Scala analysis: xen05-wilson-scott
A Scale for Scott
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 16/15 111.731285 minor diatonic 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: 45/32 590.223716 diatonic tritone 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: 225/128 976.537429 augmented sixth 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 128/125 41.0589 minor diesis, diesis 3: 135/128 92.1787 major chroma, major limma 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: 135/128 92.1787 major chroma, major limma 10: 128/125 41.0589 minor diesis, 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: 135/128 92.1787 major chroma, major limma 16: 128/125 41.0589 minor diesis, diesis 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: 7 128/125 41.059 cents minor diesis, diesis 1: 9 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 135/128 92.179 cents major chroma, major limma 2: 11 16/15 111.731 cents minor diatonic semitone 2: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 3 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: 5 256/225 223.463 cents Neapolitan diminished third 4: 4 144/125 244.969 cents classic diminished third 4: 2 125/108 253.076 cents semi-augmented whole tone 4: 8 75/64 274.582 cents classic augmented second 5: 4 32/27 294.135 cents Pythagorean minor third 5: 12 6/5 315.641 cents minor third 5: 3 625/512 345.255 cents classic neutral third 6: 1 4096/3375 335.194 cents double diminished fourth 6: 3 768/625 356.700 cents 6: 15 5/4 386.314 cents major third 7: 11 32/25 427.373 cents classic diminished fourth 7: 6 125/96 456.986 cents classic augmented third 7: 2 675/512 478.492 cents wide augmented third 8: 14 4/3 498.045 cents perfect fourth 8: 4 27/20 519.551 cents acute fourth 8: 1 5625/4096 549.165 cents double augmented third 9: 5 512/375 539.104 cents double diminished fifth 9: 1 864/625 560.610 cents 9: 6 25/18 568.717 cents classic augmented fourth 9: 7 45/32 590.224 cents diatonic tritone 10: 7 64/45 609.776 cents 2nd tritone 10: 6 36/25 631.283 cents classic diminished fifth 10: 1 625/432 639.390 cents 10: 5 375/256 660.896 cents double augmented fourth 11: 1 8192/5625 650.835 cents double diminished sixth 11: 4 40/27 680.449 cents grave fifth 11: 14 3/2 701.955 cents perfect fifth 12: 2 1024/675 721.508 cents narrow diminished sixth 12: 6 192/125 743.014 cents classic diminished sixth 12: 11 25/16 772.627 cents classic augmented fifth 13: 15 8/5 813.686 cents minor sixth 13: 3 625/384 843.300 cents 13: 1 3375/2048 864.806 cents double augmented fifth 14: 3 1024/625 854.745 cents two (classic diminished fourth) 14: 12 5/3 884.359 cents major sixth, BP sixth 14: 4 27/16 905.865 cents Pythagorean major sixth 15: 8 128/75 925.418 cents diminished seventh 15: 2 216/125 946.924 cents semi-augmented sixth 15: 4 125/72 955.031 cents classic augmented sixth 15: 5 225/128 976.537 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: 3 2048/1125 1037.149 cents double diminished octave 17: 2 1152/625 1058.655 cents 17: 3 50/27 1066.762 cents grave major seventh 17: 11 15/8 1088.269 cents classic major seventh 18: 3 256/135 1107.821 cents octave - major chroma 18: 9 48/25 1129.328 cents classic diminished octave 18: 7 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 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 : 70.7 111.7 203.9 274.6 315.6 386.3 427.4 498.0 590.2 631.3 702.0 772.6 813.7 884.4 976.5 1017.6 1088.3 1129.3 1200.0 70.7 : 41.1 133.2 203.9 245.0 315.6 356.7 427.4 519.6 560.6 631.3 702.0 743.0 813.7 905.9 946.9 1017.6 1058.7 1129.3 1200.0 111.7 : 92.2 162.9 203.9 274.6 315.6 386.3 478.5 519.6 590.2 660.9 702.0 772.6 864.8 905.9 976.5 1017.6 1088.3 1158.9 1200.0 203.9 : 70.7 111.7 182.4 223.5 294.1 386.3 427.4 498.0 568.7 609.8 680.4 772.6 813.7 884.4 925.4 996.1 1066.8 1107.8 1200.0 274.6 : 41.1 111.7 152.8 223.5 315.6 356.7 427.4 498.0 539.1 609.8 702.0 743.0 813.7 854.7 925.4 996.1 1037.1 1129.3 1200.0 315.6 : 70.7 111.7 182.4 274.6 315.6 386.3 457.0 498.0 568.7 660.9 702.0 772.6 813.7 884.4 955.0 996.1 1088.3 1158.9 1200.0 386.3 : 41.1 111.7 203.9 245.0 315.6 386.3 427.4 498.0 590.2 631.3 702.0 743.0 813.7 884.4 925.4 1017.6 1088.3 1129.3 1200.0 427.4 : 70.7 162.9 203.9 274.6 345.3 386.3 457.0 549.2 590.2 660.9 702.0 772.6 843.3 884.4 976.5 1047.2 1088.3 1158.9 1200.0 498.0 : 92.2 133.2 203.9 274.6 315.6 386.3 478.5 519.6 590.2 631.3 702.0 772.6 813.7 905.9 976.5 1017.6 1088.3 1129.3 1200.0 590.2 : 41.1 111.7 182.4 223.5 294.1 386.3 427.4 498.0 539.1 609.8 680.4 721.5 813.7 884.4 925.4 996.1 1037.1 1107.8 1200.0 631.3 : 70.7 141.3 182.4 253.1 345.3 386.3 457.0 498.0 568.7 639.4 680.4 772.6 843.3 884.4 955.0 996.1 1066.8 1158.9 1200.0 702.0 : 70.7 111.7 182.4 274.6 315.6 386.3 427.4 498.0 568.7 609.8 702.0 772.6 813.7 884.4 925.4 996.1 1088.3 1129.3 1200.0 772.6 : 41.1 111.7 203.9 245.0 315.6 356.7 427.4 498.0 539.1 631.3 702.0 743.0 813.7 854.7 925.4 1017.6 1058.7 1129.3 1200.0 813.7 : 70.7 162.9 203.9 274.6 315.6 386.3 457.0 498.0 590.2 660.9 702.0 772.6 813.7 884.4 976.5 1017.6 1088.3 1158.9 1200.0 884.4 : 92.2 133.2 203.9 245.0 315.6 386.3 427.4 519.6 590.2 631.3 702.0 743.0 813.7 905.9 946.9 1017.6 1088.3 1129.3 1200.0 976.5 : 41.1 111.7 152.8 223.5 294.1 335.2 427.4 498.0 539.1 609.8 650.8 721.5 813.7 854.7 925.4 996.1 1037.1 1107.8 1200.0 1017.6: 70.7 111.7 182.4 253.1 294.1 386.3 457.0 498.0 568.7 609.8 680.4 772.6 813.7 884.4 955.0 996.1 1066.8 1158.9 1200.0 1088.3: 41.1 111.7 182.4 223.5 315.6 386.3 427.4 498.0 539.1 609.8 702.0 743.0 813.7 884.4 925.4 996.1 1088.3 1129.3 1200.0 1129.3: 70.7 141.3 182.4 274.6 345.3 386.3 457.0 498.0 568.7 660.9 702.0 772.6 843.3 884.4 955.0 1047.2 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 .. 345.2549 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 6: 335.1939 .. 386.3137 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 7: 427.3726 .. 478.4924 cents 16875/16384, 51.1199 cents 128/125, 41.0589 cents 8: 498.0450 .. 549.1649 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 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 .. 701.9550 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 cents 12: 721.5076 .. 772.6274 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 13: 813.6863 .. 864.8061 cents 16875/16384, 51.1199 cents 128/125, 41.0589 cents 14: 854.7451 .. 905.8650 cents 16875/16384, 51.1199 cents 2097152/2109375,-10.0610 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: 9 Most common interval of one step : 25/24, 70.6724 cents, amount: 9 Least squares average step : 63.56726 cents, oct.: 1207.77796 cents Scale is not proper Step pattern alph. order: ABCABABACBAABACBABA Step pattern size order : MSLMSMSMLSMMSMLSMSM Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.339973 Lumma stability : 0.283507 Lumma impropriety factor : 0.050305 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 : 15625/15552, 8.1073 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 15 Most common triad is 0.0 386.314 813.686 cents, amount: 11 Number of recognisable fifths : 14, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 5 15 25 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 13 = 68.4211% Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 5 Odd number limit : 5625 (O: 5625 U: 5625) Highest odd numerator or denominator: 225 Scale harmonicity : 0.021930 Average absolute harmonicity : 0.142301 Specific harmonicity : 0.119755 Fundamental : 1/9600, -13.2288 octaves, 0.0273 Hz. Guide tone : 7200, 12.8138 octaves, 1883704.070 Hz. Exponens Consonantiae : 6.912000E+07, 26.04260 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 495.5, average 26.07895 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.88095, average 1.09900 Sum of Tenney's harmonic distance : 41.30032, average 2.17370 Vogel's harmonic complexity : 21.63158 Wille's k value : 8437 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 913.51644, average 4.80798 Lattice compactness (without 2's) : 433.63531, average 2.28229 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 5 -0.63158 56 1 3: -1 .. 2 0.57895 19 3 5: -2 .. 2 0.10526 22 15 Average exponent except 2's : 13 / 19 = 0.68421 Average absolute exponent except 2's: 41 / 19 = 2.15789 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: 13.0822 c. M: 29.1690 c. 20: 1 1 1 2 0 1 1 1 2 1 1 1 1 1 1 1 1 1 1 N D3 SD: 16.8833 c. M:-28.7174 c. 22: 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 P M ME S SD: 11.0801 c. M:-23.2629 c. 26: 2 0 2 2 1 1 1 2 2 1 1 2 1 1 2 1 2 0 2 N T3 SD: 13.7865 c. M:-21.6353 c. 28: 2 1 2 1 1 2 1 2 2 1 1 2 1 2 2 1 1 1 2 N D3 SD: 12.3248 c. M: 17.4396 c. 30: 2 1 2 2 1 2 1 1 3 1 2 1 1 2 2 1 2 1 2 N D3 SD: 11.4544 c. M:-18.0450 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: 6.5562 c. M: 11.9277 c. 34: 2 1 3 2 1 2 1 2 3 1 2 2 1 2 3 1 2 1 2 N T3 SD: 5.3805 c. M:-11.6979 c. 52: 3 2 4 3 2 3 2 3 4 1 3 3 2 3 4 2 3 2 3 P SD: 6.8300 c. M:-11.0890 c. 53: 3 2 4 3 2 3 2 3 4 2 3 3 2 3 4 2 3 2 3 P T3 SD: 1.9348 c. M: 2.9525 c. 87: 5 3 7 5 3 5 3 5 7 3 5 5 3 5 7 3 5 3 5 N T3 SD: 1.8598 c. M:-3.2002 c. 118: 7 4 9 7 4 7 4 7 9 4 7 7 4 7 9 4 7 4 7 N SD: 0.3752 c. M: 0.7741 c. 289: 17 10 22 17 10 17 10 17 22 10 17 17 10 17 22 10 17 10 17 N SD: 0.3393 c. M: 0.7589 c. 323: 19 11 25 19 11 19 11 19 25 11 19 19 11 19 25 11 19 11 19 N SD: 0.2713 c. M:-0.5524 c. 441: 26 15 34 26 15 26 15 26 34 15 26 26 15 26 34 15 26 15 26 N SD: 0.1489 c. M:-0.3333 c. 494: 29 17 38 29 17 29 17 29 38 17 29 29 17 29 38 17 29 17 29 N SD: 0.1424 c. M:-0.2964 c. 559: 33 19 43 33 19 33 19 33 43 19 33 33 19 33 43 19 33 19 33 N SD: 0.1247 c. M:-0.2068 c. 612: 36 21 47 36 21 36 21 36 47 21 36 36 21 36 47 21 36 21 36 N SD: 0.0549 c. M:-0.0900 c. 730: 43 25 56 43 25 43 25 43 56 25 43 43 25 43 56 25 43 25 43 N SD: 0.0480 c. M: 0.0991 c. 1171: 69 40 90 69 40 69 40 69 90 40 69 69 40 69 90 40 69 40 69 N SD: 0.0326 c. M:-0.0638 c. 1783: 105 61 137 105 61 105 61 105 137 61 105 105 61 105 137 61 105 61 105 N SD: 0.0099 c. M:-0.0189 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: 1.9279 cents 5 .. 10 match: 5 H SD: 1.5423 cents 6 .. 12 match: 6 H SD: 5.4482 cents 7 .. 14 match: 7 H SD: 8.1430 cents 8 .. 16 match: 8 H SD: 5.9864 cents 9 .. 18 match: 9 H SD: 5.0980 cents 10 .. 20 match: 10 H SD: 6.1624 cents 11 .. 22 match: 11 H SD: 7.2339 cents 12 .. 24 match: 12 H SD: 4.0393 cents 13 .. 26 match: 13 H SD: 6.3311 cents 14 .. 28 match: 13 SD: 4.6494 cents 15 .. 30 match: 15 H SD: 3.8971 cents 16 .. 32 match: 15 SD: 3.5022 cents 17 .. 34 match: 15 S SD: 4.4593 cents 18 .. 36 match: 16 S SD: 3.7438 cents 19 .. 38 match: 14 SD: 5.3157 cents 20 .. 40 match: 16 SD: 3.7106 cents 21 .. 42 match: 16 SD: 3.6336 cents 22 .. 44 match: 16 SD: 3.3001 cents 23 .. 46 match: 18 SD: 3.6703 cents 24 .. 48 match: 18 SD: 2.6497 cents 25 .. 50 match: 19 SD: 2.4381 cents 26 .. 52 match: 17 SD: 3.3524 cents 27 .. 54 match: 18 SD: 3.0302 cents 28 .. 56 match: 19 SD: 2.9165 cents 29 .. 58 match: 19 SD: 2.5881 cents 30 .. 60 match: 18 SD: 1.8992 cents 32 .. 64 match: 18 SD: 2.0729 cents 36 .. 72 match: 18 SD: 2.1998 cents 37 .. 74 match: 18 SD: 2.5993 cents 39 .. 78 match: 19 SD: 1.9533 cents 40 .. 80 match: 19 SD: 1.7491 cents 45 .. 90 match: 19 SD: 1.5814 cents 46 .. 92 match: 19 SD: 1.5004 cents 48 .. 96 match: 19 SD: 1.4214 cents 57 .. 114 match: 19 SD: 1.2613 cents 64 .. 128 match: 19 SD: 0.9769 cents 71 .. 142 match: 19 SD: 0.9576 cents 75 .. 150 match: 19 SD: 0.8239 cents 89 .. 178 match: 19 SD: 0.8046 cents 96 .. 192 match: 19 SD: 0.6775 cents 104 .. 208 match: 19 SD: 0.6394 cents 120 .. 240 match: 19 SD: 0.4786 cents 135 .. 270 match: 19 SD: 0.4693 cents 150 .. 300 match: 19 SD: 0.3907 cents 168 .. 336 match: 19 SD: 0.3616 cents 192 .. 384 match: 19 SD: 0.3266 cents 210 .. 420 match: 19 SD: 0.2961 cents 239 .. 478 match: 19 SD: 0.2670 cents 240 .. 480 match: 19 SD: 0.2042 cents 315 .. 630 match: 19 SD: 0.2015 cents 336 .. 672 match: 19 SD: 0.1880 cents 360 .. 720 match: 19 SD: 0.1313 cents 450 .. 900 match: 19 SD: 0.1273 cents 480 .. 960 match: 19 SD: 0.1143 cents 576 .. 1152 match: 19 SD: 0.1081 cents 600 .. 1200 match: 19 SD: 0.0639 cents