Scala analysis: xen18-erlich-catler-24
12L 12s MOS for Catler, L=75.22, s=24.59
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24.590 cents 24.590000 2: 99.810 cents 99.810000 3: 124.400 cents 124.400000 4: 199.620 cents 199.620000 5: 224.210 cents 224.210000 6: 299.430 cents 299.430000 7: 324.020 cents 324.020000 8: 399.240 cents 399.240000 9: 423.830 cents 423.830000 10: 499.050 cents 499.050000 11: 523.640 cents 523.640000 12: 598.860 cents 598.860000 13: 623.450 cents 623.450000 14: 698.670 cents 698.670000 15: 723.260 cents 723.260000 16: 798.480 cents 798.480000 17: 823.070 cents 823.070000 18: 898.290 cents 898.290000 19: 922.880 cents 922.880000 20: 998.100 cents 998.100000 21: 1022.690 cents 1022.690000 22: 1097.910 cents 1097.910000 23: 1122.500 cents 1122.500000 24: 1197.720 cents 1197.720000
SHOW/INTERVAL
0: 75.2200 cents 75.2200 1: 24.5900 cents 24.5900 2: 75.2200 cents 75.2200 3: 24.5900 cents 24.5900 4: 75.2200 cents 75.2200 5: 24.5900 cents 24.5900 6: 75.2200 cents 75.2200 7: 24.5900 cents 24.5900 8: 75.2200 cents 75.2200 9: 24.5900 cents 24.5900 10: 75.2200 cents 75.2200 11: 24.5900 cents 24.5900 12: 75.2200 cents 75.2200 13: 24.5900 cents 24.5900 14: 75.2200 cents 75.2200 15: 24.5900 cents 24.5900 16: 75.2200 cents 75.2200 17: 24.5900 cents 24.5900 18: 75.2200 cents 75.2200 19: 24.5900 cents 24.5900 20: 75.2200 cents 75.2200 21: 24.5900 cents 24.5900 22: 75.2200 cents 75.2200 23: 24.5900 cents 24.5900 24: 75.2200 cents 75.2200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 24.59000 cents 1: 12 75.22000 cents 2: 24 99.81000 cents 3: 12 124.40000 cents 3: 12 175.03000 cents 4: 24 199.62000 cents 5: 12 224.21000 cents 5: 12 274.84000 cents 6: 24 299.43000 cents 7: 12 324.02000 cents 7: 12 374.65000 cents 8: 24 399.24000 cents 9: 12 423.83000 cents 9: 12 474.46000 cents 10: 24 499.05000 cents 11: 12 523.64000 cents 11: 12 574.27000 cents 12: 24 598.86000 cents 13: 12 623.45000 cents 13: 12 674.08000 cents 14: 24 698.67000 cents 15: 12 723.26000 cents 15: 12 773.89000 cents 16: 24 798.48000 cents 17: 12 823.07000 cents 17: 12 873.70000 cents 18: 24 898.29000 cents 19: 12 922.88000 cents 19: 12 973.51000 cents 20: 24 998.10000 cents 21: 12 1022.69000 cents 21: 12 1073.32000 cents 22: 24 1097.91000 cents 23: 12 1122.50000 cents 23: 12 1173.13000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.52174 = 35/23
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 0.0 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.5 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 24.6 : 75.2 99.8 175.0 199.6 274.8 299.4 374.6 399.2 474.5 499.0 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 99.8 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.4 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 124.4 : 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 199.6 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.5 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 224.2 : 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.0 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 299.4 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.4 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 324.0 : 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 399.2 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.5 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 423.8 : 75.2 99.8 175.0 199.6 274.8 299.4 374.6 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 499.1 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.0 523.6 598.9 623.4 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 523.6 : 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 598.9 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.4 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 623.5 : 75.2 99.8 175.0 199.6 274.8 299.4 374.6 399.2 474.5 499.0 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 698.7 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.5 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 723.3 : 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 798.5 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.5 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 823.1 : 75.2 99.8 175.0 199.6 274.8 299.4 374.6 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 898.3 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.4 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 922.9 : 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 998.1 : 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.1 523.6 598.9 623.5 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 1022.7: 75.2 99.8 175.0 199.6 274.8 299.4 374.7 399.2 474.5 499.0 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 1097.9: 24.6 99.8 124.4 199.6 224.2 299.4 324.0 399.2 423.8 499.0 523.6 598.9 623.4 698.7 723.3 798.5 823.1 898.3 922.9 998.1 1022.7 1097.9 1122.5 1197.7 1122.5: 75.2 99.8 175.0 199.6 274.8 299.4 374.6 399.2 474.5 499.1 574.3 598.9 674.1 698.7 773.9 798.5 873.7 898.3 973.5 998.1 1073.3 1097.9 1173.1 1197.7 1197.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.5900 .. 75.2200 cents 50.63000 cents 24.59000 cents 2: 99.8100 .. 99.8100 cents 1/1, 0.0000 cents 24.59000 cents 3: 124.4000 .. 175.0300 cents 50.63000 cents 24.59000 cents 4: 199.6200 .. 199.6200 cents 1/1, 0.0000 cents 24.59000 cents 5: 224.2100 .. 274.8400 cents 50.63000 cents 24.59000 cents 6: 299.4300 .. 299.4300 cents 1/1, 0.0000 cents 24.59000 cents 7: 324.0200 .. 374.6500 cents 50.63000 cents 24.59000 cents 8: 399.2400 .. 399.2400 cents 1/1, 0.0000 cents 24.59000 cents 9: 423.8300 .. 474.4600 cents 50.63000 cents 24.59000 cents 10: 499.0500 .. 499.0500 cents 1/1, 0.0000 cents 24.59000 cents 11: 523.6400 .. 574.2700 cents 50.63000 cents 24.59000 cents 12: 598.8600 .. 598.8600 cents 1/1, 0.0000 cents 24.59000 cents 13: 623.4500 .. 674.0800 cents 50.63000 cents 24.59000 cents 14: 698.6700 .. 698.6700 cents 1/1, 0.0000 cents 24.59000 cents 15: 723.2600 .. 773.8900 cents 50.63000 cents 24.59000 cents 16: 798.4800 .. 798.4800 cents 1/1, 0.0000 cents 24.59000 cents 17: 823.0700 .. 873.7000 cents 50.63000 cents 24.59000 cents 18: 898.2900 .. 898.2900 cents 1/1, 0.0000 cents 24.59000 cents 19: 922.8800 .. 973.5100 cents 50.63000 cents 24.59000 cents 20: 998.1000 .. 998.1000 cents 1/1, 0.0000 cents 24.59000 cents 21: 1022.6900 .. 1073.3200 cents 50.63000 cents 24.59000 cents 22: 1097.9100 .. 1097.9100 cents 1/1, 0.0000 cents 24.59000 cents 23: 1122.5000 .. 1173.1300 cents 50.63000 cents 24.59000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 24.59000 cents, class 1 Average step (divided formal octave): 49.9050 cents Largest one step interval : 75.22000 cents Average / Smallest step : 2.029484 Largest / Average step : 1.507264 Largest / Smallest step : 3.058967 Median interval of one step : 49.90500 cents, amount: 0 Least squares average step : 49.16105 cents, oct.: 1179.86518 cents Scale is strictly proper Scale has 12 repeating blocks of 2 notes Blocks have Myhill's property chromas: 50.63000 cents and 26.04000 cents, ratio: 1.944316 generator: 1 of 24.59000 cents ET pair of linear temperament : 780&828 Scale is distributional even Scale is a mode of a 828-tone equal temperament with octave 1197.720 cents degrees: 17 69 86 138 155 207 224 276 293 345 362 414 431 483 500 552 569 621 638 690 707 759 776 828 Least number of segments generator : 419 of 606.093 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 431 of 623.451 cents and inv. generated superset size: 761 = 737 more = 3170.833% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABABABABABABAB Step pattern size order : SLSLSLSLSLSLSLSLSLSLSLSL Scale is a Constant Structure, by a margin of 24.59000 cents Scale diversity : 1.088166 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.492736 Number of different interval sizes : 35 = 1.52174 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.52174 = 35/23 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 24.59000 cents Scale is a chain of 12 triads 0.0 1022.690 1097.910 cents Most common triad is 0.0 99.810 199.620 cents, amount: 24 Number of recognisable fifths : 24, average 698.6700 cents Number of recognisable fourths : 24, average 499.0500 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 12 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 2 4 6 8 10 12 14 16 18 20 22 Limited inverse transpositions : 1 3 5 7 9 11 13 15 17 19 21 23 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24 -- Rational properties --
FIT/MODE
24: 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 P B DE SD: 17.3878 c. M: 24.5900 c. 28: 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 2 0 2 P B D3 SD: 11.9687 c. M:-18.1857 c. 32: 1 2 0 2 1 2 1 2 0 2 1 2 1 2 0 2 1 2 1 2 0 2 1 2 P B D3 SD: 10.1900 c. M:-12.8388 c. 36: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 6.1377 c. M:-8.6800 c. 48: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 SP B DE SD: 0.2563 c. M:-0.3625 c. 444: 9 28 9 28 9 28 9 28 9 28 9 28 9 28 9 28 9 28 9 28 9 28 9 28 SP B DE SD: 0.2205 c. M: 0.3119 c. 492: 10 31 10 31 10 31 10 31 10 31 10 31 10 31 10 31 10 31 10 31 10 31 10 31 SP B DE SD: 0.1740 c. M: 0.2461 c. 540: 11 34 11 34 11 34 11 34 11 34 11 34 11 34 11 34 11 34 11 34 11 34 11 34 SP B DE SD: 0.1358 c. M: 0.1920 c. 588: 12 37 12 37 12 37 12 37 12 37 12 37 12 37 12 37 12 37 12 37 12 37 12 37 SP B DE SD: 0.1038 c. M: 0.1467 c. 636: 13 40 13 40 13 40 13 40 13 40 13 40 13 40 13 40 13 40 13 40 13 40 13 40 SP B DE SD: 0.0766 c. M: 0.1083 c. 684: 14 43 14 43 14 43 14 43 14 43 14 43 14 43 14 43 14 43 14 43 14 43 14 43 SP B DE SD: 0.0532 c. M: 0.0753 c. 732: 15 46 15 46 15 46 15 46 15 46 15 46 15 46 15 46 15 46 15 46 15 46 15 46 SP B DE SD: 0.0329 c. M: 0.0466 c. 780: 16 49 16 49 16 49 16 49 16 49 16 49 16 49 16 49 16 49 16 49 16 49 16 49 SP B DE SD: 0.0151 c. M: 0.0214 c. 828: 17 52 17 52 17 52 17 52 17 52 17 52 17 52 17 52 17 52 17 52 17 52 17 52 SP B DE SD: 0.0006 c. M:-0.0009 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 2.2800 cents 2 .. 4 match: 2 H SD: 1.9994 cents 3 .. 6 match: 3 H SD: 4.7175 cents 4 .. 8 match: 4 H SD: 8.0625 cents 5 .. 10 match: 5 H SD: 4.2739 cents 6 .. 12 match: 6 H SD: 7.4211 cents 7 .. 14 match: 7 H SD: 5.0778 cents 8 .. 16 match: 8 H SD: 5.8926 cents 9 .. 18 match: 9 H SD: 5.3949 cents 10 .. 20 match: 10 H SD: 5.2293 cents 11 .. 22 match: 11 H SD: 5.8567 cents 12 .. 24 match: 12 H SD: 4.7491 cents 13 .. 26 match: 12 SD: 6.6236 cents 14 .. 28 match: 14 H SD: 3.9371 cents 15 .. 30 match: 15 H SD: 4.2257 cents 16 .. 32 match: 16 H SD: 4.1249 cents 17 .. 34 match: 16 SD: 4.1114 cents 18 .. 36 match: 15 SD: 3.9938 cents 19 .. 38 match: 16 S SD: 4.1777 cents 20 .. 40 match: 15 S SD: 4.1427 cents 21 .. 42 match: 18 S SD: 3.6181 cents 22 .. 44 match: 18 SD: 3.6136 cents 23 .. 46 match: 18 SD: 3.3985 cents 24 .. 48 match: 17 SD: 2.8921 cents 25 .. 50 match: 20 SD: 3.1139 cents 26 .. 52 match: 16 SD: 2.4777 cents 27 .. 54 match: 20 SD: 2.5625 cents 28 .. 56 match: 22 SD: 2.9508 cents 29 .. 58 match: 17 SD: 3.2477 cents 30 .. 60 match: 18 SD: 2.9827 cents 31 .. 62 match: 20 SD: 2.4336 cents 32 .. 64 match: 20 SD: 2.4466 cents 33 .. 66 match: 21 SD: 2.3987 cents 34 .. 68 match: 22 SD: 2.2421 cents 35 .. 70 match: 21 SD: 2.2762 cents 36 .. 72 match: 23 SD: 1.9675 cents 37 .. 74 match: 22 SD: 1.9599 cents 38 .. 76 match: 21 SD: 2.0309 cents 39 .. 78 match: 22 SD: 1.9194 cents 40 .. 80 match: 22 SD: 2.0470 cents 41 .. 82 match: 21 SD: 1.8107 cents 42 .. 84 match: 24 SD: 1.7680 cents 43 .. 86 match: 23 SD: 1.5356 cents 44 .. 88 match: 23 SD: 1.5917 cents 45 .. 90 match: 21 SD: 1.9193 cents 46 .. 92 match: 21 SD: 1.4201 cents 50 .. 100 match: 24 SD: 1.2974 cents 51 .. 102 match: 23 SD: 1.1230 cents 54 .. 108 match: 23 SD: 1.0732 cents 59 .. 118 match: 23 SD: 1.2618 cents 60 .. 120 match: 23 SD: 1.2372 cents 62 .. 124 match: 24 SD: 1.1699 cents 63 .. 126 match: 24 SD: 1.0853 cents 65 .. 130 match: 24 SD: 0.8802 cents 68 .. 136 match: 24 SD: 0.8638 cents 79 .. 158 match: 24 SD: 0.8448 cents 80 .. 160 match: 24 SD: 0.8340 cents 81 .. 162 match: 24 SD: 0.7928 cents 87 .. 174 match: 24 SD: 0.7741 cents 96 .. 192 match: 24 SD: 0.7364 cents 97 .. 194 match: 24 SD: 0.6877 cents 104 .. 208 match: 24 SD: 0.6795 cents 107 .. 214 match: 24 SD: 0.6790 cents 108 .. 216 match: 24 SD: 0.6471 cents 115 .. 230 match: 24 SD: 0.6397 cents 116 .. 232 match: 24 SD: 0.5231 cents 122 .. 244 match: 24 SD: 0.4828 cents 123 .. 246 match: 24 SD: 0.4670 cents 131 .. 262 match: 24 SD: 0.4255 cents 138 .. 276 match: 24 SD: 0.4186 cents 147 .. 294 match: 24 SD: 0.4134 cents 150 .. 300 match: 24 SD: 0.3857 cents 185 .. 370 match: 24 SD: 0.3828 cents 189 .. 378 match: 24 SD: 0.3217 cents 201 .. 401 match: 24 SD: 0.2986 cents 203 .. 405 match: 24 SD: 0.2908 cents 227 .. 453 match: 24 SD: 0.2865 cents 237 .. 473 match: 24 SD: 0.2716 cents 253 .. 505 match: 24 SD: 0.2579 cents 254 .. 507 match: 24 SD: 0.2346 cents 270 .. 539 match: 24 SD: 0.2317 cents 281 .. 561 match: 24 SD: 0.1878 cents 332 .. 663 match: 24 SD: 0.1878 cents 334 .. 667 match: 24 SD: 0.1782 cents 335 .. 669 match: 24 SD: 0.1757 cents 350 .. 699 match: 24 SD: 0.1681 cents 360 .. 719 match: 24 SD: 0.1604 cents 404 .. 807 match: 24 SD: 0.1482 cents 418 .. 835 match: 24 SD: 0.1419 cents 419 .. 837 match: 24 SD: 0.1317 cents 482 .. 963 match: 24 SD: 0.1274 cents 491 .. 981 match: 24 SD: 0.1202 cents 509 .. 1017 match: 24 SD: 0.1199 cents 540 .. 1079 match: 24 SD: 0.1159 cents 551 .. 1101 match: 24 SD: 0.1119 cents 563 .. 1125 match: 24 SD: 0.1055 cents