Scala analysis: xen07-chalmers-hanson-just
Hanson-19
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: 9/8 203.910002 major 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: 125/96 456.986141 classic augmented third 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: 125/72 955.031140 classic 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: 648/625 62.5651 major diesis 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 250/243 49.1661 maximal diesis, Porcupine comma 5: 648/625 62.5651 major diesis 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 128/125 41.0589 minor diesis, diesis 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: 25/24 70.6724 classic chromatic semitone, minor chroma 16: 648/625 62.5651 major 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: 3 128/125 41.059 cents minor diesis, diesis 1: 1 250/243 49.166 cents maximal diesis, Porcupine comma 1: 4 648/625 62.565 cents major diesis 1: 11 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 7 16/15 111.731 cents minor diatonic semitone 2: 1 3125/2916 119.839 cents quasi-equal 10-tone semitone 2: 7 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 4 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 3: 2 3456/3125 174.296 cents 3: 10 10/9 182.404 cents minor whole tone 3: 7 9/8 203.910 cents major whole tone 4: 9 144/125 244.969 cents classic diminished third 4: 7 125/108 253.076 cents semi-augmented whole tone 4: 3 75/64 274.582 cents classic augmented second 5: 1 32/27 294.135 cents Pythagorean minor third 5: 15 6/5 315.641 cents minor third 5: 3 3125/2592 323.749 cents 6: 2 768/625 356.700 cents 6: 3 100/81 364.807 cents grave major third 6: 2 3888/3125 378.206 cents 6: 12 5/4 386.314 cents major third 7: 7 32/25 427.373 cents classic diminished fourth 7: 2 625/486 435.480 cents 7: 4 162/125 448.879 cents 7: 6 125/96 456.986 cents classic augmented third 8: 13 4/3 498.045 cents perfect fourth 8: 5 27/20 519.551 cents acute fourth 8: 1 3125/2304 527.659 cents 9: 6 864/625 560.610 cents 9: 11 25/18 568.717 cents classic augmented fourth 9: 2 45/32 590.224 cents diatonic tritone 10: 2 64/45 609.776 cents 2nd tritone 10: 11 36/25 631.283 cents classic diminished fifth 10: 6 625/432 639.390 cents 11: 1 4608/3125 672.341 cents 11: 5 40/27 680.449 cents grave fifth 11: 13 3/2 701.955 cents perfect fifth 12: 6 192/125 743.014 cents classic diminished sixth 12: 4 125/81 751.121 cents 12: 2 972/625 764.520 cents 12: 7 25/16 772.627 cents classic augmented fifth 13: 12 8/5 813.686 cents minor sixth 13: 2 3125/1944 821.794 cents 13: 3 81/50 835.193 cents acute minor sixth 13: 2 625/384 843.300 cents 14: 3 5184/3125 876.251 cents 14: 15 5/3 884.359 cents major sixth, BP sixth 14: 1 27/16 905.865 cents Pythagorean major sixth 15: 3 128/75 925.418 cents diminished seventh 15: 7 216/125 946.924 cents semi-augmented sixth 15: 9 125/72 955.031 cents classic augmented sixth 16: 7 16/9 996.090 cents Pythagorean minor seventh 16: 10 9/5 1017.596 cents just minor seventh, BP seventh 16: 2 3125/1728 1025.704 cents 17: 4 1152/625 1058.655 cents 17: 7 50/27 1066.762 cents grave major seventh 17: 1 5832/3125 1080.161 cents 17: 7 15/8 1088.269 cents classic major seventh 18: 11 48/25 1129.328 cents classic diminished octave 18: 4 625/324 1137.435 cents octave - major diesis 18: 1 243/125 1150.834 cents octave - maximal diesis 18: 3 125/64 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 : 70.7 133.2 203.9 253.1 315.6 386.3 457.0 498.0 568.7 631.3 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1129.3 1200.0 70.7 : 62.6 133.2 182.4 245.0 315.6 386.3 427.4 498.0 560.6 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1058.7 1129.3 1200.0 133.2 : 70.7 119.8 182.4 253.1 323.7 364.8 435.5 498.0 568.7 639.4 680.4 751.1 821.8 884.4 955.0 996.1 1066.8 1137.4 1200.0 203.9 : 49.2 111.7 182.4 253.1 294.1 364.8 427.4 498.0 568.7 609.8 680.4 751.1 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 253.1 : 62.6 133.2 203.9 245.0 315.6 378.2 448.9 519.6 560.6 631.3 702.0 764.5 835.2 876.3 946.9 1017.6 1080.2 1150.8 1200.0 315.6 : 70.7 141.3 182.4 253.1 315.6 386.3 457.0 498.0 568.7 639.4 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1137.4 1200.0 386.3 : 70.7 111.7 182.4 245.0 315.6 386.3 427.4 498.0 568.7 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1066.8 1129.3 1200.0 457.0 : 41.1 111.7 174.3 245.0 315.6 356.7 427.4 498.0 560.6 631.3 672.3 743.0 813.7 876.3 946.9 996.1 1058.7 1129.3 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 457.0 519.6 590.2 631.3 702.0 772.6 835.2 905.9 955.0 1017.6 1088.3 1158.9 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 386.3 448.9 519.6 560.6 631.3 702.0 764.5 835.2 884.4 946.9 1017.6 1088.3 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 323.7 386.3 457.0 498.0 568.7 639.4 702.0 772.6 821.8 884.4 955.0 1025.7 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 253.1 315.6 386.3 427.4 498.0 568.7 631.3 702.0 751.1 813.7 884.4 955.0 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 182.4 245.0 315.6 356.7 427.4 498.0 560.6 631.3 680.4 743.0 813.7 884.4 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 141.3 203.9 274.6 315.6 386.3 457.0 519.6 590.2 639.4 702.0 772.6 843.3 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 70.7 133.2 203.9 245.0 315.6 386.3 448.9 519.6 568.7 631.3 702.0 772.6 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 955.0 : 62.6 133.2 174.3 245.0 315.6 378.2 448.9 498.0 560.6 631.3 702.0 743.0 813.7 876.3 946.9 1017.6 1058.7 1129.3 1200.0 1017.6: 70.7 111.7 182.4 253.1 315.6 386.3 435.5 498.0 568.7 639.4 680.4 751.1 813.7 884.4 955.0 996.1 1066.8 1137.4 1200.0 1088.3: 41.1 111.7 182.4 245.0 315.6 364.8 427.4 498.0 568.7 609.8 680.4 743.0 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 1129.3: 70.7 141.3 203.9 274.6 323.7 386.3 457.0 527.7 568.7 639.4 702.0 772.6 843.3 884.4 955.0 1025.7 1088.3 1158.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 70.6724 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 2: 111.7313 .. 141.3449 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 3: 174.2964 .. 203.9100 cents 3125/3072, 29.6136 cents 1990656/1953125, 32.9516 cents 4: 244.9689 .. 274.5824 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 5: 294.1350 .. 323.7486 cents 3125/3072, 29.6136 cents 2048/2025, 19.5526 cents 6: 356.7001 .. 386.3137 cents 3125/3072, 29.6136 cents 1990656/1953125, 32.9516 cents 7: 427.3726 .. 456.9861 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 8: 498.0450 .. 527.6586 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 9: 560.6101 .. 590.2237 cents 3125/3072, 29.6136 cents 1990656/1953125, 32.9516 cents 10: 609.7763 .. 639.3899 cents 3125/3072, 29.6136 cents 2048/2025, 19.5526 cents 11: 672.3414 .. 701.9550 cents 3125/3072, 29.6136 cents 1990656/1953125, 32.9516 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: 876.2514 .. 905.8650 cents 3125/3072, 29.6136 cents 1990656/1953125, 32.9516 cents 15: 925.4176 .. 955.0311 cents 3125/3072, 29.6136 cents 2048/2025, 19.5526 cents 16: 996.0900 .. 1025.7036 cents 3125/3072, 29.6136 cents 128/125, 41.0589 cents 17: 1058.6551 .. 1088.2687 cents 3125/3072, 29.6136 cents 1990656/1953125, 32.9516 cents 18: 1129.3276 .. 1158.9411 cents 3125/3072, 29.6136 cents 128/125, 41.0589 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 : 25/24, 70.6724 cents Average / Smallest step : 1.538228 Largest / Average step : 1.118980 Largest / Smallest step : 1.721247 Median interval of one step : 25/24, 70.6724 cents, amount: 11 Most common interval of one step : 25/24, 70.6724 cents, amount: 11 Least squares average step : 63.42480 cents, oct.: 1205.07128 cents Scale is strictly proper Step pattern alph. order: ABACBAADABAADAABADA Step pattern size order : DCDBCDDADCDDADDCDAD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.289762 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555796 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 Most common intervals : 6/5, 315.6413 cents & inv., amount: 15 Most common triad is 0.0 315.641 884.359 cents, amount: 11 Number of recognisable fifths : 13, average 701.9550 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 15 25 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 57.8947% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions with margin 29.6136 cents: 11 -- Rational properties -- Prime limit : 5 Odd number limit : 3125 (O: 3125 U: 3125) Highest odd numerator or denominator: 125 Scale harmonicity : 0.017544 Average absolute harmonicity : 0.138579 Specific harmonicity : 0.105089 Fundamental : 1/21600, -14.3987 octaves, 0.0121 Hz. Guide tone : 54000, 15.7207 octaves, 14127780.526 Hz. Exponens Consonantiae : 1.166400E+09, 30.11942 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 540.0, average 28.42105 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 21.54649, average 1.13403 Sum of Tenney's harmonic distance : 42.36430, average 2.22970 Vogel's harmonic complexity : 25.94737 Wille's k value : 14062 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 11 Triangular lattice diameter : 6 Lattice compactness : 808.72666, average 4.25646 Lattice compactness (without 2's) : 535.78385, average 2.81992 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 4 -0.73684 40 1 3: -3 .. 3 0.10526 24 3 5: -2 .. 3 0.47368 27 15 Average exponent except 2's : 11 / 19 = 0.57895 Average absolute exponent except 2's: 51 / 19 = 2.68421 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: 8.4052 c. M: 14.8809 c. 34: 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 P M ME S SD: 4.1760 c. M:-7.9389 c. 53: 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 3 3 2 3 SP M ME S SD: 2.3590 c. M: 4.1560 c. 84: 5 4 5 4 4 5 5 3 5 4 5 5 3 5 5 4 5 3 5 SP T3 SD: 2.3496 c. M: 4.6661 c. 99: 6 5 6 4 5 6 6 3 6 5 6 6 3 6 6 5 6 3 6 SP SD: 1.7997 c. M:-3.6199 c. 118: 7 6 7 5 6 7 7 4 7 6 7 7 4 7 7 6 7 4 7 SP SD: 0.5897 c. M:-1.1611 c. 171: 10 9 10 7 9 10 10 6 10 9 10 10 6 10 10 9 10 6 10 SP SD: 0.4185 c. M: 0.8458 c. 270: 16 14 16 11 14 16 16 9 16 14 16 16 9 16 16 14 16 9 16 SP SD: 0.3993 c. M:-0.7916 c. 289: 17 15 17 12 15 17 17 10 17 15 17 17 10 17 17 15 17 10 17 SP SD: 0.2268 c. M: 0.4498 c. 441: 26 23 26 18 23 26 26 15 26 23 26 26 15 26 26 23 26 15 26 SP SD: 0.0946 c. M:-0.1716 c. 612: 36 32 36 25 32 36 36 21 36 32 36 36 21 36 36 32 36 21 36 SP SD: 0.0750 c. M: 0.1350 c. 730: 43 38 43 30 38 43 43 25 43 38 43 43 25 43 43 38 43 25 43 SP SD: 0.0438 c. M: 0.0869 c. 1171: 69 61 69 48 61 69 69 40 69 61 69 69 40 69 69 61 69 40 69 SP SD: 0.0300 c. M:-0.0591 c. 1342: 79 70 79 55 70 79 79 46 79 70 79 79 46 79 79 70 79 46 79 SP SD: 0.0281 c. M: 0.0562 c. 1783: 105 93 105 73 93 105 105 61 105 93 105 105 61 105 105 93 105 61 105 SP SD: 0.0106 c. M:-0.0210 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: 3.4487 cents 5 .. 10 match: 5 H SD: 2.7590 cents 6 .. 12 match: 6 H SD: 5.7721 cents 7 .. 14 match: 7 H SD: 6.3906 cents 8 .. 16 match: 8 H SD: 4.3544 cents 9 .. 18 match: 9 H SD: 5.1942 cents 10 .. 20 match: 10 H SD: 5.2068 cents 11 .. 22 match: 11 H SD: 6.5139 cents 12 .. 24 match: 12 H SD: 4.2129 cents 13 .. 26 match: 13 H SD: 5.3463 cents 14 .. 28 match: 14 H SD: 4.7490 cents 15 .. 30 match: 15 H SD: 4.0143 cents 16 .. 32 match: 16 H SD: 3.6412 cents 17 .. 34 match: 15 S SD: 5.6273 cents 18 .. 36 match: 17 S SD: 4.0679 cents 19 .. 38 match: 15 SD: 4.8701 cents 20 .. 40 match: 17 SD: 3.2973 cents 21 .. 42 match: 18 S SD: 3.8034 cents 22 .. 44 match: 17 SD: 4.1295 cents 23 .. 46 match: 19 SD: 3.0503 cents 24 .. 48 match: 18 SD: 2.4410 cents 25 .. 50 match: 18 SD: 2.3400 cents 28 .. 56 match: 18 SD: 3.1139 cents 30 .. 60 match: 19 SD: 2.3712 cents 36 .. 72 match: 19 SD: 2.2966 cents 39 .. 78 match: 19 SD: 1.6741 cents 46 .. 92 match: 19 SD: 1.5958 cents 48 .. 96 match: 19 SD: 1.4682 cents 50 .. 100 match: 19 SD: 1.2569 cents 64 .. 128 match: 19 SD: 0.9187 cents 72 .. 144 match: 19 SD: 0.9061 cents 75 .. 150 match: 19 SD: 0.8216 cents 90 .. 180 match: 19 SD: 0.7342 cents 96 .. 192 match: 19 SD: 0.5611 cents 120 .. 240 match: 19 SD: 0.5049 cents 150 .. 300 match: 19 SD: 0.4813 cents 152 .. 304 match: 19 SD: 0.4397 cents 159 .. 318 match: 19 SD: 0.4377 cents 160 .. 320 match: 19 SD: 0.3864 cents 185 .. 370 match: 19 SD: 0.3495 cents 210 .. 420 match: 19 SD: 0.3481 cents 215 .. 430 match: 19 SD: 0.3048 cents 216 .. 432 match: 19 SD: 0.2427 cents 240 .. 480 match: 19 SD: 0.2404 cents 265 .. 530 match: 19 SD: 0.2337 cents 285 .. 570 match: 19 SD: 0.2321 cents 288 .. 576 match: 19 SD: 0.1729 cents 336 .. 672 match: 19 SD: 0.1676 cents 360 .. 720 match: 19 SD: 0.1485 cents 375 .. 750 match: 19 SD: 0.1460 cents 400 .. 800 match: 19 SD: 0.1423 cents 450 .. 900 match: 19 SD: 0.1172 cents 552 .. 1104 match: 19 SD: 0.1113 cents 560 .. 1120 match: 19 SD: 0.1032 cents 576 .. 1152 match: 19 SD: 0.0846 cents