Scala analysis: xen18-erlich-wurschmidt-22
3L 19s MOS for Wurschmidt, L=167.02, 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: 277.330 cents 277.330000 5: 314.100 cents 314.100000 6: 350.870 cents 350.870000 7: 387.640 cents 387.640000 8: 424.410 cents 424.410000 9: 461.180 cents 461.180000 10: 497.950 cents 497.950000 11: 664.970 cents 664.970000 12: 701.740 cents 701.740000 13: 738.510 cents 738.510000 14: 775.280 cents 775.280000 15: 812.050 cents 812.050000 16: 848.820 cents 848.820000 17: 885.590 cents 885.590000 18: 922.360 cents 922.360000 19: 1089.380 cents 1089.380000 20: 1126.150 cents 1126.150000 21: 1162.920 cents 1162.920000 22: 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: 167.0200 cents 167.0200 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: 36.7700 cents 36.7700 11: 167.0200 cents 167.0200 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: 36.7700 cents 36.7700 17: 36.7700 cents 36.7700 18: 36.7700 cents 36.7700 19: 167.0200 cents 167.0200 20: 36.7700 cents 36.7700 21: 36.7700 cents 36.7700 22: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 19 36.77000 cents 1: 3 167.02000 cents 2: 16 73.54000 cents 2: 6 203.79000 cents 3: 13 110.31000 cents 3: 9 240.56000 cents 4: 10 147.08000 cents 4: 12 277.33000 cents 5: 7 183.85000 cents 5: 15 314.10000 cents 6: 4 220.62000 cents 6: 18 350.87000 cents 7: 1 257.39000 cents 7: 21 387.64000 cents 8: 20 424.41000 cents 8: 2 554.66000 cents 9: 17 461.18000 cents 9: 5 591.43000 cents 10: 14 497.95000 cents 10: 8 628.20000 cents 11: 11 534.72000 cents 11: 11 664.97000 cents 12: 8 571.49000 cents 12: 14 701.74000 cents 13: 5 608.26000 cents 13: 17 738.51000 cents 14: 2 645.03000 cents 14: 20 775.28000 cents 15: 21 812.05000 cents 15: 1 942.30000 cents 16: 18 848.82000 cents 16: 4 979.07000 cents 17: 15 885.59000 cents 17: 7 1015.84000 cents 18: 12 922.36000 cents 18: 10 1052.61000 cents 19: 9 959.13000 cents 19: 13 1089.38000 cents 20: 6 995.90000 cents 20: 16 1126.15000 cents 21: 3 1032.67000 cents 21: 19 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 20 21 22 0.0 : 36.8 73.5 110.3 277.3 314.1 350.9 387.6 424.4 461.2 497.9 665.0 701.7 738.5 775.3 812.0 848.8 885.6 922.4 1089.4 1126.2 1162.9 1199.7 36.8 : 36.8 73.5 240.6 277.3 314.1 350.9 387.6 424.4 461.2 628.2 665.0 701.7 738.5 775.3 812.1 848.8 885.6 1052.6 1089.4 1126.2 1162.9 1199.7 73.5 : 36.8 203.8 240.6 277.3 314.1 350.9 387.6 424.4 591.4 628.2 665.0 701.7 738.5 775.3 812.0 848.8 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 110.3 : 167.0 203.8 240.6 277.3 314.1 350.9 387.6 554.7 591.4 628.2 665.0 701.7 738.5 775.3 812.1 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 277.3 : 36.8 73.5 110.3 147.1 183.8 220.6 387.6 424.4 461.2 497.9 534.7 571.5 608.3 645.0 812.0 848.8 885.6 922.4 959.1 995.9 1032.7 1199.7 314.1 : 36.8 73.5 110.3 147.1 183.8 350.9 387.6 424.4 461.2 497.9 534.7 571.5 608.3 775.3 812.0 848.8 885.6 922.4 959.1 995.9 1162.9 1199.7 350.9 : 36.8 73.5 110.3 147.1 314.1 350.9 387.6 424.4 461.2 497.9 534.7 571.5 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1126.2 1162.9 1199.7 387.6 : 36.8 73.5 110.3 277.3 314.1 350.9 387.6 424.4 461.2 497.9 534.7 701.7 738.5 775.3 812.1 848.8 885.6 922.4 1089.4 1126.2 1162.9 1199.7 424.4 : 36.8 73.5 240.6 277.3 314.1 350.9 387.6 424.4 461.2 497.9 665.0 701.7 738.5 775.3 812.0 848.8 885.6 1052.6 1089.4 1126.2 1162.9 1199.7 461.2 : 36.8 203.8 240.6 277.3 314.1 350.9 387.6 424.4 461.2 628.2 665.0 701.7 738.5 775.3 812.1 848.8 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 497.9 : 167.0 203.8 240.6 277.3 314.1 350.9 387.6 424.4 591.4 628.2 665.0 701.7 738.5 775.3 812.1 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 665.0 : 36.8 73.5 110.3 147.1 183.9 220.6 257.4 424.4 461.2 498.0 534.7 571.5 608.3 645.0 812.1 848.8 885.6 922.4 959.1 995.9 1032.7 1199.7 701.7 : 36.8 73.5 110.3 147.1 183.8 220.6 387.6 424.4 461.2 497.9 534.7 571.5 608.3 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1162.9 1199.7 738.5 : 36.8 73.5 110.3 147.1 183.9 350.9 387.6 424.4 461.2 497.9 534.7 571.5 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1126.2 1162.9 1199.7 775.3 : 36.8 73.5 110.3 147.1 314.1 350.9 387.6 424.4 461.2 498.0 534.7 701.7 738.5 775.3 812.1 848.8 885.6 922.4 1089.4 1126.2 1162.9 1199.7 812.0 : 36.8 73.5 110.3 277.3 314.1 350.9 387.6 424.4 461.2 498.0 665.0 701.7 738.5 775.3 812.1 848.8 885.6 1052.6 1089.4 1126.2 1162.9 1199.7 848.8 : 36.8 73.5 240.6 277.3 314.1 350.9 387.6 424.4 461.2 628.2 665.0 701.7 738.5 775.3 812.1 848.8 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 885.6 : 36.8 203.8 240.6 277.3 314.1 350.9 387.6 424.4 591.4 628.2 665.0 701.7 738.5 775.3 812.1 979.1 1015.8 1052.6 1089.4 1126.1 1162.9 1199.7 922.4 : 167.0 203.8 240.6 277.3 314.1 350.9 387.6 554.7 591.4 628.2 665.0 701.7 738.5 775.3 942.3 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 1089.4: 36.8 73.5 110.3 147.1 183.9 220.6 387.6 424.4 461.2 498.0 534.7 571.5 608.3 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1032.7 1199.7 1126.2: 36.8 73.5 110.3 147.1 183.9 350.9 387.6 424.4 461.2 497.9 534.7 571.5 738.5 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1162.9 1199.7 1162.9: 36.8 73.5 110.3 147.1 314.1 350.9 387.6 424.4 461.2 498.0 534.7 701.7 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1126.1 1162.9 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 167.0200 cents 130.25000 cents 36.77000 cents 2: 73.5400 .. 203.7900 cents 130.25000 cents -93.48000 cents 3: 110.3100 .. 240.5600 cents 130.25000 cents -93.48000 cents 4: 147.0800 .. 277.3300 cents 130.25000 cents -93.48000 cents 5: 183.8500 .. 314.1000 cents 130.25000 cents -93.48000 cents 6: 220.6200 .. 350.8700 cents 130.25000 cents -93.48000 cents 7: 257.3900 .. 387.6400 cents 130.25000 cents -93.48000 cents 8: 424.4100 .. 554.6600 cents 130.25000 cents 36.77000 cents 9: 461.1800 .. 591.4300 cents 130.25000 cents -93.48000 cents 10: 497.9500 .. 628.2000 cents 130.25000 cents -93.48000 cents 11: 534.7200 .. 664.9700 cents 130.25000 cents -93.48000 cents 12: 571.4900 .. 701.7400 cents 130.25000 cents -93.48000 cents 13: 608.2600 .. 738.5100 cents 130.25000 cents -93.48000 cents 14: 645.0300 .. 775.2800 cents 130.25000 cents -93.48000 cents 15: 812.0500 .. 942.3000 cents 130.25000 cents 36.77000 cents 16: 848.8200 .. 979.0700 cents 130.25000 cents -93.48000 cents 17: 885.5900 .. 1015.8400 cents 130.25000 cents -93.48000 cents 18: 922.3600 .. 1052.6100 cents 130.25000 cents -93.48000 cents 19: 959.1300 .. 1089.3800 cents 130.25000 cents -93.48000 cents 20: 995.9000 .. 1126.1500 cents 130.25000 cents -93.48000 cents 21: 1032.6700 .. 1162.9200 cents 130.25000 cents -93.48000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 54.5314 cents Largest one step interval : 167.02000 cents Average / Smallest step : 1.483040 Largest / Average step : 3.062825 Largest / Smallest step : 4.542290 Median interval of one step : 36.77000 cents, amount: 19 Most common interval of one step : 36.77000 cents, amount: 19 Least squares average step : 54.85742 cents, oct.: 1206.86319 cents Scale is not proper Scale has Myhill's property chromas: 130.25000 cents and 93.48000 cents, ratio: 1.393346 generators: 7 of 387.64000 cents and 15 of 812.05000 cents ET pair of linear temperament : 31&34 Scale is distributional even Scale is a mode of a 1925-tone equal temperament with octave 1199.690 cents degrees: 59 118 177 445 504 563 622 681 740 799 1067 1126 1185 1244 1303 1362 1421 1480 1748 1807 1866 1925 generators: 622 and 1303 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAAABAAAAAAABAAA Step pattern size order : SSSLSSSSSSLSSSSSSSLSSS Scale is a Constant Structure, by a margin of 16.83000 cents Scale diversity : 1.184007 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 Rothenberg efficiency : 0.696970 redundancy: 0.303030 Efficiency x scale size : 15.333333 Number of different interval sizes : 42 = 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: 21 Scale is a chain of 11 triads 0.0 277.330 812.050 cents Most common triad is 0.0 387.640 812.050 cents, amount: 20 Number of recognisable fifths : 14, average 701.7400 cents Number of recognisable fourths : 14, average 497.9500 cents Formal octave complements present : 21 = 95.4545% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 14-15 -- Rational properties --
FIT/MODE
22: 1 0 1 3 1 0 1 1 0 1 3 1 1 0 1 1 0 1 3 1 0 1 N SD: 14.5743 c. M:-24.9291 c. 23: 1 0 1 3 1 1 0 1 1 1 3 0 1 1 1 0 1 1 3 1 0 1 N SD: 15.0123 c. M:-23.6543 c. 27: 1 1 0 4 1 1 1 1 0 1 4 1 1 0 1 1 1 1 4 0 1 1 N SD: 12.8476 c. M:-21.4441 c. 29: 1 1 1 4 1 0 1 1 1 1 4 1 1 1 1 1 0 1 4 1 1 1 N SD: 11.7598 c. M: 19.9210 c. 30: 1 1 1 4 1 1 1 1 1 0 5 1 0 1 1 1 1 1 4 1 1 1 N SD: 11.4561 c. M:-18.6960 c. 31: 1 1 1 4 1 1 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 N M DE SD: 4.0935 c. M: 7.0755 c. 34: 1 1 1 5 1 1 1 1 1 1 5 1 1 1 1 1 1 1 5 1 1 1 N M DE SD: 3.1502 c. M:-5.4450 c. 65: 2 2 2 9 2 2 2 2 2 2 9 2 2 2 2 2 2 2 9 2 2 2 N M DE SD: 0.3045 c. M: 0.5263 c. 229: 7 7 7 32 7 7 7 7 7 7 32 7 7 7 7 7 7 7 32 7 7 7 N M DE SD: 0.2084 c. M:-0.3603 c. 294: 9 9 9 41 9 9 9 9 9 9 41 9 9 9 9 9 9 9 41 9 9 9 N M DE SD: 0.0950 c. M:-0.1643 c. 359: 11 11 11 50 11 11 11 11 11 11 50 11 11 11 11 11 11 11 50 11 11 11 N M DE SD: 0.0227 c. M:-0.0392 c. 783: 24 24 24 109 24 24 24 24 24 24 109 24 24 24 24 24 24 24 109 24 24 24 N M DE SD: 0.0045 c. M: 0.0077 c. 1142: 35 35 35 159 35 35 35 35 35 35 159 35 35 35 35 35 35 35 159 35 35 35 N M DE SD: 0.0041 c. M:-0.0070 c. 1925: 59 59 59 268 59 59 59 59 59 59 268 59 59 59 59 59 59 59 268 59 59 59 N M DE SD: 0.0006 c. M:-0.0010 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: 11.6216 cents 5 .. 10 match: 5 H SD: 21.8699 cents 6 .. 12 match: 6 H SD: 6.8969 cents 7 .. 14 match: 7 H SD: 10.0808 cents 8 .. 16 match: 8 H SD: 12.7901 cents 9 .. 18 match: 8 SD: 9.8888 cents 10 .. 20 match: 8 SD: 7.1617 cents 11 .. 22 match: 10 SD: 6.6764 cents 12 .. 24 match: 9 SD: 3.8226 cents 13 .. 26 match: 11 SD: 4.7083 cents 14 .. 28 match: 12 SD: 5.4019 cents 15 .. 30 match: 12 S SD: 3.1691 cents 16 .. 32 match: 12 SD: 4.0939 cents 17 .. 34 match: 13 SD: 3.3078 cents 18 .. 36 match: 14 SD: 3.2917 cents 19 .. 38 match: 13 SD: 3.8624 cents 20 .. 40 match: 15 SD: 3.8005 cents 21 .. 42 match: 15 SD: 2.6970 cents 22 .. 44 match: 15 SD: 2.5628 cents 23 .. 46 match: 17 SD: 2.9901 cents 24 .. 48 match: 18 SD: 2.5169 cents 25 .. 50 match: 18 SD: 2.7432 cents 26 .. 52 match: 18 SD: 2.5211 cents 27 .. 54 match: 18 SD: 2.3074 cents 28 .. 56 match: 19 SD: 2.2251 cents 29 .. 58 match: 19 SD: 2.7518 cents 30 .. 60 match: 20 SD: 1.7435 cents 31 .. 62 match: 19 SD: 2.9154 cents 32 .. 64 match: 20 SD: 2.0076 cents 33 .. 66 match: 20 SD: 2.3352 cents 34 .. 68 match: 20 SD: 2.2503 cents 35 .. 70 match: 21 SD: 2.1328 cents 36 .. 72 match: 21 SD: 1.7166 cents 37 .. 74 match: 21 SD: 2.3328 cents 39 .. 78 match: 22 SD: 1.8274 cents 40 .. 80 match: 22 SD: 1.4792 cents 45 .. 90 match: 22 SD: 1.4289 cents 47 .. 94 match: 22 SD: 1.3961 cents 50 .. 100 match: 22 SD: 1.3801 cents 51 .. 102 match: 22 SD: 1.3768 cents 57 .. 114 match: 22 SD: 1.2941 cents 60 .. 120 match: 22 SD: 1.1602 cents 62 .. 124 match: 22 SD: 1.0975 cents 71 .. 142 match: 22 SD: 1.0754 cents 72 .. 144 match: 22 SD: 0.9669 cents 75 .. 150 match: 22 SD: 0.8123 cents 87 .. 174 match: 22 SD: 0.7858 cents 88 .. 176 match: 22 SD: 0.7849 cents 90 .. 180 match: 22 SD: 0.6470 cents 92 .. 184 match: 22 SD: 0.6192 cents 111 .. 222 match: 22 SD: 0.5775 cents 120 .. 240 match: 22 SD: 0.4875 cents 137 .. 274 match: 22 SD: 0.4859 cents 138 .. 276 match: 22 SD: 0.4580 cents 156 .. 312 match: 22 SD: 0.3893 cents 179 .. 358 match: 22 SD: 0.3825 cents 180 .. 360 match: 22 SD: 0.3265 cents 184 .. 368 match: 22 SD: 0.3150 cents 186 .. 372 match: 22 SD: 0.2948 cents 226 .. 452 match: 22 SD: 0.2349 cents 276 .. 552 match: 22 SD: 0.1741 cents 368 .. 736 match: 22 SD: 0.1727 cents 370 .. 740 match: 22 SD: 0.1651 cents 374 .. 748 match: 22 SD: 0.1599 cents 414 .. 828 match: 22 SD: 0.1416 cents 458 .. 916 match: 22 SD: 0.1410 cents 466 .. 932 match: 22 SD: 0.1334 cents 468 .. 936 match: 22 SD: 0.1265 cents 517 .. 1034 match: 22 SD: 0.1232 cents 534 .. 1068 match: 22 SD: 0.1221 cents 547 .. 1094 match: 22 SD: 0.1026 cents 558 .. 1116 match: 22 SD: 0.1020 cents