Scala analysis: fivecrys1
First 5-limit crystal ball
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 6/5 315.6413 minor third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 2 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 36/25 631.283 cents classic diminished fifth 3: 2 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 4: 2 8/5 813.686 cents minor sixth 5: 1 25/18 568.717 cents classic augmented fourth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 386.3 498.0 702.0 813.7 884.4 1200.0 315.6 : 70.7 182.4 386.3 498.0 568.7 884.4 1200.0 386.3 : 111.7 315.6 427.4 498.0 813.7 1129.3 1200.0 498.0 : 203.9 315.6 386.3 702.0 1017.6 1088.3 1200.0 702.0 : 111.7 182.4 498.0 813.7 884.4 996.1 1200.0 813.7 : 70.7 386.3 702.0 772.6 884.4 1088.3 1200.0 884.4 : 315.6 631.3 702.0 813.7 1017.6 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 182.4037 .. 631.2826 cents 162/125, 448.8789 cents 25/27,-133.2376 cents 3: 386.3137 .. 701.9550 cents 6/5, 315.6413 cents 125/144,-244.9689 cents 4: 498.0450 .. 813.6863 cents 6/5, 315.6413 cents 8/9,-203.9100 cents 5: 568.7174 .. 1017.5963 cents 162/125, 448.8789 cents 125/144,-244.9689 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 165.46291 cents, oct.: 1158.24037 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.445234 Lumma stability : 0.117787 Lumma impropriety factor : 0.578206 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 81/80, 21.5063 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 5 Odd number limit : 25 (O: 25 U: 25) Highest odd numerator or denominator: 5 Scale harmonicity : 0.043228 Average absolute harmonicity : 0.274582 Specific harmonicity : 0.235640 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 7.200000E+03, 12.81378 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 28.0, average 4.00000 Mersenne's string divisions : 360360 Sum of van Prooijen's expressibility: 3.75012, average 0.53573 Sum of Tenney's harmonic distance : 7.71466, average 1.10209 Vogel's harmonic complexity : 10.57143 Wille's k value : 37 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 70.65645, average 2.52344 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 10 1 3: -1 .. 1 0.00000 4 2 5: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 15| Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <7 12 15| Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 28.7498 c. M: 43.4566 c. 12: 3 1 1 2 1 1 3 N I SD: 11.1584 c. M: 15.6413 c. Mela Yagapriya, Raga Kalahamsa 19: 5 1 2 3 2 1 5 N I SD: 5.5133 c. M: 7.3663 c. 31: 8 2 3 5 3 2 8 N I SD: 4.2434 c. M: 5.9639 c. 34: 9 2 3 6 3 2 9 N I SD: 2.5713 c. M:-3.9274 c. 53: 14 3 5 9 5 3 14 N I SD: 1.0396 c. M: 1.4081 c. 118: 31 7 11 20 11 7 31 N I SD: 0.2583 c. M:-0.3870 c. 171: 45 10 16 29 16 10 45 N I SD: 0.2292 c. M: 0.3488 c. 289: 76 17 27 49 27 17 76 N I SD: 0.1506 c. M:-0.2249 c. 323: 85 19 30 55 30 19 85 N I SD: 0.1425 c. M:-0.2122 c. 441: 116 26 41 75 41 26 116 N I SD: 0.0631 c. M:-0.0858 c. 612: 161 36 57 104 57 36 161 N I SD: 0.0320 c. M:-0.0450 c. 730: 192 43 68 124 68 43 192 N I SD: 0.0248 c. M:-0.0372 c. 1171: 308 69 109 199 109 69 308 N I SD: 0.0150 c. M:-0.0228 c. 1783: 469 105 166 303 166 105 469 N I SD: 0.0056 c. M:-0.0080 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5:6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 21.1168 cents 5:6 x 7 x 8 x 10 S SD: 21.1168 cents 6:7 x 8:9 x 10:12 S SD: 9.7541 cents 7:8:9 x x 11:12:14 SD: 22.6847 cents 8 x 10:11:12:13 x 16 SD: 11.9306 cents 9:11 x 12 x 14:15:18 SD: 11.6407 cents 10:12 x 13:15:16:17:20 SD: 9.2743 cents 11:13:14:15:17 x 18:22 SD: 13.8098 cents 12:14:15:16:18:19:20:24 S SD: 7.4329 cents 13 x 16:17:20:21:22:26 SD: 11.4805 cents 14:17:18:19:21:22:23:28 SD: 10.4304 cents 15:18:19:20:23:24:25:30 SD: 6.3466 cents 20:24:25:27:30:32:33:40 SD: 3.9519 cents 24:29:30:32:36:38:40:48 SD: 3.1042 cents 36:43:45:48:54:58:60:72 SD: 2.0607 cents 40:48:50:53:60:64:67:80 SD: 1.9814 cents 48:58:60:64:72:77:80:96 SD: 1.8284 cents 60:72:75:80:90:96:100:120 S SD: 0.0000 cents