Scala analysis: keenan5
11-limit with distrib 224:225 and 384:385, max err 2.7c, Dave Keenan 24-Dec-99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.601 cents 66.601065 2: 115.803 cents 115.802647 3: 151.994 cents 151.994179 4: 201.196 cents 201.195761 5: 231.605 cents 231.605294 6: 267.797 cents 267.796826 7: 316.998 cents 316.998408 8: 383.599 cents 383.599473 9: 432.801 cents 432.801054 10: 499.402 cents 499.402120 11: 584.795 cents 584.795233 12: 651.396 cents 651.396299 13: 700.598 cents 700.597880 14: 767.199 cents 767.198946 15: 816.401 cents 816.400527 16: 18/11 852.592059 undecimal neutral sixth 17: 883.002 cents 883.001592 18: 932.203 cents 932.203174 19: 968.395 cents 968.394706 20: 9/5 1017.596288 just minor seventh, BP seventh 21: 1084.197 cents 1084.197353 22: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 115.8026 cents 115.8026 1: 66.6011 cents 66.6011 2: 49.2016 cents 49.2016 3: 36.1915 cents 36.1915 4: 49.2016 cents 49.2016 5: 30.4095 cents 30.4095 6: 36.1915 cents 36.1915 7: 49.2016 cents 49.2016 8: 66.6011 cents 66.6011 9: 49.2016 cents 49.2016 10: 66.6011 cents 66.6011 11: 85.3931 cents 85.3931 12: 66.6011 cents 66.6011 13: 49.2016 cents 49.2016 14: 66.6011 cents 66.6011 15: 49.2016 cents 49.2016 16: 36.1915 cents 36.1915 17: 30.4095 cents 30.4095 18: 49.2016 cents 49.2016 19: 36.1915 cents 36.1915 20: 49.2016 cents 49.2016 21: 66.6011 cents 66.6011 22: 115.8026 cents 115.8026
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 30.40953 cents 1: 4 36.19153 cents 1: 8 49.20158 cents 1: 6 66.60107 cents 1: 1 85.39311 cents 1: 1 115.80265 cents 2: 2 66.60107 cents 2: 2 79.61111 cents 2: 6 85.39311 cents 2: 8 115.80265 cents 2: 2 151.99418 cents 2: 2 10/9 182.404 cents minor whole tone 3: 6 115.80265 cents 3: 2 134.59470 cents 3: 4 151.99418 cents 3: 2 165.00423 cents 3: 2 182.40371 cents 3: 2 201.19576 cents 3: 1 218.59524 cents 3: 2 231.60529 cents 3: 1 249.00478 cents 4: 2 151.99418 cents 4: 4 165.00423 cents 4: 2 182.40371 cents 4: 4 201.19576 cents 4: 2 231.60529 cents 4: 6 267.79683 cents 4: 2 298.20636 cents 5: 4 201.19576 cents 5: 6 231.60529 cents 5: 2 267.79683 cents 5: 5 316.99841 cents 5: 4 334.39789 cents 5: 1 347.40794 cents 6: 2 250.39734 cents 6: 4 267.79683 cents 6: 2 280.80688 cents 6: 2 298.20636 cents 6: 2 11/9 347.408 cents undecimal neutral third 6: 2 353.18994 cents 6: 8 383.59947 cents 7: 6 316.99841 cents 7: 2 347.40794 cents 7: 4 383.59947 cents 7: 2 414.00901 cents 7: 3 419.79100 cents 7: 4 432.80105 cents 7: 1 450.20054 cents 8: 2 366.19999 cents 8: 4 383.59947 cents 8: 4 432.80105 cents 8: 4 450.20054 cents 8: 2 463.21059 cents 8: 4 468.99259 cents 8: 2 499.40212 cents 9: 4 432.80105 cents 9: 2 468.99259 cents 9: 12 499.40212 cents 9: 1 518.19417 cents 9: 2 535.59365 cents 9: 1 548.60370 cents 10: 2 499.40212 cents 10: 2 518.19417 cents 10: 4 535.59365 cents 10: 8 548.60370 cents 10: 4 566.00318 cents 10: 2 584.79523 cents 11: 1 579.01323 cents 11: 10 584.79523 cents 11: 10 615.20477 cents 11: 1 620.98677 cents 12: 2 615.20477 cents 12: 4 633.99682 cents 12: 8 651.39630 cents 12: 4 664.40635 cents 12: 2 681.80583 cents 12: 2 700.59788 cents 13: 1 651.39630 cents 13: 2 664.40635 cents 13: 1 681.80583 cents 13: 12 700.59788 cents 13: 2 731.00741 cents 13: 4 767.19895 cents 14: 2 700.59788 cents 14: 4 731.00741 cents 14: 2 736.78941 cents 14: 4 749.79946 cents 14: 4 767.19895 cents 14: 4 816.40053 cents 14: 2 833.80001 cents 15: 1 749.79946 cents 15: 4 767.19895 cents 15: 3 780.20900 cents 15: 2 785.99099 cents 15: 4 816.40053 cents 15: 2 852.59206 cents 15: 6 883.00159 cents 16: 8 816.40053 cents 16: 2 846.81006 cents 16: 2 18/11 852.592 cents undecimal neutral sixth 16: 2 901.79364 cents 16: 2 919.19312 cents 16: 4 932.20317 cents 16: 2 949.60266 cents 17: 1 852.59206 cents 17: 4 865.60211 cents 17: 5 883.00159 cents 17: 2 932.20317 cents 17: 6 968.39471 cents 17: 4 998.80424 cents 18: 2 901.79364 cents 18: 6 932.20317 cents 18: 2 968.39471 cents 18: 4 998.80424 cents 18: 2 1017.59629 cents 18: 4 1034.99577 cents 18: 2 1048.00582 cents 19: 1 950.99522 cents 19: 2 968.39471 cents 19: 1 981.40476 cents 19: 2 998.80424 cents 19: 2 1017.59629 cents 19: 2 1034.99577 cents 19: 4 1048.00582 cents 19: 2 1065.40530 cents 19: 6 1084.19735 cents 20: 2 9/5 1017.596 cents just minor seventh, BP seventh 20: 2 1048.00582 cents 20: 8 1084.19735 cents 20: 6 1114.60689 cents 20: 2 1120.38889 cents 20: 2 1133.39893 cents 21: 1 1084.19735 cents 21: 1 1114.60689 cents 21: 6 1133.39893 cents 21: 8 1150.79842 cents 21: 4 1163.80847 cents 21: 2 1169.59047 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 6.57143 = 46/7
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 : 66.6 115.8 152.0 201.2 231.6 267.8 317.0 383.6 432.8 499.4 584.8 651.4 700.6 767.2 816.4 852.6 883.0 932.2 968.4 1017.6 1084.2 1200.0 66.6 : 49.2 85.4 134.6 165.0 201.2 250.4 317.0 366.2 432.8 518.2 584.8 634.0 700.6 749.8 786.0 816.4 865.6 901.8 951.0 1017.6 1133.4 1200.0 115.8 : 36.2 85.4 115.8 152.0 201.2 267.8 317.0 383.6 469.0 535.6 584.8 651.4 700.6 736.8 767.2 816.4 852.6 901.8 968.4 1084.2 1150.8 1200.0 152.0 : 49.2 79.6 115.8 165.0 231.6 280.8 347.4 432.8 499.4 548.6 615.2 664.4 700.6 731.0 780.2 816.4 865.6 932.2 1048.0 1114.6 1163.8 1200.0 201.2 : 30.4 66.6 115.8 182.4 231.6 298.2 383.6 450.2 499.4 566.0 615.2 651.4 681.8 731.0 767.2 816.4 883.0 998.8 1065.4 1114.6 1150.8 1200.0 231.6 : 36.2 85.4 152.0 201.2 267.8 353.2 419.8 469.0 535.6 584.8 621.0 651.4 700.6 736.8 786.0 852.6 968.4 1035.0 1084.2 1120.4 1169.6 1200.0 267.8 : 49.2 115.8 165.0 231.6 317.0 383.6 432.8 499.4 548.6 584.8 615.2 664.4 700.6 749.8 816.4 932.2 998.8 1048.0 1084.2 1133.4 1163.8 1200.0 317.0 : 66.6 115.8 182.4 267.8 334.4 383.6 450.2 499.4 535.6 566.0 615.2 651.4 700.6 767.2 883.0 949.6 998.8 1035.0 1084.2 1114.6 1150.8 1200.0 383.6 : 49.2 115.8 201.2 267.8 317.0 383.6 432.8 469.0 499.4 548.6 584.8 634.0 700.6 816.4 883.0 932.2 968.4 1017.6 1048.0 1084.2 1133.4 1200.0 432.8 : 66.6 152.0 218.6 267.8 334.4 383.6 419.8 450.2 499.4 535.6 584.8 651.4 767.2 833.8 883.0 919.2 968.4 998.8 1035.0 1084.2 1150.8 1200.0 499.4 : 85.4 152.0 201.2 267.8 317.0 353.2 383.6 432.8 469.0 518.2 584.8 700.6 767.2 816.4 852.6 901.8 932.2 968.4 1017.6 1084.2 1133.4 1200.0 584.8 : 66.6 115.8 182.4 231.6 267.8 298.2 347.4 383.6 432.8 499.4 615.2 681.8 731.0 767.2 816.4 846.8 883.0 932.2 998.8 1048.0 1114.6 1200.0 651.4 : 49.2 115.8 165.0 201.2 231.6 280.8 317.0 366.2 432.8 548.6 615.2 664.4 700.6 749.8 780.2 816.4 865.6 932.2 981.4 1048.0 1133.4 1200.0 700.6 : 66.6 115.8 152.0 182.4 231.6 267.8 317.0 383.6 499.4 566.0 615.2 651.4 700.6 731.0 767.2 816.4 883.0 932.2 998.8 1084.2 1150.8 1200.0 767.2 : 49.2 85.4 115.8 165.0 201.2 250.4 317.0 432.8 499.4 548.6 584.8 634.0 664.4 700.6 749.8 816.4 865.6 932.2 1017.6 1084.2 1133.4 1200.0 816.4 : 36.2 66.6 115.8 152.0 201.2 267.8 383.6 450.2 499.4 535.6 584.8 615.2 651.4 700.6 767.2 816.4 883.0 968.4 1035.0 1084.2 1150.8 1200.0 852.6 : 30.4 79.6 115.8 165.0 231.6 347.4 414.0 463.2 499.4 548.6 579.0 615.2 664.4 731.0 780.2 846.8 932.2 998.8 1048.0 1114.6 1163.8 1200.0 883.0 : 49.2 85.4 134.6 201.2 317.0 383.6 432.8 469.0 518.2 548.6 584.8 634.0 700.6 749.8 816.4 901.8 968.4 1017.6 1084.2 1133.4 1169.6 1200.0 932.2 : 36.2 85.4 152.0 267.8 334.4 383.6 419.8 469.0 499.4 535.6 584.8 651.4 700.6 767.2 852.6 919.2 968.4 1035.0 1084.2 1120.4 1150.8 1200.0 968.4 : 49.2 115.8 231.6 298.2 347.4 383.6 432.8 463.2 499.4 548.6 615.2 664.4 731.0 816.4 883.0 932.2 998.8 1048.0 1084.2 1114.6 1163.8 1200.0 1017.6: 66.6 182.4 249.0 298.2 334.4 383.6 414.0 450.2 499.4 566.0 615.2 681.8 767.2 833.8 883.0 949.6 998.8 1035.0 1065.4 1114.6 1150.8 1200.0 1084.2: 115.8 182.4 231.6 267.8 317.0 347.4 383.6 432.8 499.4 548.6 615.2 700.6 767.2 816.4 883.0 932.2 968.4 998.8 1048.0 1084.2 1133.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.4095 .. 115.8026 cents 85.39311 cents 30.40953 cents 2: 66.6011 .. 182.4037 cents 115.80265 cents -49.20158 cents 3: 115.8026 .. 249.0048 cents 133.20213 cents -66.60107 cents 4: 151.9942 .. 298.2064 cents 146.21218 cents -97.01060 cents 5: 201.1958 .. 347.4079 cents 146.21218 cents -97.01060 cents 6: 250.3973 .. 383.5995 cents 133.20213 cents -97.01060 cents 7: 316.9984 .. 450.2005 cents 133.20213 cents -66.60107 cents 8: 366.2000 .. 499.4021 cents 133.20213 cents -84.00055 cents 9: 432.8011 .. 548.6037 cents 115.80265 cents -66.60107 cents 10: 499.4021 .. 584.7952 cents 85.39311 cents -49.20158 cents 11: 579.0132 .. 620.9868 cents 41.97353 cents -5.78200 cents 12: 615.2048 .. 700.5979 cents 85.39311 cents -5.78200 cents 13: 651.3963 .. 767.1989 cents 115.80265 cents -49.20158 cents 14: 700.5979 .. 833.8000 cents 133.20213 cents -66.60107 cents 15: 749.7995 .. 883.0016 cents 133.20213 cents -84.00055 cents 16: 816.4005 .. 949.6027 cents 133.20213 cents -66.60107 cents 17: 852.5921 .. 998.8042 cents 146.21218 cents -97.01060 cents 18: 901.7936 .. 1048.0058 cents 146.21218 cents -97.01060 cents 19: 950.9952 .. 1084.1974 cents 133.20213 cents -97.01060 cents 20: 1017.5963 .. 1133.3989 cents 115.80265 cents -66.60107 cents 21: 1084.1974 .. 1169.5905 cents 85.39311 cents -49.20158 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 30.40953 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 115.80265 cents Average / Smallest step : 1.793696 Largest / Average step : 2.123049 Largest / Smallest step : 3.808103 Median interval of one step : 49.20158 cents, amount: 8 Most common interval of one step : 49.20158 cents, amount: 8 Least squares average step : 52.22572 cents, oct.: 1148.96574 cents Scale is not proper Step pattern alph. order: ABCBDCBABAEABABCDBCBAF Step pattern size order : DCBCABCDCDEDCDCBACBCDF Scale is not a Constant Structure Scale diversity : 1.344854 Lumma stability : 0.050683 Lumma impropriety factor : 0.812974 Number of different interval sizes : 76 = 3.61905 / class Number of one step interval sizes : 6 Highest interval variety : 9 Mean interval variety : 6.57143 = 46/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.39256 cents Number of recognisable fifths : 16, average 700.5979 cents Formal octave complements present : 15 = 68.1818% Limited inverse transpositions : 21 Inversional symmetry on intervals : 10-11 21-22 -- Rational properties -- Prime limit : 11 (not all pitches rational)
FIT/MODE
22: 1 1 1 1 0 1 1 1 1 1 2 1 1 1 1 1 0 1 1 1 1 2 N T3 SD: 10.5623 c. M:-20.1352 c. 30: 2 1 1 1 1 1 1 2 1 1 3 1 2 1 1 1 1 1 1 1 2 3 N SD: 11.6010 c. M: 19.4021 c. 31: 2 1 1 1 1 1 1 2 1 2 2 2 1 2 1 1 1 1 1 1 2 3 N SD: 5.4372 c. M: 11.1447 c. 41: 2 2 1 2 1 1 2 2 2 2 3 2 2 2 2 1 1 2 1 2 2 4 N SD: 4.4463 c. M: 8.0645 c. 53: 3 2 2 2 1 2 2 3 2 3 4 3 2 3 2 2 1 2 2 2 3 5 N SD: 3.5240 c. M:-7.7853 c. 72: 4 3 2 3 2 2 3 4 3 4 5 4 3 4 3 2 2 3 2 3 4 7 N SD: 1.1430 c. M: 2.5921 c. 125: 7 5 4 5 3 4 5 7 5 7 9 7 5 7 5 4 3 5 4 5 7 12 N SD: 0.8633 c. M:-1.8079 c. 166: 9 7 5 7 4 5 7 9 7 9 12 9 7 9 7 5 4 7 5 7 9 16 N SD: 0.7893 c. M:-1.6808 c. 197: 11 8 6 8 5 6 8 11 8 11 14 11 8 11 8 6 5 8 6 8 11 19 N SD: 0.2244 c. M:-0.4040 c. 435: 24 18 13 18 11 13 18 24 18 24 31 24 18 24 18 13 11 18 13 18 24 42 N SD: 0.2159 c. M: 0.3942 c. 466: 26 19 14 19 12 14 19 26 19 26 33 26 19 26 19 14 12 19 14 19 26 45 N SD: 0.2008 c. M: 0.4289 c. 560: 31 23 17 23 14 17 23 31 23 31 40 31 23 31 23 17 14 23 17 23 31 54 N SD: 0.1429 c. M:-0.2651 c. 632: 35 26 19 26 16 19 26 35 26 35 45 35 26 35 26 19 16 26 19 26 35 61 N SD: 0.0787 c. M: 0.1454 c. 829: 46 34 25 34 21 25 34 46 34 46 59 46 34 46 34 25 21 34 25 34 46 80 N SD: 0.0074 c. M:-0.0153 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.6786 cents 3 .. 6 match: 3 H SD: 0.6398 cents 4 .. 8 match: 4 H SD: 0.7663 cents 5 .. 10 match: 5 H SD: 0.7595 cents 6 .. 12 match: 6 H SD: 5.3112 cents 7 .. 14 match: 7 H SD: 5.4680 cents 8 .. 16 match: 8 H SD: 4.5063 cents 9 .. 18 match: 9 H SD: 5.2723 cents 10 .. 20 match: 10 H SD: 3.9460 cents 11 .. 22 match: 11 H SD: 5.7766 cents 12 .. 24 match: 11 S SD: 4.0340 cents 13 .. 26 match: 12 S SD: 5.5843 cents 14 .. 28 match: 13 S SD: 4.1717 cents 15 .. 30 match: 14 S SD: 3.1631 cents 16 .. 32 match: 15 S SD: 4.1347 cents 17 .. 34 match: 16 S SD: 4.0978 cents 18 .. 36 match: 16 S SD: 3.5588 cents 19 .. 38 match: 15 SD: 4.7246 cents 20 .. 40 match: 18 SD: 2.7101 cents 21 .. 42 match: 17 SD: 3.1081 cents 22 .. 44 match: 18 SD: 3.2676 cents 23 .. 46 match: 18 SD: 3.5128 cents 24 .. 48 match: 20 SD: 2.1068 cents 25 .. 50 match: 20 SD: 2.4136 cents 26 .. 52 match: 18 SD: 3.4011 cents 27 .. 54 match: 20 SD: 2.7499 cents 28 .. 56 match: 21 SD: 2.4372 cents 29 .. 58 match: 21 SD: 2.4764 cents 30 .. 60 match: 21 SD: 2.1874 cents 31 .. 62 match: 21 SD: 2.2771 cents 32 .. 64 match: 21 SD: 2.0792 cents 37 .. 74 match: 20 SD: 2.6222 cents 38 .. 76 match: 20 SD: 2.3821 cents 39 .. 78 match: 22 SD: 2.1987 cents 40 .. 80 match: 22 SD: 1.8633 cents 41 .. 82 match: 22 SD: 1.7395 cents 42 .. 84 match: 22 SD: 1.6339 cents 45 .. 90 match: 21 SD: 1.5511 cents 48 .. 96 match: 22 SD: 1.3399 cents 54 .. 108 match: 22 SD: 1.3164 cents 55 .. 110 match: 22 SD: 1.1482 cents 56 .. 112 match: 22 SD: 1.1187 cents 70 .. 140 match: 22 SD: 1.0271 cents 72 .. 144 match: 22 SD: 0.9472 cents 74 .. 148 match: 22 SD: 0.9255 cents 75 .. 150 match: 22 SD: 0.9143 cents 77 .. 154 match: 22 SD: 0.8896 cents 84 .. 168 match: 22 SD: 0.7254 cents 96 .. 192 match: 22 SD: 0.7141 cents 98 .. 196 match: 22 SD: 0.6862 cents 99 .. 198 match: 22 SD: 0.6416 cents 105 .. 210 match: 22 SD: 0.6061 cents 119 .. 238 match: 22 SD: 0.5885 cents 120 .. 240 match: 22 SD: 0.4837 cents 129 .. 258 match: 22 SD: 0.4772 cents 144 .. 288 match: 22 SD: 0.4374 cents 149 .. 298 match: 22 SD: 0.4305 cents 154 .. 308 match: 22 SD: 0.4071 cents 161 .. 322 match: 22 SD: 0.4014 cents 173 .. 346 match: 22 SD: 0.3837 cents 174 .. 348 match: 22 SD: 0.3728 cents 179 .. 358 match: 22 SD: 0.3631 cents 186 .. 372 match: 22 SD: 0.3376 cents 201 .. 402 match: 22 SD: 0.3338 cents 203 .. 406 match: 22 SD: 0.3065 cents 204 .. 408 match: 22 SD: 0.2758 cents 229 .. 458 match: 22 SD: 0.2755 cents 251 .. 502 match: 22 SD: 0.2411 cents 274 .. 548 match: 22 SD: 0.2308 cents 275 .. 550 match: 22 SD: 0.2284 cents 299 .. 598 match: 22 SD: 0.2099 cents 307 .. 614 match: 22 SD: 0.2044 cents 334 .. 668 match: 22 SD: 0.1947 cents 335 .. 670 match: 22 SD: 0.1517 cents 359 .. 718 match: 22 SD: 0.1490 cents 448 .. 896 match: 22 SD: 0.1355 cents 479 .. 958 match: 22 SD: 0.1262 cents 503 .. 1006 match: 22 SD: 0.1045 cents 592 .. 1184 match: 22 SD: 0.1014 cents