230.87000 cents and 8 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: 41 76 117 152 193 234 269 310 351 386 427 462 503 544 579 620 655 696 737 772 813 854 889 930 965 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: 516 = 490 more = 1984.615% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABAABABAABABAABAABABA Step pattern size order : LSLSLLSLLSLSLLSLSLLSLLSLSL Scale is a Constant Structure, by a margin of 34.67000 cents Scale diversity : 1.081609 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.856606 Number of different interval sizes : 49 = 1.96000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.96000 = 49/25 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 7.19000 cents Most common intervals : 601.70000 cents & inv., amount: 26 Number of recognisable fifths : 26, average 694.2692 cents Number of recognisable fourths : 26, average 509.1308 cents Scale contains two identical disjunct "tetrachords" of 12 notes Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 26 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 13 Limited inverse transpositions : 13 Inversional symmetry on degrees : 0 13 Inversional symmetry on intervals : 6-7 19-20 -- Rational properties --
FIT/MODE
26: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 2.0694 c. M: 3.3185 c. 94: 4 3 4 3 4 4 3 4 4 3 4 3 4 4 3 4 3 4 4 3 4 4 3 4 3 4 SP B ME I SD: 1.6153 c. M:-2.5902 c. 120: 5 4 5 4 5 5 4 5 5 4 5 4 5 5 4 5 4 5 5 4 5 5 4 5 4 5 SP B ME I SD: 0.8169 c. M:-1.3100 c. 146: 6 5 6 5 6 6 5 6 6 5 6 5 6 6 5 6 5 6 6 5 6 6 5 6 5 6 SP B ME I SD: 0.3029 c. M:-0.4858 c. 172: 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 SP B ME I SD: 0.0557 c. M: 0.0893 c. 490: 20 17 20 17 20 20 17 20 20 17 20 17 20 20 17 20 17 20 20 17 20 20 17 20 17 20 SP B DE I SD: 0.0512 c. M:-0.0820 c. 662: 27 23 27 23 27 27 23 27 27 23 27 23 27 27 23 27 23 27 27 23 27 27 23 27 23 27 SP B DE I SD: 0.0234 c. M:-0.0375 c. 834: 34 29 34 29 34 34 29 34 34 29 34 29 34 34 29 34 29 34 34 29 34 34 29 34 29 34 SP B DE I SD: 0.0071 c. M:-0.0114 c. 1006: 41 35 41 35 41 41 35 41 41 35 41 35 41 41 35 41 35 41 41 35 41 41 35 41 35 41 SP B DE I SD: 0.0036 c. M:-0.0058 c. 1840: 75 64 75 64 75 75 64 75 75 64 75 64 75 75 64 75 64 75 75 64 75 75 64 75 64 75 SP B DE I SD: 0.0012 c. M:-0.0020 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: 5.6210 cents 6 .. 12 match: 6 H SD: 4.2074 cents 7 .. 14 match: 7 H SD: 3.6547 cents 8 .. 16 match: 8 H SD: 4.8285 cents 9 .. 18 match: 9 H SD: 4.9220 cents 10 .. 20 match: 10 H SD: 3.5238 cents 11 .. 22 match: 11 H SD: 3.8108 cents 12 .. 24 match: 12 H SD: 2.9232 cents 13 .. 26 match: 13 H SD: 3.0050 cents 14 .. 28 match: 14 H SD: 3.7772 cents 15 .. 30 match: 15 H SD: 3.4869 cents 16 .. 32 match: 16 H SD: 3.5164 cents 17 .. 34 match: 17 H SD: 2.8671 cents 18 .. 36 match: 18 H SD: 3.0794 cents 19 .. 38 match: 19 H SD: 2.8965 cents 20 .. 40 match: 20 H SD: 2.4002 cents 21 .. 42 match: 21 H SD: 2.2767 cents 22 .. 44 match: 22 H SD: 2.8996 cents 23 .. 46 match: 22 SD: 3.0119 cents 24 .. 48 match: 23 S SD: 2.3346 cents 25 .. 50 match: 23 S SD: 3.0125 cents 26 .. 52 match: 24 SD: 2.0933 cents 27 .. 54 match: 24 SD: 2.6318 cents 28 .. 56 match: 25 SD: 2.5265 cents 29 .. 58 match: 25 SD: 2.0708 cents 30 .. 60 match: 25 SD: 2.2766 cents 31 .. 62 match: 24 SD: 2.6601 cents 32 .. 64 match: 26 SD: 2.3120 cents 33 .. 66 match: 26 SD: 1.8137 cents 34 .. 68 match: 26 SD: 1.7716 cents 35 .. 70 match: 26 SD: 1.6226 cents 45 .. 90 match: 26 SD: 1.5248 cents 50 .. 100 match: 26 SD: 1.3814 cents 53 .. 106 match: 26 SD: 1.3723 cents 55 .. 110 match: 26 SD: 1.2107 cents 58 .. 116 match: 26 SD: 1.0860 cents 62 .. 124 match: 26 SD: 1.0205 cents 63 .. 126 match: 26 SD: 0.9847 cents 70 .. 140 match: 26 SD: 0.9083 cents 72 .. 144 match: 26 SD: 0.7968 cents 79 .. 158 match: 26 SD: 0.7891 cents 91 .. 182 match: 26 SD: 0.6932 cents 92 .. 184 match: 26 SD: 0.6174 cents 98 .. 196 match: 26 SD: 0.5935 cents 108 .. 216 match: 26 SD: 0.5315 cents 128 .. 257 match: 26 SD: 0.5286 cents 131 .. 263 match: 26 SD: 0.4681 cents 138 .. 277 match: 26 SD: 0.4538 cents 142 .. 285 match: 26 SD: 0.4059 cents 154 .. 309 match: 26 SD: 0.3915 cents 163 .. 327 match: 26 SD: 0.3855 cents 167 .. 335 match: 26 SD: 0.3745 cents 170 .. 341 match: 26 SD: 0.3651 cents 180 .. 361 match: 26 SD: 0.3611 cents 181 .. 363 match: 26 SD: 0.3532 cents 183 .. 367 match: 26 SD: 0.3388 cents 189 .. 379 match: 26 SD: 0.3256 cents 200 .. 401 match: 26 SD: 0.3197 cents 204 .. 409 match: 26 SD: 0.2795 cents 210 .. 421 match: 26 SD: 0.2674 cents 236 .. 473 match: 26 SD: 0.2505 cents 245 .. 491 match: 26 SD: 0.2299 cents 272 .. 545 match: 26 SD: 0.2276 cents 274 .. 549 match: 26 SD: 0.2039 cents 309 .. 619 match: 26 SD: 0.1819 cents 342 .. 685 match: 26 SD: 0.1761 cents 353 .. 707 match: 26 SD: 0.1548 cents 393 .. 788 match: 26 SD: 0.1526 cents 405 .. 812 match: 26 SD: 0.1476 cents 423 .. 848 match: 26 SD: 0.1293 cents 426 .. 854 match: 26 SD: 0.1240 cents 449 .. 900 match: 26 SD: 0.1237 cents 460 .. 922 match: 26 SD: 0.1233 cents 484 .. 970 match: 26 SD: 0.1019 cents 524 .. 1050 match: 26 SD: 0.0928 cents