Scala analysis: xen18-erlich-dicot-17
7L 10s MOS for Dicot, L=90.78, s=57.22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.220 cents 57.220000 2: 148.000 cents 148.000000 3: 205.220 cents 205.220000 4: 296.000 cents 296.000000 5: 353.220 cents 353.220000 6: 410.440 cents 410.440000 7: 501.220 cents 501.220000 8: 558.440 cents 558.440000 9: 649.220 cents 649.220000 10: 706.440 cents 706.440000 11: 797.220 cents 797.220000 12: 854.440 cents 854.440000 13: 911.660 cents 911.660000 14: 1002.440 cents 1002.440000 15: 1059.660 cents 1059.660000 16: 1150.440 cents 1150.440000 17: 1207.660 cents 1207.660000
SHOW/INTERVAL
0: 57.2200 cents 57.2200 1: 57.2200 cents 57.2200 2: 90.7800 cents 90.7800 3: 57.2200 cents 57.2200 4: 90.7800 cents 90.7800 5: 57.2200 cents 57.2200 6: 57.2200 cents 57.2200 7: 90.7800 cents 90.7800 8: 57.2200 cents 57.2200 9: 90.7800 cents 90.7800 10: 57.2200 cents 57.2200 11: 90.7800 cents 90.7800 12: 57.2200 cents 57.2200 13: 57.2200 cents 57.2200 14: 90.7800 cents 90.7800 15: 57.2200 cents 57.2200 16: 90.7800 cents 90.7800 17: 57.2200 cents 57.2200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 57.22000 cents 1: 7 90.78000 cents 2: 3 114.44000 cents 2: 14 148.00000 cents 3: 13 205.22000 cents 3: 4 238.78000 cents 4: 6 262.44000 cents 4: 11 296.00000 cents 5: 16 353.22000 cents 5: 1 386.78000 cents 6: 9 410.44000 cents 6: 8 444.00000 cents 7: 2 467.66000 cents 7: 15 501.22000 cents 8: 12 558.44000 cents 8: 5 592.00000 cents 9: 5 615.66000 cents 9: 12 649.22000 cents 10: 15 706.44000 cents 10: 2 740.00000 cents 11: 8 763.66000 cents 11: 9 797.22000 cents 12: 1 820.88000 cents 12: 16 854.44000 cents 13: 11 911.66000 cents 13: 6 945.22000 cents 14: 4 968.88000 cents 14: 13 1002.44000 cents 15: 14 1059.66000 cents 15: 3 1093.22000 cents 16: 7 1116.88000 cents 16: 10 1150.44000 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 0.0 : 57.2 148.0 205.2 296.0 353.2 410.4 501.2 558.4 649.2 706.4 797.2 854.4 911.7 1002.4 1059.7 1150.4 1207.7 57.2 : 90.8 148.0 238.8 296.0 353.2 444.0 501.2 592.0 649.2 740.0 797.2 854.4 945.2 1002.4 1093.2 1150.4 1207.7 148.0 : 57.2 148.0 205.2 262.4 353.2 410.4 501.2 558.4 649.2 706.4 763.7 854.4 911.7 1002.4 1059.7 1116.9 1207.7 205.2 : 90.8 148.0 205.2 296.0 353.2 444.0 501.2 592.0 649.2 706.4 797.2 854.4 945.2 1002.4 1059.7 1150.4 1207.7 296.0 : 57.2 114.4 205.2 262.4 353.2 410.4 501.2 558.4 615.7 706.4 763.7 854.4 911.7 968.9 1059.7 1116.9 1207.7 353.2 : 57.2 148.0 205.2 296.0 353.2 444.0 501.2 558.4 649.2 706.4 797.2 854.4 911.7 1002.4 1059.7 1150.4 1207.7 410.4 : 90.8 148.0 238.8 296.0 386.8 444.0 501.2 592.0 649.2 740.0 797.2 854.4 945.2 1002.4 1093.2 1150.4 1207.7 501.2 : 57.2 148.0 205.2 296.0 353.2 410.4 501.2 558.4 649.2 706.4 763.7 854.4 911.7 1002.4 1059.7 1116.9 1207.7 558.4 : 90.8 148.0 238.8 296.0 353.2 444.0 501.2 592.0 649.2 706.4 797.2 854.4 945.2 1002.4 1059.7 1150.4 1207.7 649.2 : 57.2 148.0 205.2 262.4 353.2 410.4 501.2 558.4 615.7 706.4 763.7 854.4 911.7 968.9 1059.7 1116.9 1207.7 706.4 : 90.8 148.0 205.2 296.0 353.2 444.0 501.2 558.4 649.2 706.4 797.2 854.4 911.7 1002.4 1059.7 1150.4 1207.7 797.2 : 57.2 114.4 205.2 262.4 353.2 410.4 467.7 558.4 615.7 706.4 763.7 820.9 911.7 968.9 1059.7 1116.9 1207.7 854.4 : 57.2 148.0 205.2 296.0 353.2 410.4 501.2 558.4 649.2 706.4 763.7 854.4 911.7 1002.4 1059.7 1150.4 1207.7 911.7 : 90.8 148.0 238.8 296.0 353.2 444.0 501.2 592.0 649.2 706.4 797.2 854.4 945.2 1002.4 1093.2 1150.4 1207.7 1002.4: 57.2 148.0 205.2 262.4 353.2 410.4 501.2 558.4 615.7 706.4 763.7 854.4 911.7 1002.4 1059.7 1116.9 1207.7 1059.7: 90.8 148.0 205.2 296.0 353.2 444.0 501.2 558.4 649.2 706.4 797.2 854.4 945.2 1002.4 1059.7 1150.4 1207.7 1150.4: 57.2 114.4 205.2 262.4 353.2 410.4 467.7 558.4 615.7 706.4 763.7 854.4 911.7 968.9 1059.7 1116.9 1207.7 1207.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.2200 .. 90.7800 cents 33.56000 cents 57.22000 cents 2: 114.4400 .. 148.0000 cents 33.56000 cents 23.66000 cents 3: 205.2200 .. 238.7800 cents 33.56000 cents 57.22000 cents 4: 262.4400 .. 296.0000 cents 33.56000 cents 23.66000 cents 5: 353.2200 .. 386.7800 cents 33.56000 cents 57.22000 cents 6: 410.4400 .. 444.0000 cents 33.56000 cents 23.66000 cents 7: 467.6600 .. 501.2200 cents 33.56000 cents 23.66000 cents 8: 558.4400 .. 592.0000 cents 33.56000 cents 57.22000 cents 9: 615.6600 .. 649.2200 cents 33.56000 cents 23.66000 cents 10: 706.4400 .. 740.0000 cents 33.56000 cents 57.22000 cents 11: 763.6600 .. 797.2200 cents 33.56000 cents 23.66000 cents 12: 820.8800 .. 854.4400 cents 33.56000 cents 23.66000 cents 13: 911.6600 .. 945.2200 cents 33.56000 cents 57.22000 cents 14: 968.8800 .. 1002.4400 cents 33.56000 cents 23.66000 cents 15: 1059.6600 .. 1093.2200 cents 33.56000 cents 57.22000 cents 16: 1116.8800 .. 1150.4400 cents 33.56000 cents 23.66000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.22000 cents, class 1 Average step (divided formal octave): 71.0388 cents Largest one step interval : 90.78000 cents Average / Smallest step : 1.241503 Largest / Average step : 1.277893 Largest / Smallest step : 1.586508 Median interval of one step : 57.22000 cents, amount: 10 Most common interval of one step : 57.22000 cents, amount: 10 Least squares average step : 71.15163 cents, oct.: 1209.57771 cents Scale is strictly proper Scale has Myhill's property chromas: 33.56000 cents and 23.66000 cents, ratio: 1.418428 generators: 5 of 353.22000 cents and 12 of 854.44000 cents ET pair of linear temperament : 17&24 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1583-tone equal temperament with octave 1207.660 cents degrees: 75 194 269 388 463 538 657 732 851 926 1045 1120 1195 1314 1389 1508 1583 generators: 463 and 1120 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABAABABA Step pattern size order : SLSLSSLSLSLSSLSLS Scale is a Constant Structure, by a margin of 23.66000 cents Scale diversity : 1.189196 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555372 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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 : 23.66000 cents Most common intervals : 353.22000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 410.440 854.440 cents Most common triad is 0.0 353.220 854.440 cents, amount: 15 Number of recognisable fifths : 15, average 706.4400 cents Number of recognisable fourths : 15, average 501.2200 cents Scale contains two identical conjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.6712 c. M:-15.7929 c. 24: 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 P M ME I SD: 4.8296 c. M:-7.8867 c. 41: 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 3 2 SP M ME I SD: 1.1829 c. M:-1.9317 c. 65: 3 5 3 5 3 3 5 3 5 3 5 3 3 5 3 5 3 SP M DE I SD: 1.0371 c. M:-1.6935 c. 106: 5 8 5 8 5 5 8 5 8 5 8 5 5 8 5 8 5 SP M DE I SD: 0.1784 c. M: 0.2913 c. 253: 12 19 12 19 12 12 19 12 19 12 19 12 12 19 12 19 12 SP M DE I SD: 0.0422 c. M:-0.0689 c. 359: 17 27 17 27 17 17 27 17 27 17 27 17 17 27 17 27 17 SP M DE I SD: 0.0229 c. M:-0.0374 c. 612: 29 46 29 46 29 29 46 29 46 29 46 29 29 46 29 46 29 SP M DE I SD: 0.0040 c. M:-0.0065 c. 1583: 75 119 75 119 75 75 119 75 119 75 119 75 75 119 75 119 75 SP M DE I SD: 0.0021 c. M:-0.0034 c. 2195: 104 165 104 165 104 104 165 104 165 104 165 104 104 165 104 165 104 SP M DE I SD: 0.0004 c. M:-0.0007 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 7.6600 cents 2 .. 4 match: 2 H SD: 4.4382 cents 3 .. 6 match: 3 H SD: 9.5109 cents 4 .. 8 match: 4 H SD: 10.5794 cents 5 .. 10 match: 5 H SD: 7.8097 cents 6 .. 12 match: 6 H SD: 7.0490 cents 7 .. 14 match: 7 H SD: 8.0425 cents 8 .. 16 match: 8 H SD: 6.6793 cents 9 .. 18 match: 9 H SD: 7.3063 cents 10 .. 20 match: 10 H SD: 7.3067 cents 11 .. 22 match: 11 H SD: 6.6103 cents 12 .. 24 match: 12 H SD: 6.5404 cents 13 .. 26 match: 13 H SD: 6.1642 cents 14 .. 28 match: 14 H SD: 5.1795 cents 15 .. 30 match: 14 SD: 5.3292 cents 16 .. 32 match: 15 SD: 5.3123 cents 17 .. 34 match: 15 SD: 5.3025 cents 18 .. 36 match: 15 SD: 4.7024 cents 19 .. 38 match: 15 SD: 4.4788 cents 20 .. 40 match: 16 SD: 4.4839 cents 21 .. 42 match: 17 SD: 4.2460 cents 22 .. 44 match: 17 SD: 2.9722 cents 26 .. 52 match: 17 SD: 2.6297 cents 31 .. 62 match: 17 SD: 2.3476 cents 32 .. 64 match: 17 SD: 2.1953 cents 33 .. 66 match: 17 SD: 2.0891 cents 45 .. 90 match: 17 SD: 2.0479 cents 47 .. 94 match: 17 SD: 2.0044 cents 48 .. 96 match: 17 SD: 1.5934 cents 53 .. 106 match: 17 SD: 1.3213 cents 63 .. 127 match: 17 SD: 1.2111 cents 65 .. 131 match: 17 SD: 1.1923 cents 66 .. 133 match: 17 SD: 1.1089 cents 71 .. 143 match: 17 SD: 1.0832 cents 79 .. 159 match: 17 SD: 0.9462 cents 86 .. 173 match: 17 SD: 0.9125 cents 87 .. 175 match: 17 SD: 0.8628 cents 89 .. 179 match: 17 SD: 0.7305 cents 97 .. 195 match: 17 SD: 0.7021 cents 111 .. 223 match: 17 SD: 0.6218 cents 119 .. 239 match: 17 SD: 0.6019 cents 123 .. 247 match: 17 SD: 0.5774 cents 143 .. 287 match: 17 SD: 0.5168 cents 145 .. 291 match: 17 SD: 0.4871 cents 149 .. 299 match: 17 SD: 0.4376 cents 176 .. 354 match: 17 SD: 0.3327 cents 213 .. 428 match: 17 SD: 0.3222 cents 231 .. 464 match: 17 SD: 0.3198 cents 236 .. 474 match: 17 SD: 0.3036 cents 238 .. 478 match: 17 SD: 0.2936 cents 246 .. 494 match: 17 SD: 0.2804 cents 262 .. 526 match: 17 SD: 0.2780 cents 268 .. 538 match: 17 SD: 0.2145 cents 326 .. 655 match: 17 SD: 0.2096 cents 349 .. 701 match: 17 SD: 0.1775 cents 381 .. 765 match: 17 SD: 0.1474 cents 446 .. 896 match: 17 SD: 0.1413 cents 482 .. 968 match: 17 SD: 0.1403 cents 494 .. 992 match: 17 SD: 0.1391 cents 530 .. 1065 match: 17 SD: 0.1298 cents 538 .. 1081 match: 17 SD: 0.1264 cents 564 .. 1133 match: 17 SD: 0.1261 cents 583 .. 1171 match: 17 SD: 0.1194 cents