Scala analysis: cw19_5
CalkinWilf(<19 30 44|)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 9/8 203.910002 major whole tone 4: 75/64 274.582429 classic augmented second 5: 6/5 315.641287 minor third 6: 5/4 386.313714 major third 7: 32/25 427.372572 classic diminished fourth 8: 4/3 498.044999 perfect fourth 9: 25/18 568.717426 classic augmented fourth 10: 36/25 631.282574 classic diminished fifth 11: 3/2 701.955001 perfect fifth 12: 25/16 772.627428 classic augmented fifth 13: 8/5 813.686286 minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 128/75 925.417571 diminished seventh 16: 9/5 1017.596288 just minor seventh, BP seventh 17: 15/8 1088.268715 classic major seventh 18: 48/25 1129.327573 classic diminished octave 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 135/128 92.1787 major chroma, major limma 2: 128/125 41.0589 minor diesis, diesis 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 128/125 41.0589 minor diesis, diesis 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 128/125 41.0589 minor diesis, diesis 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 648/625 62.5651 major diesis 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 25/24 70.6724 classic chromatic semitone, minor chroma 13: 128/125 41.0589 minor diesis, diesis 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 128/125 41.0589 minor diesis, diesis 16: 135/128 92.1787 major chroma, major limma 17: 25/24 70.6724 classic chromatic semitone, minor chroma 18: 128/125 41.0589 minor diesis, diesis 19: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 128/125 41.059 cents minor diesis, diesis 1: 1 648/625 62.565 cents major diesis 1: 10 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 135/128 92.179 cents major chroma, major limma 2: 10 16/15 111.731 cents minor diatonic semitone 2: 4 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 3 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 2 1125/1024 162.851 cents double augmented prime 3: 2 2048/1875 152.790 cents double diminished third 3: 8 10/9 182.404 cents minor whole tone 3: 9 9/8 203.910 cents major whole tone 4: 4 256/225 223.463 cents Neapolitan diminished third 4: 5 144/125 244.969 cents classic diminished third 4: 3 125/108 253.076 cents semi-augmented whole tone 4: 7 75/64 274.582 cents classic augmented second 5: 5 32/27 294.135 cents Pythagorean minor third 5: 11 6/5 315.641 cents minor third 5: 2 625/512 345.255 cents classic neutral third 5: 1 10125/8192 366.761 cents double augmented second 6: 1 4096/3375 335.194 cents double diminished fourth 6: 3 768/625 356.700 cents 6: 2 100/81 364.807 cents grave major third 6: 11 5/4 386.314 cents major third 6: 2 81/64 407.820 cents Pythagorean major third 7: 1 512/405 405.866 cents narrow diminished fourth 7: 8 32/25 427.373 cents classic diminished fourth 7: 1 625/486 435.480 cents 7: 2 162/125 448.879 cents 7: 5 125/96 456.986 cents classic augmented third 7: 2 675/512 478.492 cents wide augmented third 8: 1 320/243 476.539 cents grave fourth 8: 12 4/3 498.045 cents perfect fourth 8: 5 27/20 519.551 cents acute fourth 8: 1 5625/4096 549.165 cents double augmented third 9: 4 512/375 539.104 cents double diminished fifth 9: 2 864/625 560.610 cents 9: 7 25/18 568.717 cents classic augmented fourth 9: 6 45/32 590.224 cents diatonic tritone 10: 6 64/45 609.776 cents 2nd tritone 10: 7 36/25 631.283 cents classic diminished fifth 10: 2 625/432 639.390 cents 10: 4 375/256 660.896 cents double augmented fourth 11: 1 8192/5625 650.835 cents double diminished sixth 11: 5 40/27 680.449 cents grave fifth 11: 12 3/2 701.955 cents perfect fifth 11: 1 243/160 723.461 cents acute fifth 12: 2 1024/675 721.508 cents narrow diminished sixth 12: 5 192/125 743.014 cents classic diminished sixth 12: 2 125/81 751.121 cents 12: 1 972/625 764.520 cents 12: 8 25/16 772.627 cents classic augmented fifth 12: 1 405/256 794.134 cents wide augmented fifth 13: 2 128/81 792.180 cents Pythagorean minor sixth 13: 11 8/5 813.686 cents minor sixth 13: 2 81/50 835.193 cents acute minor sixth 13: 3 625/384 843.300 cents 13: 1 3375/2048 864.806 cents double augmented fifth 14: 1 16384/10125 833.239 cents double diminished seventh 14: 2 1024/625 854.745 cents two (classic diminished fourth) 14: 11 5/3 884.359 cents major sixth, BP sixth 14: 5 27/16 905.865 cents Pythagorean major sixth 15: 7 128/75 925.418 cents diminished seventh 15: 3 216/125 946.924 cents semi-augmented sixth 15: 5 125/72 955.031 cents classic augmented sixth 15: 4 225/128 976.537 cents augmented sixth 16: 9 16/9 996.090 cents Pythagorean minor seventh 16: 8 9/5 1017.596 cents just minor seventh, BP seventh 16: 2 1875/1024 1047.210 cents double augmented sixth 17: 2 2048/1125 1037.149 cents double diminished octave 17: 3 1152/625 1058.655 cents 17: 4 50/27 1066.762 cents grave major seventh 17: 10 15/8 1088.269 cents classic major seventh 18: 2 256/135 1107.821 cents octave - major chroma 18: 10 48/25 1129.328 cents classic diminished octave 18: 1 625/324 1137.435 cents octave - major diesis 18: 6 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.22222 = 38/9
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 : 92.2 133.2 203.9 274.6 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 925.4 1017.6 1088.3 1129.3 1200.0 92.2 : 41.1 111.7 182.4 223.5 294.1 335.2 405.9 476.5 539.1 609.8 680.4 721.5 792.2 833.2 925.4 996.1 1037.1 1107.8 1200.0 133.2 : 70.7 141.3 182.4 253.1 294.1 364.8 435.5 498.0 568.7 639.4 680.4 751.1 792.2 884.4 955.0 996.1 1066.8 1158.9 1200.0 203.9 : 70.7 111.7 182.4 223.5 294.1 364.8 427.4 498.0 568.7 609.8 680.4 721.5 813.7 884.4 925.4 996.1 1088.3 1129.3 1200.0 274.6 : 41.1 111.7 152.8 223.5 294.1 356.7 427.4 498.0 539.1 609.8 650.8 743.0 813.7 854.7 925.4 1017.6 1058.7 1129.3 1200.0 315.6 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 498.0 568.7 609.8 702.0 772.6 813.7 884.4 976.5 1017.6 1088.3 1158.9 1200.0 386.3 : 41.1 111.7 182.4 245.0 315.6 386.3 427.4 498.0 539.1 631.3 702.0 743.0 813.7 905.9 946.9 1017.6 1088.3 1129.3 1200.0 427.4 : 70.7 141.3 203.9 274.6 345.3 386.3 457.0 498.0 590.2 660.9 702.0 772.6 864.8 905.9 976.5 1047.2 1088.3 1158.9 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 427.4 519.6 590.2 631.3 702.0 794.1 835.2 905.9 976.5 1017.6 1088.3 1129.3 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 356.7 448.9 519.6 560.6 631.3 723.5 764.5 835.2 905.9 946.9 1017.6 1058.7 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 294.1 386.3 457.0 498.0 568.7 660.9 702.0 772.6 843.3 884.4 955.0 996.1 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 223.5 315.6 386.3 427.4 498.0 590.2 631.3 702.0 772.6 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 152.8 245.0 315.6 356.7 427.4 519.6 560.6 631.3 702.0 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 111.7 203.9 274.6 315.6 386.3 478.5 519.6 590.2 660.9 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 41.1 133.2 203.9 245.0 315.6 407.8 448.9 519.6 590.2 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 925.4 : 92.2 162.9 203.9 274.6 366.8 407.8 478.5 549.2 590.2 660.9 702.0 772.6 843.3 905.9 976.5 1047.2 1088.3 1158.9 1200.0 1017.6: 70.7 111.7 182.4 274.6 315.6 386.3 457.0 498.0 568.7 609.8 680.4 751.1 813.7 884.4 955.0 996.1 1066.8 1107.8 1200.0 1088.3: 41.1 111.7 203.9 245.0 315.6 386.3 427.4 498.0 539.1 609.8 680.4 743.0 813.7 884.4 925.4 996.1 1037.1 1129.3 1200.0 1129.3: 70.7 162.9 203.9 274.6 345.3 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 996.1 1088.3 1158.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 92.1787 cents 16875/16384, 51.1199 cents 128/125, 41.0589 cents 2: 111.7313 .. 162.8511 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 3: 152.7901 .. 203.9100 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 4: 223.4626 .. 274.5824 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 5: 294.1350 .. 366.7611 cents 273375/262144, 72.6261 cents 2048/2025, 19.5526 cents 6: 335.1939 .. 407.8200 cents 273375/262144, 72.6261 cents 33554432/34171875,-31.5673 cents 7: 405.8663 .. 478.4924 cents 273375/262144, 72.6261 cents 32768/32805,-1.9537 cents 8: 476.5387 .. 549.1649 cents 273375/262144, 72.6261 cents 32768/32805,-1.9537 cents 9: 539.1039 .. 590.2237 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 10: 609.7763 .. 660.8961 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 11: 650.8351 .. 723.4613 cents 273375/262144, 72.6261 cents 2097152/2109375,-10.0610 cents 12: 721.5076 .. 794.1337 cents 273375/262144, 72.6261 cents 32768/32805,-1.9537 cents 13: 792.1800 .. 864.8061 cents 273375/262144, 72.6261 cents 32768/32805,-1.9537 cents 14: 833.2389 .. 905.8650 cents 273375/262144, 72.6261 cents 33554432/34171875,-31.5673 cents 15: 925.4176 .. 976.5374 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 16: 996.0900 .. 1047.2099 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 17: 1037.1489 .. 1088.2687 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 18: 1107.8213 .. 1158.9411 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 135/128, 92.1787 cents Average / Smallest step : 1.538228 Largest / Average step : 1.459496 Largest / Smallest step : 2.245038 Median interval of one step : 25/24, 70.6724 cents, amount: 10 Most common interval of one step : 25/24, 70.6724 cents, amount: 10 Least squares average step : 63.20457 cents, oct.: 1200.88692 cents Scale is not proper Step pattern alph. order: ABCCBCBCCDCCBCBACBC Step pattern size order : DACCACACCBCCACADCAC Scale is a Constant Structure, by a margin of 1.95372 cents Scale diversity : 1.402261 Lumma stability : 0.182488 Lumma impropriety factor : 0.092661 Number of different interval sizes : 76 = 4.22222 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.22222 = 38/9 Median interval variety : 3.5 Lowest interval variety : 3 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 12 Most common triad is 0.0 498.045 701.955 cents, amount: 7 Number of recognisable fifths : 12, average 701.9550 cents Scale contains a complete diamond : 1 3 5 Formal octave complements present : 13 = 68.4211% Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 10125 (O: 10125 U: 10125) Highest odd numerator or denominator: 135 Scale harmonicity : 0.018892 Average absolute harmonicity : 0.140267 Specific harmonicity : 0.112574 Fundamental : 1/28800, -14.8138 octaves, 0.0091 Hz. Guide tone : 86400, 16.3987 octaves, 22604448.842 Hz. Exponens Consonantiae : 2.488320E+09, 31.21252 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 521.0, average 27.42105 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 21.13622, average 1.11243 Sum of Tenney's harmonic distance : 42.22654, average 2.22245 Vogel's harmonic complexity : 24.00000 Wille's k value : 15187 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 948.15537, average 4.99029 Lattice compactness (without 2's) : 479.91051, average 2.52584 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 7 -0.10526 52 1 3: -2 .. 3 0.63158 22 3 5: -2 .. 2 -0.15789 23 15 Average exponent except 2's : 9 / 19 = 0.47368 Average absolute exponent except 2's: 45 / 19 = 2.36842 Scale is JI-epimorphic with val: <19 30 44| = patent
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: 12.6250 c. M: 29.0208 c. 20: 2 0 1 2 0 1 1 1 1 2 1 1 1 1 0 2 1 1 1 N SD: 19.5805 c. M:-28.7174 c. 22: 2 0 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 N D3 SD: 13.2898 c. M: 24.1467 c. 25: 2 1 1 2 1 1 1 1 2 1 2 1 1 1 1 2 2 1 1 N D3 SD: 12.8263 c. M:-22.6724 c. 26: 2 1 1 2 1 1 1 2 1 2 1 2 1 1 1 2 2 0 2 N D3 SD: 12.2923 c. M: 21.6353 c. 27: 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 N D3 SD: 11.7469 c. M: 21.6020 c. 30: 2 1 2 2 1 1 1 2 2 2 1 2 1 2 1 2 2 1 2 N SD: 13.8576 c. M: 27.3726 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P M ME I SD: 8.1065 c. M: 17.1085 c. 34: 3 1 2 2 1 2 1 2 2 2 2 2 1 2 1 3 2 1 2 N SD: 5.6694 c. M:-13.7036 c. 43: 3 2 2 3 1 3 1 3 2 3 2 3 1 3 1 3 3 1 3 N SD: 7.8317 c. M: 13.0485 c. 46: 4 1 3 3 1 3 1 3 3 2 3 3 1 3 2 3 3 1 3 N SD: 7.1087 c. M:-13.7129 c. 48: 4 1 3 3 2 2 2 3 3 2 3 3 2 2 2 4 3 1 3 N SD: 6.8243 c. M:-11.7313 c. 49: 4 1 3 3 2 3 1 3 3 3 3 3 1 3 2 4 2 2 3 N SD: 7.3493 c. M: 11.0460 c. 51: 4 2 3 3 1 3 2 3 3 3 3 3 2 3 1 4 3 2 3 N SD: 6.4689 c. M: 9.8431 c. 53: 4 2 3 3 2 3 2 3 3 3 3 3 2 3 2 4 3 2 3 N SD: 1.9896 c. M: 2.8843 c. 118: 9 4 7 7 4 7 4 7 7 6 7 7 4 7 4 9 7 4 7 N SD: 0.4736 c. M: 1.0342 c. 171: 13 6 10 10 6 10 6 10 10 9 10 10 6 10 6 13 10 6 10 N SD: 0.5003 c. M: 0.9506 c. 289: 22 10 17 17 10 17 10 17 17 15 17 17 10 17 10 22 17 10 17 N SD: 0.3419 c. M: 0.8292 c. 323: 25 11 19 19 11 19 11 19 19 17 19 19 11 19 11 25 19 11 19 N SD: 0.3013 c. M:-0.7005 c. 388: 30 13 23 23 13 23 13 23 23 20 23 23 13 23 13 30 23 13 23 N SD: 0.3908 c. M: 0.6753 c. 407: 31 14 24 24 14 24 14 24 24 21 24 24 14 24 14 31 24 14 24 N SD: 0.3338 c. M: 0.7782 c. 441: 34 15 26 26 15 26 15 26 26 23 26 26 15 26 15 34 26 15 26 N SD: 0.1447 c. M:-0.3383 c. 559: 43 19 33 33 19 33 19 33 33 29 33 33 19 33 19 43 33 19 33 N SD: 0.1255 c. M: 0.1940 c. 612: 47 21 36 36 21 36 21 36 36 32 36 36 21 36 21 47 36 21 36 N SD: 0.0593 c. M:-0.0958 c. 730: 56 25 43 43 25 43 25 43 43 38 43 43 25 43 25 56 43 25 43 N SD: 0.0528 c. M: 0.1239 c. 1171: 90 40 69 69 40 69 40 69 69 61 69 69 40 69 40 90 69 40 69 N SD: 0.0314 c. M: 0.0546 c. 1783: 137 61 105 105 61 105 61 105 105 93 105 105 61 105 61 137 105 61 105 N SD: 0.0114 c. M:-0.0254 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 0.0000 cents 4 .. 8 match: 4 H SD: 10.8521 cents 5 .. 10 match: 5 H SD: 2.7590 cents 6 .. 12 match: 6 H SD: 5.4482 cents 7 .. 14 match: 7 H SD: 5.3915 cents 8 .. 16 match: 8 H SD: 6.7401 cents 9 .. 18 match: 9 H SD: 5.1942 cents 10 .. 20 match: 10 H SD: 4.7900 cents 11 .. 22 match: 11 H SD: 5.8404 cents 12 .. 24 match: 11 S SD: 4.2974 cents 13 .. 26 match: 13 H SD: 6.0141 cents 14 .. 28 match: 14 H SD: 4.4284 cents 15 .. 30 match: 15 H SD: 4.2485 cents 16 .. 32 match: 15 SD: 3.6758 cents 17 .. 34 match: 15 SD: 4.7448 cents 18 .. 36 match: 17 S SD: 3.2888 cents 19 .. 38 match: 14 SD: 5.3677 cents 20 .. 40 match: 17 S SD: 3.9549 cents 21 .. 42 match: 18 S SD: 3.5782 cents 22 .. 44 match: 17 SD: 3.7728 cents 23 .. 46 match: 18 SD: 3.1464 cents 24 .. 48 match: 18 SD: 2.5629 cents 26 .. 52 match: 18 SD: 3.4277 cents 27 .. 54 match: 18 SD: 3.4977 cents 28 .. 56 match: 18 SD: 2.9675 cents 29 .. 58 match: 18 SD: 3.0095 cents 30 .. 60 match: 17 SD: 2.2466 cents 31 .. 62 match: 18 SD: 2.7801 cents 32 .. 64 match: 18 SD: 2.5331 cents 34 .. 68 match: 19 SD: 2.2850 cents 35 .. 70 match: 19 SD: 2.1778 cents 36 .. 72 match: 19 SD: 1.8246 cents 39 .. 78 match: 19 SD: 1.5914 cents 48 .. 96 match: 19 SD: 1.4219 cents 54 .. 108 match: 19 SD: 1.3153 cents 57 .. 114 match: 19 SD: 1.2898 cents 60 .. 120 match: 19 SD: 1.2662 cents 64 .. 128 match: 19 SD: 0.9916 cents 72 .. 144 match: 19 SD: 0.9122 cents 75 .. 150 match: 19 SD: 0.7176 cents 96 .. 192 match: 19 SD: 0.7093 cents 105 .. 210 match: 19 SD: 0.6475 cents 110 .. 220 match: 19 SD: 0.6080 cents 111 .. 222 match: 19 SD: 0.5634 cents 126 .. 252 match: 19 SD: 0.5514 cents 128 .. 256 match: 19 SD: 0.5058 cents 144 .. 288 match: 19 SD: 0.4763 cents 150 .. 300 match: 19 SD: 0.3909 cents 175 .. 350 match: 19 SD: 0.3891 cents 185 .. 370 match: 19 SD: 0.3437 cents 200 .. 400 match: 19 SD: 0.2788 cents 239 .. 478 match: 19 SD: 0.2691 cents 240 .. 480 match: 19 SD: 0.2144 cents 327 .. 654 match: 19 SD: 0.2082 cents 336 .. 672 match: 19 SD: 0.1781 cents 350 .. 700 match: 19 SD: 0.1679 cents 360 .. 720 match: 19 SD: 0.1607 cents 384 .. 768 match: 19 SD: 0.1564 cents 400 .. 800 match: 19 SD: 0.1253 cents 489 .. 978 match: 19 SD: 0.1245 cents 512 .. 1024 match: 19 SD: 0.1148 cents 528 .. 1056 match: 19 SD: 0.1129 cents 560 .. 1120 match: 19 SD: 0.1117 cents 576 .. 1152 match: 19 SD: 0.1092 cents 600 .. 1200 match: 19 SD: 0.0684 cents