Scala analysis: xen12-chalmers-tritriadic-mt-3-5-15
Tritriadic M->T scale built from 3:5:15
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: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 25/18 568.717426 classic augmented fourth 5: 3/2 701.955001 perfect fifth 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 144/125 244.9689 classic diminished third 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 10/9 182.4037 minor whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.4037 minor whole tone 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: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 144/125 244.969 cents classic diminished third 1: 1 6/5 315.641 cents minor third 2: 1 125/108 253.076 cents semi-augmented whole tone 2: 4 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 3: 2 5/4 386.314 cents major third 3: 2 4/3 498.045 cents perfect fourth 3: 1 25/18 568.717 cents classic augmented fourth 3: 2 36/25 631.283 cents classic diminished fifth 4: 2 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 8/5 813.686 cents minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 4 5/3 884.359 cents major sixth, BP sixth 5: 1 216/125 946.924 cents semi-augmented sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 125/72 955.031 cents classic augmented sixth 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 6: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 70.7 315.6 386.3 568.7 702.0 884.4 1200.0 70.7 : 245.0 315.6 498.0 631.3 813.7 1129.3 1200.0 315.6 : 70.7 253.1 386.3 568.7 884.4 955.0 1200.0 386.3 : 182.4 315.6 498.0 813.7 884.4 1129.3 1200.0 568.7 : 133.2 315.6 631.3 702.0 946.9 1017.6 1200.0 702.0 : 182.4 498.0 568.7 813.7 884.4 1066.8 1200.0 884.4 : 315.6 386.3 631.3 702.0 884.4 1017.6 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: 253.0761 .. 498.0450 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 15/16,-111.7313 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 701.9550 .. 946.9239 cents 144/125, 244.9689 cents 15/16,-111.7313 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 625/648,-62.5651 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 : 10/9, 182.4037 cents, amount: 2 Least squares average step : 152.51209 cents, oct.: 1067.58466 cents Scale is not proper Step pattern alph. order: ABACDCE Step pattern size order : ADACBCE Scale is not a Constant Structure Scale diversity : 1.440469 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 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 : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 884.359 cents Most common triad is 0.0 315.641 884.359 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 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 differentially coherent in interval classes 1 and 2 combined 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 -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.032051 Average absolute harmonicity : 0.243974 Specific harmonicity : 0.176958 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 150, 7.2288 octaves, 39243.835 Hz. Exponens Consonantiae : 5.400000E+04, 15.72067 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 64.0, average 9.14286 Mersenne's string divisions : 8343720 Sum of van Prooijen's expressibility: 5.36991, average 0.76713 Sum of Tenney's harmonic distance : 10.46479, average 1.49497 Vogel's harmonic complexity : 16.00000 Wille's k value : 187 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 74.98199, average 2.67793 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.71429 9 1 3: -2 .. 1 -0.28571 6 1 5: -1 .. 2 0.71429 7 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18| Scale is weakly epimorphic with val: <7 11 17| Scale is weakly epimorphic with val: <7 12 16|
FIT/MODE
7: 0 2 0 1 1 1 2 N T3 SD: 40.6923 c. M: 70.6724 c. 11: 1 2 1 1 1 2 3 N SD: 31.7139 c. M:-50.0499 c. 12: 1 2 1 2 1 2 3 N T3 SD: 18.9704 c. M:-31.2826 c. 15: 1 3 1 2 2 2 4 N SD: 10.0990 c. M:-18.0450 c. 19: 1 4 1 3 2 3 5 N SD: 4.8250 c. M: 7.5145 c. 34: 2 7 2 5 4 5 9 N SD: 2.4860 c. M: 4.0115 c. 53: 3 11 3 8 6 8 14 N SD: 1.7033 c. M: 2.7479 c. 84: 5 17 5 13 9 13 22 N SD: 1.5014 c. M:-2.7111 c. 99: 6 20 6 15 11 15 26 N SD: 1.1506 c. M:-2.0548 c. 118: 7 24 7 18 13 18 31 N SD: 0.4220 c. M:-0.7741 c. 152: 9 31 9 23 17 23 40 N SD: 0.3805 c. M:-0.6766 c. 171: 10 35 10 26 19 26 45 N SD: 0.2779 c. M: 0.4970 c. 270: 16 55 16 41 30 41 71 N SD: 0.2486 c. M:-0.4387 c. 289: 17 59 17 44 32 44 76 N SD: 0.1261 c. M: 0.2249 c. 441: 26 90 26 67 49 67 116 N SD: 0.0532 c. M:-0.0858 c. 730: 43 149 43 111 81 111 192 N SD: 0.0278 c. M:-0.0497 c. 1171: 69 239 69 178 130 178 308 N SD: 0.0208 c. M:-0.0364 c. 1342: 79 274 79 204 149 204 353 N SD: 0.0178 c. M: 0.0316 c. 1783: 105 364 105 271 198 271 469 N SD: 0.0070 c. M: 0.0130 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 0.0000 cents 3 x x x 4 x 5:6 S SD: 23.5575 cents 4 x x 5 x 6:7:8 S SD: 21.1168 cents 5 x 6 x 7 x 8:10 S SD: 18.0015 cents 6 x 7 x 8:9:10:12 S SD: 17.1734 cents 7 x 8:9:10:11:12:14 S SD: 24.0119 cents 8 x x 10:11:12:13:16 SD: 9.4317 cents 9:10:11 x x 14:15:18 SD: 26.4250 cents 10:11:12:13:14:15:17:20 SD: 17.4230 cents 11:12:13:14:15:17:18:22 SD: 16.1342 cents 12:13:14:15:17:18:20:24 SD: 12.9081 cents 13:14 x 16:18:20:22:26 SD: 13.6315 cents 14:15:17:18:19:21:23:28 SD: 12.2889 cents 15:16:18:19:21:23:25:30 SD: 8.8638 cents 16:17:19:20:22:24:27:32 SD: 6.8052 cents 20:21:24:25:28:30:33:40 SD: 3.7344 cents 24:25:29:30:33:36:40:48 SD: 3.0179 cents 44:46:53:55:61:66:73:88 SD: 1.7755 cents 64:67:77:80:89:96:107:128 SD: 1.6206 cents 72:75:86:90:100:108:120:144 SD: 1.1477 cents 95:99:114:119:132:143:158:190 SD: 1.1464 cents 96:100:115:120:133:144:160:192 SD: 0.7536 cents 100:104:120:125:139:150:167:200 SD: 0.6634 cents 120:125:144:150:167:180:200:240 SD: 0.4941 cents 144:150:173:180:200:216:240:288 SD: 0.2861 cents 216:225:259:270:300:324:360:432 SD: 0.1909 cents 360:375:432:450:500:540:600:720 SD: 0.0000 cents