Scala analysis: scott
Wilson's Scott scale, wilson1, in minimax minerva tempering
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.874 cents 75.873867 2: 115.318 cents 115.317911 3: 195.660 cents 195.660207 4: 271.534 cents 271.534074 5: 310.978 cents 310.978119 6: 386.852 cents 386.851985 7: 426.296 cents 426.296030 8: 502.170 cents 502.169896 9: 582.512 cents 582.512193 10: 621.956 cents 621.956237 11: 697.830 cents 697.830104 12: 773.704 cents 773.703970 13: 813.148 cents 813.148015 14: 889.022 cents 889.021881 15: 969.364 cents 969.364178 16: 1008.808 cents 1008.808222 17: 1084.682 cents 1084.682089 18: 1124.126 cents 1124.126133 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 75.8739 cents 75.8739 1: 75.8739 cents 75.8739 2: 39.4440 cents 39.4440 3: 80.3423 cents 80.3423 4: 75.8739 cents 75.8739 5: 39.4440 cents 39.4440 6: 75.8739 cents 75.8739 7: 39.4440 cents 39.4440 8: 75.8739 cents 75.8739 9: 80.3423 cents 80.3423 10: 39.4440 cents 39.4440 11: 75.8739 cents 75.8739 12: 75.8739 cents 75.8739 13: 39.4440 cents 39.4440 14: 75.8739 cents 75.8739 15: 80.3423 cents 80.3423 16: 39.4440 cents 39.4440 17: 75.8739 cents 75.8739 18: 39.4440 cents 39.4440 19: 75.8739 cents 75.8739
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 39.44404 cents 1: 9 75.87387 cents 1: 3 80.34230 cents 2: 11 115.31791 cents 2: 3 119.78634 cents 2: 2 151.74773 cents 2: 3 156.21616 cents 3: 2 154.76196 cents 3: 8 191.19178 cents 3: 9 195.66021 cents 4: 5 230.63582 cents 4: 4 235.10425 cents 4: 2 267.06564 cents 4: 8 271.53407 cents 5: 4 306.50969 cents 5: 12 310.97812 cents 5: 3 347.40794 cents 6: 1 345.95373 cents 6: 3 350.42216 cents 6: 15 386.85198 cents 7: 11 426.29603 cents 7: 6 462.72585 cents 7: 2 467.19428 cents 8: 14 502.16990 cents 8: 4 506.63833 cents 8: 1 543.06815 cents 9: 5 541.61394 cents 9: 1 546.08237 cents 9: 6 578.04376 cents 9: 7 582.51219 cents 10: 7 617.48781 cents 10: 6 621.95624 cents 10: 1 653.91763 cents 10: 5 658.38606 cents 11: 1 656.93185 cents 11: 4 693.36167 cents 11: 14 697.83010 cents 12: 2 732.80572 cents 12: 6 737.27415 cents 12: 11 773.70397 cents 13: 15 813.14801 cents 13: 3 849.57784 cents 13: 1 854.04627 cents 14: 3 852.59206 cents 14: 12 889.02188 cents 14: 4 893.49031 cents 15: 8 928.46593 cents 15: 2 932.93435 cents 15: 4 964.89575 cents 15: 5 969.36418 cents 16: 9 1004.33979 cents 16: 8 1008.80822 cents 16: 2 1045.23804 cents 17: 3 1043.78384 cents 17: 2 1048.25227 cents 17: 3 1080.21366 cents 17: 11 1084.68209 cents 18: 3 1119.65770 cents 18: 9 1124.12613 cents 18: 7 1160.55596 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 75.9 115.3 195.7 271.5 311.0 386.9 426.3 502.2 582.5 622.0 697.8 773.7 813.1 889.0 969.4 1008.8 1084.7 1124.1 1200.0 75.9 : 39.4 119.8 195.7 235.1 311.0 350.4 426.3 506.6 546.1 622.0 697.8 737.3 813.1 893.5 932.9 1008.8 1048.3 1124.1 1200.0 115.3 : 80.3 156.2 195.7 271.5 311.0 386.9 467.2 506.6 582.5 658.4 697.8 773.7 854.0 893.5 969.4 1008.8 1084.7 1160.6 1200.0 195.7 : 75.9 115.3 191.2 230.6 306.5 386.9 426.3 502.2 578.0 617.5 693.4 773.7 813.1 889.0 928.5 1004.3 1080.2 1119.7 1200.0 271.5 : 39.4 115.3 154.8 230.6 311.0 350.4 426.3 502.2 541.6 617.5 697.8 737.3 813.1 852.6 928.5 1004.3 1043.8 1124.1 1200.0 311.0 : 75.9 115.3 191.2 271.5 311.0 386.9 462.7 502.2 578.0 658.4 697.8 773.7 813.1 889.0 964.9 1004.3 1084.7 1160.6 1200.0 386.9 : 39.4 115.3 195.7 235.1 311.0 386.9 426.3 502.2 582.5 622.0 697.8 737.3 813.1 889.0 928.5 1008.8 1084.7 1124.1 1200.0 426.3 : 75.9 156.2 195.7 271.5 347.4 386.9 462.7 543.1 582.5 658.4 697.8 773.7 849.6 889.0 969.4 1045.2 1084.7 1160.6 1200.0 502.2 : 80.3 119.8 195.7 271.5 311.0 386.9 467.2 506.6 582.5 622.0 697.8 773.7 813.1 893.5 969.4 1008.8 1084.7 1124.1 1200.0 582.5 : 39.4 115.3 191.2 230.6 306.5 386.9 426.3 502.2 541.6 617.5 693.4 732.8 813.1 889.0 928.5 1004.3 1043.8 1119.7 1200.0 622.0 : 75.9 151.7 191.2 267.1 347.4 386.9 462.7 502.2 578.0 653.9 693.4 773.7 849.6 889.0 964.9 1004.3 1080.2 1160.6 1200.0 697.8 : 75.9 115.3 191.2 271.5 311.0 386.9 426.3 502.2 578.0 617.5 697.8 773.7 813.1 889.0 928.5 1004.3 1084.7 1124.1 1200.0 773.7 : 39.4 115.3 195.7 235.1 311.0 350.4 426.3 502.2 541.6 622.0 697.8 737.3 813.1 852.6 928.5 1008.8 1048.3 1124.1 1200.0 813.1 : 75.9 156.2 195.7 271.5 311.0 386.9 462.7 502.2 582.5 658.4 697.8 773.7 813.1 889.0 969.4 1008.8 1084.7 1160.6 1200.0 889.0 : 80.3 119.8 195.7 235.1 311.0 386.9 426.3 506.6 582.5 622.0 697.8 737.3 813.1 893.5 932.9 1008.8 1084.7 1124.1 1200.0 969.4 : 39.4 115.3 154.8 230.6 306.5 346.0 426.3 502.2 541.6 617.5 656.9 732.8 813.1 852.6 928.5 1004.3 1043.8 1119.7 1200.0 1008.8: 75.9 115.3 191.2 267.1 306.5 386.9 462.7 502.2 578.0 617.5 693.4 773.7 813.1 889.0 964.9 1004.3 1080.2 1160.6 1200.0 1084.7: 39.4 115.3 191.2 230.6 311.0 386.9 426.3 502.2 541.6 617.5 697.8 737.3 813.1 889.0 928.5 1004.3 1084.7 1124.1 1200.0 1124.1: 75.9 151.7 191.2 271.5 347.4 386.9 462.7 502.2 578.0 658.4 697.8 773.7 849.6 889.0 964.9 1045.2 1084.7 1160.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.4440 .. 80.3423 cents 40.89825 cents 39.44404 cents 2: 115.3179 .. 156.2162 cents 40.89825 cents 34.97562 cents 3: 154.7620 .. 195.6602 cents 40.89825 cents -1.45421 cents 4: 230.6358 .. 271.5341 cents 40.89825 cents 34.97562 cents 5: 306.5097 .. 347.4079 cents 40.89825 cents 34.97562 cents 6: 345.9537 .. 386.8520 cents 40.89825 cents -1.45421 cents 7: 426.2960 .. 467.1943 cents 40.89825 cents 39.44405 cents 8: 502.1699 .. 543.0681 cents 40.89825 cents 34.97561 cents 9: 541.6139 .. 582.5122 cents 40.89825 cents -1.45421 cents 10: 617.4878 .. 658.3861 cents 40.89825 cents 34.97561 cents 11: 656.9319 .. 697.8301 cents 40.89825 cents -1.45421 cents 12: 732.8057 .. 773.7040 cents 40.89825 cents 34.97561 cents 13: 813.1480 .. 854.0463 cents 40.89825 cents 39.44405 cents 14: 852.5921 .. 893.4903 cents 40.89825 cents -1.45421 cents 15: 928.4659 .. 969.3642 cents 40.89825 cents 34.97561 cents 16: 1004.3398 .. 1045.2380 cents 40.89825 cents 34.97561 cents 17: 1043.7838 .. 1084.6821 cents 40.89825 cents -1.45421 cents 18: 1119.6577 .. 1160.5560 cents 40.89825 cents 34.97562 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 39.44404 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 80.34230 cents Average / Smallest step : 1.601202 Largest / Average step : 1.272086 Largest / Smallest step : 2.036868 Median interval of one step : 75.87387 cents, amount: 9 Most common interval of one step : 75.87387 cents, amount: 9 Least squares average step : 63.34101 cents, oct.: 1203.47925 cents Scale is not proper Step pattern alph. order: ABCABABACBAABACBABA Step pattern size order : MSLMSMSMLSMMSMLSMSM Scale is a Constant Structure, by a margin of 1.45421 cents Scale diversity : 1.224851 Lumma stability : 0.393797 Lumma impropriety factor : 0.007271 Number of different interval sizes : 60 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1.45421 cents Most common intervals : 386.85198 cents & inv., amount: 15 Most common triad is 0.0 386.852 813.148 cents, amount: 11 Number of recognisable fifths : 18, average 696.8371 cents Best minor thirds form a closed circle Formal octave complements present : 13 = 68.4211% Limited inverse transpositions with margin 40.8983 cents: 3 -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.3069 c. M: 21.9958 c. 29: 2 1 2 2 1 1 1 2 2 1 2 2 1 1 2 1 2 1 2 N D3 SD: 12.2944 c. M: 20.0564 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 P M ME S SD: 1.3674 c. M: 2.6014 c. 146: 9 5 10 9 5 9 5 9 10 5 9 9 5 9 10 5 9 5 9 P SD: 1.2822 c. M:-2.7013 c. 158: 10 5 11 10 5 10 5 10 11 5 10 10 5 10 11 5 10 5 10 N SD: 1.2684 c. M:-2.7877 c. 177: 11 6 12 11 6 11 6 11 12 6 11 11 6 11 12 6 11 6 11 P SD: 0.8402 c. M:-1.7726 c. 208: 13 7 14 13 7 13 7 13 14 7 13 13 7 13 14 7 13 7 13 P SD: 0.5436 c. M:-1.1207 c. 239: 15 8 16 15 8 15 8 15 16 8 15 15 8 15 16 8 15 8 15 P SD: 0.3512 c. M:-0.6379 c. 270: 17 9 18 17 9 17 9 17 18 9 17 17 9 17 18 9 17 9 17 P SD: 0.2592 c. M: 0.4753 c. 301: 19 10 20 19 10 19 10 19 20 10 19 19 10 19 20 10 19 10 19 P SD: 0.2647 c. M: 0.5934 c. 459: 29 15 31 29 15 29 15 29 31 15 29 29 15 29 31 15 29 15 29 N SD: 0.2727 c. M:-0.5705 c. 490: 31 16 33 31 16 31 16 31 33 16 31 31 16 31 33 16 31 16 31 N SD: 0.1932 c. M:-0.4317 c. 521: 33 17 35 33 17 33 17 33 35 17 33 33 17 33 35 17 33 17 33 N SD: 0.1469 c. M:-0.3095 c. 552: 35 18 37 35 18 35 18 35 37 18 35 35 18 35 37 18 35 18 35 N SD: 0.1443 c. M: 0.2171 c. 729: 46 24 49 46 24 46 24 46 49 24 46 46 24 46 49 24 46 24 46 N SD: 0.1433 c. M:-0.2660 c. 760: 48 25 51 48 25 48 25 48 51 25 48 48 25 48 51 25 48 25 48 N SD: 0.0818 c. M:-0.1490 c. 791: 50 26 53 50 26 50 26 50 53 26 50 50 26 50 53 26 50 26 50 N SD: 0.0256 c. M:-0.0416 c. 1613: 102 53 108 102 53 102 53 102 108 53 102 102 53 102 108 53 102 53 102 N SD: 0.0066 c. M:-0.0097 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.0624 cents 3 .. 6 match: 3 H SD: 2.0752 cents 4 .. 8 match: 4 H SD: 1.0486 cents 5 .. 10 match: 5 H SD: 1.9926 cents 6 .. 12 match: 6 H SD: 6.0667 cents 7 .. 14 match: 7 H SD: 7.7158 cents 8 .. 16 match: 8 H SD: 5.3345 cents 9 .. 18 match: 9 H SD: 5.2860 cents 10 .. 20 match: 10 H SD: 5.3665 cents 11 .. 22 match: 11 H SD: 7.3492 cents 12 .. 24 match: 12 H SD: 4.1998 cents 13 .. 26 match: 13 H SD: 6.4312 cents 14 .. 28 match: 13 SD: 4.8895 cents 15 .. 30 match: 15 H SD: 4.1279 cents 16 .. 32 match: 16 H SD: 4.0929 cents 17 .. 34 match: 14 SD: 4.7675 cents 18 .. 36 match: 15 S SD: 3.6314 cents 19 .. 38 match: 14 SD: 4.6714 cents 20 .. 40 match: 18 SD: 3.8511 cents 21 .. 42 match: 17 SD: 3.7764 cents 22 .. 44 match: 16 SD: 4.2924 cents 23 .. 46 match: 18 SD: 3.3877 cents 24 .. 48 match: 17 SD: 2.6040 cents 25 .. 50 match: 19 SD: 2.4129 cents 26 .. 52 match: 18 SD: 3.2547 cents 27 .. 54 match: 18 SD: 2.9304 cents 28 .. 56 match: 19 SD: 2.6666 cents 30 .. 60 match: 18 SD: 2.3159 cents 32 .. 64 match: 19 SD: 2.3066 cents 33 .. 66 match: 18 SD: 2.4950 cents 34 .. 68 match: 17 SD: 2.6866 cents 35 .. 70 match: 18 SD: 2.1243 cents 36 .. 72 match: 18 SD: 2.1338 cents 39 .. 78 match: 19 SD: 2.0118 cents 40 .. 80 match: 19 SD: 1.6924 cents 42 .. 84 match: 19 SD: 1.6556 cents 47 .. 94 match: 19 SD: 1.5192 cents 48 .. 96 match: 19 SD: 1.3949 cents 57 .. 114 match: 19 SD: 1.2470 cents 60 .. 120 match: 19 SD: 0.9544 cents 72 .. 144 match: 19 SD: 0.8698 cents 83 .. 166 match: 19 SD: 0.7771 cents 92 .. 184 match: 19 SD: 0.6650 cents 107 .. 214 match: 19 SD: 0.5775 cents 125 .. 250 match: 19 SD: 0.5754 cents 128 .. 256 match: 19 SD: 0.5454 cents 132 .. 264 match: 19 SD: 0.5405 cents 133 .. 266 match: 19 SD: 0.5049 cents 143 .. 286 match: 19 SD: 0.4675 cents 157 .. 314 match: 19 SD: 0.4191 cents 158 .. 316 match: 19 SD: 0.4189 cents 172 .. 344 match: 19 SD: 0.3935 cents 176 .. 352 match: 19 SD: 0.3581 cents 200 .. 400 match: 19 SD: 0.3026 cents 220 .. 440 match: 19 SD: 0.2958 cents 240 .. 480 match: 19 SD: 0.2855 cents 243 .. 486 match: 19 SD: 0.2463 cents 264 .. 528 match: 19 SD: 0.2434 cents 294 .. 588 match: 19 SD: 0.2297 cents 300 .. 600 match: 19 SD: 0.2194 cents 319 .. 638 match: 19 SD: 0.2141 cents 335 .. 670 match: 19 SD: 0.1719 cents 377 .. 754 match: 19 SD: 0.1513 cents 407 .. 814 match: 19 SD: 0.1488 cents 467 .. 934 match: 19 SD: 0.1338 cents 493 .. 986 match: 19 SD: 0.1325 cents 512 .. 1024 match: 19 SD: 0.1265 cents 520 .. 1040 match: 19 SD: 0.1222 cents 534 .. 1068 match: 19 SD: 0.1187 cents 535 .. 1070 match: 19 SD: 0.1177 cents 584 .. 1168 match: 19 SD: 0.1121 cents 594 .. 1188 match: 19 SD: 0.1101 cents 595 .. 1190 match: 19 SD: 0.1096 cents