Scala analysis: xen18-erlich-amity-25
7L 18s MOS for Amity, L=111.21, s=23.41
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23.410 cents 23.410000 2: 134.620 cents 134.620000 3: 158.030 cents 158.030000 4: 181.440 cents 181.440000 5: 204.850 cents 204.850000 6: 316.060 cents 316.060000 7: 339.470 cents 339.470000 8: 362.880 cents 362.880000 9: 474.090 cents 474.090000 10: 497.500 cents 497.500000 11: 520.910 cents 520.910000 12: 544.320 cents 544.320000 13: 655.530 cents 655.530000 14: 678.940 cents 678.940000 15: 702.350 cents 702.350000 16: 725.760 cents 725.760000 17: 836.970 cents 836.970000 18: 860.380 cents 860.380000 19: 883.790 cents 883.790000 20: 995.000 cents 995.000000 21: 1018.410 cents 1018.410000 22: 1041.820 cents 1041.820000 23: 1065.230 cents 1065.230000 24: 1176.440 cents 1176.440000 25: 1199.850 cents 1199.850000
SHOW/INTERVAL
0: 23.4100 cents 23.4100 1: 23.4100 cents 23.4100 2: 111.2100 cents 111.2100 3: 23.4100 cents 23.4100 4: 23.4100 cents 23.4100 5: 23.4100 cents 23.4100 6: 111.2100 cents 111.2100 7: 23.4100 cents 23.4100 8: 23.4100 cents 23.4100 9: 111.2100 cents 111.2100 10: 23.4100 cents 23.4100 11: 23.4100 cents 23.4100 12: 23.4100 cents 23.4100 13: 111.2100 cents 111.2100 14: 23.4100 cents 23.4100 15: 23.4100 cents 23.4100 16: 23.4100 cents 23.4100 17: 111.2100 cents 111.2100 18: 23.4100 cents 23.4100 19: 23.4100 cents 23.4100 20: 111.2100 cents 111.2100 21: 23.4100 cents 23.4100 22: 23.4100 cents 23.4100 23: 23.4100 cents 23.4100 24: 111.2100 cents 111.2100 25: 23.4100 cents 23.4100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 18 23.41000 cents 1: 7 111.21000 cents 2: 11 46.82000 cents 2: 14 134.62000 cents 3: 4 70.23000 cents 3: 21 158.03000 cents 4: 22 181.44000 cents 4: 3 269.24000 cents 5: 15 204.85000 cents 5: 10 292.65000 cents 6: 8 228.26000 cents 6: 17 316.06000 cents 7: 1 251.67000 cents 7: 24 339.47000 cents 8: 19 362.88000 cents 8: 6 450.68000 cents 9: 12 386.29000 cents 9: 13 474.09000 cents 10: 5 409.70000 cents 10: 20 497.50000 cents 11: 23 520.91000 cents 11: 2 608.71000 cents 12: 16 544.32000 cents 12: 9 632.12000 cents 13: 9 567.73000 cents 13: 16 655.53000 cents 14: 2 591.14000 cents 14: 23 678.94000 cents 15: 20 702.35000 cents 15: 5 790.15000 cents 16: 13 725.76000 cents 16: 12 813.56000 cents 17: 6 749.17000 cents 17: 19 836.97000 cents 18: 24 860.38000 cents 18: 1 948.18000 cents 19: 17 883.79000 cents 19: 8 971.59000 cents 20: 10 907.20000 cents 20: 15 995.00000 cents 21: 3 930.61000 cents 21: 22 1018.41000 cents 22: 21 1041.82000 cents 22: 4 1129.62000 cents 23: 14 1065.23000 cents 23: 11 1153.03000 cents 24: 7 1088.64000 cents 24: 18 1176.44000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
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 0.0 : 23.4 134.6 158.0 181.4 204.8 316.1 339.5 362.9 474.1 497.5 520.9 544.3 655.5 678.9 702.3 725.8 837.0 860.4 883.8 995.0 1018.4 1041.8 1065.2 1176.4 1199.8 23.4 : 111.2 134.6 158.0 181.4 292.6 316.1 339.5 450.7 474.1 497.5 520.9 632.1 655.5 678.9 702.3 813.6 837.0 860.4 971.6 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 134.6 : 23.4 46.8 70.2 181.4 204.8 228.3 339.5 362.9 386.3 409.7 520.9 544.3 567.7 591.1 702.3 725.8 749.2 860.4 883.8 907.2 930.6 1041.8 1065.2 1088.6 1199.8 158.0 : 23.4 46.8 158.0 181.4 204.9 316.1 339.5 362.9 386.3 497.5 520.9 544.3 567.7 678.9 702.3 725.8 837.0 860.4 883.8 907.2 1018.4 1041.8 1065.2 1176.4 1199.8 181.4 : 23.4 134.6 158.0 181.4 292.6 316.1 339.5 362.9 474.1 497.5 520.9 544.3 655.5 678.9 702.3 813.6 837.0 860.4 883.8 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 204.8 : 111.2 134.6 158.0 269.2 292.7 316.1 339.5 450.7 474.1 497.5 520.9 632.1 655.5 678.9 790.2 813.6 837.0 860.4 971.6 995.0 1018.4 1129.6 1153.0 1176.4 1199.8 316.1 : 23.4 46.8 158.0 181.4 204.8 228.3 339.5 362.9 386.3 409.7 520.9 544.3 567.7 678.9 702.3 725.8 749.2 860.4 883.8 907.2 1018.4 1041.8 1065.2 1088.6 1199.8 339.5 : 23.4 134.6 158.0 181.4 204.8 316.1 339.5 362.9 386.3 497.5 520.9 544.3 655.5 678.9 702.3 725.8 837.0 860.4 883.8 995.0 1018.4 1041.8 1065.2 1176.4 1199.9 362.9 : 111.2 134.6 158.0 181.4 292.6 316.1 339.5 362.9 474.1 497.5 520.9 632.1 655.5 678.9 702.3 813.6 837.0 860.4 971.6 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 474.1 : 23.4 46.8 70.2 181.4 204.9 228.3 251.7 362.9 386.3 409.7 520.9 544.3 567.7 591.1 702.4 725.8 749.2 860.4 883.8 907.2 930.6 1041.8 1065.2 1088.6 1199.9 497.5 : 23.4 46.8 158.0 181.4 204.8 228.3 339.5 362.9 386.3 497.5 520.9 544.3 567.7 678.9 702.3 725.8 837.0 860.4 883.8 907.2 1018.4 1041.8 1065.2 1176.4 1199.8 520.9 : 23.4 134.6 158.0 181.4 204.8 316.1 339.5 362.9 474.1 497.5 520.9 544.3 655.5 678.9 702.3 813.6 837.0 860.4 883.8 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 544.3 : 111.2 134.6 158.0 181.4 292.7 316.1 339.5 450.7 474.1 497.5 520.9 632.1 655.5 678.9 790.1 813.6 837.0 860.4 971.6 995.0 1018.4 1129.6 1153.0 1176.4 1199.8 655.5 : 23.4 46.8 70.2 181.4 204.8 228.3 339.5 362.9 386.3 409.7 520.9 544.3 567.7 678.9 702.3 725.8 749.2 860.4 883.8 907.2 1018.4 1041.8 1065.2 1088.6 1199.8 678.9 : 23.4 46.8 158.0 181.4 204.8 316.1 339.5 362.9 386.3 497.5 520.9 544.3 655.5 678.9 702.3 725.8 837.0 860.4 883.8 995.0 1018.4 1041.8 1065.2 1176.4 1199.8 702.3 : 23.4 134.6 158.0 181.4 292.7 316.1 339.5 362.9 474.1 497.5 520.9 632.1 655.5 678.9 702.3 813.6 837.0 860.4 971.6 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 725.8 : 111.2 134.6 158.0 269.2 292.6 316.1 339.5 450.7 474.1 497.5 608.7 632.1 655.5 678.9 790.2 813.6 837.0 948.2 971.6 995.0 1018.4 1129.6 1153.0 1176.4 1199.9 837.0 : 23.4 46.8 158.0 181.4 204.8 228.3 339.5 362.9 386.3 497.5 520.9 544.3 567.7 678.9 702.4 725.8 837.0 860.4 883.8 907.2 1018.4 1041.8 1065.2 1088.6 1199.8 860.4 : 23.4 134.6 158.0 181.4 204.8 316.1 339.5 362.9 474.1 497.5 520.9 544.3 655.5 678.9 702.4 813.6 837.0 860.4 883.8 995.0 1018.4 1041.8 1065.2 1176.4 1199.8 883.8 : 111.2 134.6 158.0 181.4 292.6 316.1 339.5 450.7 474.1 497.5 520.9 632.1 655.5 678.9 790.1 813.6 837.0 860.4 971.6 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 995.0 : 23.4 46.8 70.2 181.4 204.8 228.3 339.5 362.9 386.3 409.7 520.9 544.3 567.7 678.9 702.3 725.8 749.2 860.4 883.8 907.2 930.6 1041.8 1065.2 1088.6 1199.8 1018.4: 23.4 46.8 158.0 181.4 204.8 316.1 339.5 362.9 386.3 497.5 520.9 544.3 655.5 678.9 702.3 725.8 837.0 860.4 883.8 907.2 1018.4 1041.8 1065.2 1176.4 1199.8 1041.8: 23.4 134.6 158.0 181.4 292.7 316.1 339.5 362.9 474.1 497.5 520.9 632.1 655.5 678.9 702.4 813.6 837.0 860.4 883.8 995.0 1018.4 1041.8 1153.0 1176.4 1199.8 1065.2: 111.2 134.6 158.0 269.2 292.6 316.1 339.5 450.7 474.1 497.5 608.7 632.1 655.5 678.9 790.1 813.6 837.0 860.4 971.6 995.0 1018.4 1129.6 1153.0 1176.4 1199.8 1176.4: 23.4 46.8 158.0 181.4 204.9 228.3 339.5 362.9 386.3 497.5 520.9 544.3 567.7 678.9 702.3 725.8 749.2 860.4 883.8 907.2 1018.4 1041.8 1065.2 1088.6 1199.8 1199.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.4100 .. 111.2100 cents 87.80000 cents 23.41000 cents 2: 46.8200 .. 134.6200 cents 87.80000 cents -64.39000 cents 3: 70.2300 .. 158.0300 cents 87.80000 cents -64.39000 cents 4: 181.4400 .. 269.2400 cents 87.80000 cents 23.41000 cents 5: 204.8500 .. 292.6500 cents 87.80000 cents -64.39000 cents 6: 228.2600 .. 316.0600 cents 87.80000 cents -64.39000 cents 7: 251.6700 .. 339.4700 cents 87.80000 cents -64.39000 cents 8: 362.8800 .. 450.6800 cents 87.80000 cents 23.41000 cents 9: 386.2900 .. 474.0900 cents 87.80000 cents -64.39000 cents 10: 409.7000 .. 497.5000 cents 87.80000 cents -64.39000 cents 11: 520.9100 .. 608.7100 cents 87.80000 cents 23.41000 cents 12: 544.3200 .. 632.1200 cents 87.80000 cents -64.39000 cents 13: 567.7300 .. 655.5300 cents 87.80000 cents -64.39000 cents 14: 591.1400 .. 678.9400 cents 87.80000 cents -64.39000 cents 15: 702.3500 .. 790.1500 cents 87.80000 cents 23.41000 cents 16: 725.7600 .. 813.5600 cents 87.80000 cents -64.39000 cents 17: 749.1700 .. 836.9700 cents 87.80000 cents -64.39000 cents 18: 860.3800 .. 948.1800 cents 87.80000 cents 23.41000 cents 19: 883.7900 .. 971.5900 cents 87.80000 cents -64.39000 cents 20: 907.2000 .. 995.0000 cents 87.80000 cents -64.39000 cents 21: 930.6100 .. 1018.4100 cents 87.80000 cents -64.39000 cents 22: 1041.8200 .. 1129.6200 cents 87.80000 cents 23.41000 cents 23: 1065.2300 .. 1153.0300 cents 87.80000 cents -64.39000 cents 24: 1088.6400 .. 1176.4400 cents 87.80000 cents -64.39000 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 23.41000 cents, class 1 Average step (divided formal octave): 47.9940 cents Largest one step interval : 111.21000 cents Average / Smallest step : 2.050150 Largest / Average step : 2.317165 Largest / Smallest step : 4.750534 Median interval of one step : 23.41000 cents, amount: 18 Most common interval of one step : 23.41000 cents, amount: 18 Least squares average step : 47.93043 cents, oct.: 1198.26086 cents Scale is not proper Scale has Myhill's property chromas: 87.80000 cents and 64.39000 cents, ratio: 1.363566 generators: 7 of 339.47000 cents and 18 of 860.38000 cents ET pair of linear temperament : 46&53 Scale is distributional even Scale is a mode of a 205-tone equal temperament with octave 1199.850 cents degrees: 4 23 27 31 35 54 58 62 81 85 89 93 112 116 120 124 143 147 151 170 174 178 182 201 205 generators: 58 and 147 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABAAABAAABAABAAABA Step pattern size order : SLSSSLSSLSSSLSSSLSSLSSSLS Scale is a Constant Structure, by a margin of 17.57000 cents Scale diversity : 1.195881 Lumma stability : 0.156086 Lumma impropriety factor : 0.570763 Rothenberg efficiency : 0.693333 redundancy: 0.306667 Efficiency x scale size : 17.333333 Number of different interval sizes : 48 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 17.57000 cents Most common intervals : 339.47000 cents & inv., amount: 24 Scale is a chain of 12 triads 0.0 474.090 860.380 cents Most common triad is 0.0 339.470 860.380 cents, amount: 23 Number of recognisable fifths : 20, average 702.3500 cents Number of recognisable fourths : 20, average 497.5000 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 25 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 12-13 -- Rational properties --
FIT/MODE
25: 0 3 0 1 0 2 1 0 3 0 1 0 2 1 0 1 2 1 0 2 1 0 1 2 1 N SD: 19.3356 c. M: 35.1200 c. 27: 1 2 1 0 1 2 1 0 3 0 1 0 3 0 1 0 3 0 1 2 1 0 1 2 1 N I SD: 12.8099 c. M: 21.0289 c. 28: 1 2 1 0 1 2 1 0 3 1 0 1 2 1 0 1 3 0 1 2 1 0 1 2 1 N I SD: 12.4907 c. M: 20.0657 c. 29: 1 2 1 0 1 3 0 1 2 1 1 0 3 0 1 1 2 1 0 3 1 0 1 2 1 N I SD: 12.0730 c. M:-18.9745 c. 33: 1 3 0 1 1 3 0 1 3 1 0 1 3 1 0 1 3 1 0 3 1 1 0 3 1 N I SD: 9.6860 c. M:-13.3045 c. 35: 1 3 1 0 1 3 1 1 3 0 1 1 3 1 0 1 3 1 1 3 1 0 1 3 1 N SD: 9.2310 c. M: 17.5600 c. 36: 1 3 1 0 1 3 1 1 3 1 1 0 4 0 1 1 3 1 1 3 1 0 1 3 1 N I SD: 9.2305 c. M:-16.0975 c. 37: 1 3 1 1 0 4 0 1 4 0 1 1 3 1 1 0 4 1 0 4 0 1 1 3 1 N I SD: 9.2269 c. M:-15.1862 c. 39: 1 3 1 1 1 3 1 1 3 1 1 1 3 1 1 1 3 1 1 3 1 1 1 3 1 N M DE I SD: 7.5772 c. M:-12.6092 c. 41: 1 4 0 1 1 4 1 0 4 1 1 1 3 1 1 1 4 0 1 4 1 1 0 4 1 N I SD: 8.2773 c. M:-11.7080 c. 42: 1 4 1 0 1 4 1 1 4 0 1 1 4 1 1 0 4 1 1 4 1 0 1 4 1 N I SD: 8.0271 c. M:-13.3771 c. 45: 1 4 1 1 1 4 1 1 4 1 1 0 5 0 1 1 4 1 1 4 1 1 1 4 1 N I SD: 7.3827 c. M: 12.3567 c. 46: 1 4 1 1 1 4 1 1 4 1 1 1 4 1 1 1 4 1 1 4 1 1 1 4 1 N M DE I SD: 2.7543 c. M:-4.5835 c. 53: 1 5 1 1 1 5 1 1 5 1 1 1 5 1 1 1 5 1 1 5 1 1 1 5 1 N M DE I SD: 0.7946 c. M:-1.3223 c. 152: 3 14 3 3 3 14 3 3 14 3 3 3 14 3 3 3 14 3 3 14 3 3 3 14 3 N M DE I SD: 0.2794 c. M:-0.4650 c. 205: 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 N M DE I SD: 0.0018 c. M:-0.0029 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.1500 cents 2 .. 4 match: 2 H SD: 0.2113 cents 3 .. 6 match: 3 H SD: 0.2673 cents 4 .. 8 match: 4 H SD: 8.7835 cents 5 .. 10 match: 5 H SD: 8.9479 cents 6 .. 12 match: 6 H SD: 8.2954 cents 7 .. 14 match: 7 H SD: 13.6320 cents 8 .. 16 match: 8 H SD: 5.3439 cents 9 .. 18 match: 9 H SD: 6.3239 cents 10 .. 20 match: 10 H SD: 7.5982 cents 11 .. 22 match: 9 S SD: 7.6541 cents 12 .. 24 match: 10 S SD: 7.3770 cents 13 .. 26 match: 12 S SD: 4.9947 cents 14 .. 28 match: 11 SD: 5.8097 cents 15 .. 30 match: 13 SD: 5.6055 cents 16 .. 32 match: 14 S SD: 4.7475 cents 17 .. 34 match: 12 SD: 5.1087 cents 18 .. 36 match: 12 SD: 4.4767 cents 19 .. 38 match: 12 SD: 3.1108 cents 20 .. 40 match: 14 SD: 4.2377 cents 21 .. 42 match: 15 SD: 2.8625 cents 22 .. 44 match: 16 SD: 4.3785 cents 23 .. 46 match: 16 SD: 4.1886 cents 24 .. 48 match: 16 SD: 3.8834 cents 25 .. 50 match: 16 SD: 3.4415 cents 26 .. 52 match: 18 SD: 3.1767 cents 27 .. 54 match: 17 SD: 3.1403 cents 28 .. 56 match: 19 SD: 3.3066 cents 29 .. 58 match: 19 SD: 2.9554 cents 30 .. 60 match: 20 SD: 2.7535 cents 31 .. 62 match: 18 SD: 2.4249 cents 32 .. 64 match: 18 SD: 2.4576 cents 33 .. 66 match: 18 SD: 2.3362 cents 34 .. 68 match: 20 SD: 2.2389 cents 35 .. 70 match: 19 SD: 1.8463 cents 36 .. 72 match: 21 SD: 2.0735 cents 37 .. 74 match: 21 SD: 2.1166 cents 38 .. 76 match: 20 SD: 2.0272 cents 39 .. 78 match: 21 SD: 1.6340 cents 40 .. 80 match: 22 SD: 1.5486 cents 41 .. 82 match: 22 SD: 1.7903 cents 42 .. 84 match: 24 SD: 1.6676 cents 43 .. 86 match: 21 SD: 1.9716 cents 44 .. 88 match: 22 SD: 1.6426 cents 45 .. 90 match: 22 SD: 1.4665 cents 46 .. 92 match: 24 SD: 1.3744 cents 47 .. 94 match: 22 SD: 1.6527 cents 48 .. 96 match: 23 SD: 1.1849 cents 49 .. 98 match: 23 SD: 1.7290 cents 50 .. 100 match: 23 SD: 1.2557 cents 51 .. 102 match: 24 SD: 1.3168 cents 53 .. 106 match: 24 SD: 1.5297 cents 54 .. 108 match: 25 SD: 1.0579 cents 56 .. 112 match: 24 SD: 1.1424 cents 57 .. 114 match: 24 SD: 1.2999 cents 58 .. 116 match: 24 SD: 1.4045 cents 59 .. 118 match: 24 SD: 1.2413 cents 60 .. 120 match: 25 SD: 1.0102 cents 63 .. 126 match: 25 SD: 0.9305 cents 68 .. 136 match: 24 SD: 1.1961 cents 69 .. 138 match: 25 SD: 1.0223 cents 70 .. 140 match: 25 SD: 0.9752 cents 71 .. 142 match: 25 SD: 0.9192 cents 72 .. 144 match: 25 SD: 0.8933 cents 73 .. 146 match: 25 SD: 0.7833 cents 85 .. 170 match: 25 SD: 0.7601 cents 90 .. 180 match: 25 SD: 0.7499 cents 96 .. 192 match: 25 SD: 0.6840 cents 98 .. 196 match: 25 SD: 0.6537 cents 102 .. 204 match: 25 SD: 0.6065 cents 111 .. 222 match: 25 SD: 0.5602 cents 120 .. 240 match: 25 SD: 0.5340 cents 125 .. 250 match: 25 SD: 0.5008 cents 126 .. 252 match: 25 SD: 0.4938 cents 134 .. 268 match: 25 SD: 0.4517 cents 135 .. 270 match: 25 SD: 0.4407 cents 144 .. 288 match: 25 SD: 0.4336 cents 146 .. 292 match: 25 SD: 0.3678 cents 171 .. 342 match: 25 SD: 0.3568 cents 190 .. 380 match: 25 SD: 0.3450 cents 198 .. 396 match: 25 SD: 0.3039 cents 200 .. 400 match: 25 SD: 0.2697 cents 219 .. 438 match: 25 SD: 0.2582 cents 261 .. 522 match: 25 SD: 0.2561 cents 270 .. 540 match: 25 SD: 0.2215 cents 273 .. 546 match: 25 SD: 0.2110 cents 296 .. 592 match: 25 SD: 0.1912 cents 333 .. 666 match: 25 SD: 0.1870 cents 336 .. 672 match: 25 SD: 0.1724 cents 360 .. 720 match: 25 SD: 0.1660 cents 365 .. 730 match: 25 SD: 0.1657 cents 368 .. 736 match: 25 SD: 0.1650 cents 373 .. 746 match: 25 SD: 0.1603 cents 396 .. 792 match: 25 SD: 0.1552 cents 420 .. 840 match: 25 SD: 0.1495 cents 430 .. 860 match: 25 SD: 0.1489 cents 438 .. 876 match: 25 SD: 0.1387 cents 444 .. 888 match: 25 SD: 0.1369 cents 447 .. 894 match: 25 SD: 0.1311 cents 471 .. 942 match: 25 SD: 0.1276 cents 493 .. 986 match: 25 SD: 0.1258 cents 508 .. 1016 match: 25 SD: 0.1248 cents 515 .. 1030 match: 25 SD: 0.1244 cents 523 .. 1046 match: 25 SD: 0.1177 cents 533 .. 1066 match: 25 SD: 0.1128 cents 558 .. 1116 match: 25 SD: 0.1127 cents 578 .. 1156 match: 25 SD: 0.1094 cents 582 .. 1164 match: 25 SD: 0.1092 cents 587 .. 1174 match: 25 SD: 0.1015 cents 595 .. 1190 match: 25 SD: 0.0884 cents