Scala analysis: xen09-chalmers-tritriadic-1-3-5
Tritriadic scale built from 1:3:5
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: 3/2 701.955001 perfect fifth 4: 25/16 772.627428 classic augmented fifth 5: 8/5 813.686286 minor sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 6/5 315.6413 minor third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 6/5 315.6413 minor third 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 128/125 41.0589 minor diesis, diesis 6: 75/64 274.5824 classic augmented second 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 75/64 274.582 cents classic augmented second 1: 2 6/5 315.641 cents minor third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 6/5 315.641 cents minor third 2: 4 5/4 386.314 cents major third 2: 1 32/25 427.373 cents classic diminished fourth 3: 1 5/4 386.314 cents major third 3: 2 32/25 427.373 cents classic diminished fourth 3: 1 125/96 456.986 cents classic augmented third 3: 1 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: 1 3/2 701.955 cents perfect fifth 4: 1 192/125 743.014 cents classic diminished sixth 4: 2 25/16 772.627 cents classic augmented fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 25/16 772.627 cents classic augmented fifth 5: 4 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 15/8 1088.269 cents classic major seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 128/75 925.418 cents diminished seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 2 48/25 1129.328 cents classic diminished octave 6: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 386.3 702.0 772.6 813.7 1088.3 1200.0 315.6 : 70.7 386.3 457.0 498.0 772.6 884.4 1200.0 386.3 : 315.6 386.3 427.4 702.0 813.7 1129.3 1200.0 702.0 : 70.7 111.7 386.3 498.0 813.7 884.4 1200.0 772.6 : 41.1 315.6 427.4 743.0 813.7 1129.3 1200.0 813.7 : 274.6 386.3 702.0 772.6 1088.3 1158.9 1200.0 1088.3: 111.7 427.4 498.0 813.7 884.4 925.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 315.6413 cents 75/64, 274.5824 cents 128/125, 41.0589 cents 2: 111.7313 .. 427.3726 cents 6/5, 315.6413 cents 8/9,-203.9100 cents 3: 386.3137 .. 701.9550 cents 6/5, 315.6413 cents 125/128,-41.0589 cents 4: 498.0450 .. 813.6863 cents 6/5, 315.6413 cents 8/9,-203.9100 cents 5: 772.6274 .. 1088.2687 cents 6/5, 315.6413 cents 125/128,-41.0589 cents 6: 884.3587 .. 1158.9411 cents 75/64, 274.5824 cents 8/9,-203.9100 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 4.175191 Largest / Average step : 1.841241 Largest / Smallest step : 7.687532 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 180.59062 cents, oct.: 1264.13436 cents Scale is not proper Step pattern alph. order: ABABCDE Step pattern size order : EBEBADC Scale is not a Constant Structure Scale diversity : 1.256111 Lumma stability : 0.068431 Lumma impropriety factor : 0.578206 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 3125/3072, 29.6136 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 315.641 813.686 cents Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale contains two identical conjunct "tetrachords" of 3 notes Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.034642 Average absolute harmonicity : 0.248556 Specific harmonicity : 0.190136 Fundamental : 1/80, -6.3219 octaves, 3.2703 Hz. Guide tone : 600, 9.2288 octaves, 156975.339 Hz. Exponens Consonantiae : 4.800000E+04, 15.55075 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 52.5, average 7.50000 Mersenne's string divisions : 6068205 Sum of van Prooijen's expressibility: 5.14806, average 0.73544 Sum of Tenney's harmonic distance : 10.14063, average 1.44866 Vogel's harmonic complexity : 11.00000 Wille's k value : 62 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 91.35062, average 3.26252 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.71429 15 1 3: 0 .. 1 0.42857 3 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 2 0 2 1 0 1 1 N T3 SD: 47.0380 c. M:-84.5154 c. 8: 2 1 2 0 0 2 1 N S SD: 42.4960 c. M: 63.6863 c. 9: 2 1 2 1 0 2 1 N T3 SD: 27.3452 c. M: 48.9746 c. 12: 3 1 3 1 0 3 1 N T3 SD: 14.6871 c. M:-27.3726 c. 19: 5 1 5 1 1 4 2 N SD: 9.1839 c. M: 14.7327 c. 22: 6 1 6 1 1 5 2 N SD: 6.7023 c. M:-11.6314 c. 31: 8 2 8 2 1 7 3 N SD: 3.4934 c. M: 5.9639 c. 34: 9 2 9 2 1 8 3 N SD: 3.2909 c. M:-5.8489 c. 53: 14 3 14 3 2 12 5 N SD: 1.5059 c. M: 2.8161 c. 65: 17 4 17 4 2 15 6 N SD: 1.4988 c. M:-2.7572 c. 84: 22 5 22 5 3 19 8 N SD: 1.4313 c. M: 2.5544 c. 87: 23 5 23 5 3 20 8 N SD: 0.9842 c. M:-1.6001 c. 118: 31 7 31 7 4 27 11 N SD: 0.2177 c. M: 0.3870 c. 289: 76 17 76 17 10 66 27 N SD: 0.2213 c. M: 0.3794 c. 323: 85 19 85 19 11 74 30 N SD: 0.1548 c. M:-0.2762 c. 441: 116 26 116 26 15 101 41 N SD: 0.1031 c. M:-0.1667 c. 494: 130 29 130 29 17 113 46 N SD: 0.0958 c. M: 0.1578 c. 612: 161 36 161 36 21 140 57 N SD: 0.0421 c. M: 0.0784 c. 730: 192 43 192 43 25 167 68 N SD: 0.0277 c. M: 0.0495 c. 1171: 308 69 308 69 40 268 109 N SD: 0.0250 c. M:-0.0455 c. 1665: 438 98 438 98 57 381 155 N SD: 0.0194 c. M:-0.0344 c. 1783: 469 105 469 105 61 408 166 N SD: 0.0055 c. M:-0.0095 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 0.0000 cents 3 x 4 x x 5 x 6 S SD: 44.0687 cents 4 x 5:6 x x x 8 S SD: 0.0000 cents 5:6 x x x 8:9:10 S SD: 17.6681 cents 6:7:8:9 x 10:11:12 S SD: 24.3645 cents 7:8:9 x 11 x 13:14 SD: 19.8847 cents 8 x 10:12 x 13:15:16 SD: 5.3683 cents 9:11 x x 14 x 17:18 SD: 8.7744 cents 10:12:13:15 x 16:19:20 SD: 11.9446 cents 11:13:14 x 17:18:21:22 SD: 11.2040 cents 12:14:15:18 x 19:23:24 SD: 10.7433 cents 13 x 16 x 20:21:24:26 SD: 9.8709 cents 14:17:18:21:22 x 26:28 SD: 9.3839 cents 15:18:19 x 23:24:28:30 SD: 6.7689 cents 16:19:20:24:25:26:30:32 SD: 4.6271 cents 17:20:21:26 x 27:32:34 SD: 9.0283 cents 18:22:23:27:28:29:34:36 SD: 7.5906 cents 19:23:24:29:30 x 36:38 SD: 7.6759 cents 20:24:25:30:31:32:38:40 SD: 3.8311 cents 24:29:30:36 x 38:45:48 SD: 3.6216 cents 30:36:38:45:47:48:56:60 SD: 3.5183 cents 32:38:40:48:50:51:60:64 SD: 2.7647 cents 40:48:50:60:63:64:75:80 SD: 1.9707 cents 48:58:60:72:75:77:90:96 SD: 1.8284 cents 55:66:69:83:86:88:103:110 SD: 1.7780 cents 60:72:75:90:94:96:113:120 SD: 1.2793 cents 64:77:80:96:100:102:120:128 SD: 1.1622 cents 80:96:100:120:125:128:150:160 SD: 0.0000 cents