Scala analysis: xen07-chalmers-fokker-h
Fokker-H
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: 10/9 182.403712 minor 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 128/125 41.0589 minor diesis, diesis 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 135/128 92.1787 major chroma, major limma 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: 3 256/225 223.463 cents Neapolitan diminished third 4: 6 144/125 244.969 cents classic diminished third 4: 4 125/108 253.076 cents semi-augmented whole tone 4: 6 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: 1 100/81 364.807 cents grave major third 6: 14 5/4 386.314 cents major third 7: 9 32/25 427.373 cents classic diminished fourth 7: 2 162/125 448.879 cents 7: 8 125/96 456.986 cents classic 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: 8 192/125 743.014 cents classic diminished sixth 12: 2 125/81 751.121 cents 12: 9 25/16 772.627 cents classic augmented fifth 13: 14 8/5 813.686 cents minor sixth 13: 1 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: 6 128/75 925.418 cents diminished seventh 15: 4 216/125 946.924 cents semi-augmented sixth 15: 6 125/72 955.031 cents classic augmented sixth 15: 3 225/128 976.537 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: 3.44444 = 31/9
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 : 70.7 111.7 182.4 274.6 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 925.4 1017.6 1088.3 1129.3 1200.0 70.7 : 41.1 111.7 203.9 245.0 315.6 356.7 427.4 498.0 560.6 631.3 702.0 743.0 813.7 854.7 946.9 1017.6 1058.7 1129.3 1200.0 111.7 : 70.7 162.9 203.9 274.6 315.6 386.3 457.0 519.6 590.2 660.9 702.0 772.6 813.7 905.9 976.5 1017.6 1088.3 1158.9 1200.0 182.4 : 92.2 133.2 203.9 245.0 315.6 386.3 448.9 519.6 590.2 631.3 702.0 743.0 835.2 905.9 946.9 1017.6 1088.3 1129.3 1200.0 274.6 : 41.1 111.7 152.8 223.5 294.1 356.7 427.4 498.0 539.1 609.8 650.8 743.0 813.7 854.7 925.4 996.1 1037.1 1107.8 1200.0 315.6 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 498.0 568.7 609.8 702.0 772.6 813.7 884.4 955.0 996.1 1066.8 1158.9 1200.0 386.3 : 41.1 111.7 182.4 245.0 315.6 386.3 427.4 498.0 539.1 631.3 702.0 743.0 813.7 884.4 925.4 996.1 1088.3 1129.3 1200.0 427.4 : 70.7 141.3 203.9 274.6 345.3 386.3 457.0 498.0 590.2 660.9 702.0 772.6 843.3 884.4 955.0 1047.2 1088.3 1158.9 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 427.4 519.6 590.2 631.3 702.0 772.6 813.7 884.4 976.5 1017.6 1088.3 1129.3 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 356.7 448.9 519.6 560.6 631.3 702.0 743.0 813.7 905.9 946.9 1017.6 1058.7 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 294.1 386.3 457.0 498.0 568.7 639.4 680.4 751.1 843.3 884.4 955.0 996.1 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 223.5 315.6 386.3 427.4 498.0 568.7 609.8 680.4 772.6 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 152.8 245.0 315.6 356.7 427.4 498.0 539.1 609.8 702.0 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 111.7 203.9 274.6 315.6 386.3 457.0 498.0 568.7 660.9 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 41.1 133.2 203.9 245.0 315.6 386.3 427.4 498.0 590.2 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 925.4 : 92.2 162.9 203.9 274.6 345.3 386.3 457.0 549.2 590.2 660.9 702.0 772.6 843.3 905.9 976.5 1047.2 1088.3 1158.9 1200.0 1017.6: 70.7 111.7 182.4 253.1 294.1 364.8 457.0 498.0 568.7 609.8 680.4 751.1 813.7 884.4 955.0 996.1 1066.8 1107.8 1200.0 1088.3: 41.1 111.7 182.4 223.5 294.1 386.3 427.4 498.0 539.1 609.8 680.4 743.0 813.7 884.4 925.4 996.1 1037.1 1129.3 1200.0 1129.3: 70.7 141.3 182.4 253.1 345.3 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 996.1 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 .. 345.2549 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 6: 356.7001 .. 386.3137 cents 3125/3072, 29.6136 cents 393216/390625, 11.4453 cents 7: 427.3726 .. 456.9861 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 8: 498.0450 .. 549.1649 cents 16875/16384, 51.1199 cents 128/125, 41.0589 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: 743.0139 .. 772.6274 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 13: 813.6863 .. 843.2999 cents 3125/3072, 29.6136 cents 128/125, 41.0589 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 : 63.15233 cents, oct.: 1199.89432 cents Scale is not proper Step pattern alph. order: ABACBABAADAABABCABA Step pattern size order : CACDACACCBCCACADCAC Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.335412 Lumma stability : 0.338426 Lumma impropriety factor : 0.033537 Number of different interval sizes : 62 = 3.44444 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.44444 = 31/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15625/15552, 8.1073 cents 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 : 0.139973 Specific harmonicity : 0.116504 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 : 404.5, average 21.28947 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 : 40.41496, average 2.12710 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 : 880.36294, average 4.63349 Lattice compactness (without 2's) : 455.12347, average 2.39539 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.52632 50 1 3: -2 .. 2 0.00000 18 2 5: -2 .. 2 0.00000 24 16 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 42 / 19 = 2.21053 Scale is weakly epimorphic with val: <19 27 45| Scale is weakly epimorphic with val: <19 29 42| Scale is JI-epimorphic with val: <19 30 44| = patent Scale is weakly epimorphic with val: <19 32 47|
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: 10.8799 c. M: 21.9508 c. 26: 2 0 2 2 1 1 1 2 1 2 1 2 1 1 1 2 2 0 2 N D3 I SD: 13.2219 c. M:-21.6353 c. 27: 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 P D3 I SD: 12.7641 c. M:-21.6020 c. 28: 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 P D3 I SD: 12.8907 c. M: 17.4396 c. 29: 2 1 1 3 1 1 1 2 2 1 2 2 1 1 1 3 1 1 2 N D3 I SD: 12.7376 c. M: 16.8865 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: 11.5245 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: 6.5685 c. M:-11.9277 c. 34: 2 1 2 3 1 2 1 2 2 2 2 2 1 2 1 3 2 1 2 N D3 I SD: 4.3986 c. M: 7.7705 c. 53: 3 2 3 4 2 3 2 3 3 3 3 3 2 3 2 4 3 2 3 P D3 I SD: 2.0147 c. M: 2.8843 c. 87: 5 3 5 7 3 5 3 5 5 5 5 5 3 5 3 7 5 3 5 N D3 I SD: 1.8102 c. M:-3.2002 c. 118: 7 4 7 9 4 7 4 7 7 6 7 7 4 7 4 9 7 4 7 N I SD: 0.4101 c. M:-0.7741 c. 289: 17 10 17 22 10 17 10 17 17 15 17 17 10 17 10 22 17 10 17 N I SD: 0.2749 c. M: 0.5340 c. 323: 19 11 19 25 11 19 11 19 19 17 19 19 11 19 11 25 19 11 19 N I SD: 0.2304 c. M: 0.3604 c. 441: 26 15 26 34 15 26 15 26 26 23 26 26 15 26 15 34 26 15 26 N I SD: 0.1228 c. M: 0.2475 c. 559: 33 19 33 43 19 33 19 33 33 29 33 33 19 33 19 43 33 19 33 N I SD: 0.1266 c. M: 0.1940 c. 612: 36 21 36 47 21 36 21 36 36 32 36 36 21 36 21 47 36 21 36 N I SD: 0.0597 c. M:-0.0900 c. 730: 43 25 43 56 25 43 25 43 43 38 43 43 25 43 25 56 43 25 43 N I SD: 0.0404 c. M: 0.0620 c. 1171: 69 40 69 90 40 69 40 69 69 61 69 69 40 69 40 90 69 40 69 N I SD: 0.0307 c. M: 0.0546 c. 1783: 105 61 105 137 61 105 61 105 105 93 105 105 61 105 61 137 105 61 105 N I SD: 0.0088 c. M: 0.0145 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: 7.2355 cents 8 .. 16 match: 8 H SD: 7.2565 cents 9 .. 18 match: 9 H SD: 4.6119 cents 10 .. 20 match: 10 H SD: 3.9850 cents 11 .. 22 match: 11 H SD: 6.3205 cents 12 .. 24 match: 11 S SD: 4.9180 cents 13 .. 26 match: 13 H SD: 6.1359 cents 14 .. 28 match: 14 H SD: 4.9763 cents 15 .. 30 match: 15 H SD: 4.5661 cents 16 .. 32 match: 15 SD: 3.8789 cents 17 .. 34 match: 15 SD: 4.7875 cents 18 .. 36 match: 17 S SD: 3.2165 cents 19 .. 38 match: 14 SD: 5.1055 cents 20 .. 40 match: 17 S SD: 3.6945 cents 21 .. 42 match: 17 SD: 3.4294 cents 22 .. 44 match: 16 SD: 4.1103 cents 23 .. 46 match: 18 SD: 3.7829 cents 24 .. 48 match: 18 SD: 2.9503 cents 25 .. 50 match: 19 SD: 2.6756 cents 26 .. 52 match: 18 SD: 3.1368 cents 27 .. 54 match: 18 SD: 2.9186 cents 28 .. 56 match: 19 SD: 2.4209 cents 30 .. 60 match: 18 SD: 2.0855 cents 32 .. 64 match: 18 SD: 2.6336 cents 34 .. 68 match: 19 SD: 2.4817 cents 35 .. 70 match: 19 SD: 2.4022 cents 36 .. 72 match: 18 SD: 1.7991 cents 37 .. 74 match: 18 SD: 2.5802 cents 39 .. 78 match: 19 SD: 2.0658 cents 40 .. 80 match: 19 SD: 2.0549 cents 41 .. 82 match: 19 SD: 2.0209 cents 43 .. 86 match: 19 SD: 1.9391 cents 44 .. 88 match: 19 SD: 1.7039 cents 45 .. 90 match: 19 SD: 1.5663 cents 46 .. 92 match: 19 SD: 1.4935 cents 48 .. 96 match: 19 SD: 1.3944 cents 54 .. 108 match: 19 SD: 1.3767 cents 57 .. 114 match: 19 SD: 1.3539 cents 60 .. 120 match: 19 SD: 1.2811 cents 64 .. 128 match: 19 SD: 0.9274 cents 72 .. 144 match: 19 SD: 0.8965 cents 75 .. 150 match: 19 SD: 0.7008 cents 100 .. 200 match: 19 SD: 0.5779 cents 120 .. 240 match: 19 SD: 0.5506 cents 135 .. 270 match: 19 SD: 0.5284 cents 136 .. 272 match: 19 SD: 0.4998 cents 144 .. 288 match: 19 SD: 0.4456 cents 150 .. 300 match: 19 SD: 0.4187 cents 164 .. 328 match: 19 SD: 0.3713 cents 180 .. 360 match: 19 SD: 0.3592 cents 200 .. 400 match: 19 SD: 0.3562 cents 208 .. 416 match: 19 SD: 0.3503 cents 210 .. 420 match: 19 SD: 0.3256 cents 215 .. 430 match: 19 SD: 0.3179 cents 216 .. 432 match: 19 SD: 0.3169 cents 225 .. 450 match: 19 SD: 0.3061 cents 239 .. 478 match: 19 SD: 0.3036 cents 240 .. 480 match: 19 SD: 0.2279 cents 286 .. 572 match: 19 SD: 0.2268 cents 304 .. 608 match: 19 SD: 0.2235 cents 314 .. 628 match: 19 SD: 0.2035 cents 332 .. 664 match: 19 SD: 0.2024 cents 336 .. 672 match: 19 SD: 0.1961 cents 360 .. 720 match: 19 SD: 0.1342 cents 432 .. 864 match: 19 SD: 0.1231 cents 450 .. 900 match: 19 SD: 0.1159 cents 525 .. 1050 match: 19 SD: 0.1084 cents 576 .. 1152 match: 19 SD: 0.0984 cents 600 .. 1200 match: 19 SD: 0.0776 cents