Scala analysis: xen07-chalmers-wurschmidt-1
Wurschmidt-1
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: 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: 16/9 996.089998 Pythagorean minor 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: 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: 25/24 70.6724 classic chromatic semitone, minor chroma 17: 135/128 92.1787 major chroma, major limma 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: 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: 4 768/625 356.700 cents 6: 2 100/81 364.807 cents grave major third 6: 12 5/4 386.314 cents major third 6: 1 81/64 407.820 cents Pythagorean 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: 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: 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: 1 128/81 792.180 cents Pythagorean minor sixth 13: 12 8/5 813.686 cents minor sixth 13: 2 81/50 835.193 cents acute minor sixth 13: 4 625/384 843.300 cents 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: 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: 4 Average number of different intervals per interval class: 3.55556 = 32/9
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 : 70.7 111.7 203.9 274.6 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 925.4 996.1 1088.3 1129.3 1200.0 70.7 : 41.1 133.2 203.9 245.0 315.6 356.7 427.4 498.0 560.6 631.3 702.0 743.0 813.7 854.7 925.4 1017.6 1058.7 1129.3 1200.0 111.7 : 92.2 162.9 203.9 274.6 315.6 386.3 457.0 519.6 590.2 660.9 702.0 772.6 813.7 884.4 976.5 1017.6 1088.3 1158.9 1200.0 203.9 : 70.7 111.7 182.4 223.5 294.1 364.8 427.4 498.0 568.7 609.8 680.4 721.5 792.2 884.4 925.4 996.1 1066.8 1107.8 1200.0 274.6 : 41.1 111.7 152.8 223.5 294.1 356.7 427.4 498.0 539.1 609.8 650.8 721.5 813.7 854.7 925.4 996.1 1037.1 1129.3 1200.0 315.6 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 498.0 568.7 609.8 680.4 772.6 813.7 884.4 955.0 996.1 1088.3 1158.9 1200.0 386.3 : 41.1 111.7 182.4 245.0 315.6 386.3 427.4 498.0 539.1 609.8 702.0 743.0 813.7 884.4 925.4 1017.6 1088.3 1129.3 1200.0 427.4 : 70.7 141.3 203.9 274.6 345.3 386.3 457.0 498.0 568.7 660.9 702.0 772.6 843.3 884.4 976.5 1047.2 1088.3 1158.9 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 427.4 498.0 590.2 631.3 702.0 772.6 813.7 905.9 976.5 1017.6 1088.3 1129.3 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 356.7 427.4 519.6 560.6 631.3 702.0 743.0 835.2 905.9 946.9 1017.6 1058.7 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 294.1 364.8 457.0 498.0 568.7 639.4 680.4 772.6 843.3 884.4 955.0 996.1 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 223.5 294.1 386.3 427.4 498.0 568.7 609.8 702.0 772.6 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 152.8 223.5 315.6 356.7 427.4 498.0 539.1 631.3 702.0 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 111.7 182.4 274.6 315.6 386.3 457.0 498.0 590.2 660.9 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 41.1 111.7 203.9 245.0 315.6 386.3 427.4 519.6 590.2 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 925.4 : 70.7 162.9 203.9 274.6 345.3 386.3 478.5 549.2 590.2 660.9 702.0 772.6 843.3 905.9 976.5 1047.2 1088.3 1158.9 1200.0 996.1 : 92.2 133.2 203.9 274.6 315.6 407.8 478.5 519.6 590.2 631.3 702.0 772.6 835.2 905.9 976.5 1017.6 1088.3 1129.3 1200.0 1088.3: 41.1 111.7 182.4 223.5 315.6 386.3 427.4 498.0 539.1 609.8 680.4 743.0 813.7 884.4 925.4 996.1 1037.1 1107.8 1200.0 1129.3: 70.7 141.3 182.4 274.6 345.3 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 996.1 1066.8 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: 356.7001 .. 407.8200 cents 16875/16384, 51.1199 cents 393216/390625, 11.4453 cents 7: 427.3726 .. 478.4924 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 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: 792.1800 .. 843.2999 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 14: 854.7451 .. 905.8650 cents 16875/16384, 51.1199 cents 393216/390625, 11.4453 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 : 63.03914 cents, oct.: 1197.74369 cents Scale is not proper Step pattern alph. order: ABCABABAADAABABACBA Step pattern size order : CADCACACCBCCACACDAC Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.369111 Lumma stability : 0.266739 Lumma impropriety factor : 0.033537 Number of different interval sizes : 64 = 3.55556 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.55556 = 32/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 14 Most common triad is 0.0 498.045 701.955 cents, amount: 9 Number of recognisable fifths : 14, average 701.9550 cents Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 5 15 25 75 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 19 = 100.0000% Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 5 Odd number limit : 5625 (O: 5625 U: 5625) Highest odd numerator or denominator: 75 Scale harmonicity : 0.020298 Average absolute harmonicity : 0.143309 Specific harmonicity : 0.116981 Fundamental : 1/14400, -13.8138 octaves, 0.0182 Hz. Guide tone : 28800, 14.8138 octaves, 7534816.281 Hz. Exponens Consonantiae : 4.147200E+08, 28.62756 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 409.0, average 21.52632 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.14855, average 1.06045 Sum of Tenney's harmonic distance : 40.82320, average 2.14859 Vogel's harmonic complexity : 22.52632 Wille's k value : 8437 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 917.24138, average 4.82759 Lattice compactness (without 2's) : 450.44262, average 2.37075 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.52632 56 1 3: -2 .. 2 0.00000 18 4 5: -2 .. 2 0.00000 22 14 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 40 / 19 = 2.10526 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: 11.6210 c. M: 21.9508 c. 28: 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 P D3 I SD: 12.8383 c. M: 17.4396 c. 29: 2 1 2 2 1 1 1 2 2 1 2 2 1 1 1 2 2 1 2 N D3 I SD: 11.5399 c. M:-15.3932 c. 30: 2 1 2 2 1 2 1 1 2 2 2 1 1 2 1 2 2 1 2 N D3 I SD: 10.0911 c. M:-18.0450 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: 6.4321 c. M:-11.9277 c. 34: 2 1 3 2 1 2 1 2 2 2 2 2 1 2 1 2 3 1 2 N T3 I SD: 4.7049 c. M:-7.8547 c. 53: 3 2 4 3 2 3 2 3 3 3 3 3 2 3 2 3 4 2 3 P T3 I SD: 1.9725 c. M: 2.8843 c. 87: 5 3 7 5 3 5 3 5 5 5 5 5 3 5 3 5 7 3 5 N T3 I SD: 1.7912 c. M:-3.2002 c. 118: 7 4 9 7 4 7 4 7 7 6 7 7 4 7 4 7 9 4 7 N I SD: 0.3907 c. M:-0.7741 c. 289: 17 10 22 17 10 17 10 17 17 15 17 17 10 17 10 17 22 10 17 N I SD: 0.2962 c. M: 0.5340 c. 323: 19 11 25 19 11 19 11 19 19 17 19 19 11 19 11 19 25 11 19 N I SD: 0.2416 c. M:-0.4244 c. 441: 26 15 34 26 15 26 15 26 26 23 26 26 15 26 15 26 34 15 26 N I SD: 0.1316 c. M: 0.2475 c. 559: 33 19 43 33 19 33 19 33 33 29 33 33 19 33 19 33 43 19 33 N I SD: 0.1251 c. M: 0.1940 c. 612: 36 21 47 36 21 36 21 36 36 32 36 36 21 36 21 36 47 21 36 N I SD: 0.0575 c. M:-0.0900 c. 730: 43 25 56 43 25 43 25 43 43 38 43 43 25 43 25 43 56 25 43 N I SD: 0.0426 c. M:-0.0744 c. 1171: 69 40 90 69 40 69 40 69 69 61 69 69 40 69 40 69 90 40 69 N I SD: 0.0312 c. M: 0.0546 c. 1783: 105 61 137 105 61 105 61 105 105 93 105 105 61 105 61 105 137 61 105 N I SD: 0.0090 c. M:-0.0160 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: 6.8160 cents 5 .. 10 match: 5 H SD: 5.1101 cents 6 .. 12 match: 6 H SD: 6.6104 cents 7 .. 14 match: 7 H SD: 5.3915 cents 8 .. 16 match: 8 H SD: 5.2538 cents 9 .. 18 match: 9 H SD: 4.6119 cents 10 .. 20 match: 10 H SD: 5.7109 cents 11 .. 22 match: 11 H SD: 7.3570 cents 12 .. 24 match: 11 SD: 4.6894 cents 13 .. 26 match: 13 H SD: 5.7261 cents 14 .. 28 match: 14 H SD: 4.2750 cents 15 .. 30 match: 15 H SD: 4.2903 cents 16 .. 32 match: 15 S SD: 3.9567 cents 17 .. 34 match: 15 S SD: 4.6383 cents 18 .. 36 match: 17 S SD: 3.2165 cents 19 .. 38 match: 14 SD: 5.5283 cents 20 .. 40 match: 16 SD: 4.0041 cents 21 .. 42 match: 17 SD: 3.5681 cents 22 .. 44 match: 16 SD: 3.6121 cents 23 .. 46 match: 18 SD: 3.3123 cents 24 .. 48 match: 18 SD: 2.7637 cents 25 .. 50 match: 19 SD: 2.7632 cents 26 .. 52 match: 18 SD: 3.2298 cents 27 .. 54 match: 18 SD: 3.0536 cents 28 .. 56 match: 19 SD: 2.7297 cents 30 .. 60 match: 18 SD: 2.0694 cents 32 .. 64 match: 18 SD: 2.2584 cents 36 .. 72 match: 18 SD: 2.1311 cents 37 .. 74 match: 18 SD: 2.6659 cents 38 .. 76 match: 19 SD: 2.6579 cents 39 .. 78 match: 19 SD: 1.9912 cents 40 .. 80 match: 19 SD: 1.8451 cents 41 .. 82 match: 19 SD: 1.8223 cents 45 .. 90 match: 19 SD: 1.7046 cents 46 .. 92 match: 19 SD: 1.5482 cents 48 .. 96 match: 19 SD: 1.2515 cents 64 .. 128 match: 19 SD: 0.9200 cents 72 .. 144 match: 19 SD: 0.8514 cents 75 .. 150 match: 19 SD: 0.7580 cents 96 .. 192 match: 19 SD: 0.7220 cents 100 .. 200 match: 19 SD: 0.7084 cents 105 .. 210 match: 19 SD: 0.6286 cents 120 .. 240 match: 19 SD: 0.5210 cents 136 .. 272 match: 19 SD: 0.4967 cents 144 .. 288 match: 19 SD: 0.4400 cents 150 .. 300 match: 19 SD: 0.4163 cents 168 .. 336 match: 19 SD: 0.3644 cents 192 .. 384 match: 19 SD: 0.3259 cents 210 .. 420 match: 19 SD: 0.3240 cents 215 .. 430 match: 19 SD: 0.3229 cents 216 .. 432 match: 19 SD: 0.3134 cents 225 .. 450 match: 19 SD: 0.3094 cents 239 .. 478 match: 19 SD: 0.2637 cents 240 .. 480 match: 19 SD: 0.2099 cents 336 .. 672 match: 19 SD: 0.1831 cents 360 .. 720 match: 19 SD: 0.1342 cents 432 .. 864 match: 19 SD: 0.1138 cents 528 .. 1056 match: 19 SD: 0.1072 cents 576 .. 1152 match: 19 SD: 0.0968 cents 600 .. 1200 match: 19 SD: 0.0690 cents