Scala analysis: xen07-chalmers-fokker-k
Fokker-K
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: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.403712 minor whole tone 4: 125/108 253.076139 semi-augmented whole tone 5: 6/5 315.641287 minor third 6: 5/4 386.313714 major third 7: 162/125 448.878862 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: 125/81 751.121138 13: 8/5 813.686286 minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 216/125 946.923861 semi-augmented sixth 16: 9/5 1017.596288 just minor seventh, BP seventh 17: 50/27 1066.762425 grave 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: 648/625 62.5651 major diesis 3: 250/243 49.1661 maximal diesis, Porcupine comma 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 648/625 62.5651 major diesis 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 648/625 62.5651 major diesis 8: 250/243 49.1661 maximal diesis, Porcupine comma 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: 250/243 49.1661 maximal diesis, Porcupine comma 13: 648/625 62.5651 major diesis 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 648/625 62.5651 major diesis 16: 25/24 70.6724 classic chromatic semitone, minor chroma 17: 250/243 49.1661 maximal diesis, Porcupine comma 18: 648/625 62.5651 major diesis 19: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 250/243 49.166 cents maximal diesis, Porcupine comma 1: 7 648/625 62.565 cents major diesis 1: 8 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 4 16/15 111.731 cents minor diatonic semitone 2: 4 3125/2916 119.839 cents quasi-equal 10-tone semitone 2: 10 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 3: 12 10/9 182.404 cents minor whole tone 3: 2 17496/15625 195.803 cents 3: 5 9/8 203.910 cents major whole tone 4: 6 144/125 244.969 cents classic diminished third 4: 10 125/108 253.076 cents semi-augmented whole tone 4: 3 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 5: 1 15625/13122 302.242 cents 5: 16 6/5 315.641 cents minor third 5: 2 3125/2592 323.749 cents 6: 5 100/81 364.807 cents grave major third 6: 4 3888/3125 378.206 cents 6: 10 5/4 386.314 cents major third 7: 3 32/25 427.373 cents classic diminished fourth 7: 6 625/486 435.480 cents 7: 8 162/125 448.879 cents 7: 2 125/96 456.986 cents classic augmented third 8: 12 4/3 498.045 cents perfect fourth 8: 1 15625/11664 506.152 cents two (semi-augmented whole tone) 8: 6 27/20 519.551 cents acute fourth 9: 4 864/625 560.610 cents 9: 13 25/18 568.717 cents classic augmented fourth 9: 2 4374/3125 582.116 cents 10: 2 3125/2187 617.884 cents 10: 13 36/25 631.283 cents classic diminished fifth 10: 4 625/432 639.390 cents 11: 6 40/27 680.449 cents grave fifth 11: 1 23328/15625 693.848 cents 11: 12 3/2 701.955 cents perfect fifth 12: 2 192/125 743.014 cents classic diminished sixth 12: 8 125/81 751.121 cents 12: 6 972/625 764.520 cents 12: 3 25/16 772.627 cents classic augmented fifth 13: 10 8/5 813.686 cents minor sixth 13: 4 3125/1944 821.794 cents 13: 5 81/50 835.193 cents acute minor sixth 14: 2 5184/3125 876.251 cents 14: 16 5/3 884.359 cents major sixth, BP sixth 14: 1 26244/15625 897.758 cents 15: 3 1250/729 933.525 cents 15: 10 216/125 946.924 cents semi-augmented sixth 15: 6 125/72 955.031 cents classic augmented sixth 16: 5 16/9 996.090 cents Pythagorean minor seventh 16: 2 15625/8748 1004.197 cents 16: 12 9/5 1017.596 cents just minor seventh, BP seventh 17: 1 1152/625 1058.655 cents 17: 10 50/27 1066.762 cents grave major seventh 17: 4 5832/3125 1080.161 cents 17: 4 15/8 1088.269 cents classic major seventh 18: 8 48/25 1129.328 cents classic diminished octave 18: 7 625/324 1137.435 cents octave - major diesis 18: 4 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.22222 = 29/9
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 : 70.7 133.2 182.4 253.1 315.6 386.3 448.9 498.0 568.7 631.3 702.0 751.1 813.7 884.4 946.9 1017.6 1066.8 1129.3 1200.0 70.7 : 62.6 111.7 182.4 245.0 315.6 378.2 427.4 498.0 560.6 631.3 680.4 743.0 813.7 876.3 946.9 996.1 1058.7 1129.3 1200.0 133.2 : 49.2 119.8 182.4 253.1 315.6 364.8 435.5 498.0 568.7 617.9 680.4 751.1 813.7 884.4 933.5 996.1 1066.8 1137.4 1200.0 182.4 : 70.7 133.2 203.9 266.5 315.6 386.3 448.9 519.6 568.7 631.3 702.0 764.5 835.2 884.4 946.9 1017.6 1088.3 1150.8 1200.0 253.1 : 62.6 133.2 195.8 245.0 315.6 378.2 448.9 498.0 560.6 631.3 693.8 764.5 813.7 876.3 946.9 1017.6 1080.2 1129.3 1200.0 315.6 : 70.7 133.2 182.4 253.1 315.6 386.3 435.5 498.0 568.7 631.3 702.0 751.1 813.7 884.4 955.0 1017.6 1066.8 1137.4 1200.0 386.3 : 62.6 111.7 182.4 245.0 315.6 364.8 427.4 498.0 560.6 631.3 680.4 743.0 813.7 884.4 946.9 996.1 1066.8 1129.3 1200.0 448.9 : 49.2 119.8 182.4 253.1 302.2 364.8 435.5 498.0 568.7 617.9 680.4 751.1 821.8 884.4 933.5 1004.2 1066.8 1137.4 1200.0 498.0 : 70.7 133.2 203.9 253.1 315.6 386.3 448.9 519.6 568.7 631.3 702.0 772.6 835.2 884.4 955.0 1017.6 1088.3 1150.8 1200.0 568.7 : 62.6 133.2 182.4 245.0 315.6 378.2 448.9 498.0 560.6 631.3 702.0 764.5 813.7 884.4 946.9 1017.6 1080.2 1129.3 1200.0 631.3 : 70.7 119.8 182.4 253.1 315.6 386.3 435.5 498.0 568.7 639.4 702.0 751.1 821.8 884.4 955.0 1017.6 1066.8 1137.4 1200.0 702.0 : 49.2 111.7 182.4 245.0 315.6 364.8 427.4 498.0 568.7 631.3 680.4 751.1 813.7 884.4 946.9 996.1 1066.8 1129.3 1200.0 751.1 : 62.6 133.2 195.8 266.5 315.6 378.2 448.9 519.6 582.1 631.3 702.0 764.5 835.2 897.8 946.9 1017.6 1080.2 1150.8 1200.0 813.7 : 70.7 133.2 203.9 253.1 315.6 386.3 457.0 519.6 568.7 639.4 702.0 772.6 835.2 884.4 955.0 1017.6 1088.3 1137.4 1200.0 884.4 : 62.6 133.2 182.4 245.0 315.6 386.3 448.9 498.0 568.7 631.3 702.0 764.5 813.7 884.4 946.9 1017.6 1066.8 1129.3 1200.0 946.9 : 70.7 119.8 182.4 253.1 323.7 386.3 435.5 506.2 568.7 639.4 702.0 751.1 821.8 884.4 955.0 1004.2 1066.8 1137.4 1200.0 1017.6: 49.2 111.7 182.4 253.1 315.6 364.8 435.5 498.0 568.7 631.3 680.4 751.1 813.7 884.4 933.5 996.1 1066.8 1129.3 1200.0 1066.8: 62.6 133.2 203.9 266.5 315.6 386.3 448.9 519.6 582.1 631.3 702.0 764.5 835.2 884.4 946.9 1017.6 1080.2 1150.8 1200.0 1129.3: 70.7 141.3 203.9 253.1 323.7 386.3 457.0 519.6 568.7 639.4 702.0 772.6 821.8 884.4 955.0 1017.6 1088.3 1137.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 70.6724 cents 81/80, 21.5063 cents 250/243, 49.1661 cents 2: 111.7313 .. 141.3449 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 3: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 4: 244.9689 .. 266.4751 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 5: 302.2423 .. 323.7486 cents 81/80, 21.5063 cents 9765625/9565938, 35.7671 cents 6: 364.8074 .. 386.3137 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 7: 427.3726 .. 456.9861 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 8: 498.0450 .. 519.5513 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 9: 560.6101 .. 582.1164 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 10: 617.8836 .. 639.3899 cents 81/80, 21.5063 cents 9765625/9565938, 35.7671 cents 11: 680.4487 .. 701.9550 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 12: 743.0139 .. 772.6274 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 13: 813.6863 .. 835.1926 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 14: 876.2514 .. 897.7577 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 15: 933.5249 .. 955.0311 cents 81/80, 21.5063 cents 9765625/9565938, 35.7671 cents 16: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 17: 1058.6551 .. 1088.2687 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 18: 1129.3276 .. 1150.8339 cents 81/80, 21.5063 cents 128/125, 41.0589 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 25/24, 70.6724 cents Average / Smallest step : 1.284581 Largest / Average step : 1.118980 Largest / Smallest step : 1.437421 Median interval of one step : 648/625, 62.5651 cents, amount: 7 Most common interval of one step : 25/24, 70.6724 cents, amount: 8 Least squares average step : 63.07397 cents, oct.: 1198.40542 cents Scale is strictly proper Step pattern alph. order: ABCABABCABACBABACBA Step pattern size order : LMSLMLMSLMLSMLMLSML Scale is a Constant Structure, by a margin of 35.76713 cents Scale diversity : 1.243967 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.650381 Number of different interval sizes : 58 = 3.22222 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.22222 = 29/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 16 Most common triad is 0.0 315.641 884.359 cents, amount: 13 Number of recognisable fifths : 13, average 701.3314 cents Best fifths form a closed circle 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 : 3 5 9 25 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 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 : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 125 Scale harmonicity : 0.014985 Average absolute harmonicity : 0.132656 Specific harmonicity : 0.092487 Fundamental : 1/81000, -16.3056 octaves, 0.0032 Hz. Guide tone : 162000, 17.3056 octaves, 42383341.579 Hz. Exponens Consonantiae : 1.312200E+10, 33.61127 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 755.5, average 39.76316 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 22.50074, average 1.18425 Sum of Tenney's harmonic distance : 45.62006, average 2.40106 Vogel's harmonic complexity : 30.52632 Wille's k value : 42187 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 818.19931, average 4.30631 Lattice compactness (without 2's) : 656.58176, average 3.45569 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.52632 28 1 3: -4 .. 4 0.00000 34 2 5: -3 .. 3 0.00000 30 16 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 64 / 19 = 3.36842 Scale is weakly epimorphic with val: <19 29 44| Scale is JI-epimorphic with val: <19 30 44| = patent Scale is weakly epimorphic with val: <19 32 42|
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: 5.6839 c. M: 7.5145 c. 34: 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 P M ME I SD: 5.3565 c. M:-9.9447 c. 46: 3 2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 2 3 SP D3 I SD: 4.8097 c. M: 7.7934 c. 53: 3 3 2 3 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 SP M ME I SD: 2.4862 c. M: 4.0195 c. 72: 4 4 3 4 4 4 4 3 4 4 4 3 4 4 4 4 3 4 4 SP M ME I SD: 2.1909 c. M: 4.0058 c. 99: 6 5 4 6 5 6 5 4 6 5 6 4 5 6 5 6 4 5 6 SP I SD: 1.1095 c. M:-2.0548 c. 118: 7 6 5 7 6 7 6 5 7 6 7 5 6 7 6 7 5 6 7 SP I SD: 0.7916 c. M:-1.4212 c. 152: 9 8 6 9 8 9 8 6 9 8 9 6 8 9 8 9 6 8 9 SP I SD: 0.6548 c. M:-1.1211 c. 171: 10 9 7 10 9 10 9 7 10 9 10 7 9 10 9 10 7 9 10 SP I SD: 0.2880 c. M: 0.4970 c. 270: 16 14 11 16 14 16 14 11 16 14 16 11 14 16 14 16 11 14 16 SP I SD: 0.2370 c. M:-0.4387 c. 289: 17 15 12 17 15 17 15 12 17 15 17 12 15 17 15 17 12 15 17 SP I SD: 0.2432 c. M:-0.4360 c. 422: 25 22 17 25 22 25 22 17 25 22 25 17 22 25 22 25 17 22 25 SP I SD: 0.3290 c. M:-0.4176 c. 441: 26 23 18 26 23 26 23 18 26 23 26 18 23 26 23 26 18 23 26 SP I SD: 0.0708 c. M:-0.1007 c. 730: 43 38 30 43 38 43 38 30 43 38 43 30 38 43 38 43 30 38 43 SP I SD: 0.0600 c. M:-0.1117 c. 901: 53 47 37 53 47 53 47 37 53 47 53 37 47 53 47 53 37 47 53 SP I SD: 0.0531 c. M: 0.0842 c. 1171: 69 61 48 69 61 69 61 48 69 61 69 48 61 69 61 69 48 61 69 SP I SD: 0.0249 c. M: 0.0409 c. 1342: 79 70 55 79 70 79 70 55 79 70 79 55 70 79 70 79 55 70 79 SP I SD: 0.0170 c. M: 0.0316 c. 1783: 105 93 73 105 93 105 93 73 105 93 105 73 93 105 93 105 73 93 105 SP I SD: 0.0148 c. M:-0.0275 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: 5.4755 cents 5 .. 10 match: 5 H SD: 2.7590 cents 6 .. 12 match: 6 H SD: 3.7007 cents 7 .. 14 match: 7 H SD: 6.4651 cents 8 .. 16 match: 8 H SD: 6.1593 cents 9 .. 18 match: 9 H SD: 5.5447 cents 10 .. 20 match: 10 H SD: 4.0620 cents 11 .. 22 match: 11 H SD: 6.2340 cents 12 .. 24 match: 12 H SD: 3.8539 cents 13 .. 26 match: 13 H SD: 4.6364 cents 14 .. 28 match: 14 H SD: 4.7742 cents 15 .. 30 match: 15 H SD: 4.1360 cents 16 .. 32 match: 16 H SD: 4.5760 cents 17 .. 34 match: 14 SD: 5.4191 cents 18 .. 36 match: 17 SD: 3.7050 cents 19 .. 38 match: 16 SD: 4.2803 cents 20 .. 40 match: 18 SD: 2.8400 cents 21 .. 42 match: 17 S SD: 3.4786 cents 22 .. 44 match: 17 SD: 4.2470 cents 23 .. 46 match: 18 SD: 3.7738 cents 24 .. 48 match: 19 SD: 2.7558 cents 25 .. 50 match: 19 SD: 2.6925 cents 26 .. 52 match: 19 SD: 2.6272 cents 30 .. 60 match: 19 SD: 2.6019 cents 33 .. 66 match: 19 SD: 2.5928 cents 34 .. 68 match: 19 SD: 2.5281 cents 36 .. 72 match: 19 SD: 2.0240 cents 39 .. 78 match: 19 SD: 2.0002 cents 40 .. 80 match: 19 SD: 1.9165 cents 44 .. 88 match: 19 SD: 1.6635 cents 48 .. 96 match: 19 SD: 1.3927 cents 51 .. 102 match: 19 SD: 1.3585 cents 52 .. 104 match: 19 SD: 1.3372 cents 63 .. 126 match: 19 SD: 1.2619 cents 64 .. 128 match: 19 SD: 1.0110 cents 72 .. 144 match: 19 SD: 0.9195 cents 75 .. 150 match: 19 SD: 0.7750 cents 88 .. 176 match: 19 SD: 0.7476 cents 96 .. 192 match: 19 SD: 0.6933 cents 100 .. 200 match: 19 SD: 0.5440 cents 125 .. 250 match: 19 SD: 0.5315 cents 136 .. 272 match: 19 SD: 0.4870 cents 152 .. 304 match: 19 SD: 0.4733 cents 160 .. 320 match: 19 SD: 0.4417 cents 164 .. 328 match: 19 SD: 0.4137 cents 165 .. 330 match: 19 SD: 0.4012 cents 180 .. 360 match: 19 SD: 0.3965 cents 188 .. 376 match: 19 SD: 0.3679 cents 189 .. 378 match: 19 SD: 0.3661 cents 190 .. 380 match: 19 SD: 0.3415 cents 210 .. 420 match: 19 SD: 0.3115 cents 216 .. 432 match: 19 SD: 0.2158 cents 324 .. 648 match: 19 SD: 0.1874 cents 360 .. 720 match: 19 SD: 0.1675 cents 412 .. 824 match: 19 SD: 0.1476 cents 440 .. 880 match: 19 SD: 0.1423 cents 450 .. 900 match: 19 SD: 0.1329 cents 460 .. 920 match: 19 SD: 0.1289 cents 504 .. 1008 match: 19 SD: 0.1150 cents 540 .. 1080 match: 19 SD: 0.1093 cents 600 .. 1200 match: 19 SD: 0.0972 cents