Scala analysis: xen18-erlich-wurschmidt-25
3L 22s MOS for Wurschmidt, L=130.25, 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: 147.080 cents 147.080000 5: 277.330 cents 277.330000 6: 314.100 cents 314.100000 7: 350.870 cents 350.870000 8: 387.640 cents 387.640000 9: 424.410 cents 424.410000 10: 461.180 cents 461.180000 11: 497.950 cents 497.950000 12: 534.720 cents 534.720000 13: 664.970 cents 664.970000 14: 701.740 cents 701.740000 15: 738.510 cents 738.510000 16: 775.280 cents 775.280000 17: 812.050 cents 812.050000 18: 848.820 cents 848.820000 19: 885.590 cents 885.590000 20: 922.360 cents 922.360000 21: 1052.610 cents 1052.610000 22: 1089.380 cents 1089.380000 23: 1126.150 cents 1126.150000 24: 1162.920 cents 1162.920000 25: 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: 36.7700 cents 36.7700 5: 130.2500 cents 130.2500 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: 36.7700 cents 36.7700 12: 36.7700 cents 36.7700 13: 130.2500 cents 130.2500 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: 36.7700 cents 36.7700 20: 36.7700 cents 36.7700 21: 130.2500 cents 130.2500 22: 36.7700 cents 36.7700 23: 36.7700 cents 36.7700 24: 36.7700 cents 36.7700 25: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 22 36.77000 cents 1: 3 130.25000 cents 2: 19 73.54000 cents 2: 6 167.02000 cents 3: 16 110.31000 cents 3: 9 203.79000 cents 4: 13 147.08000 cents 4: 12 240.56000 cents 5: 10 183.85000 cents 5: 15 277.33000 cents 6: 7 220.62000 cents 6: 18 314.10000 cents 7: 4 257.39000 cents 7: 21 350.87000 cents 8: 1 294.16000 cents 8: 24 387.64000 cents 9: 23 424.41000 cents 9: 2 517.89000 cents 10: 20 461.18000 cents 10: 5 554.66000 cents 11: 17 497.95000 cents 11: 8 591.43000 cents 12: 14 534.72000 cents 12: 11 628.20000 cents 13: 11 571.49000 cents 13: 14 664.97000 cents 14: 8 608.26000 cents 14: 17 701.74000 cents 15: 5 645.03000 cents 15: 20 738.51000 cents 16: 2 681.80000 cents 16: 23 775.28000 cents 17: 24 812.05000 cents 17: 1 905.53000 cents 18: 21 848.82000 cents 18: 4 942.30000 cents 19: 18 885.59000 cents 19: 7 979.07000 cents 20: 15 922.36000 cents 20: 10 1015.84000 cents 21: 12 959.13000 cents 21: 13 1052.61000 cents 22: 9 995.90000 cents 22: 16 1089.38000 cents 23: 6 1032.67000 cents 23: 19 1126.15000 cents 24: 3 1069.44000 cents 24: 22 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 23 24 25 0.0 : 36.8 73.5 110.3 147.1 277.3 314.1 350.9 387.6 424.4 461.2 497.9 534.7 665.0 701.7 738.5 775.3 812.0 848.8 885.6 922.4 1052.6 1089.4 1126.2 1162.9 1199.7 36.8 : 36.8 73.5 110.3 240.6 277.3 314.1 350.9 387.6 424.4 461.2 498.0 628.2 665.0 701.7 738.5 775.3 812.1 848.8 885.6 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 73.5 : 36.8 73.5 203.8 240.6 277.3 314.1 350.9 387.6 424.4 461.2 591.4 628.2 665.0 701.7 738.5 775.3 812.0 848.8 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 110.3 : 36.8 167.0 203.8 240.6 277.3 314.1 350.9 387.6 424.4 554.7 591.4 628.2 665.0 701.7 738.5 775.3 812.1 942.3 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 147.1 : 130.3 167.0 203.8 240.6 277.3 314.1 350.9 387.6 517.9 554.7 591.4 628.2 665.0 701.7 738.5 775.3 905.5 942.3 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 277.3 : 36.8 73.5 110.3 147.1 183.8 220.6 257.4 387.6 424.4 461.2 497.9 534.7 571.5 608.3 645.0 775.3 812.0 848.8 885.6 922.4 959.1 995.9 1032.7 1069.4 1199.7 314.1 : 36.8 73.5 110.3 147.1 183.8 220.6 350.9 387.6 424.4 461.2 497.9 534.7 571.5 608.3 738.5 775.3 812.0 848.8 885.6 922.4 959.1 995.9 1032.7 1162.9 1199.7 350.9 : 36.8 73.5 110.3 147.1 183.8 314.1 350.9 387.6 424.4 461.2 497.9 534.7 571.5 701.7 738.5 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1126.2 1162.9 1199.7 387.6 : 36.8 73.5 110.3 147.1 277.3 314.1 350.9 387.6 424.4 461.2 497.9 534.7 665.0 701.7 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1089.4 1126.2 1162.9 1199.7 424.4 : 36.8 73.5 110.3 240.6 277.3 314.1 350.9 387.6 424.4 461.2 497.9 628.2 665.0 701.7 738.5 775.3 812.0 848.8 885.6 922.4 1052.6 1089.4 1126.2 1162.9 1199.7 461.2 : 36.8 73.5 203.8 240.6 277.3 314.1 350.9 387.6 424.4 461.2 591.4 628.2 665.0 701.7 738.5 775.3 812.1 848.8 885.6 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 497.9 : 36.8 167.0 203.8 240.6 277.3 314.1 350.9 387.6 424.4 554.7 591.4 628.2 665.0 701.7 738.5 775.3 812.1 848.8 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 534.7 : 130.2 167.0 203.8 240.6 277.3 314.1 350.9 387.6 517.9 554.7 591.4 628.2 665.0 701.7 738.5 775.3 812.1 942.3 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 665.0 : 36.8 73.5 110.3 147.1 183.9 220.6 257.4 387.6 424.4 461.2 498.0 534.7 571.5 608.3 645.0 681.8 812.1 848.8 885.6 922.4 959.1 995.9 1032.7 1069.4 1199.7 701.7 : 36.8 73.5 110.3 147.1 183.8 220.6 350.9 387.6 424.4 461.2 497.9 534.7 571.5 608.3 645.0 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1032.7 1162.9 1199.7 738.5 : 36.8 73.5 110.3 147.1 183.9 314.1 350.9 387.6 424.4 461.2 497.9 534.7 571.5 608.3 738.5 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1126.2 1162.9 1199.7 775.3 : 36.8 73.5 110.3 147.1 277.3 314.1 350.9 387.6 424.4 461.2 498.0 534.7 571.5 701.7 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1089.4 1126.2 1162.9 1199.7 812.0 : 36.8 73.5 110.3 240.6 277.3 314.1 350.9 387.6 424.4 461.2 498.0 534.7 665.0 701.7 738.5 775.3 812.1 848.8 885.6 922.4 1052.6 1089.4 1126.2 1162.9 1199.7 848.8 : 36.8 73.5 203.8 240.6 277.3 314.1 350.9 387.6 424.4 461.2 497.9 628.2 665.0 701.7 738.5 775.3 812.1 848.8 885.6 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 885.6 : 36.8 167.0 203.8 240.6 277.3 314.1 350.9 387.6 424.4 461.2 591.4 628.2 665.0 701.7 738.5 775.3 812.1 848.8 979.1 1015.8 1052.6 1089.4 1126.1 1162.9 1199.7 922.4 : 130.2 167.0 203.8 240.6 277.3 314.1 350.9 387.6 424.4 554.7 591.4 628.2 665.0 701.7 738.5 775.3 812.1 942.3 979.1 1015.8 1052.6 1089.4 1126.2 1162.9 1199.7 1052.6: 36.8 73.5 110.3 147.1 183.9 220.6 257.4 294.2 424.4 461.2 498.0 534.7 571.5 608.3 645.0 681.8 812.1 848.8 885.6 922.4 959.1 995.9 1032.7 1069.4 1199.7 1089.4: 36.8 73.5 110.3 147.1 183.9 220.6 257.4 387.6 424.4 461.2 498.0 534.7 571.5 608.3 645.0 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1032.7 1162.9 1199.7 1126.2: 36.8 73.5 110.3 147.1 183.9 220.6 350.9 387.6 424.4 461.2 497.9 534.7 571.5 608.3 738.5 775.3 812.1 848.8 885.6 922.4 959.1 995.9 1126.1 1162.9 1199.7 1162.9: 36.8 73.5 110.3 147.1 183.8 314.1 350.9 387.6 424.4 461.2 498.0 534.7 571.5 701.7 738.5 775.3 812.1 848.8 885.6 922.4 959.1 1089.4 1126.1 1162.9 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 130.2500 cents 93.48000 cents 36.77000 cents 2: 73.5400 .. 167.0200 cents 93.48000 cents -56.71000 cents 3: 110.3100 .. 203.7900 cents 93.48000 cents -56.71000 cents 4: 147.0800 .. 240.5600 cents 93.48000 cents -56.71000 cents 5: 183.8500 .. 277.3300 cents 93.48000 cents -56.71000 cents 6: 220.6200 .. 314.1000 cents 93.48000 cents -56.71000 cents 7: 257.3900 .. 350.8700 cents 93.48000 cents -56.71000 cents 8: 294.1600 .. 387.6400 cents 93.48000 cents -56.71000 cents 9: 424.4100 .. 517.8900 cents 93.48000 cents 36.77000 cents 10: 461.1800 .. 554.6600 cents 93.48000 cents -56.71000 cents 11: 497.9500 .. 591.4300 cents 93.48000 cents -56.71000 cents 12: 534.7200 .. 628.2000 cents 93.48000 cents -56.71000 cents 13: 571.4900 .. 664.9700 cents 93.48000 cents -56.71000 cents 14: 608.2600 .. 701.7400 cents 93.48000 cents -56.71000 cents 15: 645.0300 .. 738.5100 cents 93.48000 cents -56.71000 cents 16: 681.8000 .. 775.2800 cents 93.48000 cents -56.71000 cents 17: 812.0500 .. 905.5300 cents 93.48000 cents 36.77000 cents 18: 848.8200 .. 942.3000 cents 93.48000 cents -56.71000 cents 19: 885.5900 .. 979.0700 cents 93.48000 cents -56.71000 cents 20: 922.3600 .. 1015.8400 cents 93.48000 cents -56.71000 cents 21: 959.1300 .. 1052.6100 cents 93.48000 cents -56.71000 cents 22: 995.9000 .. 1089.3800 cents 93.48000 cents -56.71000 cents 23: 1032.6700 .. 1126.1500 cents 93.48000 cents -56.71000 cents 24: 1069.4400 .. 1162.9200 cents 93.48000 cents -56.71000 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 47.9876 cents Largest one step interval : 130.25000 cents Average / Smallest step : 1.305075 Largest / Average step : 2.714243 Largest / Smallest step : 3.542290 Median interval of one step : 36.77000 cents, amount: 22 Most common interval of one step : 36.77000 cents, amount: 22 Least squares average step : 48.22447 cents, oct.: 1205.61181 cents Scale is not proper Scale has Myhill's property chromas: 93.48000 cents and 56.71000 cents, ratio: 1.648387 generators: 8 of 387.64000 cents and 17 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: 59 118 177 236 445 504 563 622 681 740 799 858 1067 1126 1185 1244 1303 1362 1421 1480 1689 1748 1807 1866 1925 generators: 622 and 1303 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAAAABAAAAAAABAAAA Step pattern size order : SSSSLSSSSSSSLSSSSSSSLSSSS Scale is a Constant Structure, by a margin of 16.83000 cents Scale diversity : 1.172741 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 Rothenberg efficiency : 0.693333 redundancy: 0.306667 Efficiency x scale size : 17.333333 Number of different interval sizes : 48 = 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: 24 Scale is a chain of 12 triads 0.0 387.640 775.280 cents Most common triad is 0.0 387.640 812.050 cents, amount: 23 Number of recognisable fifths : 17, average 701.7400 cents Number of recognisable fourths : 17, average 497.9500 cents Formal octave complements present : 25 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 12-13 -- Rational properties --
FIT/MODE
25: 0 1 1 1 2 1 1 1 0 1 1 1 2 1 1 1 0 1 1 1 2 1 1 1 1 N T3 SD: 26.6968 c. M: 44.8704 c. 26: 1 1 0 1 3 1 1 0 1 1 1 1 2 1 1 1 1 0 1 1 3 1 0 1 1 N I SD: 13.0555 c. M:-18.9831 c. 27: 1 1 0 1 3 1 1 1 1 0 1 1 3 1 1 0 1 1 1 1 3 1 0 1 1 N I SD: 12.6705 c. M:-21.4441 c. 31: 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 N M DE I SD: 4.6384 c. M:-7.7187 c. 34: 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1 N M DE I SD: 3.5695 c. M:-5.9400 c. 65: 2 2 2 2 7 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 7 2 2 2 2 N M DE I SD: 0.3450 c. M:-0.5742 c. 229: 7 7 7 7 25 7 7 7 7 7 7 7 25 7 7 7 7 7 7 7 25 7 7 7 7 N M DE I SD: 0.2362 c. M:-0.3930 c. 294: 9 9 9 9 32 9 9 9 9 9 9 9 32 9 9 9 9 9 9 9 32 9 9 9 9 N M DE I SD: 0.1077 c. M:-0.1792 c. 359: 11 11 11 11 39 11 11 11 11 11 11 11 39 11 11 11 11 11 11 11 39 11 11 11 11 N M DE I SD: 0.0257 c. M:-0.0428 c. 783: 24 24 24 24 85 24 24 24 24 24 24 24 85 24 24 24 24 24 24 24 85 24 24 24 24 N M DE I SD: 0.0051 c. M:-0.0084 c. 1142: 35 35 35 35 124 35 35 35 35 35 35 35 124 35 35 35 35 35 35 35 124 35 35 35 35 N M DE I SD: 0.0046 c. M:-0.0077 c. 1925: 59 59 59 59 209 59 59 59 59 59 59 59 209 59 59 59 59 59 59 59 209 59 59 59 59 N M DE I SD: 0.0007 c. M:-0.0011 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: 11.8578 cents 6 .. 12 match: 6 H SD: 1.8379 cents 7 .. 14 match: 7 H SD: 10.0808 cents 8 .. 16 match: 8 H SD: 9.4671 cents 9 .. 18 match: 8 SD: 6.0061 cents 10 .. 20 match: 10 H SD: 6.4206 cents 11 .. 22 match: 11 H SD: 3.6792 cents 12 .. 24 match: 10 S SD: 2.1628 cents 13 .. 26 match: 12 S SD: 4.4098 cents 14 .. 28 match: 12 SD: 4.7825 cents 15 .. 30 match: 12 S SD: 3.1691 cents 16 .. 32 match: 14 SD: 4.0529 cents 17 .. 34 match: 15 SD: 3.9781 cents 18 .. 36 match: 17 SD: 3.9626 cents 19 .. 38 match: 16 SD: 3.5909 cents 20 .. 40 match: 17 SD: 3.4745 cents 21 .. 42 match: 17 SD: 2.8362 cents 22 .. 44 match: 18 SD: 2.3607 cents 23 .. 46 match: 18 SD: 2.1539 cents 24 .. 48 match: 20 SD: 2.0075 cents 25 .. 50 match: 20 SD: 2.3016 cents 26 .. 52 match: 19 SD: 2.4331 cents 27 .. 54 match: 20 SD: 2.2589 cents 28 .. 56 match: 21 SD: 2.1480 cents 29 .. 58 match: 21 SD: 2.7578 cents 30 .. 60 match: 23 SD: 1.7308 cents 31 .. 62 match: 22 SD: 2.6179 cents 32 .. 64 match: 23 SD: 1.9423 cents 33 .. 66 match: 23 SD: 2.0941 cents 34 .. 68 match: 23 SD: 2.0910 cents 35 .. 70 match: 24 SD: 1.9696 cents 36 .. 72 match: 24 SD: 1.5497 cents 37 .. 74 match: 24 SD: 2.1763 cents 38 .. 76 match: 24 SD: 2.2545 cents 39 .. 78 match: 24 SD: 1.7219 cents 40 .. 80 match: 25 SD: 1.6658 cents 43 .. 86 match: 25 SD: 1.6056 cents 44 .. 88 match: 25 SD: 1.3518 cents 45 .. 90 match: 25 SD: 1.3298 cents 47 .. 94 match: 25 SD: 1.2769 cents 57 .. 114 match: 25 SD: 1.2045 cents 58 .. 116 match: 25 SD: 1.1920 cents 60 .. 120 match: 25 SD: 1.1109 cents 64 .. 128 match: 25 SD: 1.0695 cents 66 .. 132 match: 25 SD: 1.0681 cents 71 .. 142 match: 25 SD: 1.0304 cents 72 .. 144 match: 25 SD: 0.9264 cents 75 .. 150 match: 25 SD: 0.7890 cents 87 .. 174 match: 25 SD: 0.7807 cents 88 .. 176 match: 25 SD: 0.7277 cents 90 .. 180 match: 25 SD: 0.6327 cents 92 .. 184 match: 25 SD: 0.5789 cents 111 .. 222 match: 25 SD: 0.5234 cents 120 .. 240 match: 25 SD: 0.5194 cents 122 .. 244 match: 25 SD: 0.5057 cents 132 .. 264 match: 25 SD: 0.4944 cents 134 .. 268 match: 25 SD: 0.4892 cents 135 .. 270 match: 25 SD: 0.4586 cents 136 .. 272 match: 25 SD: 0.4561 cents 138 .. 276 match: 25 SD: 0.4378 cents 147 .. 294 match: 25 SD: 0.4093 cents 156 .. 312 match: 25 SD: 0.3955 cents 166 .. 332 match: 25 SD: 0.3746 cents 177 .. 354 match: 25 SD: 0.3615 cents 179 .. 358 match: 25 SD: 0.3485 cents 180 .. 360 match: 25 SD: 0.3011 cents 212 .. 424 match: 25 SD: 0.3007 cents 216 .. 432 match: 25 SD: 0.2904 cents 226 .. 452 match: 25 SD: 0.2134 cents 276 .. 552 match: 25 SD: 0.1895 cents 324 .. 648 match: 25 SD: 0.1753 cents 338 .. 676 match: 25 SD: 0.1677 cents 368 .. 736 match: 25 SD: 0.1667 cents 370 .. 740 match: 25 SD: 0.1550 cents 374 .. 748 match: 25 SD: 0.1509 cents 406 .. 812 match: 25 SD: 0.1493 cents 414 .. 828 match: 25 SD: 0.1397 cents 442 .. 884 match: 25 SD: 0.1329 cents 453 .. 906 match: 25 SD: 0.1310 cents 506 .. 1012 match: 25 SD: 0.1226 cents 508 .. 1016 match: 25 SD: 0.1218 cents 517 .. 1034 match: 25 SD: 0.1141 cents 547 .. 1094 match: 25 SD: 0.1091 cents 553 .. 1106 match: 25 SD: 0.1068 cents 558 .. 1116 match: 25 SD: 0.1054 cents 594 .. 1188 match: 25 SD: 0.1049 cents 597 .. 1194 match: 25 SD: 0.0980 cents