Scala analysis: xen18-erlich-liese-17
2L 15s MOS for Liese, L=117.41, s=64.52
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: 375.490 cents 375.490000 6: 440.010 cents 440.010000 7: 504.530 cents 504.530000 8: 569.050 cents 569.050000 9: 633.570 cents 633.570000 10: 698.090 cents 698.090000 11: 762.610 cents 762.610000 12: 827.130 cents 827.130000 13: 944.540 cents 944.540000 14: 1009.060 cents 1009.060000 15: 1073.580 cents 1073.580000 16: 1138.100 cents 1138.100000 17: 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: 117.4100 cents 117.4100 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: 117.4100 cents 117.4100 14: 64.5200 cents 64.5200 15: 64.5200 cents 64.5200 16: 64.5200 cents 64.5200 17: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 64.52000 cents 1: 2 117.41000 cents 2: 13 129.04000 cents 2: 4 181.93000 cents 3: 11 193.56000 cents 3: 6 246.45000 cents 4: 9 258.08000 cents 4: 8 310.97000 cents 5: 7 322.60000 cents 5: 10 375.49000 cents 6: 5 387.12000 cents 6: 12 440.01000 cents 7: 3 451.64000 cents 7: 14 504.53000 cents 8: 1 516.16000 cents 8: 16 569.05000 cents 9: 16 633.57000 cents 9: 1 686.46000 cents 10: 14 698.09000 cents 10: 3 750.98000 cents 11: 12 762.61000 cents 11: 5 815.50000 cents 12: 10 827.13000 cents 12: 7 880.02000 cents 13: 8 891.65000 cents 13: 9 944.54000 cents 14: 6 956.17000 cents 14: 11 1009.06000 cents 15: 4 1020.69000 cents 15: 13 1073.58000 cents 16: 2 1085.21000 cents 16: 15 1138.10000 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 0.0 : 64.5 129.0 193.6 258.1 375.5 440.0 504.5 569.0 633.6 698.1 762.6 827.1 944.5 1009.1 1073.6 1138.1 1202.6 64.5 : 64.5 129.0 193.6 311.0 375.5 440.0 504.5 569.1 633.6 698.1 762.6 880.0 944.5 1009.1 1073.6 1138.1 1202.6 129.0 : 64.5 129.0 246.4 311.0 375.5 440.0 504.5 569.0 633.6 698.1 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 193.6 : 64.5 181.9 246.4 311.0 375.5 440.0 504.5 569.0 633.6 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 258.1 : 117.4 181.9 246.5 311.0 375.5 440.0 504.5 569.1 686.5 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 375.5 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 569.0 633.6 698.1 762.6 827.1 891.6 956.2 1020.7 1085.2 1202.6 440.0 : 64.5 129.0 193.6 258.1 322.6 387.1 504.5 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1138.1 1202.6 504.5 : 64.5 129.0 193.6 258.1 322.6 440.0 504.5 569.0 633.6 698.1 762.6 827.1 891.6 956.2 1073.6 1138.1 1202.6 569.0 : 64.5 129.0 193.6 258.1 375.5 440.0 504.5 569.1 633.6 698.1 762.6 827.1 891.6 1009.1 1073.6 1138.1 1202.6 633.6 : 64.5 129.0 193.6 311.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 827.1 944.5 1009.1 1073.6 1138.1 1202.6 698.1 : 64.5 129.0 246.4 311.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 880.0 944.5 1009.1 1073.6 1138.1 1202.6 762.6 : 64.5 181.9 246.4 311.0 375.5 440.0 504.5 569.1 633.6 698.1 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 827.1 : 117.4 181.9 246.4 311.0 375.5 440.0 504.5 569.1 633.6 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 944.5 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 516.2 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1085.2 1202.6 1009.1: 64.5 129.0 193.6 258.1 322.6 387.1 451.6 569.1 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1138.1 1202.6 1073.6: 64.5 129.0 193.6 258.1 322.6 387.1 504.5 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1073.6 1138.1 1202.6 1138.1: 64.5 129.0 193.6 258.1 322.6 440.0 504.5 569.1 633.6 698.1 762.6 827.1 891.7 1009.1 1073.6 1138.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.5200 .. 117.4100 cents 52.89000 cents 64.52000 cents 2: 129.0400 .. 181.9300 cents 52.89000 cents 11.63000 cents 3: 193.5600 .. 246.4500 cents 52.89000 cents 11.63000 cents 4: 258.0800 .. 310.9700 cents 52.89000 cents 11.63000 cents 5: 322.6000 .. 375.4900 cents 52.89000 cents 11.63000 cents 6: 387.1200 .. 440.0100 cents 52.89000 cents 11.63000 cents 7: 451.6400 .. 504.5300 cents 52.89000 cents 11.63000 cents 8: 516.1600 .. 569.0500 cents 52.89000 cents 11.63000 cents 9: 633.5700 .. 686.4600 cents 52.89000 cents 64.52000 cents 10: 698.0900 .. 750.9800 cents 52.89000 cents 11.63000 cents 11: 762.6100 .. 815.5000 cents 52.89000 cents 11.63000 cents 12: 827.1300 .. 880.0200 cents 52.89000 cents 11.63000 cents 13: 891.6500 .. 944.5400 cents 52.89000 cents 11.63000 cents 14: 956.1700 .. 1009.0600 cents 52.89000 cents 11.63000 cents 15: 1020.6900 .. 1073.5800 cents 52.89000 cents 11.63000 cents 16: 1085.2100 .. 1138.1000 cents 52.89000 cents 11.63000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 64.52000 cents, class 1 Average step (divided formal octave): 70.7424 cents Largest one step interval : 117.41000 cents Average / Smallest step : 1.096441 Largest / Average step : 1.659685 Largest / Smallest step : 1.819746 Median interval of one step : 64.52000 cents, amount: 15 Most common interval of one step : 64.52000 cents, amount: 15 Least squares average step : 70.97939 cents, oct.: 1206.64971 cents Scale is strictly proper Scale has Myhill's property chromas: 52.89000 cents and 11.63000 cents, ratio: 4.547721 generators: 8 of 569.05000 cents and 9 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: 61 122 183 244 355 416 477 538 599 660 721 782 893 954 1015 1076 1137 generators: 538 and 599 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAAAABAAAA Step pattern size order : SSSSLSSSSSSSLSSSS Scale is a Constant Structure, by a margin of 11.63000 cents Scale diversity : 1.126293 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.296336 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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: 16 Scale is a chain of 8 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 15 Number of recognisable fifths : 15, average 697.3147 cents Number of appreciable fifths : 14, average 698.0900 cents Number of recognisable fourths : 14, average 504.5300 cents Scale contains two identical disjunct "tetrachords" of 8 notes Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.2416 c. M:-24.8894 c. 19: 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 P M ME I SD: 2.9987 c. M: 4.8968 c. 55: 3 3 3 3 5 3 3 3 3 3 3 3 5 3 3 3 3 SP M DE I SD: 2.6392 c. M: 4.3098 c. 74: 4 4 4 4 7 4 4 4 4 4 4 4 7 4 4 4 4 SP M DE I SD: 1.1916 c. M:-1.9459 c. 93: 5 5 5 5 9 5 5 5 5 5 5 5 9 5 5 5 5 SP M DE I SD: 0.3356 c. M:-0.5480 c. 112: 6 6 6 6 11 6 6 6 6 6 6 6 11 6 6 6 6 SP M DE I SD: 0.2301 c. M:-0.3757 c. 205: 11 11 11 11 20 11 11 11 11 11 11 11 20 11 11 11 11 SP M DE I SD: 0.0265 c. M:-0.0433 c. 727: 39 39 39 39 71 39 39 39 39 39 39 39 71 39 39 39 39 SP M DE I SD: 0.0130 c. M:-0.0212 c. 932: 50 50 50 50 91 50 50 50 50 50 50 50 91 50 50 50 50 SP M DE I SD: 0.0043 c. M:-0.0070 c. 1137: 61 61 61 61 111 61 61 61 61 61 61 61 111 61 61 61 61 SP M DE I SD: 0.0012 c. M:-0.0020 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: 19.2182 cents 4 .. 8 match: 4 H SD: 6.7489 cents 5 .. 10 match: 5 H SD: 12.2556 cents 6 .. 12 match: 6 H SD: 10.5445 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: 7.9925 cents 10 .. 20 match: 10 H SD: 7.8622 cents 11 .. 22 match: 11 H SD: 6.4018 cents 12 .. 24 match: 11 SD: 5.4511 cents 13 .. 26 match: 13 H SD: 4.6265 cents 14 .. 28 match: 14 H SD: 4.9774 cents 15 .. 30 match: 13 SD: 4.7189 cents 16 .. 32 match: 15 S SD: 4.8189 cents 17 .. 34 match: 15 SD: 5.4534 cents 18 .. 36 match: 16 SD: 3.4801 cents 19 .. 38 match: 15 SD: 5.4157 cents 20 .. 40 match: 16 SD: 3.7358 cents 21 .. 42 match: 16 SD: 4.0148 cents 23 .. 46 match: 17 SD: 3.5130 cents 24 .. 48 match: 17 SD: 2.7689 cents 25 .. 50 match: 17 SD: 2.6842 cents 29 .. 58 match: 17 SD: 2.6507 cents 33 .. 66 match: 17 SD: 2.6248 cents 34 .. 68 match: 17 SD: 2.5077 cents 36 .. 72 match: 17 SD: 2.1606 cents 38 .. 76 match: 17 SD: 2.1502 cents 41 .. 82 match: 17 SD: 1.8985 cents 44 .. 88 match: 17 SD: 1.7964 cents 48 .. 96 match: 17 SD: 1.7285 cents 49 .. 98 match: 17 SD: 1.4532 cents 51 .. 102 match: 17 SD: 1.4061 cents 52 .. 104 match: 17 SD: 1.3637 cents 54 .. 108 match: 17 SD: 1.3126 cents 62 .. 124 match: 17 SD: 1.1086 cents 74 .. 148 match: 17 SD: 1.0338 cents 75 .. 150 match: 17 SD: 1.0144 cents 77 .. 154 match: 17 SD: 0.8589 cents 100 .. 200 match: 17 SD: 0.6538 cents 124 .. 248 match: 17 SD: 0.6524 cents 125 .. 250 match: 17 SD: 0.6420 cents 127 .. 254 match: 17 SD: 0.5870 cents 129 .. 258 match: 17 SD: 0.5467 cents 153 .. 306 match: 17 SD: 0.5363 cents 154 .. 308 match: 17 SD: 0.5040 cents 157 .. 314 match: 17 SD: 0.4561 cents 177 .. 355 match: 17 SD: 0.4539 cents 179 .. 359 match: 17 SD: 0.4479 cents 181 .. 363 match: 17 SD: 0.4397 cents 183 .. 367 match: 17 SD: 0.3945 cents 186 .. 373 match: 17 SD: 0.3448 cents 210 .. 421 match: 17 SD: 0.3416 cents 211 .. 423 match: 17 SD: 0.2878 cents 255 .. 511 match: 17 SD: 0.2743 cents 260 .. 521 match: 17 SD: 0.2269 cents 298 .. 597 match: 17 SD: 0.2169 cents 322 .. 645 match: 17 SD: 0.1974 cents 372 .. 745 match: 17 SD: 0.1733 cents 398 .. 797 match: 17 SD: 0.1593 cents 441 .. 883 match: 17 SD: 0.1395 cents 455 .. 911 match: 17 SD: 0.1321 cents 529 .. 1060 match: 17 SD: 0.1294 cents 532 .. 1066 match: 17 SD: 0.1287 cents 573 .. 1148 match: 17 SD: 0.1233 cents 583 .. 1168 match: 17 SD: 0.1166 cents 598 .. 1198 match: 17 SD: 0.1101 cents