Scala analysis: xen18-erlich-dominant-17
12L 5s MOS for Dominant, L=88.94, s=25.59
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.940 cents 88.940000 2: 114.530 cents 114.530000 3: 203.470 cents 203.470000 4: 292.410 cents 292.410000 5: 381.350 cents 381.350000 6: 406.940 cents 406.940000 7: 495.880 cents 495.880000 8: 584.820 cents 584.820000 9: 610.410 cents 610.410000 10: 699.350 cents 699.350000 11: 788.290 cents 788.290000 12: 813.880 cents 813.880000 13: 902.820 cents 902.820000 14: 991.760 cents 991.760000 15: 1080.700 cents 1080.700000 16: 1106.290 cents 1106.290000 17: 1195.230 cents 1195.230000
SHOW/INTERVAL
0: 88.9400 cents 88.9400 1: 88.9400 cents 88.9400 2: 25.5900 cents 25.5900 3: 88.9400 cents 88.9400 4: 88.9400 cents 88.9400 5: 88.9400 cents 88.9400 6: 25.5900 cents 25.5900 7: 88.9400 cents 88.9400 8: 88.9400 cents 88.9400 9: 25.5900 cents 25.5900 10: 88.9400 cents 88.9400 11: 88.9400 cents 88.9400 12: 25.5900 cents 25.5900 13: 88.9400 cents 88.9400 14: 88.9400 cents 88.9400 15: 88.9400 cents 88.9400 16: 25.5900 cents 25.5900 17: 88.9400 cents 88.9400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 25.59000 cents 1: 12 88.94000 cents 2: 10 114.53000 cents 2: 7 177.88000 cents 3: 15 203.47000 cents 3: 2 266.82000 cents 4: 3 229.06000 cents 4: 14 292.41000 cents 5: 8 318.00000 cents 5: 9 381.35000 cents 6: 13 406.94000 cents 6: 4 470.29000 cents 7: 1 432.53000 cents 7: 16 495.88000 cents 8: 6 521.47000 cents 8: 11 584.82000 cents 9: 11 610.41000 cents 9: 6 673.76000 cents 10: 16 699.35000 cents 10: 1 762.70000 cents 11: 4 724.94000 cents 11: 13 788.29000 cents 12: 9 813.88000 cents 12: 8 877.23000 cents 13: 14 902.82000 cents 13: 3 966.17000 cents 14: 2 928.41000 cents 14: 15 991.76000 cents 15: 7 1017.35000 cents 15: 10 1080.70000 cents 16: 12 1106.29000 cents 16: 5 1169.64000 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 : 88.9 114.5 203.5 292.4 381.3 406.9 495.9 584.8 610.4 699.4 788.3 813.9 902.8 991.8 1080.7 1106.3 1195.2 88.9 : 25.6 114.5 203.5 292.4 318.0 406.9 495.9 521.5 610.4 699.3 724.9 813.9 902.8 991.8 1017.3 1106.3 1195.2 114.5 : 88.9 177.9 266.8 292.4 381.3 470.3 495.9 584.8 673.8 699.4 788.3 877.2 966.2 991.8 1080.7 1169.6 1195.2 203.5 : 88.9 177.9 203.5 292.4 381.3 406.9 495.9 584.8 610.4 699.3 788.3 877.2 902.8 991.8 1080.7 1106.3 1195.2 292.4 : 88.9 114.5 203.5 292.4 318.0 406.9 495.9 521.5 610.4 699.3 788.3 813.9 902.8 991.8 1017.3 1106.3 1195.2 381.3 : 25.6 114.5 203.5 229.1 318.0 406.9 432.5 521.5 610.4 699.4 724.9 813.9 902.8 928.4 1017.4 1106.3 1195.2 406.9 : 88.9 177.9 203.5 292.4 381.3 406.9 495.9 584.8 673.8 699.4 788.3 877.2 902.8 991.8 1080.7 1169.6 1195.2 495.9 : 88.9 114.5 203.5 292.4 318.0 406.9 495.9 584.8 610.4 699.4 788.3 813.9 902.8 991.8 1080.7 1106.3 1195.2 584.8 : 25.6 114.5 203.5 229.1 318.0 406.9 495.9 521.5 610.4 699.4 724.9 813.9 902.8 991.8 1017.4 1106.3 1195.2 610.4 : 88.9 177.9 203.5 292.4 381.3 470.3 495.9 584.8 673.8 699.3 788.3 877.2 966.2 991.8 1080.7 1169.6 1195.2 699.4 : 88.9 114.5 203.5 292.4 381.4 406.9 495.9 584.8 610.4 699.4 788.3 877.2 902.8 991.8 1080.7 1106.3 1195.2 788.3 : 25.6 114.5 203.5 292.4 318.0 406.9 495.9 521.5 610.4 699.4 788.3 813.9 902.8 991.8 1017.4 1106.3 1195.2 813.9 : 88.9 177.9 266.8 292.4 381.3 470.3 495.9 584.8 673.8 762.7 788.3 877.2 966.2 991.8 1080.7 1169.6 1195.2 902.8 : 88.9 177.9 203.5 292.4 381.3 406.9 495.9 584.8 673.8 699.4 788.3 877.2 902.8 991.8 1080.7 1106.3 1195.2 991.8 : 88.9 114.5 203.5 292.4 318.0 406.9 495.9 584.8 610.4 699.4 788.3 813.9 902.8 991.8 1017.4 1106.3 1195.2 1080.7: 25.6 114.5 203.5 229.1 318.0 406.9 495.9 521.5 610.4 699.3 724.9 813.9 902.8 928.4 1017.3 1106.3 1195.2 1106.3: 88.9 177.9 203.5 292.4 381.3 470.3 495.9 584.8 673.8 699.4 788.3 877.2 902.8 991.8 1080.7 1169.6 1195.2 1195.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.5900 .. 88.9400 cents 63.35000 cents 25.59000 cents 2: 114.5300 .. 177.8800 cents 63.35000 cents 25.59000 cents 3: 203.4700 .. 266.8200 cents 63.35000 cents 25.59000 cents 4: 229.0600 .. 292.4100 cents 63.35000 cents -37.76000 cents 5: 318.0000 .. 381.3500 cents 63.35000 cents 25.59000 cents 6: 406.9400 .. 470.2900 cents 63.35000 cents 25.59000 cents 7: 432.5300 .. 495.8800 cents 63.35000 cents -37.76000 cents 8: 521.4700 .. 584.8200 cents 63.35000 cents 25.59000 cents 9: 610.4100 .. 673.7600 cents 63.35000 cents 25.59000 cents 10: 699.3500 .. 762.7000 cents 63.35000 cents 25.59000 cents 11: 724.9400 .. 788.2900 cents 63.35000 cents -37.76000 cents 12: 813.8800 .. 877.2300 cents 63.35000 cents 25.59000 cents 13: 902.8200 .. 966.1700 cents 63.35000 cents 25.59000 cents 14: 928.4100 .. 991.7600 cents 63.35000 cents -37.76000 cents 15: 1017.3500 .. 1080.7000 cents 63.35000 cents 25.59000 cents 16: 1106.2900 .. 1169.6400 cents 63.35000 cents 25.59000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 25.59000 cents, class 1 Average step (divided formal octave): 70.3076 cents Largest one step interval : 88.94000 cents Average / Smallest step : 2.747466 Largest / Average step : 1.265012 Largest / Smallest step : 3.475576 Median interval of one step : 88.94000 cents, amount: 12 Most common interval of one step : 88.94000 cents, amount: 12 Least squares average step : 70.23667 cents, oct.: 1194.02333 cents Scale is not proper Scale has Myhill's property chromas: 63.35000 cents and 37.76000 cents, ratio: 1.677701 generators: 7 of 495.88000 cents and 10 of 699.35000 cents ET pair of linear temperament : 12&41 Scale is distributional even Scale is a mode of a 981-tone equal temperament with octave 1195.230 cents degrees: 73 94 167 240 313 334 407 480 501 574 647 668 741 814 887 908 981 generators: 407 and 574 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABAABAAABA Step pattern size order : LSLLLSLLSLLSLLLSL Scale is a Constant Structure, by a margin of 25.59000 cents Scale diversity : 1.173917 Lumma stability : 0.278331 Lumma impropriety factor : 0.126369 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 : 25.59000 cents Most common intervals : 495.88000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 495.880 991.760 cents Most common triad is 0.0 495.880 699.350 cents, amount: 15 Number of recognisable fifths : 16, average 699.3500 cents Number of recognisable fourths : 16, average 495.8800 cents Scale contains two identical disjunct "tetrachords" of 8 notes 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: 18.2559 c. M:-29.8118 c. 21: 2 0 2 1 2 0 2 1 1 1 2 0 2 1 2 0 2 N T3 I SD: 15.8801 c. M: 24.8914 c. 22: 2 0 2 1 2 0 2 2 0 2 2 0 2 1 2 0 2 N I SD: 15.2184 c. M:-26.6395 c. 23: 2 0 2 2 1 1 2 1 1 1 2 1 1 2 2 0 2 N D3 I SD: 14.7868 c. M:-23.7852 c. 24: 2 0 2 2 2 0 2 2 0 2 2 0 2 2 2 0 2 N M DE I SD: 10.4471 c. M:-17.0600 c. 29: 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 P M ME I SD: 6.3788 c. M:-10.4166 c. 41: 3 1 3 3 3 1 3 3 1 3 3 1 3 3 3 1 3 N M DE I SD: 1.4542 c. M:-2.3746 c. 53: 4 1 4 4 4 1 4 4 1 4 4 1 4 4 4 1 4 N M DE I SD: 1.2405 c. M:-2.0257 c. 94: 7 2 7 7 7 2 7 7 2 7 7 2 7 7 7 2 7 N M DE I SD: 0.0651 c. M:-0.1064 c. 511: 38 11 38 38 38 11 38 38 11 38 38 11 38 38 38 11 38 N M DE I SD: 0.0568 c. M: 0.0927 c. 605: 45 13 45 45 45 13 45 45 13 45 45 13 45 45 45 13 45 N M DE I SD: 0.0378 c. M:-0.0618 c. 699: 52 15 52 52 52 15 52 52 15 52 52 15 52 52 52 15 52 N M DE I SD: 0.0240 c. M:-0.0391 c. 793: 59 17 59 59 59 17 59 59 17 59 59 17 59 59 59 17 59 N M DE I SD: 0.0134 c. M:-0.0219 c. 887: 66 19 66 66 66 19 66 66 19 66 66 19 66 66 66 19 66 N M DE I SD: 0.0051 c. M:-0.0083 c. 981: 73 21 73 73 73 21 73 73 21 73 73 21 73 73 73 21 73 N M DE I SD: 0.0016 c. M: 0.0027 c. 1868: 139 40 139 139 139 40 139 139 40 139 139 40 139 139 139 40 139 N M DE I SD: 0.0015 c. M: 0.0025 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 4.7700 cents 2 .. 4 match: 2 H SD: 2.7175 cents 3 .. 6 match: 3 H SD: 6.3967 cents 4 .. 8 match: 4 H SD: 6.0216 cents 5 .. 10 match: 5 H SD: 7.0294 cents 6 .. 12 match: 6 H SD: 7.4709 cents 7 .. 14 match: 7 H SD: 7.3757 cents 8 .. 16 match: 8 H SD: 6.2125 cents 9 .. 18 match: 9 H SD: 6.3280 cents 10 .. 20 match: 10 H SD: 6.8791 cents 11 .. 22 match: 11 H SD: 9.6311 cents 12 .. 24 match: 12 H SD: 5.0324 cents 13 .. 26 match: 12 SD: 7.1101 cents 14 .. 28 match: 13 S SD: 6.3315 cents 15 .. 30 match: 12 SD: 4.6296 cents 16 .. 32 match: 14 S SD: 4.3982 cents 17 .. 34 match: 13 SD: 5.3827 cents 18 .. 36 match: 15 S SD: 4.5344 cents 19 .. 38 match: 13 SD: 5.1130 cents 20 .. 40 match: 13 SD: 4.6823 cents 21 .. 42 match: 16 SD: 4.1063 cents 22 .. 44 match: 15 SD: 3.8394 cents 23 .. 46 match: 16 SD: 3.7242 cents 24 .. 48 match: 13 SD: 3.8043 cents 25 .. 50 match: 16 SD: 3.7940 cents 26 .. 52 match: 16 SD: 3.3572 cents 27 .. 54 match: 14 SD: 3.4611 cents 28 .. 56 match: 16 SD: 3.0549 cents 29 .. 58 match: 14 SD: 3.2504 cents 30 .. 60 match: 16 SD: 2.5808 cents 31 .. 62 match: 15 SD: 2.5651 cents 32 .. 64 match: 15 SD: 2.4010 cents 33 .. 66 match: 16 SD: 2.3327 cents 34 .. 68 match: 14 SD: 2.7350 cents 35 .. 70 match: 15 SD: 2.5294 cents 36 .. 72 match: 16 SD: 2.6089 cents 37 .. 74 match: 17 SD: 2.3401 cents 38 .. 76 match: 17 SD: 1.8766 cents 39 .. 78 match: 15 SD: 2.2303 cents 40 .. 80 match: 17 SD: 1.6865 cents 43 .. 86 match: 16 SD: 2.0422 cents 45 .. 90 match: 17 SD: 1.5243 cents 47 .. 94 match: 16 SD: 1.9930 cents 48 .. 96 match: 16 SD: 1.3926 cents 49 .. 98 match: 16 SD: 1.6742 cents 50 .. 100 match: 16 SD: 1.6061 cents 51 .. 102 match: 16 SD: 2.2427 cents 52 .. 104 match: 17 SD: 1.7783 cents 53 .. 106 match: 17 SD: 1.7264 cents 54 .. 108 match: 17 SD: 1.3408 cents 57 .. 114 match: 17 SD: 1.0906 cents 72 .. 144 match: 17 SD: 1.0553 cents 73 .. 146 match: 17 SD: 1.0375 cents 75 .. 150 match: 17 SD: 0.9854 cents 87 .. 174 match: 17 SD: 0.9196 cents 88 .. 176 match: 17 SD: 0.8647 cents 90 .. 180 match: 17 SD: 0.8569 cents 97 .. 193 match: 17 SD: 0.6742 cents 102 .. 203 match: 17 SD: 0.6702 cents 113 .. 225 match: 17 SD: 0.6647 cents 114 .. 227 match: 17 SD: 0.5218 cents 130 .. 259 match: 17 SD: 0.5057 cents 135 .. 269 match: 17 SD: 0.4822 cents 151 .. 301 match: 17 SD: 0.4224 cents 175 .. 349 match: 17 SD: 0.3641 cents 191 .. 381 match: 17 SD: 0.3575 cents 207 .. 413 match: 17 SD: 0.3340 cents 208 .. 415 match: 17 SD: 0.3252 cents 234 .. 467 match: 17 SD: 0.3207 cents 247 .. 493 match: 17 SD: 0.3168 cents 248 .. 495 match: 17 SD: 0.2724 cents 265 .. 529 match: 17 SD: 0.2526 cents 305 .. 608 match: 17 SD: 0.1823 cents 378 .. 754 match: 17 SD: 0.1763 cents 418 .. 834 match: 17 SD: 0.1563 cents 456 .. 909 match: 17 SD: 0.1444 cents 495 .. 987 match: 17 SD: 0.1241 cents 555 .. 1107 match: 17 SD: 0.1069 cents 570 .. 1137 match: 17 SD: 0.0919 cents