Scala analysis: xen07-chalmers-ariel
Ariel
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: 125/108 253.076139 semi-augmented whole tone 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: 216/125 946.923861 semi-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: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 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: 648/625 62.5651 major diesis 16: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 4 128/125 41.059 cents minor diesis, diesis 1: 3 648/625 62.565 cents major diesis 1: 12 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 8 16/15 111.731 cents minor diatonic semitone 2: 6 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 5 625/576 141.345 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: 1 256/225 223.463 cents Neapolitan diminished third 4: 8 144/125 244.969 cents classic diminished third 4: 6 125/108 253.076 cents semi-augmented whole tone 4: 4 75/64 274.582 cents classic augmented second 5: 2 32/27 294.135 cents Pythagorean minor third 5: 14 6/5 315.641 cents minor third 5: 2 3125/2592 323.749 cents 5: 1 625/512 345.255 cents classic neutral third 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: 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: 2 512/375 539.104 cents double diminished fifth 9: 4 864/625 560.610 cents 9: 9 25/18 568.717 cents classic augmented fourth 9: 4 45/32 590.224 cents diatonic tritone 10: 4 64/45 609.776 cents 2nd tritone 10: 9 36/25 631.283 cents classic diminished fifth 10: 4 625/432 639.390 cents 10: 2 375/256 660.896 cents double augmented fourth 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: 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: 1 1024/625 854.745 cents two (classic diminished fourth) 14: 2 5184/3125 876.251 cents 14: 14 5/3 884.359 cents major sixth, BP sixth 14: 2 27/16 905.865 cents Pythagorean major sixth 15: 4 128/75 925.418 cents diminished seventh 15: 6 216/125 946.924 cents semi-augmented sixth 15: 8 125/72 955.031 cents classic augmented sixth 15: 1 225/128 976.537 cents 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: 5 1152/625 1058.655 cents 17: 6 50/27 1066.762 cents grave major seventh 17: 8 15/8 1088.269 cents classic major seventh 18: 12 48/25 1129.328 cents classic diminished octave 18: 3 625/324 1137.435 cents octave - major diesis 18: 4 125/64 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 : 70.7 111.7 182.4 253.1 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 70.7 : 41.1 111.7 182.4 245.0 315.6 356.7 427.4 498.0 560.6 631.3 702.0 743.0 813.7 876.3 946.9 1017.6 1058.7 1129.3 1200.0 111.7 : 70.7 141.3 203.9 274.6 315.6 386.3 457.0 519.6 590.2 660.9 702.0 772.6 835.2 905.9 976.5 1017.6 1088.3 1158.9 1200.0 182.4 : 70.7 133.2 203.9 245.0 315.6 386.3 448.9 519.6 590.2 631.3 702.0 764.5 835.2 905.9 946.9 1017.6 1088.3 1129.3 1200.0 253.1 : 62.6 133.2 174.3 245.0 315.6 378.2 448.9 519.6 560.6 631.3 693.8 764.5 835.2 876.3 946.9 1017.6 1058.7 1129.3 1200.0 315.6 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 498.0 568.7 631.3 702.0 772.6 813.7 884.4 955.0 996.1 1066.8 1137.4 1200.0 386.3 : 41.1 111.7 182.4 245.0 315.6 386.3 427.4 498.0 560.6 631.3 702.0 743.0 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 427.4 : 70.7 141.3 203.9 274.6 345.3 386.3 457.0 519.6 590.2 660.9 702.0 772.6 843.3 884.4 955.0 1025.7 1088.3 1158.9 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 448.9 519.6 590.2 631.3 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1129.3 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 378.2 448.9 519.6 560.6 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1058.7 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 315.6 386.3 457.0 498.0 568.7 639.4 680.4 751.1 821.8 884.4 955.0 996.1 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 245.0 315.6 386.3 427.4 498.0 568.7 609.8 680.4 751.1 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 174.3 245.0 315.6 356.7 427.4 498.0 539.1 609.8 680.4 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 133.2 203.9 274.6 315.6 386.3 457.0 498.0 568.7 639.4 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 62.6 133.2 203.9 245.0 315.6 386.3 427.4 498.0 568.7 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 946.9 : 70.7 141.3 182.4 253.1 323.7 364.8 435.5 506.2 568.7 639.4 680.4 751.1 821.8 884.4 955.0 1025.7 1066.8 1137.4 1200.0 1017.6: 70.7 111.7 182.4 253.1 294.1 364.8 435.5 498.0 568.7 609.8 680.4 751.1 813.7 884.4 955.0 996.1 1066.8 1129.3 1200.0 1088.3: 41.1 111.7 182.4 223.5 294.1 364.8 427.4 498.0 539.1 609.8 680.4 743.0 813.7 884.4 925.4 996.1 1058.7 1129.3 1200.0 1129.3: 70.7 141.3 182.4 253.1 323.7 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 1017.6 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: 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 .. 519.5513 cents 81/80, 21.5063 cents 128/125, 41.0589 cents 9: 539.1039 .. 590.2237 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 10: 609.7763 .. 660.8961 cents 16875/16384, 51.1199 cents 2048/2025, 19.5526 cents 11: 680.4487 .. 701.9550 cents 81/80, 21.5063 cents 2048/2025, 19.5526 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 .. 1025.7036 cents 3125/3072, 29.6136 cents 2048/2025, 19.5526 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: 12 Most common interval of one step : 25/24, 70.6724 cents, amount: 12 Least squares average step : 63.24811 cents, oct.: 1201.71408 cents Scale is strictly proper Step pattern alph. order: ABAACABAACAABACAABA Step pattern size order : LSLLMLSLLMLLSLMLLSL Scale is a Constant Structure, by a margin of 11.44529 cents Scale diversity : 1.321092 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.461777 Number of different interval sizes : 64 = 3.55556 / class Number of one step interval sizes : 3 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 : 6/5, 315.6413 cents & inv., amount: 14 Most common triad is 0.0 315.641 884.359 cents, amount: 9 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 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 : 19 = 100.0000% 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 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 : 0.015773 Average absolute harmonicity : 0.138724 Specific harmonicity : 0.107473 Fundamental : 1/54000, -15.7207 octaves, 0.0048 Hz. Guide tone : 108000, 16.7207 octaves, 28255561.053 Hz. Exponens Consonantiae : 5.832000E+09, 32.44134 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 520.5, average 27.39474 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.59225, average 1.08380 Sum of Tenney's harmonic distance : 41.31315, average 2.17438 Vogel's harmonic complexity : 28.52632 Wille's k value : 42187 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 12 Triangular lattice diameter : 6 Lattice compactness : 817.45182, average 4.30238 Lattice compactness (without 2's) : 518.32340, average 2.72802 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.52632 42 1 3: -3 .. 3 0.00000 22 2 5: -3 .. 3 0.00000 26 16 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 48 / 19 = 2.52632 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: 8.2263 c. M: 14.7327 c. 33: 2 1 2 2 2 2 1 2 2 1 2 2 1 2 2 2 2 1 2 P D3 I SD: 8.6498 c. M:-13.6863 c. 34: 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 P D3 I SD: 4.0992 c. M: 6.0173 c. 53: 3 2 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 2 3 SP D3 I SD: 2.2100 c. M: 4.0195 c. 99: 6 3 6 6 5 6 3 6 6 5 6 6 3 6 5 6 6 3 6 P I SD: 1.7259 c. M:-3.1301 c. 118: 7 4 7 7 6 7 4 7 7 6 7 7 4 7 6 7 7 4 7 SP I SD: 0.5569 c. M:-1.1611 c. 171: 10 6 10 10 9 10 6 10 10 9 10 10 6 10 9 10 10 6 10 SP I SD: 0.3984 c. M: 0.6976 c. 270: 16 9 16 16 14 16 9 16 16 14 16 16 9 16 14 16 16 9 16 SP I SD: 0.3849 c. M: 0.7059 c. 289: 17 10 17 17 15 17 10 17 17 15 17 17 10 17 15 17 17 10 17 SP I SD: 0.2242 c. M:-0.3794 c. 441: 26 15 26 26 23 26 15 26 26 23 26 26 15 26 23 26 26 15 26 SP I SD: 0.0930 c. M:-0.1667 c. 612: 36 21 36 36 32 36 21 36 36 32 36 36 21 36 32 36 36 21 36 SP I SD: 0.0702 c. M: 0.1350 c. 730: 43 25 43 43 38 43 25 43 43 38 43 43 25 43 38 43 43 25 43 SP I SD: 0.0426 c. M: 0.0745 c. 1171: 69 40 69 69 61 69 40 69 69 61 69 69 40 69 61 69 69 40 69 SP I SD: 0.0283 c. M: 0.0455 c. 1342: 79 46 79 79 70 79 46 79 79 70 79 79 46 79 70 79 79 46 79 SP I SD: 0.0270 c. M: 0.0492 c. 1783: 105 61 105 105 93 105 61 105 105 93 105 105 61 105 93 105 105 61 105 SP I SD: 0.0102 c. M:-0.0195 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: 5.7721 cents 7 .. 14 match: 7 H SD: 5.1340 cents 8 .. 16 match: 8 H SD: 5.5416 cents 9 .. 18 match: 9 H SD: 4.6119 cents 10 .. 20 match: 10 H SD: 4.8394 cents 11 .. 22 match: 11 H SD: 6.3553 cents 12 .. 24 match: 12 H SD: 4.9562 cents 13 .. 26 match: 13 H SD: 6.0351 cents 14 .. 28 match: 14 H SD: 4.2738 cents 15 .. 30 match: 15 H SD: 4.2159 cents 16 .. 32 match: 16 H SD: 3.9257 cents 17 .. 34 match: 15 SD: 5.3366 cents 18 .. 36 match: 17 S SD: 3.1719 cents 19 .. 38 match: 15 SD: 4.5975 cents 20 .. 40 match: 17 SD: 3.4490 cents 21 .. 42 match: 18 S SD: 3.5178 cents 22 .. 44 match: 17 SD: 4.3177 cents 23 .. 46 match: 18 SD: 4.0163 cents 24 .. 48 match: 18 SD: 3.2111 cents 25 .. 50 match: 19 SD: 2.4526 cents 26 .. 52 match: 18 SD: 2.6584 cents 30 .. 60 match: 18 SD: 2.1678 cents 36 .. 72 match: 18 SD: 1.8074 cents 37 .. 74 match: 18 SD: 2.4761 cents 39 .. 78 match: 19 SD: 1.9800 cents 43 .. 86 match: 19 SD: 1.8286 cents 44 .. 88 match: 19 SD: 1.5221 cents 45 .. 90 match: 19 SD: 1.5125 cents 55 .. 110 match: 19 SD: 1.4558 cents 56 .. 112 match: 19 SD: 1.4256 cents 57 .. 114 match: 19 SD: 1.3787 cents 60 .. 120 match: 19 SD: 1.3305 cents 63 .. 126 match: 19 SD: 1.3181 cents 64 .. 128 match: 19 SD: 0.9722 cents 72 .. 144 match: 19 SD: 0.9261 cents 75 .. 150 match: 19 SD: 0.7737 cents 89 .. 178 match: 19 SD: 0.7708 cents 90 .. 180 match: 19 SD: 0.7172 cents 96 .. 192 match: 19 SD: 0.6500 cents 100 .. 200 match: 19 SD: 0.5777 cents 120 .. 240 match: 19 SD: 0.5165 cents 136 .. 272 match: 19 SD: 0.5076 cents 144 .. 288 match: 19 SD: 0.4576 cents 150 .. 300 match: 19 SD: 0.4571 cents 160 .. 320 match: 19 SD: 0.4349 cents 164 .. 328 match: 19 SD: 0.3906 cents 165 .. 330 match: 19 SD: 0.3672 cents 190 .. 380 match: 19 SD: 0.3588 cents 195 .. 390 match: 19 SD: 0.3558 cents 196 .. 392 match: 19 SD: 0.3321 cents 210 .. 420 match: 19 SD: 0.3095 cents 216 .. 432 match: 19 SD: 0.3069 cents 224 .. 448 match: 19 SD: 0.2941 cents 236 .. 472 match: 19 SD: 0.2741 cents 240 .. 480 match: 19 SD: 0.2158 cents 288 .. 576 match: 19 SD: 0.2121 cents 332 .. 664 match: 19 SD: 0.2073 cents 336 .. 672 match: 19 SD: 0.1863 cents 360 .. 720 match: 19 SD: 0.1386 cents 432 .. 864 match: 19 SD: 0.1248 cents 450 .. 900 match: 19 SD: 0.1138 cents 540 .. 1080 match: 19 SD: 0.1124 cents 600 .. 1200 match: 19 SD: 0.0973 cents