Scala analysis: xen09-chalmers-tritriadic-10-13-15
Tritriadic scale built from 10:13:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 13/10 454.213948 tridecimal semi-diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 26/15 952.258947 tridecimal semi-augmented sixth 6: 39/20 1156.168949 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 9/8 203.9100 major whole tone 2: 52/45 250.3039 3: 40/39 43.8311 tridecimal minor diesis 4: 9/8 203.9100 major whole tone 5: 52/45 250.3039 6: 9/8 203.9100 major whole tone 7: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 3 9/8 203.910 cents major whole tone 1: 2 52/45 250.304 cents 2: 3 15/13 247.741 cents tridecimal 5/4-tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 135/104 451.651 cents 3: 5 4/3 498.045 cents perfect fourth 3: 1 117/80 658.124 cents 4: 1 160/117 541.876 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 208/135 748.349 cents 5: 3 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 45/26 949.696 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 39/20 1156.169 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 454.2 498.0 702.0 952.3 1156.2 1200.0 203.9 : 250.3 294.1 498.0 748.3 952.3 996.1 1200.0 454.2 : 43.8 247.7 498.0 702.0 745.8 949.7 1200.0 498.0 : 203.9 454.2 658.1 702.0 905.9 1156.2 1200.0 702.0 : 250.3 454.2 498.0 702.0 952.3 996.1 1200.0 952.3 : 203.9 247.7 451.7 702.0 745.8 949.7 1200.0 1156.2: 43.8 247.7 498.0 541.9 745.8 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 250.3039 cents 169/150, 206.4729 cents 40/39, 43.8311 cents 2: 247.7411 .. 454.2139 cents 169/150, 206.4729 cents 675/676,-2.5629 cents 3: 451.6511 .. 658.1239 cents 169/150, 206.4729 cents 675/676,-2.5629 cents 4: 541.8761 .. 748.3489 cents 169/150, 206.4729 cents 12800/13689,-116.2479 cents 5: 745.7861 .. 952.2589 cents 169/150, 206.4729 cents 675/676,-2.5629 cents 6: 949.6961 .. 1156.1689 cents 169/150, 206.4729 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 3.911122 Largest / Average step : 1.460106 Largest / Smallest step : 5.710654 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 182.23287 cents, oct.: 1275.63007 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MLSMLMS Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.221723 Lumma stability : 0.073052 Lumma impropriety factor : 0.105416 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 454.214 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Scale contains a complete diamond : 1 3 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 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 39 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.243141 Specific harmonicity : 0.111116 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 77.5, average 11.07143 Mersenne's string divisions : 99312045 Sum of van Prooijen's expressibility: 5.78958, average 0.82708 Sum of Tenney's harmonic distance : 11.61280, average 1.65897 Vogel's harmonic complexity : 14.85714 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 76.20148, average 2.72148 Lattice compactness (without 2's) : 46.44630, average 1.65880 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 11 1 3: -1 .. 2 0.28571 6 3 5: -1 .. 0 -0.42857 3 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 17 29| Scale is JI-epimorphic with val: <7 11 15 24| Scale is JI-epimorphic with val: <7 11 16 25| Scale is JI-epimorphic with val: <7 11 17 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 12 15 28| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 18 24|
FIT/MODE
7: 1 2 0 1 2 1 0 N T3 SD: 42.9883 c. M:-76.3125 c. 10: 2 2 0 2 2 2 0 N M DE S SD: 25.6341 c. M:-43.8311 c. 14: 2 3 1 2 3 2 1 P T3 SD: 24.1504 c. M: 41.8832 c. 17: 3 3 1 3 3 3 1 N M DE S SD: 20.5218 c. M: 34.6119 c. Seventeen-tone Major 18: 3 4 0 3 4 3 1 N SD: 21.6461 c. M: 35.2883 c. 19: 3 4 1 3 4 3 1 N T3 SD: 11.0626 c. M: 19.3268 c. 24: 4 5 1 4 5 4 1 N T3 SD: 3.4610 c. M: 6.1689 c. 29: 5 6 1 5 6 5 1 N T3 SD: 1.7153 c. M:-2.9865 c. 53: 9 11 2 9 11 9 2 N T3 SD: 0.9088 c. M: 1.4520 c. 82: 14 17 3 14 17 14 3 N T3 SD: 0.6324 c. M: 1.0394 c. 135: 23 28 5 23 28 23 5 N T3 SD: 0.6434 c. M: 1.1478 c. 217: 37 45 8 37 45 37 8 N T3 SD: 0.6208 c. M: 1.1069 c. 248: 42 52 9 42 52 42 9 N T3 SD: 0.5487 c. M:-0.9669 c. 272: 46 57 10 46 57 46 10 N T3 SD: 0.5338 c. M: 0.9688 c. 277: 47 58 10 47 58 47 10 N T3 SD: 0.4607 c. M:-0.8096 c. 301: 51 63 11 51 63 51 11 N T3 SD: 0.3608 c. M: 0.5877 c. 330: 56 69 12 56 69 56 12 N T3 SD: 0.2617 c. M:-0.4683 c. 359: 61 75 13 61 75 61 13 N T3 SD: 0.2502 c. M:-0.3873 c. 383: 65 80 14 65 80 65 14 N T3 SD: 0.1494 c. M: 0.2546 c. 412: 70 86 15 70 86 70 15 N T3 SD: 0.1024 c. M:-0.1682 c. 465: 79 97 17 79 97 79 17 N T3 SD: 0.0248 c. M: 0.0399 c. 1424: 242 297 52 242 297 242 52 N T3 SD: 0.0121 c. M:-0.0226 c. 1889: 321 394 69 321 394 321 69 N T3 SD: 0.0053 c. M: 0.0091 c. 2354: 400 491 86 400 491 400 86 N T3 SD: 0.0055 c. M: 0.0092 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 5 x 6 S SD: 22.6334 cents 4 x 5 x 6:7 x 8 S SD: 17.4730 cents 5:6 x 7:8:9 x 10 S SD: 38.1426 cents 6:7 x 8:9:10 x 12 S SD: 18.5197 cents 7:8:9 x 11:12 x 14 SD: 17.8454 cents 8:9:10:11:12:14 x 16 S SD: 14.6467 cents 9:10 x 12:14:16 x 18 S SD: 15.9346 cents 10:11:13 x 15:17 x 20 SD: 10.2835 cents 12:14 x 16:18:21:23:24 SD: 11.9368 cents 13:15:17 x 20:23:25:26 SD: 12.6769 cents 14:16:18:19:21:24:27:28 SD: 7.5324 cents 15:17 x 20:23:26:29:30 SD: 7.1335 cents 16:18:21 x 24:28:31:32 SD: 4.3233 cents 19:21:25 x 29:33:37:38 SD: 7.9931 cents 20:23:26:27:30:35:39:40 SD: 6.6775 cents 22:25 x 29:33:38:43:44 SD: 4.5559 cents 24:27:31:32:36:42:47:48 SD: 3.0403 cents 25:28 x 33:38:43:49:50 SD: 5.6400 cents 26:29:34:35:39:45:51:52 SD: 3.8079 cents 30:34:39:40:45:52:59:60 SD: 2.7860 cents 40:45:52:53:60:69:78:80 SD: 1.9558 cents 54:61:70:72:81:94:105:108 SD: 1.7719 cents 56:63:73:75:84:97:109:112 SD: 1.3815 cents 64:72:83:85:96:111:125:128 SD: 1.2125 cents 80:90:104:107:120:139:156:160 SD: 0.9737 cents 90:101:117:120:135:156:176:180 SD: 0.9321 cents 96:108:125:128:144:166:187:192 SD: 0.7623 cents 120:135:156:160:180:208:234:240 SD: 0.0000 cents