Scala analysis: xen09-chalmers-tritriadic-12-13-18
Tritriadic scale built from 12:13:18
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 13/9 636.617660 tridecimal diminished fifth 5: 3/2 701.955001 perfect fifth 6: 13/8 840.527662 tridecimal neutral sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 13/12 138.5727 tridecimal 2/3-tone 2: 27/26 65.3373 tridecimal comma 3: 32/27 294.1350 Pythagorean minor third 4: 13/12 138.5727 tridecimal 2/3-tone 5: 27/26 65.3373 tridecimal comma 6: 13/12 138.5727 tridecimal 2/3-tone 7: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/26 65.337 cents tridecimal comma 1: 3 13/12 138.573 cents tridecimal 2/3-tone 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 16/13 359.472 cents tridecimal neutral third 2: 3 9/8 203.910 cents major whole tone 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 104/81 432.708 cents 2: 2 4/3 498.045 cents perfect fourth 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 3 4/3 498.045 cents perfect fourth 3: 2 18/13 563.382 cents tridecimal augmented fourth 3: 1 13/9 636.618 cents tridecimal diminished fifth 4: 1 18/13 563.382 cents tridecimal augmented fourth 4: 2 13/9 636.618 cents tridecimal diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 64/39 857.517 cents 39th subharmonic 5: 2 3/2 701.955 cents perfect fifth 5: 1 81/52 767.292 cents 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 13/8 840.528 cents tridecimal neutral sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 24/13 1061.427 cents tridecimal neutral seventh 6: 2 52/27 1134.663 cents 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 : 138.6 203.9 498.0 636.6 702.0 840.5 1200.0 138.6 : 65.3 359.5 498.0 563.4 702.0 1061.4 1200.0 203.9 : 294.1 432.7 498.0 636.6 996.1 1134.7 1200.0 498.0 : 138.6 203.9 342.5 702.0 840.5 905.9 1200.0 636.6 : 65.3 203.9 563.4 702.0 767.3 1061.4 1200.0 702.0 : 138.6 498.0 636.6 702.0 996.1 1134.7 1200.0 840.5 : 359.5 498.0 563.4 857.5 996.1 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.3373 .. 359.4723 cents 32/27, 294.1350 cents 27/26, 65.3373 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 117/128,-155.5623 cents 3: 342.4827 .. 636.6177 cents 32/27, 294.1350 cents 117/128,-155.5623 cents 4: 563.3823 .. 857.5173 cents 32/27, 294.1350 cents 162/169,-73.2353 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 117/128,-155.5623 cents 6: 840.5277 .. 1134.6627 cents 32/27, 294.1350 cents 117/128,-155.5623 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/26, 65.3373 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 2.623746 Largest / Average step : 2.096922 Largest / Smallest step : 5.501790 Median interval of one step : 13/12, 138.5727 cents, amount: 3 Most common interval of one step : 13/12, 138.5727 cents, amount: 3 Least squares average step : 153.85671 cents, oct.: 1076.99696 cents Scale is not proper Step pattern alph. order: ABCABAD Step pattern size order : BACBABD Scale is not a Constant Structure Scale diversity : 1.469530 Lumma stability : 0.108896 Lumma impropriety factor : 0.551254 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 512/507, 16.9897 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 138.573 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale 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 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 -- Rational properties -- Prime limit : 13 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 13 Scale harmonicity : 0.026441 Average absolute harmonicity : 0.245776 Specific harmonicity : 0.127074 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 3.369600E+04, 15.04029 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 50.0, average 7.14286 Mersenne's string divisions : 196350 Sum of van Prooijen's expressibility: 5.25032, average 0.75005 Sum of Tenney's harmonic distance : 10.29404, average 1.47058 Vogel's harmonic complexity : 13.28571 Wille's k value : 58 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 83.67977, average 2.98856 Lattice compactness (without 2's) : 47.46300, average 1.69511 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.85714 12 1 3: -2 .. 2 -0.14286 7 3 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 29| Scale is weakly epimorphic with val: <7 11 27| Scale is weakly epimorphic with val: <7 12 25|
FIT/MODE
7: 1 0 2 1 0 1 2 N T3 SD: 27.6422 c. M:-49.0966 c. 10: 1 1 2 1 1 1 3 N T3 SD: 22.8029 c. M: 36.6177 c. 12: 1 1 3 1 1 1 4 N T3 SD: 25.3381 c. M: 40.5277 c. 14: 2 0 4 1 1 2 4 N SD: 24.7242 c. M: 36.6177 c. 15: 2 1 3 2 1 2 4 N SD: 23.8518 c. M:-39.4723 c. 16: 2 1 4 2 0 2 5 N SD: 23.1234 c. M:-38.3823 c. 17: 2 1 4 2 1 2 5 N SD: 4.5314 c. M:-7.8547 c. 36: 4 2 9 4 2 4 11 N SD: 4.0165 c. M: 7.1943 c. 53: 6 3 13 6 3 6 16 N SD: 1.7845 c. M: 2.7918 c. 70: 8 4 17 8 4 8 21 N SD: 1.3440 c. M: 2.3319 c. 77: 9 4 19 9 4 9 23 N SD: 1.3085 c. M:-2.3434 c. 94: 11 5 23 11 5 11 28 N SD: 1.2270 c. M:-2.0255 c. 113: 13 6 28 13 6 13 34 N SD: 1.1934 c. M: 2.1401 c. 130: 15 7 32 15 7 15 39 N SD: 0.4512 c. M: 0.8331 c. 147: 17 8 36 17 8 17 44 N SD: 0.1614 c. M:-0.2887 c. 424: 49 23 104 49 23 49 127 N SD: 0.1009 c. M:-0.1748 c. 571: 66 31 140 66 31 66 171 N SD: 0.0913 c. M:-0.1599 c. 624: 72 34 153 72 34 72 187 N SD: 0.0804 c. M: 0.1430 c. 771: 89 42 189 89 42 89 231 N SD: 0.0351 c. M: 0.0607 c. 918: 106 50 225 106 50 106 275 N SD: 0.0093 c. M: 0.0164 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 4 x x 5:6 S SD: 14.6104 cents 4 x x 5 x 6:7:8 S SD: 42.5326 cents 5 x 6 x 7 x 8:10 S SD: 31.7527 cents 6 x 7:8 x 9:10:12 S SD: 15.3431 cents 7 x 8:9:10 x 11:14 SD: 18.3755 cents 8 x 9:11 x 12:13:16 SD: 10.6546 cents 9 x 10:12:13:14:15:18 S SD: 13.2788 cents 10:11 x 13:14:15:16:20 SD: 13.1947 cents 11:12 x 15:16:17:18:22 SD: 11.3301 cents 13:14:15:17:19:20:21:26 SD: 10.6889 cents 14:15:16:19:20:21:23:28 SD: 7.5216 cents 16:17:18:21:23:24:26:32 SD: 6.2972 cents 18 x 20:24:26:27:29:36 SD: 4.3568 cents 19 x 21:25:27:29:31:38 SD: 9.4563 cents 20:22:23:27:29:30:33:40 SD: 8.2707 cents 21:23:24:28:30:32:34:42 SD: 6.7778 cents 22:24:25:29:32:33:36:44 SD: 4.8041 cents 24:26:27:32:35:36:39:48 SD: 2.3667 cents 48:52:54:64:69:72:78:96 SD: 1.1919 cents 72:78:81:96:104:108:117:144 SD: 0.0000 cents