Scala analysis: xen18-erlich-orson-22
9L 13s MOS for Orson, L=69.27, s=44.37
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44.370 cents 44.370000 2: 113.640 cents 113.640000 3: 158.010 cents 158.010000 4: 227.280 cents 227.280000 5: 271.650 cents 271.650000 6: 316.020 cents 316.020000 7: 385.290 cents 385.290000 8: 429.660 cents 429.660000 9: 498.930 cents 498.930000 10: 543.300 cents 543.300000 11: 612.570 cents 612.570000 12: 656.940 cents 656.940000 13: 701.310 cents 701.310000 14: 770.580 cents 770.580000 15: 814.950 cents 814.950000 16: 884.220 cents 884.220000 17: 928.590 cents 928.590000 18: 972.960 cents 972.960000 19: 1042.230 cents 1042.230000 20: 1086.600 cents 1086.600000 21: 1155.870 cents 1155.870000 22: 1200.240 cents 1200.240000
SHOW/INTERVAL
0: 44.3700 cents 44.3700 1: 44.3700 cents 44.3700 2: 69.2700 cents 69.2700 3: 44.3700 cents 44.3700 4: 69.2700 cents 69.2700 5: 44.3700 cents 44.3700 6: 44.3700 cents 44.3700 7: 69.2700 cents 69.2700 8: 44.3700 cents 44.3700 9: 69.2700 cents 69.2700 10: 44.3700 cents 44.3700 11: 69.2700 cents 69.2700 12: 44.3700 cents 44.3700 13: 44.3700 cents 44.3700 14: 69.2700 cents 69.2700 15: 44.3700 cents 44.3700 16: 69.2700 cents 69.2700 17: 44.3700 cents 44.3700 18: 44.3700 cents 44.3700 19: 69.2700 cents 69.2700 20: 44.3700 cents 44.3700 21: 69.2700 cents 69.2700 22: 44.3700 cents 44.3700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 44.37000 cents 1: 9 69.27000 cents 2: 4 88.74000 cents 2: 18 113.64000 cents 3: 17 158.01000 cents 3: 5 182.91000 cents 4: 8 202.38000 cents 4: 14 227.28000 cents 5: 21 271.65000 cents 5: 1 296.55000 cents 6: 12 316.02000 cents 6: 10 340.92000 cents 7: 3 360.39000 cents 7: 19 385.29000 cents 8: 16 429.66000 cents 8: 6 454.56000 cents 9: 7 474.03000 cents 9: 15 498.93000 cents 10: 20 543.30000 cents 10: 2 568.20000 cents 11: 11 587.67000 cents 11: 11 612.57000 cents 12: 2 632.04000 cents 12: 20 656.94000 cents 13: 15 701.31000 cents 13: 7 726.21000 cents 14: 6 745.68000 cents 14: 16 770.58000 cents 15: 19 814.95000 cents 15: 3 839.85000 cents 16: 10 859.32000 cents 16: 12 884.22000 cents 17: 1 903.69000 cents 17: 21 928.59000 cents 18: 14 972.96000 cents 18: 8 997.86000 cents 19: 5 1017.33000 cents 19: 17 1042.23000 cents 20: 18 1086.60000 cents 20: 4 1111.50000 cents 21: 9 1130.97000 cents 21: 13 1155.87000 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 0.0 : 44.4 113.6 158.0 227.3 271.6 316.0 385.3 429.7 498.9 543.3 612.6 656.9 701.3 770.6 814.9 884.2 928.6 973.0 1042.2 1086.6 1155.9 1200.2 44.4 : 69.3 113.6 182.9 227.3 271.6 340.9 385.3 454.6 498.9 568.2 612.6 656.9 726.2 770.6 839.8 884.2 928.6 997.9 1042.2 1111.5 1155.9 1200.2 113.6 : 44.4 113.6 158.0 202.4 271.6 316.0 385.3 429.7 498.9 543.3 587.7 656.9 701.3 770.6 814.9 859.3 928.6 973.0 1042.2 1086.6 1131.0 1200.2 158.0 : 69.3 113.6 158.0 227.3 271.6 340.9 385.3 454.6 498.9 543.3 612.6 656.9 726.2 770.6 814.9 884.2 928.6 997.9 1042.2 1086.6 1155.9 1200.2 227.3 : 44.4 88.7 158.0 202.4 271.6 316.0 385.3 429.7 474.0 543.3 587.7 656.9 701.3 745.7 814.9 859.3 928.6 973.0 1017.3 1086.6 1131.0 1200.2 271.6 : 44.4 113.6 158.0 227.3 271.6 340.9 385.3 429.7 498.9 543.3 612.6 656.9 701.3 770.6 814.9 884.2 928.6 973.0 1042.2 1086.6 1155.9 1200.2 316.0 : 69.3 113.6 182.9 227.3 296.6 340.9 385.3 454.6 498.9 568.2 612.6 656.9 726.2 770.6 839.8 884.2 928.6 997.9 1042.2 1111.5 1155.9 1200.2 385.3 : 44.4 113.6 158.0 227.3 271.7 316.0 385.3 429.7 498.9 543.3 587.7 656.9 701.3 770.6 815.0 859.3 928.6 973.0 1042.2 1086.6 1131.0 1200.2 429.7 : 69.3 113.6 182.9 227.3 271.6 340.9 385.3 454.6 498.9 543.3 612.6 656.9 726.2 770.6 814.9 884.2 928.6 997.9 1042.2 1086.6 1155.9 1200.2 498.9 : 44.4 113.6 158.0 202.4 271.7 316.0 385.3 429.7 474.0 543.3 587.7 656.9 701.3 745.7 815.0 859.3 928.6 973.0 1017.3 1086.6 1131.0 1200.2 543.3 : 69.3 113.6 158.0 227.3 271.7 340.9 385.3 429.7 498.9 543.3 612.6 656.9 701.3 770.6 815.0 884.2 928.6 973.0 1042.2 1086.6 1155.9 1200.2 612.6 : 44.4 88.7 158.0 202.4 271.6 316.0 360.4 429.7 474.0 543.3 587.7 632.0 701.3 745.7 815.0 859.3 903.7 973.0 1017.3 1086.6 1131.0 1200.2 656.9 : 44.4 113.6 158.0 227.3 271.6 316.0 385.3 429.7 498.9 543.3 587.7 656.9 701.3 770.6 814.9 859.3 928.6 973.0 1042.2 1086.6 1155.9 1200.2 701.3 : 69.3 113.6 182.9 227.3 271.6 340.9 385.3 454.6 498.9 543.3 612.6 656.9 726.2 770.6 814.9 884.2 928.6 997.9 1042.2 1111.5 1155.9 1200.2 770.6 : 44.4 113.6 158.0 202.4 271.6 316.0 385.3 429.7 474.0 543.3 587.7 656.9 701.3 745.7 814.9 859.3 928.6 973.0 1042.2 1086.6 1131.0 1200.2 814.9 : 69.3 113.6 158.0 227.3 271.6 340.9 385.3 429.7 498.9 543.3 612.6 656.9 701.3 770.6 815.0 884.2 928.6 997.9 1042.2 1086.6 1155.9 1200.2 884.2 : 44.4 88.7 158.0 202.4 271.6 316.0 360.4 429.7 474.0 543.3 587.7 632.0 701.3 745.7 814.9 859.3 928.6 973.0 1017.3 1086.6 1131.0 1200.2 928.6 : 44.4 113.6 158.0 227.3 271.6 316.0 385.3 429.7 498.9 543.3 587.7 656.9 701.3 770.6 814.9 884.2 928.6 973.0 1042.2 1086.6 1155.9 1200.2 973.0 : 69.3 113.6 182.9 227.3 271.6 340.9 385.3 454.6 498.9 543.3 612.6 656.9 726.2 770.6 839.9 884.2 928.6 997.9 1042.2 1111.5 1155.9 1200.2 1042.2: 44.4 113.6 158.0 202.4 271.7 316.0 385.3 429.7 474.0 543.3 587.7 656.9 701.3 770.6 815.0 859.3 928.6 973.0 1042.2 1086.6 1131.0 1200.2 1086.6: 69.3 113.6 158.0 227.3 271.7 340.9 385.3 429.7 498.9 543.3 612.6 656.9 726.2 770.6 815.0 884.2 928.6 997.9 1042.2 1086.6 1155.9 1200.2 1155.9: 44.4 88.7 158.0 202.4 271.7 316.0 360.4 429.7 474.0 543.3 587.7 656.9 701.3 745.7 815.0 859.3 928.6 973.0 1017.3 1086.6 1131.0 1200.2 1200.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.3700 .. 69.2700 cents 24.90000 cents 44.37000 cents 2: 88.7400 .. 113.6400 cents 24.90000 cents 19.47000 cents 3: 158.0100 .. 182.9100 cents 24.90000 cents 44.37000 cents 4: 202.3800 .. 227.2800 cents 24.90000 cents 19.47000 cents 5: 271.6500 .. 296.5500 cents 24.90000 cents 44.37000 cents 6: 316.0200 .. 340.9200 cents 24.90000 cents 19.47000 cents 7: 360.3900 .. 385.2900 cents 24.90000 cents 19.47000 cents 8: 429.6600 .. 454.5600 cents 24.90000 cents 44.37000 cents 9: 474.0300 .. 498.9300 cents 24.90000 cents 19.47000 cents 10: 543.3000 .. 568.2000 cents 24.90000 cents 44.37000 cents 11: 587.6700 .. 612.5700 cents 24.90000 cents 19.47000 cents 12: 632.0400 .. 656.9400 cents 24.90000 cents 19.47000 cents 13: 701.3100 .. 726.2100 cents 24.90000 cents 44.37000 cents 14: 745.6800 .. 770.5800 cents 24.90000 cents 19.47000 cents 15: 814.9500 .. 839.8500 cents 24.90000 cents 44.37000 cents 16: 859.3200 .. 884.2200 cents 24.90000 cents 19.47000 cents 17: 903.6900 .. 928.5900 cents 24.90000 cents 19.47000 cents 18: 972.9600 .. 997.8600 cents 24.90000 cents 44.37000 cents 19: 1017.3300 .. 1042.2300 cents 24.90000 cents 19.47000 cents 20: 1086.6000 .. 1111.5000 cents 24.90000 cents 44.37000 cents 21: 1130.9700 .. 1155.8700 cents 24.90000 cents 19.47000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 44.37000 cents, class 1 Average step (divided formal octave): 54.5564 cents Largest one step interval : 69.27000 cents Average / Smallest step : 1.229578 Largest / Average step : 1.269696 Largest / Smallest step : 1.561190 Median interval of one step : 44.37000 cents, amount: 13 Most common interval of one step : 44.37000 cents, amount: 13 Least squares average step : 54.64494 cents, oct.: 1202.18870 cents Scale is strictly proper Scale has Myhill's property chromas: 24.90000 cents and 19.47000 cents, ratio: 1.278891 generators: 5 of 271.65000 cents and 17 of 928.59000 cents ET pair of linear temperament : 22&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1109-tone equal temperament with octave 1200.240 cents degrees: 41 105 146 210 251 292 356 397 461 502 566 607 648 712 753 817 858 899 963 1004 1068 1109 generators: 251 and 858 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABAABABAABABA Step pattern size order : SLSLSSLSLSLSSLSLSSLSLS Scale is a Constant Structure, by a margin of 19.47000 cents Scale diversity : 1.182258 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.564337 Rothenberg efficiency : 0.696970 redundancy: 0.303030 Efficiency x scale size : 15.333333 Number of different interval sizes : 42 = 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 : 19.47000 cents Most common intervals : 271.65000 cents & inv., amount: 21 Scale is a chain of 11 triads 0.0 316.020 928.590 cents Most common triad is 0.0 271.650 928.590 cents, amount: 20 Number of recognisable fifths : 15, average 701.3100 cents Number of recognisable fourths : 15, average 498.9300 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 21 = 95.4545% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 17 Inversional symmetry on intervals : 8-9 19-20 -- Rational properties --
FIT/MODE
22: 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: 7.2028 c. M: 12.4500 c. 31: 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 P M ME SD: 3.9970 c. M:-6.9087 c. 53: 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 SP M ME SD: 0.6520 c. M: 1.1270 c. 137: 5 8 5 8 5 5 8 5 8 5 8 5 5 8 5 8 5 5 8 5 8 5 SP M DE SD: 0.4000 c. M:-0.6913 c. 190: 7 11 7 11 7 7 11 7 11 7 11 7 7 11 7 11 7 7 11 7 11 7 SP M DE SD: 0.1065 c. M:-0.1841 c. 243: 9 14 9 14 9 9 14 9 14 9 14 9 9 14 9 14 9 9 14 9 14 9 SP M DE SD: 0.0589 c. M: 0.1019 c. 433: 16 25 16 25 16 16 25 16 25 16 25 16 16 25 16 25 16 16 25 16 25 16 SP M DE SD: 0.0137 c. M:-0.0236 c. 676: 25 39 25 39 25 25 39 25 39 25 39 25 25 39 25 39 25 25 39 25 39 25 SP M DE SD: 0.0124 c. M: 0.0215 c. 1109: 41 64 41 64 41 41 64 41 64 41 64 41 41 64 41 64 41 41 64 41 64 41 SP M DE SD: 0.0022 c. M: 0.0039 c. 1542: 57 89 57 89 57 57 89 57 89 57 89 57 57 89 57 89 57 57 89 57 89 57 SP M DE SD: 0.0022 c. M:-0.0039 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.2400 cents 2 .. 4 match: 2 H SD: 0.3441 cents 3 .. 6 match: 3 H SD: 0.3091 cents 4 .. 8 match: 4 H SD: 1.0786 cents 5 .. 10 match: 5 H SD: 7.7771 cents 6 .. 12 match: 6 H SD: 1.4433 cents 7 .. 14 match: 7 H SD: 3.0415 cents 8 .. 16 match: 8 H SD: 4.4827 cents 9 .. 18 match: 9 H SD: 5.8477 cents 10 .. 20 match: 10 H SD: 5.3558 cents 11 .. 22 match: 11 H SD: 5.2606 cents 12 .. 24 match: 12 H SD: 3.5471 cents 13 .. 26 match: 13 H SD: 5.5533 cents 14 .. 28 match: 14 H SD: 3.9284 cents 15 .. 30 match: 15 H SD: 4.0523 cents 16 .. 32 match: 16 H SD: 3.6939 cents 17 .. 34 match: 16 SD: 3.8453 cents 18 .. 36 match: 18 H SD: 3.6060 cents 19 .. 38 match: 16 SD: 4.0571 cents 20 .. 40 match: 18 SD: 3.6249 cents 21 .. 42 match: 19 SD: 2.9801 cents 22 .. 44 match: 20 SD: 3.4987 cents 23 .. 46 match: 18 SD: 3.4340 cents 24 .. 48 match: 21 SD: 2.6439 cents 25 .. 50 match: 19 SD: 2.9971 cents 26 .. 52 match: 20 SD: 3.3901 cents 27 .. 54 match: 21 SD: 3.1297 cents 28 .. 56 match: 22 SD: 2.2946 cents 30 .. 60 match: 22 SD: 2.0357 cents 35 .. 70 match: 22 SD: 1.8994 cents 40 .. 80 match: 22 SD: 1.6197 cents 41 .. 82 match: 22 SD: 1.5358 cents 45 .. 90 match: 22 SD: 1.4247 cents 52 .. 104 match: 22 SD: 1.4139 cents 54 .. 108 match: 22 SD: 1.3731 cents 57 .. 114 match: 22 SD: 1.3171 cents 60 .. 120 match: 22 SD: 1.1875 cents 63 .. 126 match: 22 SD: 1.1121 cents 64 .. 128 match: 22 SD: 1.0918 cents 65 .. 130 match: 22 SD: 1.0795 cents 70 .. 140 match: 22 SD: 0.9779 cents 71 .. 142 match: 22 SD: 0.9136 cents 75 .. 150 match: 22 SD: 0.9011 cents 76 .. 152 match: 22 SD: 0.8486 cents 84 .. 168 match: 22 SD: 0.7603 cents 93 .. 186 match: 22 SD: 0.7343 cents 100 .. 200 match: 22 SD: 0.6968 cents 104 .. 208 match: 22 SD: 0.6585 cents 106 .. 212 match: 22 SD: 0.6211 cents 113 .. 226 match: 22 SD: 0.5881 cents 114 .. 228 match: 22 SD: 0.5513 cents 117 .. 234 match: 22 SD: 0.5460 cents 120 .. 240 match: 22 SD: 0.5188 cents 135 .. 270 match: 22 SD: 0.4909 cents 146 .. 292 match: 22 SD: 0.4811 cents 148 .. 296 match: 22 SD: 0.4458 cents 149 .. 298 match: 22 SD: 0.4361 cents 158 .. 316 match: 22 SD: 0.4223 cents 160 .. 320 match: 22 SD: 0.3981 cents 165 .. 330 match: 22 SD: 0.3876 cents 176 .. 352 match: 22 SD: 0.3834 cents 180 .. 360 match: 22 SD: 0.3640 cents 188 .. 376 match: 22 SD: 0.3414 cents 189 .. 378 match: 22 SD: 0.3410 cents 195 .. 390 match: 22 SD: 0.3224 cents 200 .. 400 match: 22 SD: 0.2860 cents 228 .. 456 match: 22 SD: 0.2662 cents 234 .. 468 match: 22 SD: 0.2589 cents 264 .. 528 match: 22 SD: 0.2069 cents 294 .. 588 match: 22 SD: 0.2060 cents 306 .. 612 match: 22 SD: 0.1839 cents 341 .. 682 match: 22 SD: 0.1753 cents 369 .. 738 match: 22 SD: 0.1731 cents 384 .. 768 match: 22 SD: 0.1608 cents 386 .. 772 match: 22 SD: 0.1563 cents 419 .. 838 match: 22 SD: 0.1558 cents 426 .. 852 match: 22 SD: 0.1472 cents 429 .. 858 match: 22 SD: 0.1358 cents 458 .. 916 match: 22 SD: 0.1302 cents 459 .. 918 match: 22 SD: 0.1268 cents 500 .. 1000 match: 22 SD: 0.1151 cents 535 .. 1070 match: 22 SD: 0.1148 cents 542 .. 1084 match: 22 SD: 0.1095 cents 575 .. 1150 match: 22 SD: 0.0984 cents