Scala analysis: xen18-erlich-august-21
12L 9s MOS for August, L=78.06, s=29.25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.060 cents 78.060000 2: 107.310 cents 107.310000 3: 185.370 cents 185.370000 4: 214.620 cents 214.620000 5: 292.680 cents 292.680000 6: 321.930 cents 321.930000 7: 399.990 cents 399.990000 8: 478.050 cents 478.050000 9: 507.300 cents 507.300000 10: 585.360 cents 585.360000 11: 614.610 cents 614.610000 12: 692.670 cents 692.670000 13: 721.920 cents 721.920000 14: 799.980 cents 799.980000 15: 878.040 cents 878.040000 16: 907.290 cents 907.290000 17: 985.350 cents 985.350000 18: 1014.600 cents 1014.600000 19: 1092.660 cents 1092.660000 20: 1121.910 cents 1121.910000 21: 1199.970 cents 1199.970000
SHOW/INTERVAL
0: 78.0600 cents 78.0600 1: 78.0600 cents 78.0600 2: 29.2500 cents 29.2500 3: 78.0600 cents 78.0600 4: 29.2500 cents 29.2500 5: 78.0600 cents 78.0600 6: 29.2500 cents 29.2500 7: 78.0600 cents 78.0600 8: 78.0600 cents 78.0600 9: 29.2500 cents 29.2500 10: 78.0600 cents 78.0600 11: 29.2500 cents 29.2500 12: 78.0600 cents 78.0600 13: 29.2500 cents 29.2500 14: 78.0600 cents 78.0600 15: 78.0600 cents 78.0600 16: 29.2500 cents 29.2500 17: 78.0600 cents 78.0600 18: 29.2500 cents 29.2500 19: 78.0600 cents 78.0600 20: 29.2500 cents 29.2500 21: 78.0600 cents 78.0600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 29.25000 cents 1: 12 78.06000 cents 2: 18 107.31000 cents 2: 3 156.12000 cents 3: 6 136.56000 cents 3: 15 185.37000 cents 4: 15 214.62000 cents 4: 6 263.43000 cents 5: 3 243.87000 cents 5: 18 292.68000 cents 6: 12 321.93000 cents 6: 9 370.74000 cents 7: 21 399.99000 cents 8: 9 429.24000 cents 8: 12 478.05000 cents 9: 18 507.30000 cents 9: 3 556.11000 cents 10: 6 536.55000 cents 10: 15 585.36000 cents 11: 15 614.61000 cents 11: 6 663.42000 cents 12: 3 643.86000 cents 12: 18 692.67000 cents 13: 12 721.92000 cents 13: 9 770.73000 cents 14: 21 799.98000 cents 15: 9 829.23000 cents 15: 12 878.04000 cents 16: 18 907.29000 cents 16: 3 956.10000 cents 17: 6 936.54000 cents 17: 15 985.35000 cents 18: 15 1014.60000 cents 18: 6 1063.41000 cents 19: 3 1043.85000 cents 19: 18 1092.66000 cents 20: 12 1121.91000 cents 20: 9 1170.72000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.90000 = 19/10
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 0.0 : 78.1 107.3 185.4 214.6 292.7 321.9 400.0 478.1 507.3 585.4 614.6 692.7 721.9 800.0 878.0 907.3 985.4 1014.6 1092.7 1121.9 1200.0 78.1 : 29.2 107.3 136.6 214.6 243.9 321.9 400.0 429.2 507.3 536.5 614.6 643.9 721.9 800.0 829.2 907.3 936.5 1014.6 1043.8 1121.9 1200.0 107.3 : 78.1 107.3 185.4 214.6 292.7 370.7 400.0 478.1 507.3 585.4 614.6 692.7 770.7 800.0 878.0 907.3 985.4 1014.6 1092.7 1170.7 1200.0 185.4 : 29.2 107.3 136.6 214.6 292.7 321.9 400.0 429.2 507.3 536.5 614.6 692.7 721.9 800.0 829.2 907.3 936.5 1014.6 1092.7 1121.9 1200.0 214.6 : 78.1 107.3 185.4 263.4 292.7 370.7 400.0 478.1 507.3 585.4 663.4 692.7 770.7 800.0 878.0 907.3 985.4 1063.4 1092.7 1170.7 1200.0 292.7 : 29.2 107.3 185.4 214.6 292.7 321.9 400.0 429.2 507.3 585.4 614.6 692.7 721.9 800.0 829.2 907.3 985.4 1014.6 1092.7 1121.9 1200.0 321.9 : 78.1 156.1 185.4 263.4 292.7 370.7 400.0 478.1 556.1 585.4 663.4 692.7 770.7 800.0 878.0 956.1 985.4 1063.4 1092.7 1170.7 1200.0 400.0 : 78.1 107.3 185.4 214.6 292.7 321.9 400.0 478.0 507.3 585.4 614.6 692.7 721.9 800.0 878.0 907.3 985.4 1014.6 1092.7 1121.9 1200.0 478.1 : 29.2 107.3 136.6 214.6 243.9 321.9 400.0 429.2 507.3 536.5 614.6 643.9 721.9 800.0 829.2 907.3 936.5 1014.6 1043.8 1121.9 1200.0 507.3 : 78.1 107.3 185.4 214.6 292.7 370.7 400.0 478.1 507.3 585.4 614.6 692.7 770.7 800.0 878.0 907.3 985.4 1014.6 1092.7 1170.7 1200.0 585.4 : 29.2 107.3 136.6 214.6 292.7 321.9 400.0 429.2 507.3 536.6 614.6 692.7 721.9 800.0 829.2 907.3 936.5 1014.6 1092.7 1121.9 1200.0 614.6 : 78.1 107.3 185.4 263.4 292.7 370.7 400.0 478.1 507.3 585.4 663.4 692.7 770.7 800.0 878.0 907.3 985.4 1063.4 1092.7 1170.7 1200.0 692.7 : 29.2 107.3 185.4 214.6 292.7 321.9 400.0 429.2 507.3 585.4 614.6 692.7 721.9 800.0 829.2 907.3 985.4 1014.6 1092.7 1121.9 1200.0 721.9 : 78.1 156.1 185.4 263.4 292.7 370.7 400.0 478.1 556.1 585.4 663.4 692.7 770.7 800.0 878.0 956.1 985.3 1063.4 1092.7 1170.7 1200.0 800.0 : 78.1 107.3 185.4 214.6 292.7 321.9 400.0 478.1 507.3 585.4 614.6 692.7 721.9 800.0 878.0 907.3 985.4 1014.6 1092.7 1121.9 1200.0 878.0 : 29.2 107.3 136.6 214.6 243.9 321.9 400.0 429.2 507.3 536.6 614.6 643.9 721.9 800.0 829.2 907.3 936.5 1014.6 1043.9 1121.9 1200.0 907.3 : 78.1 107.3 185.4 214.6 292.7 370.7 400.0 478.1 507.3 585.4 614.6 692.7 770.7 800.0 878.0 907.3 985.4 1014.6 1092.7 1170.7 1200.0 985.4 : 29.2 107.3 136.6 214.6 292.7 321.9 400.0 429.2 507.3 536.5 614.6 692.7 721.9 800.0 829.2 907.3 936.5 1014.6 1092.7 1121.9 1200.0 1014.6: 78.1 107.3 185.4 263.4 292.7 370.7 400.0 478.1 507.3 585.4 663.4 692.7 770.7 800.0 878.0 907.3 985.4 1063.4 1092.7 1170.7 1200.0 1092.7: 29.2 107.3 185.4 214.6 292.7 321.9 400.0 429.2 507.3 585.4 614.6 692.7 721.9 800.0 829.2 907.3 985.3 1014.6 1092.7 1121.9 1200.0 1121.9: 78.1 156.1 185.4 263.4 292.7 370.7 400.0 478.0 556.1 585.4 663.4 692.7 770.7 800.0 878.0 956.1 985.3 1063.4 1092.7 1170.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.2500 .. 78.0600 cents 48.81000 cents 29.25000 cents 2: 107.3100 .. 156.1200 cents 48.81000 cents 29.25000 cents 3: 136.5600 .. 185.3700 cents 48.81000 cents -19.56000 cents 4: 214.6200 .. 263.4300 cents 48.81000 cents 29.25000 cents 5: 243.8700 .. 292.6800 cents 48.81000 cents -19.56000 cents 6: 321.9300 .. 370.7400 cents 48.81000 cents 29.25000 cents 7: 399.9900 .. 399.9900 cents 1/1, 0.0000 cents 29.25000 cents 8: 429.2400 .. 478.0500 cents 48.81000 cents 29.25000 cents 9: 507.3000 .. 556.1100 cents 48.81000 cents 29.25000 cents 10: 536.5500 .. 585.3600 cents 48.81000 cents -19.56000 cents 11: 614.6100 .. 663.4200 cents 48.81000 cents 29.25000 cents 12: 643.8600 .. 692.6700 cents 48.81000 cents -19.56000 cents 13: 721.9200 .. 770.7300 cents 48.81000 cents 29.25000 cents 14: 799.9800 .. 799.9800 cents 1/1, 0.0000 cents 29.25000 cents 15: 829.2300 .. 878.0400 cents 48.81000 cents 29.25000 cents 16: 907.2900 .. 956.1000 cents 48.81000 cents 29.25000 cents 17: 936.5400 .. 985.3500 cents 48.81000 cents -19.56000 cents 18: 1014.6000 .. 1063.4100 cents 48.81000 cents 29.25000 cents 19: 1043.8500 .. 1092.6600 cents 48.81000 cents -19.56000 cents 20: 1121.9100 .. 1170.7200 cents 48.81000 cents 29.25000 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 29.25000 cents, class 1 Average step (divided formal octave): 57.1414 cents Largest one step interval : 78.06000 cents Average / Smallest step : 1.953553 Largest / Average step : 1.366084 Largest / Smallest step : 2.668718 Median interval of one step : 78.06000 cents, amount: 12 Most common interval of one step : 78.06000 cents, amount: 12 Least squares average step : 57.05298 cents, oct.: 1198.11254 cents Scale is not proper Scale has 3 repeating blocks of 7 notes Blocks have Myhill's property chromas: 48.81000 cents and 19.56000 cents, ratio: 2.495399 generators: 2 of 107.31000 cents and 5 of 292.68000 cents ET pair of linear temperament : 33&45 Scale is distributional even Step pattern alph. order: ABABABAABABABAABABABA Step pattern size order : LSLSLSLLSLSLSLLSLSLSL Scale is a Constant Structure, by a margin of 19.56000 cents Scale diversity : 1.179590 Lumma stability : 0.365634 Lumma impropriety factor : 0.097802 Number of different interval sizes : 38 = 1.90000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.90000 = 19/10 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 19.56000 cents Most common intervals : 399.99000 cents & inv., amount: 21 Most common triad is 0.0 399.990 799.980 cents, amount: 21 Number of recognisable fifths : 18, average 692.6700 cents Number of recognisable fourths : 18, average 507.3000 cents Formal octave complements present : 21 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 7 14 Limited inverse transpositions : 7 14 Inversional symmetry on degrees : 0 7 14 Inversional symmetry on intervals : 3-4 10-11 17-18 -- Rational properties --
FIT/MODE
21: 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: 13.9457 c. M:-20.9186 c. 25: 2 0 2 0 2 1 1 2 1 1 1 1 1 2 1 1 2 0 2 0 2 N D3 I SD: 13.8040 c. M:-22.6248 c. 26: 2 0 2 1 1 1 2 1 1 2 0 2 1 1 2 1 1 1 2 0 2 N D3 I SD: 12.5841 c. M: 16.5231 c. 27: 2 0 2 1 2 0 2 2 0 2 1 2 0 2 2 0 2 1 2 0 2 N B D3 I SD: 12.1225 c. M:-18.4233 c. 30: 2 1 2 0 2 1 2 2 1 2 0 2 1 2 2 1 2 0 2 1 2 N B D3 I SD: 10.4006 c. M:-14.6250 c. 33: 2 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 2 P B ME I SD: 3.5564 c. M:-5.3345 c. 45: 3 1 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 1 3 N B DE I SD: 1.2920 c. M: 1.9380 c. 78: 5 2 5 2 5 2 5 5 2 5 2 5 2 5 5 2 5 2 5 2 5 N B DE I SD: 0.7592 c. M:-1.1388 c. 123: 8 3 8 3 8 3 8 8 3 8 3 8 3 8 8 3 8 3 8 3 8 N B DE I SD: 0.0088 c. M:-0.0132 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0300 cents 2 .. 4 match: 2 H SD: 4.6425 cents 3 .. 6 match: 3 H SD: 3.7354 cents 4 .. 8 match: 4 H SD: 5.8433 cents 5 .. 10 match: 5 H SD: 3.1273 cents 6 .. 12 match: 6 H SD: 7.6128 cents 7 .. 14 match: 7 H SD: 7.7284 cents 8 .. 16 match: 8 H SD: 7.1221 cents 9 .. 18 match: 9 H SD: 5.7553 cents 10 .. 20 match: 10 H SD: 3.9462 cents 11 .. 22 match: 11 H SD: 7.6895 cents 12 .. 24 match: 12 H SD: 5.0673 cents 13 .. 26 match: 13 H SD: 6.6494 cents 14 .. 28 match: 14 H SD: 4.7970 cents 15 .. 30 match: 14 SD: 3.3555 cents 16 .. 32 match: 15 SD: 4.0094 cents 17 .. 34 match: 17 H SD: 4.3556 cents 18 .. 36 match: 14 SD: 4.4748 cents 19 .. 38 match: 13 SD: 2.7890 cents 20 .. 40 match: 17 S SD: 3.6734 cents 21 .. 42 match: 17 SD: 3.8320 cents 22 .. 44 match: 16 SD: 3.7171 cents 23 .. 46 match: 18 SD: 2.7942 cents 24 .. 48 match: 17 SD: 3.2900 cents 25 .. 50 match: 18 SD: 3.1351 cents 26 .. 52 match: 18 SD: 2.5888 cents 27 .. 54 match: 20 SD: 2.9434 cents 28 .. 56 match: 20 SD: 2.9568 cents 29 .. 58 match: 19 SD: 2.5166 cents 30 .. 60 match: 19 SD: 2.4830 cents 31 .. 62 match: 19 SD: 2.5555 cents 32 .. 64 match: 20 SD: 2.5105 cents 33 .. 66 match: 19 SD: 2.1916 cents 34 .. 68 match: 18 SD: 2.0759 cents 35 .. 70 match: 20 SD: 1.7313 cents 36 .. 72 match: 19 SD: 2.3886 cents 37 .. 74 match: 20 SD: 2.2449 cents 38 .. 76 match: 20 SD: 1.6193 cents 39 .. 78 match: 20 SD: 1.7565 cents 40 .. 80 match: 20 SD: 2.1979 cents 41 .. 82 match: 19 SD: 2.0514 cents 42 .. 84 match: 21 SD: 1.8276 cents 43 .. 86 match: 21 SD: 1.5509 cents 44 .. 88 match: 21 SD: 1.2431 cents 49 .. 98 match: 20 SD: 1.5153 cents 50 .. 100 match: 21 SD: 1.4388 cents 53 .. 106 match: 21 SD: 1.4378 cents 54 .. 108 match: 21 SD: 1.4286 cents 58 .. 116 match: 21 SD: 1.4094 cents 59 .. 118 match: 21 SD: 1.1083 cents 65 .. 130 match: 21 SD: 0.9713 cents 77 .. 154 match: 21 SD: 0.8626 cents 82 .. 164 match: 21 SD: 0.7763 cents 89 .. 178 match: 21 SD: 0.7012 cents 97 .. 194 match: 21 SD: 0.6751 cents 104 .. 208 match: 21 SD: 0.6575 cents 107 .. 214 match: 21 SD: 0.5926 cents 108 .. 216 match: 21 SD: 0.5778 cents 112 .. 224 match: 21 SD: 0.5436 cents 124 .. 248 match: 21 SD: 0.5020 cents 126 .. 252 match: 21 SD: 0.4906 cents 141 .. 282 match: 21 SD: 0.4867 cents 150 .. 300 match: 21 SD: 0.4590 cents 151 .. 302 match: 21 SD: 0.4113 cents 157 .. 314 match: 21 SD: 0.3734 cents 167 .. 334 match: 21 SD: 0.3632 cents 176 .. 352 match: 21 SD: 0.3569 cents 189 .. 378 match: 21 SD: 0.3473 cents 197 .. 394 match: 21 SD: 0.3201 cents 211 .. 422 match: 21 SD: 0.3065 cents 218 .. 436 match: 21 SD: 0.3018 cents 232 .. 464 match: 21 SD: 0.3015 cents 235 .. 470 match: 21 SD: 0.2810 cents 264 .. 528 match: 21 SD: 0.2628 cents 265 .. 530 match: 21 SD: 0.2210 cents 282 .. 564 match: 21 SD: 0.2207 cents 303 .. 606 match: 21 SD: 0.2071 cents 309 .. 618 match: 21 SD: 0.1988 cents 326 .. 652 match: 21 SD: 0.1987 cents 327 .. 654 match: 21 SD: 0.1754 cents 373 .. 746 match: 21 SD: 0.1565 cents 408 .. 816 match: 21 SD: 0.1312 cents 485 .. 970 match: 21 SD: 0.1306 cents 500 .. 1000 match: 21 SD: 0.1250 cents 543 .. 1086 match: 21 SD: 0.1248 cents 547 .. 1094 match: 21 SD: 0.0990 cents 582 .. 1164 match: 21 SD: 0.0951 cents