Scala analysis: xen18-erlich-wurschmidt-19
3L 16s MOS for Wurschmidt, L=203.79, s=36.77
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36.770 cents 36.770000 2: 73.540 cents 73.540000 3: 110.310 cents 110.310000 4: 314.100 cents 314.100000 5: 350.870 cents 350.870000 6: 387.640 cents 387.640000 7: 424.410 cents 424.410000 8: 461.180 cents 461.180000 9: 497.950 cents 497.950000 10: 701.740 cents 701.740000 11: 738.510 cents 738.510000 12: 775.280 cents 775.280000 13: 812.050 cents 812.050000 14: 848.820 cents 848.820000 15: 885.590 cents 885.590000 16: 1089.380 cents 1089.380000 17: 1126.150 cents 1126.150000 18: 1162.920 cents 1162.920000 19: 1199.690 cents 1199.690000
SHOW/INTERVAL
0: 36.7700 cents 36.7700 1: 36.7700 cents 36.7700 2: 36.7700 cents 36.7700 3: 36.7700 cents 36.7700 4: 203.7900 cents 203.7900 5: 36.7700 cents 36.7700 6: 36.7700 cents 36.7700 7: 36.7700 cents 36.7700 8: 36.7700 cents 36.7700 9: 36.7700 cents 36.7700 10: 203.7900 cents 203.7900 11: 36.7700 cents 36.7700 12: 36.7700 cents 36.7700 13: 36.7700 cents 36.7700 14: 36.7700 cents 36.7700 15: 36.7700 cents 36.7700 16: 203.7900 cents 203.7900 17: 36.7700 cents 36.7700 18: 36.7700 cents 36.7700 19: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 36.77000 cents 1: 3 203.79000 cents 2: 13 73.54000 cents 2: 6 240.56000 cents 3: 10 110.31000 cents 3: 9 277.33000 cents 4: 7 147.08000 cents 4: 12 314.10000 cents 5: 4 183.85000 cents 5: 15 350.87000 cents 6: 1 220.62000 cents 6: 18 387.64000 cents 7: 17 424.41000 cents 7: 2 591.43000 cents 8: 14 461.18000 cents 8: 5 628.20000 cents 9: 11 497.95000 cents 9: 8 664.97000 cents 10: 8 534.72000 cents 10: 11 701.74000 cents 11: 5 571.49000 cents 11: 14 738.51000 cents 12: 2 608.26000 cents 12: 17 775.28000 cents 13: 18 812.05000 cents 13: 1 979.07000 cents 14: 15 848.82000 cents 14: 4 1015.84000 cents 15: 12 885.59000 cents 15: 7 1052.61000 cents 16: 9 922.36000 cents 16: 10 1089.38000 cents 17: 6 959.13000 cents 17: 13 1126.15000 cents 18: 3 995.90000 cents 18: 16 1162.92000 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 : 36.8 73.5 110.3 314.1 350.9 387.6 424.4 461.2 497.9 701.7 738.5 775.3 812.0 848.8 885.6 1089.4 1126.2 1162.9 1199.7 36.8 : 36.8 73.5 277.3 314.1 350.9 387.6 424.4 461.2 665.0 701.7 738.5 775.3 812.1 848.8 1052.6 1089.4 1126.2 1162.9 1199.7 73.5 : 36.8 240.6 277.3 314.1 350.9 387.6 424.4 628.2 665.0 701.7 738.5 775.3 812.0 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 110.3 : 203.8 240.6 277.3 314.1 350.9 387.6 591.4 628.2 665.0 701.7 738.5 775.3 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 314.1 : 36.8 73.5 110.3 147.1 183.8 387.6 424.4 461.2 497.9 534.7 571.5 775.3 812.0 848.8 885.6 922.4 959.1 995.9 1199.7 350.9 : 36.8 73.5 110.3 147.1 350.9 387.6 424.4 461.2 497.9 534.7 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1162.9 1199.7 387.6 : 36.8 73.5 110.3 314.1 350.9 387.6 424.4 461.2 497.9 701.7 738.5 775.3 812.1 848.8 885.6 922.4 1126.2 1162.9 1199.7 424.4 : 36.8 73.5 277.3 314.1 350.9 387.6 424.4 461.2 665.0 701.7 738.5 775.3 812.0 848.8 885.6 1089.4 1126.2 1162.9 1199.7 461.2 : 36.8 240.6 277.3 314.1 350.9 387.6 424.4 628.2 665.0 701.7 738.5 775.3 812.1 848.8 1052.6 1089.4 1126.2 1162.9 1199.7 497.9 : 203.8 240.6 277.3 314.1 350.9 387.6 591.4 628.2 665.0 701.7 738.5 775.3 812.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 701.7 : 36.8 73.5 110.3 147.1 183.8 387.6 424.4 461.2 497.9 534.7 571.5 608.3 812.1 848.8 885.6 922.4 959.1 995.9 1199.7 738.5 : 36.8 73.5 110.3 147.1 350.9 387.6 424.4 461.2 497.9 534.7 571.5 775.3 812.1 848.8 885.6 922.4 959.1 1162.9 1199.7 775.3 : 36.8 73.5 110.3 314.1 350.9 387.6 424.4 461.2 498.0 534.7 738.5 775.3 812.1 848.8 885.6 922.4 1126.2 1162.9 1199.7 812.0 : 36.8 73.5 277.3 314.1 350.9 387.6 424.4 461.2 498.0 701.7 738.5 775.3 812.1 848.8 885.6 1089.4 1126.2 1162.9 1199.7 848.8 : 36.8 240.6 277.3 314.1 350.9 387.6 424.4 461.2 665.0 701.7 738.5 775.3 812.1 848.8 1052.6 1089.4 1126.2 1162.9 1199.7 885.6 : 203.8 240.6 277.3 314.1 350.9 387.6 424.4 628.2 665.0 701.7 738.5 775.3 812.1 1015.8 1052.6 1089.4 1126.1 1162.9 1199.7 1089.4: 36.8 73.5 110.3 147.1 183.9 220.6 424.4 461.2 498.0 534.7 571.5 608.3 812.1 848.8 885.6 922.4 959.1 995.9 1199.7 1126.2: 36.8 73.5 110.3 147.1 183.9 387.6 424.4 461.2 497.9 534.7 571.5 775.3 812.1 848.8 885.6 922.4 959.1 1162.9 1199.7 1162.9: 36.8 73.5 110.3 147.1 350.9 387.6 424.4 461.2 498.0 534.7 738.5 775.3 812.1 848.8 885.6 922.4 1126.1 1162.9 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 203.7900 cents 167.02000 cents 36.77000 cents 2: 73.5400 .. 240.5600 cents 167.02000 cents -130.25000 cents 3: 110.3100 .. 277.3300 cents 167.02000 cents -130.25000 cents 4: 147.0800 .. 314.1000 cents 167.02000 cents -130.25000 cents 5: 183.8500 .. 350.8700 cents 167.02000 cents -130.25000 cents 6: 220.6200 .. 387.6400 cents 167.02000 cents -130.25000 cents 7: 424.4100 .. 591.4300 cents 167.02000 cents 36.77000 cents 8: 461.1800 .. 628.2000 cents 167.02000 cents -130.25000 cents 9: 497.9500 .. 664.9700 cents 167.02000 cents -130.25000 cents 10: 534.7200 .. 701.7400 cents 167.02000 cents -130.25000 cents 11: 571.4900 .. 738.5100 cents 167.02000 cents -130.25000 cents 12: 608.2600 .. 775.2800 cents 167.02000 cents -130.25000 cents 13: 812.0500 .. 979.0700 cents 167.02000 cents 36.77000 cents 14: 848.8200 .. 1015.8400 cents 167.02000 cents -130.25000 cents 15: 885.5900 .. 1052.6100 cents 167.02000 cents -130.25000 cents 16: 922.3600 .. 1089.3800 cents 167.02000 cents -130.25000 cents 17: 959.1300 .. 1126.1500 cents 167.02000 cents -130.25000 cents 18: 995.9000 .. 1162.9200 cents 167.02000 cents -130.25000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 63.1416 cents Largest one step interval : 203.79000 cents Average / Smallest step : 1.717204 Largest / Average step : 3.227509 Largest / Smallest step : 5.542290 Median interval of one step : 36.77000 cents, amount: 16 Most common interval of one step : 36.77000 cents, amount: 16 Least squares average step : 63.75015 cents, oct.: 1211.25292 cents Scale is not proper Scale has Myhill's property chromas: 167.02000 cents and 130.25000 cents, ratio: 1.282303 generators: 6 of 387.64000 cents and 13 of 812.05000 cents ET pair of linear temperament : 31&34 Scale is distributional even Scale is a mode of a 1142-tone equal temperament with octave 1199.690 cents degrees: 35 70 105 299 334 369 404 439 474 668 703 738 773 808 843 1037 1072 1107 1142 generators: 369 and 773 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAABAAAAABAAA Step pattern size order : SSSLSSSSSLSSSSSLSSS Scale is a Constant Structure, by a margin of 16.83000 cents Scale diversity : 1.207909 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 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 : 16.83000 cents Most common intervals : 387.64000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 387.640 775.280 cents Most common triad is 0.0 387.640 812.050 cents, amount: 17 Number of recognisable fifths : 11, average 701.7400 cents Number of recognisable fourths : 11, average 497.9500 cents 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 0 1 3 1 0 1 0 1 3 1 0 1 0 1 3 1 0 1 N I SD: 16.7028 c. M:-27.9795 c. 20: 1 0 1 3 1 0 1 1 0 4 0 1 1 0 1 3 1 0 1 N I SD: 16.4297 c. M:-27.7330 c. 22: 1 0 1 4 0 1 1 0 1 4 1 0 1 1 0 4 1 0 1 N I SD: 15.4190 c. M:-24.9291 c. 23: 1 0 1 4 1 0 1 1 1 3 1 1 1 0 1 4 1 0 1 N I SD: 14.9381 c. M:-23.6543 c. 24: 1 0 1 4 1 1 0 1 1 4 1 1 0 1 1 4 1 0 1 N I SD: 14.2186 c. M:-24.5133 c. 28: 1 1 1 4 1 1 1 1 1 4 1 1 1 1 1 4 1 1 1 N M DE I SD: 11.0933 c. M:-18.2282 c. 31: 1 1 1 5 1 1 1 1 1 5 1 1 1 1 1 5 1 1 1 N M DE I SD: 3.5231 c. M:-5.7890 c. 34: 1 1 1 6 1 1 1 1 1 6 1 1 1 1 1 6 1 1 1 N M DE I SD: 2.7112 c. M:-4.4550 c. 65: 2 2 2 11 2 2 2 2 2 11 2 2 2 2 2 11 2 2 2 N M DE I SD: 0.2621 c. M:-0.4306 c. 229: 7 7 7 39 7 7 7 7 7 39 7 7 7 7 7 39 7 7 7 N M DE I SD: 0.1794 c. M:-0.2948 c. 294: 9 9 9 50 9 9 9 9 9 50 9 9 9 9 9 50 9 9 9 N M DE I SD: 0.0818 c. M:-0.1344 c. 359: 11 11 11 61 11 11 11 11 11 61 11 11 11 11 11 61 11 11 11 N M DE I SD: 0.0195 c. M:-0.0321 c. 783: 24 24 24 133 24 24 24 24 24 133 24 24 24 24 24 133 24 24 24 N M DE I SD: 0.0038 c. M:-0.0063 c. 1142: 35 35 35 194 35 35 35 35 35 194 35 35 35 35 35 194 35 35 35 N M DE I SD: 0.0035 c. M:-0.0058 c. 1925: 59 59 59 327 59 59 59 59 59 327 59 59 59 59 59 327 59 59 59 N M DE I SD: 0.0005 c. M:-0.0008 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.3100 cents 2 .. 4 match: 2 H SD: 0.1886 cents 3 .. 6 match: 3 H SD: 0.4244 cents 4 .. 8 match: 4 H SD: 20.8118 cents 5 .. 10 match: 5 H SD: 22.1890 cents 6 .. 12 match: 6 H SD: 10.3194 cents 7 .. 14 match: 6 SD: 16.3429 cents 8 .. 16 match: 7 SD: 15.4398 cents 9 .. 18 match: 7 SD: 10.5508 cents 10 .. 20 match: 8 SD: 8.2548 cents 11 .. 22 match: 8 SD: 8.0062 cents 12 .. 24 match: 9 SD: 6.3875 cents 13 .. 26 match: 9 SD: 5.2638 cents 14 .. 28 match: 10 SD: 4.4222 cents 15 .. 30 match: 10 SD: 2.3421 cents 16 .. 32 match: 11 SD: 3.1568 cents 17 .. 34 match: 11 SD: 4.8892 cents 18 .. 36 match: 11 SD: 2.6634 cents 19 .. 38 match: 11 SD: 3.9912 cents 20 .. 40 match: 12 SD: 3.2423 cents 21 .. 42 match: 13 SD: 2.9134 cents 22 .. 44 match: 14 SD: 2.9372 cents 23 .. 46 match: 15 SD: 3.6565 cents 24 .. 48 match: 15 SD: 2.8140 cents 25 .. 50 match: 16 SD: 2.8577 cents 26 .. 52 match: 16 SD: 2.6968 cents 27 .. 54 match: 17 SD: 2.6665 cents 28 .. 56 match: 16 SD: 2.4987 cents 29 .. 58 match: 17 SD: 3.0166 cents 30 .. 60 match: 17 SD: 1.9412 cents 31 .. 62 match: 17 SD: 3.0560 cents 32 .. 64 match: 18 SD: 2.0629 cents 33 .. 66 match: 17 SD: 2.4456 cents 34 .. 68 match: 17 SD: 2.6286 cents 35 .. 70 match: 18 SD: 2.2935 cents 36 .. 72 match: 18 SD: 1.8263 cents 37 .. 74 match: 18 SD: 2.4817 cents 39 .. 78 match: 19 SD: 1.9318 cents 40 .. 80 match: 19 SD: 1.6472 cents 44 .. 88 match: 19 SD: 1.5399 cents 46 .. 92 match: 19 SD: 1.4875 cents 48 .. 96 match: 19 SD: 1.3726 cents 49 .. 98 match: 19 SD: 1.3687 cents 60 .. 120 match: 19 SD: 1.2054 cents 62 .. 124 match: 19 SD: 1.1953 cents 71 .. 142 match: 19 SD: 1.1693 cents 72 .. 144 match: 19 SD: 0.9237 cents 75 .. 150 match: 19 SD: 0.9207 cents 87 .. 174 match: 19 SD: 0.8749 cents 88 .. 176 match: 19 SD: 0.8583 cents 89 .. 178 match: 19 SD: 0.8510 cents 90 .. 180 match: 19 SD: 0.6439 cents 111 .. 222 match: 19 SD: 0.6361 cents 120 .. 240 match: 19 SD: 0.5104 cents 138 .. 276 match: 19 SD: 0.5009 cents 141 .. 282 match: 19 SD: 0.4906 cents 147 .. 294 match: 19 SD: 0.4389 cents 177 .. 354 match: 19 SD: 0.4147 cents 180 .. 360 match: 19 SD: 0.3295 cents 186 .. 372 match: 19 SD: 0.3112 cents 226 .. 452 match: 19 SD: 0.2522 cents 276 .. 552 match: 19 SD: 0.1888 cents 366 .. 732 match: 19 SD: 0.1856 cents 370 .. 740 match: 19 SD: 0.1685 cents 406 .. 812 match: 19 SD: 0.1655 cents 414 .. 828 match: 19 SD: 0.1572 cents 458 .. 916 match: 19 SD: 0.1271 cents 547 .. 1094 match: 19 SD: 0.1170 cents 558 .. 1116 match: 19 SD: 0.1073 cents