Scala analysis: xen18-erlich-wurschmidt-16
3L 13s MOS for Wurschmidt, L=240.56, 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: 314.100 cents 314.100000 4: 350.870 cents 350.870000 5: 387.640 cents 387.640000 6: 424.410 cents 424.410000 7: 461.180 cents 461.180000 8: 701.740 cents 701.740000 9: 738.510 cents 738.510000 10: 775.280 cents 775.280000 11: 812.050 cents 812.050000 12: 848.820 cents 848.820000 13: 885.590 cents 885.590000 14: 1126.150 cents 1126.150000 15: 1162.920 cents 1162.920000 16: 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: 240.5600 cents 240.5600 4: 36.7700 cents 36.7700 5: 36.7700 cents 36.7700 6: 36.7700 cents 36.7700 7: 36.7700 cents 36.7700 8: 240.5600 cents 240.5600 9: 36.7700 cents 36.7700 10: 36.7700 cents 36.7700 11: 36.7700 cents 36.7700 12: 36.7700 cents 36.7700 13: 36.7700 cents 36.7700 14: 240.5600 cents 240.5600 15: 36.7700 cents 36.7700 16: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 36.77000 cents 1: 3 240.56000 cents 2: 10 73.54000 cents 2: 6 277.33000 cents 3: 7 110.31000 cents 3: 9 314.10000 cents 4: 4 147.08000 cents 4: 12 350.87000 cents 5: 1 183.85000 cents 5: 15 387.64000 cents 6: 14 424.41000 cents 6: 2 628.20000 cents 7: 11 461.18000 cents 7: 5 664.97000 cents 8: 8 497.95000 cents 8: 8 701.74000 cents 9: 5 534.72000 cents 9: 11 738.51000 cents 10: 2 571.49000 cents 10: 14 775.28000 cents 11: 15 812.05000 cents 11: 1 1015.84000 cents 12: 12 848.82000 cents 12: 4 1052.61000 cents 13: 9 885.59000 cents 13: 7 1089.38000 cents 14: 6 922.36000 cents 14: 10 1126.15000 cents 15: 3 959.13000 cents 15: 13 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 0.0 : 36.8 73.5 314.1 350.9 387.6 424.4 461.2 701.7 738.5 775.3 812.0 848.8 885.6 1126.2 1162.9 1199.7 36.8 : 36.8 277.3 314.1 350.9 387.6 424.4 665.0 701.7 738.5 775.3 812.1 848.8 1089.4 1126.2 1162.9 1199.7 73.5 : 240.6 277.3 314.1 350.9 387.6 628.2 665.0 701.7 738.5 775.3 812.0 1052.6 1089.4 1126.2 1162.9 1199.7 314.1 : 36.8 73.5 110.3 147.1 387.6 424.4 461.2 497.9 534.7 571.5 812.0 848.8 885.6 922.4 959.1 1199.7 350.9 : 36.8 73.5 110.3 350.9 387.6 424.4 461.2 497.9 534.7 775.3 812.1 848.8 885.6 922.4 1162.9 1199.7 387.6 : 36.8 73.5 314.1 350.9 387.6 424.4 461.2 497.9 738.5 775.3 812.1 848.8 885.6 1126.2 1162.9 1199.7 424.4 : 36.8 277.3 314.1 350.9 387.6 424.4 461.2 701.7 738.5 775.3 812.0 848.8 1089.4 1126.2 1162.9 1199.7 461.2 : 240.6 277.3 314.1 350.9 387.6 424.4 665.0 701.7 738.5 775.3 812.1 1052.6 1089.4 1126.2 1162.9 1199.7 701.7 : 36.8 73.5 110.3 147.1 183.8 424.4 461.2 497.9 534.7 571.5 812.1 848.8 885.6 922.4 959.1 1199.7 738.5 : 36.8 73.5 110.3 147.1 387.6 424.4 461.2 497.9 534.7 775.3 812.1 848.8 885.6 922.4 1162.9 1199.7 775.3 : 36.8 73.5 110.3 350.9 387.6 424.4 461.2 498.0 738.5 775.3 812.1 848.8 885.6 1126.2 1162.9 1199.7 812.0 : 36.8 73.5 314.1 350.9 387.6 424.4 461.2 701.7 738.5 775.3 812.1 848.8 1089.4 1126.2 1162.9 1199.7 848.8 : 36.8 277.3 314.1 350.9 387.6 424.4 665.0 701.7 738.5 775.3 812.1 1052.6 1089.4 1126.2 1162.9 1199.7 885.6 : 240.6 277.3 314.1 350.9 387.6 628.2 665.0 701.7 738.5 775.3 1015.8 1052.6 1089.4 1126.1 1162.9 1199.7 1126.2: 36.8 73.5 110.3 147.1 387.6 424.4 461.2 497.9 534.7 775.3 812.1 848.8 885.6 922.4 959.1 1199.7 1162.9: 36.8 73.5 110.3 350.9 387.6 424.4 461.2 498.0 738.5 775.3 812.1 848.8 885.6 922.4 1162.9 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 240.5600 cents 203.79000 cents 36.77000 cents 2: 73.5400 .. 277.3300 cents 203.79000 cents -167.02000 cents 3: 110.3100 .. 314.1000 cents 203.79000 cents -167.02000 cents 4: 147.0800 .. 350.8700 cents 203.79000 cents -167.02000 cents 5: 183.8500 .. 387.6400 cents 203.79000 cents -167.02000 cents 6: 424.4100 .. 628.2000 cents 203.79000 cents 36.77000 cents 7: 461.1800 .. 664.9700 cents 203.79000 cents -167.02000 cents 8: 497.9500 .. 701.7400 cents 203.79000 cents -167.02000 cents 9: 534.7200 .. 738.5100 cents 203.79000 cents -167.02000 cents 10: 571.4900 .. 775.2800 cents 203.79000 cents -167.02000 cents 11: 812.0500 .. 1015.8400 cents 203.79000 cents 36.77000 cents 12: 848.8200 .. 1052.6100 cents 203.79000 cents -167.02000 cents 13: 885.5900 .. 1089.3800 cents 203.79000 cents -167.02000 cents 14: 922.3600 .. 1126.1500 cents 203.79000 cents -167.02000 cents 15: 959.1300 .. 1162.9200 cents 203.79000 cents -167.02000 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 74.9806 cents Largest one step interval : 240.56000 cents Average / Smallest step : 2.039179 Largest / Average step : 3.208295 Largest / Smallest step : 6.542290 Median interval of one step : 36.77000 cents, amount: 13 Most common interval of one step : 36.77000 cents, amount: 13 Least squares average step : 75.72985 cents, oct.: 1211.67765 cents Scale is not proper Scale has Myhill's property chromas: 203.79000 cents and 167.02000 cents, ratio: 1.220153 generators: 5 of 387.64000 cents and 11 of 812.05000 cents ET pair of linear temperament : 31&34 Scale is distributional even Scale is a mode of a 783-tone equal temperament with octave 1199.690 cents degrees: 24 48 205 229 253 277 301 458 482 506 530 554 578 735 759 783 generators: 253 and 530 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAAAAABAA Step pattern size order : SSLSSSSLSSSSSLSS Scale is a Constant Structure, by a margin of 36.77000 cents Scale diversity : 1.230447 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 36.77000 cents Most common intervals : 387.64000 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 314.100 812.050 cents Most common triad is 0.0 387.640 812.050 cents, amount: 14 Number of recognisable fifths : 8, average 701.7400 cents Number of recognisable fourths : 8, average 497.9500 cents Formal octave complements present : 15 = 93.7500% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 10-11 -- Rational properties --
FIT/MODE
16: 0 1 3 1 0 1 0 3 1 0 1 0 1 3 0 1 N SD: 20.8796 c. M: 38.2106 c. 18: 1 0 4 0 1 0 1 4 0 1 0 1 0 4 0 1 N SD: 19.0081 c. M:-31.4039 c. 19: 1 0 4 1 0 1 0 4 1 0 1 0 1 4 0 1 N SD: 17.2097 c. M:-27.9795 c. 26: 1 0 6 0 1 1 1 5 1 1 0 1 1 5 1 1 N SD: 15.6367 c. M: 27.8765 c. 27: 1 1 5 1 1 1 0 6 1 0 1 1 1 5 1 1 N SD: 12.2336 c. M:-19.9196 c. 28: 1 1 5 1 1 1 1 5 1 1 1 1 1 5 1 1 N M DE SD: 9.3912 c. M: 16.2029 c. 31: 1 1 6 1 1 1 1 6 1 1 1 1 1 6 1 1 N M DE SD: 2.9825 c. M: 5.1458 c. 34: 1 1 7 1 1 1 1 7 1 1 1 1 1 7 1 1 N M DE SD: 2.2952 c. M:-3.9600 c. 65: 2 2 13 2 2 2 2 13 2 2 2 2 2 13 2 2 N M DE SD: 0.2219 c. M: 0.3828 c. 229: 7 7 46 7 7 7 7 46 7 7 7 7 7 46 7 7 N M DE SD: 0.1519 c. M:-0.2620 c. 294: 9 9 59 9 9 9 9 59 9 9 9 9 9 59 9 9 N M DE SD: 0.0692 c. M:-0.1195 c. 359: 11 11 72 11 11 11 11 72 11 11 11 11 11 72 11 11 N M DE SD: 0.0165 c. M:-0.0285 c. 783: 24 24 157 24 24 24 24 157 24 24 24 24 24 157 24 24 N M DE SD: 0.0033 c. M: 0.0056 c. 1142: 35 35 229 35 35 35 35 229 35 35 35 35 35 229 35 35 N M DE SD: 0.0030 c. M:-0.0051 c. 1925: 59 59 386 59 59 59 59 386 59 59 59 59 59 386 59 59 N M DE SD: 0.0004 c. M:-0.0007 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: 12.2956 cents 4 .. 8 match: 4 H SD: 20.8118 cents 5 .. 10 match: 3 S SD: 0.7564 cents 6 .. 12 match: 5 S SD: 11.9854 cents 7 .. 14 match: 6 SD: 18.4597 cents 8 .. 16 match: 5 SD: 7.7606 cents 9 .. 18 match: 7 SD: 16.8799 cents 10 .. 20 match: 8 SD: 12.3335 cents 11 .. 22 match: 7 SD: 11.8657 cents 12 .. 24 match: 9 SD: 9.9965 cents 13 .. 26 match: 8 SD: 8.0408 cents 14 .. 28 match: 8 SD: 6.5216 cents 15 .. 30 match: 9 SD: 6.3696 cents 16 .. 32 match: 10 SD: 4.6507 cents 17 .. 34 match: 9 SD: 5.8095 cents 18 .. 36 match: 9 SD: 3.2312 cents 19 .. 38 match: 11 SD: 4.0940 cents 20 .. 40 match: 11 SD: 2.9418 cents 21 .. 42 match: 11 SD: 3.0450 cents 22 .. 44 match: 13 SD: 3.0338 cents 23 .. 46 match: 12 SD: 3.1817 cents 24 .. 48 match: 12 SD: 2.6109 cents 25 .. 50 match: 14 SD: 2.8857 cents 26 .. 52 match: 13 SD: 2.6653 cents 27 .. 54 match: 14 SD: 2.9788 cents 28 .. 56 match: 14 SD: 2.7646 cents 29 .. 58 match: 14 SD: 3.3566 cents 30 .. 60 match: 14 SD: 2.2691 cents 31 .. 62 match: 14 SD: 3.5553 cents 32 .. 64 match: 15 SD: 2.2752 cents 33 .. 66 match: 14 SD: 2.9027 cents 34 .. 68 match: 14 SD: 2.9234 cents 35 .. 70 match: 16 SD: 2.6429 cents 36 .. 72 match: 16 SD: 2.0425 cents 39 .. 78 match: 16 SD: 1.9833 cents 40 .. 80 match: 16 SD: 1.5820 cents 49 .. 98 match: 16 SD: 1.4560 cents 60 .. 120 match: 16 SD: 1.3685 cents 62 .. 124 match: 16 SD: 1.3083 cents 68 .. 136 match: 16 SD: 1.3024 cents 71 .. 142 match: 16 SD: 1.2367 cents 72 .. 144 match: 16 SD: 1.0301 cents 76 .. 152 match: 16 SD: 1.0109 cents 84 .. 168 match: 16 SD: 0.9879 cents 85 .. 170 match: 16 SD: 0.9053 cents 90 .. 180 match: 16 SD: 0.7540 cents 92 .. 184 match: 16 SD: 0.7311 cents 94 .. 188 match: 16 SD: 0.7195 cents 111 .. 222 match: 16 SD: 0.6896 cents 112 .. 224 match: 16 SD: 0.6542 cents 115 .. 230 match: 16 SD: 0.6443 cents 120 .. 240 match: 16 SD: 0.5955 cents 134 .. 268 match: 16 SD: 0.5651 cents 140 .. 280 match: 16 SD: 0.5560 cents 141 .. 282 match: 16 SD: 0.5149 cents 144 .. 288 match: 16 SD: 0.4721 cents 147 .. 294 match: 16 SD: 0.4628 cents 177 .. 354 match: 16 SD: 0.4476 cents 180 .. 360 match: 16 SD: 0.3701 cents 184 .. 368 match: 16 SD: 0.3578 cents 186 .. 372 match: 16 SD: 0.3460 cents 190 .. 380 match: 16 SD: 0.3413 cents 226 .. 452 match: 16 SD: 0.2706 cents 276 .. 552 match: 16 SD: 0.2135 cents 324 .. 648 match: 16 SD: 0.2073 cents 338 .. 676 match: 16 SD: 0.1963 cents 368 .. 736 match: 16 SD: 0.1926 cents 370 .. 740 match: 16 SD: 0.1605 cents 418 .. 836 match: 16 SD: 0.1561 cents 458 .. 916 match: 16 SD: 0.1275 cents 558 .. 1116 match: 16 SD: 0.1157 cents