Scala analysis: xen18-erlich-liese-19
17L 2s MOS for Liese, L=64.52, s=52.89
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64.520 cents 64.520000 2: 129.040 cents 129.040000 3: 193.560 cents 193.560000 4: 258.080 cents 258.080000 5: 310.970 cents 310.970000 6: 375.490 cents 375.490000 7: 440.010 cents 440.010000 8: 504.530 cents 504.530000 9: 569.050 cents 569.050000 10: 633.570 cents 633.570000 11: 698.090 cents 698.090000 12: 762.610 cents 762.610000 13: 827.130 cents 827.130000 14: 891.650 cents 891.650000 15: 944.540 cents 944.540000 16: 1009.060 cents 1009.060000 17: 1073.580 cents 1073.580000 18: 1138.100 cents 1138.100000 19: 1202.620 cents 1202.620000
SHOW/INTERVAL
0: 64.5200 cents 64.5200 1: 64.5200 cents 64.5200 2: 64.5200 cents 64.5200 3: 64.5200 cents 64.5200 4: 64.5200 cents 64.5200 5: 52.8900 cents 52.8900 6: 64.5200 cents 64.5200 7: 64.5200 cents 64.5200 8: 64.5200 cents 64.5200 9: 64.5200 cents 64.5200 10: 64.5200 cents 64.5200 11: 64.5200 cents 64.5200 12: 64.5200 cents 64.5200 13: 64.5200 cents 64.5200 14: 64.5200 cents 64.5200 15: 52.8900 cents 52.8900 16: 64.5200 cents 64.5200 17: 64.5200 cents 64.5200 18: 64.5200 cents 64.5200 19: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 52.89000 cents 1: 17 64.52000 cents 2: 4 117.41000 cents 2: 15 129.04000 cents 3: 6 181.93000 cents 3: 13 193.56000 cents 4: 8 246.45000 cents 4: 11 258.08000 cents 5: 10 310.97000 cents 5: 9 322.60000 cents 6: 12 375.49000 cents 6: 7 387.12000 cents 7: 14 440.01000 cents 7: 5 451.64000 cents 8: 16 504.53000 cents 8: 3 516.16000 cents 9: 18 569.05000 cents 9: 1 580.68000 cents 10: 1 621.94000 cents 10: 18 633.57000 cents 11: 3 686.46000 cents 11: 16 698.09000 cents 12: 5 750.98000 cents 12: 14 762.61000 cents 13: 7 815.50000 cents 13: 12 827.13000 cents 14: 9 880.02000 cents 14: 10 891.65000 cents 15: 11 944.54000 cents 15: 8 956.17000 cents 16: 13 1009.06000 cents 16: 6 1020.69000 cents 17: 15 1073.58000 cents 17: 4 1085.21000 cents 18: 17 1138.10000 cents 18: 2 1149.73000 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 0.0 : 64.5 129.0 193.6 258.1 311.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 827.1 891.7 944.5 1009.1 1073.6 1138.1 1202.6 64.5 : 64.5 129.0 193.6 246.4 311.0 375.5 440.0 504.5 569.1 633.6 698.1 762.6 827.1 880.0 944.5 1009.1 1073.6 1138.1 1202.6 129.0 : 64.5 129.0 181.9 246.4 311.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 193.6 : 64.5 117.4 181.9 246.4 311.0 375.5 440.0 504.5 569.0 633.6 698.1 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 258.1 : 52.9 117.4 181.9 246.5 311.0 375.5 440.0 504.5 569.1 633.6 686.5 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 311.0 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 516.2 580.7 633.6 698.1 762.6 827.1 891.6 956.2 1020.7 1085.2 1149.7 1202.6 375.5 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 516.2 569.0 633.6 698.1 762.6 827.1 891.6 956.2 1020.7 1085.2 1138.1 1202.6 440.0 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 504.5 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1073.6 1138.1 1202.6 504.5 : 64.5 129.0 193.6 258.1 322.6 387.1 440.0 504.5 569.0 633.6 698.1 762.6 827.1 891.6 956.2 1009.1 1073.6 1138.1 1202.6 569.0 : 64.5 129.0 193.6 258.1 322.6 375.5 440.0 504.5 569.1 633.6 698.1 762.6 827.1 891.6 944.5 1009.1 1073.6 1138.1 1202.6 633.6 : 64.5 129.0 193.6 258.1 311.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 827.1 880.0 944.5 1009.1 1073.6 1138.1 1202.6 698.1 : 64.5 129.0 193.6 246.4 311.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 762.6 : 64.5 129.0 181.9 246.4 311.0 375.5 440.0 504.5 569.1 633.6 698.1 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 827.1 : 64.5 117.4 181.9 246.4 311.0 375.5 440.0 504.5 569.1 633.6 686.5 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 891.7 : 52.9 117.4 181.9 246.4 311.0 375.5 440.0 504.5 569.0 621.9 686.5 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 944.5 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 516.2 569.1 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1085.2 1149.7 1202.6 1009.1: 64.5 129.0 193.6 258.1 322.6 387.1 451.6 504.5 569.1 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1085.2 1138.1 1202.6 1073.6: 64.5 129.0 193.6 258.1 322.6 387.1 440.0 504.5 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1073.6 1138.1 1202.6 1138.1: 64.5 129.0 193.6 258.1 322.6 375.5 440.0 504.5 569.1 633.6 698.1 762.6 827.1 891.7 956.2 1009.1 1073.6 1138.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.8900 .. 64.5200 cents 11.63000 cents 52.89000 cents 2: 117.4100 .. 129.0400 cents 11.63000 cents 52.89000 cents 3: 181.9300 .. 193.5600 cents 11.63000 cents 52.89000 cents 4: 246.4500 .. 258.0800 cents 11.63000 cents 52.89000 cents 5: 310.9700 .. 322.6000 cents 11.63000 cents 52.89000 cents 6: 375.4900 .. 387.1200 cents 11.63000 cents 52.89000 cents 7: 440.0100 .. 451.6400 cents 11.63000 cents 52.89000 cents 8: 504.5300 .. 516.1600 cents 11.63000 cents 52.89000 cents 9: 569.0500 .. 580.6800 cents 11.63000 cents 52.89000 cents 10: 621.9400 .. 633.5700 cents 11.63000 cents 41.26000 cents 11: 686.4600 .. 698.0900 cents 11.63000 cents 52.89000 cents 12: 750.9800 .. 762.6100 cents 11.63000 cents 52.89000 cents 13: 815.5000 .. 827.1300 cents 11.63000 cents 52.89000 cents 14: 880.0200 .. 891.6500 cents 11.63000 cents 52.89000 cents 15: 944.5400 .. 956.1700 cents 11.63000 cents 52.89000 cents 16: 1009.0600 .. 1020.6900 cents 11.63000 cents 52.89000 cents 17: 1073.5800 .. 1085.2100 cents 11.63000 cents 52.89000 cents 18: 1138.1000 .. 1149.7300 cents 11.63000 cents 52.89000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 52.89000 cents, class 1 Average step (divided formal octave): 63.2958 cents Largest one step interval : 64.52000 cents Average / Smallest step : 1.196744 Largest / Average step : 1.019341 Largest / Smallest step : 1.219890 Median interval of one step : 64.52000 cents, amount: 17 Most common interval of one step : 64.52000 cents, amount: 17 Least squares average step : 63.27225 cents, oct.: 1202.17269 cents Scale is strictly proper Scale has Myhill's property chromas: 11.63000 cents and 41.26000 cents, ratio: 3.547721 generators: 9 of 569.05000 cents and 10 of 633.57000 cents ET pair of linear temperament : 17&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1137-tone equal temperament with octave 1202.620 cents degrees: 61 122 183 244 294 355 416 477 538 599 660 721 782 843 893 954 1015 1076 1137 generators: 538 and 599 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAAAAAABAAAA Step pattern size order : LLLLSLLLLLLLLLSLLLL Scale is a Constant Structure, by a margin of 41.26000 cents Scale diversity : 1.111772 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.825930 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 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 : 11.63000 cents Most common intervals : 569.05000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 17 Number of recognisable fifths : 19, average 696.2537 cents Number of appreciable fifths : 16, average 698.0900 cents Number of recognisable fourths : 16, average 504.5300 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 19 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 3.3526 c. M: 5.5089 c. 55: 3 3 3 3 2 3 3 3 3 3 3 3 3 3 2 3 3 3 3 SP M ME I SD: 2.9507 c. M: 4.8485 c. 74: 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 4 4 4 4 SP M ME I SD: 1.3323 c. M: 2.1892 c. 93: 5 5 5 5 4 5 5 5 5 5 5 5 5 5 4 5 5 5 5 SP M ME I SD: 0.3752 c. M: 0.6165 c. 112: 6 6 6 6 5 6 6 6 6 6 6 6 6 6 5 6 6 6 6 SP M ME I SD: 0.2572 c. M: 0.4227 c. 205: 11 11 11 11 9 11 11 11 11 11 11 11 11 11 9 11 11 11 11 SP M DE I SD: 0.0297 c. M: 0.0487 c. 727: 39 39 39 39 32 39 39 39 39 39 39 39 39 39 32 39 39 39 39 SP M DE I SD: 0.0145 c. M: 0.0239 c. 932: 50 50 50 50 41 50 50 50 50 50 50 50 50 50 41 50 50 50 50 SP M DE I SD: 0.0048 c. M: 0.0079 c. 1137: 61 61 61 61 50 61 61 61 61 61 61 61 61 61 50 61 61 61 61 SP M DE I SD: 0.0014 c. M: 0.0023 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 2.6200 cents 2 .. 4 match: 2 H SD: 2.3347 cents 3 .. 6 match: 3 H SD: 3.3679 cents 4 .. 8 match: 4 H SD: 6.7489 cents 5 .. 10 match: 5 H SD: 4.3059 cents 6 .. 12 match: 6 H SD: 4.6570 cents 7 .. 14 match: 7 H SD: 5.6111 cents 8 .. 16 match: 8 H SD: 4.9142 cents 9 .. 18 match: 9 H SD: 4.9095 cents 10 .. 20 match: 10 H SD: 5.3759 cents 11 .. 22 match: 11 H SD: 6.0735 cents 12 .. 24 match: 12 H SD: 5.0337 cents 13 .. 26 match: 13 H SD: 4.1027 cents 14 .. 28 match: 14 H SD: 4.4790 cents 15 .. 30 match: 15 H SD: 4.1302 cents 16 .. 32 match: 16 H SD: 3.9790 cents 17 .. 34 match: 16 S SD: 5.3993 cents 18 .. 36 match: 17 SD: 3.3033 cents 19 .. 38 match: 17 SD: 4.9595 cents 20 .. 40 match: 18 SD: 3.6022 cents 21 .. 42 match: 18 SD: 3.6272 cents 22 .. 44 match: 18 SD: 4.2090 cents 23 .. 46 match: 19 SD: 3.7007 cents 24 .. 48 match: 19 SD: 2.6558 cents 25 .. 50 match: 19 SD: 2.4383 cents 34 .. 68 match: 19 SD: 2.3527 cents 36 .. 72 match: 19 SD: 1.9789 cents 41 .. 82 match: 19 SD: 1.7754 cents 44 .. 88 match: 19 SD: 1.7681 cents 48 .. 96 match: 19 SD: 1.7438 cents 49 .. 98 match: 19 SD: 1.4138 cents 51 .. 102 match: 19 SD: 1.3164 cents 52 .. 104 match: 19 SD: 1.2671 cents 56 .. 112 match: 19 SD: 1.2479 cents 61 .. 122 match: 19 SD: 1.2308 cents 62 .. 124 match: 19 SD: 1.0416 cents 74 .. 148 match: 19 SD: 1.0346 cents 75 .. 150 match: 19 SD: 1.0007 cents 76 .. 152 match: 19 SD: 0.9252 cents 77 .. 154 match: 19 SD: 0.7879 cents 100 .. 200 match: 19 SD: 0.6659 cents 101 .. 202 match: 19 SD: 0.6408 cents 125 .. 250 match: 19 SD: 0.6317 cents 127 .. 254 match: 19 SD: 0.5580 cents 128 .. 256 match: 19 SD: 0.5506 cents 129 .. 258 match: 19 SD: 0.5403 cents 141 .. 282 match: 19 SD: 0.5306 cents 142 .. 284 match: 19 SD: 0.5229 cents 152 .. 304 match: 19 SD: 0.5187 cents 153 .. 306 match: 19 SD: 0.4834 cents 154 .. 308 match: 19 SD: 0.4832 cents 157 .. 314 match: 19 SD: 0.4190 cents 183 .. 367 match: 19 SD: 0.3632 cents 186 .. 373 match: 19 SD: 0.3610 cents 193 .. 387 match: 19 SD: 0.3179 cents 211 .. 423 match: 19 SD: 0.3132 cents 219 .. 439 match: 19 SD: 0.2953 cents 242 .. 485 match: 19 SD: 0.2952 cents 244 .. 489 match: 19 SD: 0.2798 cents 255 .. 511 match: 19 SD: 0.2548 cents 260 .. 521 match: 19 SD: 0.2111 cents 310 .. 621 match: 19 SD: 0.1960 cents 346 .. 693 match: 19 SD: 0.1804 cents 372 .. 745 match: 19 SD: 0.1697 cents 387 .. 775 match: 19 SD: 0.1626 cents 398 .. 797 match: 19 SD: 0.1557 cents 441 .. 883 match: 19 SD: 0.1314 cents 529 .. 1060 match: 19 SD: 0.1232 cents 573 .. 1148 match: 19 SD: 0.1153 cents 583 .. 1168 match: 19 SD: 0.1129 cents 598 .. 1198 match: 19 SD: 0.1079 cents