Scala analysis: fivecrys2
Second 5-limit crystal ball
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: 9/8 203.910002 major 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: 16/9 996.089998 Pythagorean minor 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: 81/80 21.5063 syntonic comma, Didymus comma 5: 16/15 111.7313 minor diatonic semitone 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: 16/15 111.7313 minor diatonic semitone 16: 81/80 21.5063 syntonic comma, Didymus comma 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: 2 81/80 21.506 cents syntonic comma, Didymus comma 1: 4 128/125 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 16/15 111.731 cents minor diatonic semitone 2: 2 135/128 92.179 cents major chroma, major limma 2: 8 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 10/9 182.404 cents minor whole tone 3: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 3: 8 10/9 182.404 cents minor whole tone 3: 7 9/8 203.910 cents major whole tone 3: 2 256/225 223.463 cents Neapolitan diminished third 4: 2 9/8 203.910 cents major whole tone 4: 1 256/225 223.463 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: 4 75/64 274.582 cents classic augmented second 4: 2 32/27 294.135 cents Pythagorean minor third 5: 2 75/64 274.582 cents classic augmented second 5: 2 32/27 294.135 cents Pythagorean minor third 5: 12 6/5 315.641 cents minor third 5: 1 625/512 345.255 cents classic neutral third 5: 2 100/81 364.807 cents grave major third 6: 2 6/5 315.641 cents minor third 6: 2 768/625 356.700 cents 6: 1 100/81 364.807 cents grave major third 6: 12 5/4 386.314 cents major third 6: 2 32/25 427.373 cents classic diminished fourth 7: 2 5/4 386.314 cents major third 7: 7 32/25 427.373 cents classic diminished fourth 7: 2 162/125 448.879 cents 7: 6 125/96 456.986 cents classic augmented third 7: 2 4/3 498.045 cents perfect fourth 8: 1 81/64 407.820 cents Pythagorean major third 8: 12 4/3 498.045 cents perfect fourth 8: 4 27/20 519.551 cents acute fourth 8: 2 25/18 568.717 cents classic augmented fourth 9: 2 27/20 519.551 cents acute fourth 9: 2 512/375 539.104 cents double diminished fifth 9: 2 864/625 560.610 cents 9: 7 25/18 568.717 cents classic augmented fourth 9: 4 45/32 590.224 cents diatonic tritone 9: 2 64/45 609.776 cents 2nd tritone 10: 2 45/32 590.224 cents diatonic tritone 10: 4 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: 2 375/256 660.896 cents double augmented fourth 10: 2 40/27 680.449 cents grave fifth 11: 2 36/25 631.283 cents classic diminished fifth 11: 4 40/27 680.449 cents grave fifth 11: 12 3/2 701.955 cents perfect fifth 11: 1 128/81 792.180 cents Pythagorean minor sixth 12: 2 3/2 701.955 cents perfect fifth 12: 6 192/125 743.014 cents classic diminished sixth 12: 2 125/81 751.121 cents 12: 7 25/16 772.627 cents classic augmented fifth 12: 2 8/5 813.686 cents minor sixth 13: 2 25/16 772.627 cents classic augmented fifth 13: 12 8/5 813.686 cents minor sixth 13: 1 81/50 835.193 cents acute minor sixth 13: 2 625/384 843.300 cents 13: 2 5/3 884.359 cents major sixth, BP sixth 14: 2 81/50 835.193 cents acute minor sixth 14: 1 1024/625 854.745 cents two (classic diminished fourth) 14: 12 5/3 884.359 cents major sixth, BP sixth 14: 2 27/16 905.865 cents Pythagorean major sixth 14: 2 128/75 925.418 cents diminished seventh 15: 2 27/16 905.865 cents Pythagorean major sixth 15: 4 128/75 925.418 cents diminished seventh 15: 4 216/125 946.924 cents semi-augmented sixth 15: 6 125/72 955.031 cents classic augmented sixth 15: 1 225/128 976.537 cents augmented sixth 15: 2 16/9 996.090 cents Pythagorean minor seventh 16: 2 225/128 976.537 cents augmented sixth 16: 7 16/9 996.090 cents Pythagorean minor seventh 16: 8 9/5 1017.596 cents just minor seventh, BP seventh 16: 2 50/27 1066.762 cents grave major seventh 17: 2 9/5 1017.596 cents just minor seventh, BP seventh 17: 3 1152/625 1058.655 cents 17: 4 50/27 1066.762 cents grave major seventh 17: 8 15/8 1088.269 cents classic major seventh 17: 2 256/135 1107.821 cents octave - major chroma 18: 2 15/8 1088.269 cents classic major seventh 18: 10 48/25 1129.328 cents classic diminished octave 18: 1 625/324 1137.435 cents octave - major diesis 18: 4 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 18: 2 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.00000 = 5
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 : 70.7 111.7 182.4 203.9 315.6 386.3 427.4 498.0 568.7 631.3 702.0 772.6 813.7 884.4 996.1 1017.6 1088.3 1129.3 1200.0 70.7 : 41.1 111.7 133.2 245.0 315.6 356.7 427.4 498.0 560.6 631.3 702.0 743.0 813.7 925.4 946.9 1017.6 1058.7 1129.3 1200.0 111.7 : 70.7 92.2 203.9 274.6 315.6 386.3 457.0 519.6 590.2 660.9 702.0 772.6 884.4 905.9 976.5 1017.6 1088.3 1158.9 1200.0 182.4 : 21.5 133.2 203.9 245.0 315.6 386.3 448.9 519.6 590.2 631.3 702.0 813.7 835.2 905.9 946.9 1017.6 1088.3 1129.3 1200.0 203.9 : 111.7 182.4 223.5 294.1 364.8 427.4 498.0 568.7 609.8 680.4 792.2 813.7 884.4 925.4 996.1 1066.8 1107.8 1178.5 1200.0 315.6 : 70.7 111.7 182.4 253.1 315.6 386.3 457.0 498.0 568.7 680.4 702.0 772.6 813.7 884.4 955.0 996.1 1066.8 1088.3 1200.0 386.3 : 41.1 111.7 182.4 245.0 315.6 386.3 427.4 498.0 609.8 631.3 702.0 743.0 813.7 884.4 925.4 996.1 1017.6 1129.3 1200.0 427.4 : 70.7 141.3 203.9 274.6 345.3 386.3 457.0 568.7 590.2 660.9 702.0 772.6 843.3 884.4 955.0 976.5 1088.3 1158.9 1200.0 498.0 : 70.7 133.2 203.9 274.6 315.6 386.3 498.0 519.6 590.2 631.3 702.0 772.6 813.7 884.4 905.9 1017.6 1088.3 1129.3 1200.0 568.7 : 62.6 133.2 203.9 245.0 315.6 427.4 448.9 519.6 560.6 631.3 702.0 743.0 813.7 835.2 946.9 1017.6 1058.7 1129.3 1200.0 631.3 : 70.7 141.3 182.4 253.1 364.8 386.3 457.0 498.0 568.7 639.4 680.4 751.1 772.6 884.4 955.0 996.1 1066.8 1137.4 1200.0 702.0 : 70.7 111.7 182.4 294.1 315.6 386.3 427.4 498.0 568.7 609.8 680.4 702.0 813.7 884.4 925.4 996.1 1066.8 1129.3 1200.0 772.6 : 41.1 111.7 223.5 245.0 315.6 356.7 427.4 498.0 539.1 609.8 631.3 743.0 813.7 854.7 925.4 996.1 1058.7 1129.3 1200.0 813.7 : 70.7 182.4 203.9 274.6 315.6 386.3 457.0 498.0 568.7 590.2 702.0 772.6 813.7 884.4 955.0 1017.6 1088.3 1158.9 1200.0 884.4 : 111.7 133.2 203.9 245.0 315.6 386.3 427.4 498.0 519.6 631.3 702.0 743.0 813.7 884.4 946.9 1017.6 1088.3 1129.3 1200.0 996.1 : 21.5 92.2 133.2 203.9 274.6 315.6 386.3 407.8 519.6 590.2 631.3 702.0 772.6 835.2 905.9 976.5 1017.6 1088.3 1200.0 1017.6: 70.7 111.7 182.4 253.1 294.1 364.8 386.3 498.0 568.7 609.8 680.4 751.1 813.7 884.4 955.0 996.1 1066.8 1178.5 1200.0 1088.3: 41.1 111.7 182.4 223.5 294.1 315.6 427.4 498.0 539.1 609.8 680.4 743.0 813.7 884.4 925.4 996.1 1107.8 1129.3 1200.0 1129.3: 70.7 141.3 182.4 253.1 274.6 386.3 457.0 498.0 568.7 639.4 702.0 772.6 843.3 884.4 955.0 1066.8 1088.3 1158.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 111.7313 cents 256/243, 90.2250 cents 81/80, 21.5063 cents 2: 92.1787 .. 182.4037 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 3: 133.2376 .. 223.4626 cents 256/243, 90.2250 cents 243/250,-49.1661 cents 4: 203.9100 .. 294.1350 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 5: 274.5824 .. 364.8074 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 6: 315.6413 .. 427.3726 cents 16/15, 111.7313 cents 243/250,-49.1661 cents 7: 386.3137 .. 498.0450 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 8: 407.8200 .. 568.7174 cents 800/729, 160.8974 cents 243/256,-90.2250 cents 9: 519.5513 .. 609.7763 cents 256/243, 90.2250 cents 243/250,-49.1661 cents 10: 590.2237 .. 680.4487 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 11: 631.2826 .. 792.1800 cents 800/729, 160.8974 cents 243/250,-49.1661 cents 12: 701.9550 .. 813.6863 cents 16/15, 111.7313 cents 243/256,-90.2250 cents 13: 772.6274 .. 884.3587 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 14: 835.1926 .. 925.4176 cents 256/243, 90.2250 cents 243/250,-49.1661 cents 15: 905.8650 .. 996.0900 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 16: 976.5374 .. 1066.7624 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 17: 1017.5963 .. 1107.8213 cents 256/243, 90.2250 cents 243/250,-49.1661 cents 18: 1088.2687 .. 1178.4937 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 2.936717 Largest / Average step : 1.769079 Largest / Smallest step : 5.195284 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 : 63.46707 cents, oct.: 1205.87429 cents Scale is not proper Step pattern alph. order: ABACDABAAEAABADCABA Step pattern size order : DBDAEDBDDCDDBDEADBD Scale is not a Constant Structure Scale diversity : 1.344690 Lumma stability : 0.035844 Lumma impropriety factor : 0.546106 Number of different interval sizes : 60 = 3.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 15625/15552, 8.1073 cents Number of recognisable fifths : 14, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete diamond : 1 3 5 9 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 class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 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 : 625 (O: 625 U: 625) Highest odd numerator or denominator: 25 Scale harmonicity : 0.022091 Average absolute harmonicity : 0.147133 Specific harmonicity : 0.126066 Fundamental : 1/3600, -11.8138 octaves, 0.0727 Hz. Guide tone : 7200, 12.8138 octaves, 1883704.070 Hz. Exponens Consonantiae : 2.592000E+07, 24.62756 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 254.5, average 13.39474 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 18.30692, average 0.96352 Sum of Tenney's harmonic distance : 36.76714, average 1.93511 Vogel's harmonic complexity : 20.52632 Wille's k value : 2812 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 789.58826, average 4.15573 Lattice compactness (without 2's) : 447.51012, average 2.35532 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.52632 44 1 3: -2 .. 2 0.00000 20 4 5: -2 .. 2 0.00000 20 14 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 40 / 19 = 2.10526 Scale is weakly epimorphic with val: <19 27 45| Scale is weakly epimorphic with val: <19 29 42| Scale is weakly epimorphic with val: <19 29 44| Scale is weakly epimorphic with val: <19 32 42| Scale is weakly epimorphic with val: <19 32 47|
FIT/MODE
19: 1 1 1 0 2 1 1 1 1 1 1 1 1 1 2 0 1 1 1 N T3 I SD: 9.4651 c. M: 14.7327 c. 31: 2 1 2 0 3 2 1 2 2 1 2 2 1 2 3 0 2 1 2 N I SD: 7.2850 c. M:-11.9277 c. 34: 2 1 2 1 3 2 1 2 2 2 2 2 1 2 3 1 2 1 2 N I SD: 4.4143 c. M:-7.8547 c. 53: 3 2 3 1 5 3 2 3 3 3 3 3 2 3 5 1 3 2 3 N I SD: 1.7847 c. M: 2.8161 c. 118: 7 4 7 2 11 7 4 7 7 6 7 7 4 7 11 2 7 4 7 N I SD: 0.4435 c. M:-0.7741 c. 171: 10 6 10 3 16 10 6 10 10 9 10 10 6 10 16 3 10 6 10 N I SD: 0.3935 c. M: 0.6976 c. 289: 17 10 17 5 27 17 10 17 17 15 17 17 10 17 27 5 17 10 17 N I SD: 0.2586 c. M:-0.4498 c. 323: 19 11 19 6 30 19 11 19 19 17 19 19 11 19 30 6 19 11 19 N I SD: 0.2446 c. M:-0.4244 c. 441: 26 15 26 8 41 26 15 26 26 23 26 26 15 26 41 8 26 15 26 N I SD: 0.1083 c. M:-0.1716 c. 612: 36 21 36 11 57 36 21 36 36 32 36 36 21 36 57 11 36 21 36 N I SD: 0.0550 c. M:-0.0900 c. 730: 43 25 43 13 68 43 25 43 43 38 43 43 25 43 68 13 43 25 43 N I SD: 0.0426 c. M:-0.0744 c. 1171: 69 40 69 21 109 69 40 69 69 61 69 69 40 69 109 21 69 40 69 N I SD: 0.0257 c. M: 0.0455 c. 1783: 105 61 105 32 166 105 61 105 105 93 105 105 61 105 166 32 105 61 105 N I SD: 0.0095 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: 2.7590 cents 6 .. 12 match: 6 H SD: 9.7006 cents 7 .. 14 match: 7 H SD: 8.7405 cents 8 .. 16 match: 8 H SD: 5.2538 cents 9 .. 18 match: 9 H SD: 3.9445 cents 10 .. 20 match: 10 H SD: 5.2129 cents 11 .. 22 match: 10 S SD: 6.9905 cents 12 .. 24 match: 12 H SD: 6.4491 cents 13 .. 26 match: 13 H SD: 6.5392 cents 14 .. 28 match: 13 SD: 4.5654 cents 15 .. 30 match: 14 SD: 3.8851 cents 16 .. 32 match: 16 H SD: 3.8254 cents 17 .. 34 match: 15 S SD: 5.3538 cents 18 .. 36 match: 15 S SD: 3.1420 cents 19 .. 38 match: 13 SD: 5.2608 cents 20 .. 40 match: 16 S SD: 4.0900 cents 21 .. 42 match: 18 SD: 3.6531 cents 22 .. 44 match: 17 SD: 4.0349 cents 23 .. 46 match: 16 SD: 3.6550 cents 24 .. 48 match: 16 SD: 2.9944 cents 25 .. 50 match: 18 SD: 2.6433 cents 26 .. 52 match: 17 SD: 2.8353 cents 27 .. 54 match: 18 SD: 2.9560 cents 28 .. 56 match: 18 SD: 2.8172 cents 29 .. 58 match: 18 SD: 2.8426 cents 30 .. 60 match: 18 SD: 2.2117 cents 32 .. 64 match: 18 SD: 2.2546 cents 33 .. 66 match: 17 SD: 2.7023 cents 34 .. 68 match: 18 SD: 2.6874 cents 35 .. 70 match: 18 SD: 2.5226 cents 36 .. 72 match: 18 SD: 1.9920 cents 37 .. 74 match: 18 SD: 2.6107 cents 38 .. 76 match: 18 SD: 2.6434 cents 39 .. 78 match: 19 SD: 1.9542 cents 41 .. 82 match: 18 SD: 1.9385 cents 42 .. 84 match: 18 SD: 2.0827 cents 43 .. 86 match: 18 SD: 1.9198 cents 44 .. 88 match: 19 SD: 1.7898 cents 45 .. 90 match: 19 SD: 1.6248 cents 46 .. 92 match: 19 SD: 1.4608 cents 48 .. 96 match: 19 SD: 1.3780 cents 50 .. 100 match: 18 SD: 1.4220 cents 51 .. 102 match: 18 SD: 1.6559 cents 54 .. 108 match: 19 SD: 1.3585 cents 57 .. 114 match: 19 SD: 1.3451 cents 59 .. 118 match: 18 SD: 1.5361 cents 60 .. 120 match: 19 SD: 1.3719 cents 62 .. 124 match: 19 SD: 1.3436 cents 63 .. 126 match: 19 SD: 1.3188 cents 64 .. 128 match: 19 SD: 0.9251 cents 72 .. 144 match: 19 SD: 0.7944 cents 89 .. 178 match: 19 SD: 0.7800 cents 90 .. 180 match: 19 SD: 0.6819 cents 96 .. 192 match: 19 SD: 0.6648 cents 118 .. 236 match: 19 SD: 0.6336 cents 120 .. 240 match: 19 SD: 0.5066 cents 135 .. 270 match: 19 SD: 0.4961 cents 136 .. 272 match: 19 SD: 0.4571 cents 144 .. 288 match: 19 SD: 0.4153 cents 168 .. 336 match: 19 SD: 0.4031 cents 190 .. 380 match: 19 SD: 0.3665 cents 192 .. 384 match: 19 SD: 0.3601 cents 200 .. 400 match: 19 SD: 0.3326 cents 210 .. 420 match: 19 SD: 0.3322 cents 215 .. 430 match: 19 SD: 0.3248 cents 216 .. 432 match: 19 SD: 0.3008 cents 224 .. 448 match: 19 SD: 0.2837 cents 240 .. 480 match: 19 SD: 0.2062 cents 288 .. 576 match: 19 SD: 0.1813 cents 336 .. 672 match: 19 SD: 0.1812 cents 360 .. 720 match: 19 SD: 0.1173 cents 432 .. 864 match: 19 SD: 0.1092 cents 576 .. 1152 match: 19 SD: 0.0983 cents 600 .. 1200 match: 19 SD: 0.0811 cents