Scala analysis: xen11-chalmers-tetrachordal-08-12
Tetrachordal Hexany, 6 tones, A-Mode
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 16/15 111.731285 minor diatonic semitone 3: 9/7 435.084095 septimal major third, BP third 4: 4/3 498.044999 perfect fourth 5: 48/35 546.815381 septimal semi-augmented fourth 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 35/24 653.1846 septimal semi-diminished fifth 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 135/112 323.3528 septimal wide minor third 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 35/24 653.1846 septimal semi-diminished fifth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 135/112 323.353 cents septimal wide minor third 1: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 5/4 386.314 cents major third 2: 2 3/2 701.955 cents perfect fifth 3: 2 9/7 435.084 cents septimal major third, BP third 3: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 54/35 750.725 cents septimal semi-augmented fifth 3: 2 14/9 764.916 cents septimal minor sixth 4: 2 4/3 498.045 cents perfect fourth 4: 2 8/5 813.686 cents minor sixth 4: 2 15/8 1088.269 cents classic major seventh 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 224/135 876.647 cents narrow septimal major sixth 5: 2 27/14 1137.039 cents septimal major seventh 5: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 48.8 111.7 435.1 498.0 546.8 1200.0 48.8 : 63.0 386.3 449.3 498.0 1151.2 1200.0 111.7 : 323.4 386.3 435.1 1088.3 1137.0 1200.0 435.1 : 63.0 111.7 764.9 813.7 876.6 1200.0 498.0 : 48.8 702.0 750.7 813.7 1137.0 1200.0 546.8 : 653.2 702.0 764.9 1088.3 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 653.1846 cents 1225/864, 604.4142 cents 36/35, 48.7704 cents 2: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 128/175,-541.4533 cents 3: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 6/7,-266.8709 cents 4: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 6/7,-266.8709 cents 5: 546.8154 .. 1151.2296 cents 1225/864, 604.4142 cents 128/175,-541.4533 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 35/24, 653.1846 cents Average / Smallest step : 4.100850 Largest / Average step : 3.265923 Largest / Smallest step : 13.393059 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 148.39277 cents, oct.: 890.35662 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : ABCBAD Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.327767 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 2.800000 Number of different interval sizes : 18 = 3.60000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 245/243, 14.1905 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval class 2 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 35 Scale harmonicity : 0.034861 Average absolute harmonicity : 0.239882 Specific harmonicity : 0.149590 Fundamental : 1/105, -6.7142 octaves, 2.4917 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 1.512000E+04, 13.88417 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 105.5, average 17.58333 Mersenne's string divisions : 61381488 Sum of van Prooijen's expressibility: 5.69559, average 0.94927 Sum of Tenney's harmonic distance : 11.88544, average 1.98091 Vogel's harmonic complexity : 12.66667 Wille's k value : 67 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 62.87142, average 2.99388 Lattice compactness (without 2's) : 39.72122, average 1.89149 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 2.16667 13 1 3: -1 .. 2 0.50000 7 1 5: -1 .. 0 -0.50000 3 1 7: -1 .. 0 -0.50000 3 3 Average exponent except 2's :-3 / 6 =-0.50000 Average absolute exponent except 2's: 13 / 6 = 2.16667 Scale is weakly epimorphic with val: <6 9 13 19| Scale is weakly epimorphic with val: <6 10 13 16| Scale is weakly epimorphic with val: <6 10 15 16| Scale is weakly epimorphic with val: <6 11 14 18| Scale is weakly epimorphic with val: <6 11 15 17|
FIT/MODE
6: 0 0 2 0 0 4 N D3 SD: 88.7514 c. M: 146.8154 c. 7: 0 1 2 0 0 4 N SD: 47.4994 c. M:-79.2016 c. 8: 0 1 2 0 1 4 N SD: 39.1630 c. M:-53.1846 c. 9: 0 1 2 1 0 5 N SD: 30.2851 c. M: 48.7704 c. 11: 0 1 3 1 0 6 N SD: 27.7989 c. M: 48.7704 c. 12: 0 1 3 1 0 7 N SD: 31.4711 c. M: 48.7704 c. 13: 1 0 4 0 1 7 N SD: 26.9406 c. M:-43.5373 c. 15: 1 0 4 1 1 8 N SD: 24.8747 c. M: 35.0841 c. 17: 1 1 4 1 1 9 N D3 SD: 17.3784 c. M:-29.4452 c. 19: 1 1 5 1 1 10 N D3 SD: 12.8317 c. M:-21.6057 c. 20: 1 1 5 1 1 11 N D3 SD: 11.5042 c. M: 18.0450 c. 22: 1 1 6 1 1 12 N D3 SD: 3.9735 c. M: 7.1359 c. 53: 2 3 14 3 2 29 N SD: 2.8868 c. M: 4.8954 c. 72: 3 4 19 4 3 39 N SD: 2.6739 c. M:-4.9354 c. 74: 3 4 20 4 3 40 N SD: 2.9733 c. M:-4.6577 c. 75: 3 4 20 4 3 41 N SD: 1.9272 c. M: 3.0841 c. 77: 3 4 21 4 3 42 N SD: 1.5790 c. M: 2.6404 c. 99: 4 5 27 5 4 54 N SD: 1.3963 c. M: 2.6404 c. 118: 5 6 32 6 5 64 N SD: 1.5663 c. M:-2.3372 c. 127: 5 7 34 7 5 69 N SD: 1.5416 c. M:-2.7424 c. 147: 6 8 39 8 6 80 N SD: 1.4435 c. M:-2.5544 c. 149: 6 8 40 8 6 81 N SD: 0.7770 c. M:-1.2839 c. 171: 7 9 46 9 7 93 N SD: 0.3587 c. M:-0.5530 c. 248: 10 13 67 13 10 135 N SD: 0.3214 c. M: 0.4410 c. 419: 17 22 113 22 17 228 N SD: 0.1762 c. M:-0.2844 c. 441: 18 23 119 23 18 240 N SD: 0.1724 c. M:-0.2901 c. 494: 20 26 133 26 20 269 N SD: 0.1717 c. M: 0.2663 c. 590: 24 31 159 31 24 321 N SD: 0.1863 c. M:-0.3033 c. 612: 25 32 165 32 25 333 N SD: 0.1667 c. M:-0.2492 c. 643: 26 34 173 34 26 350 N SD: 0.2007 c. M: 0.2478 c. 665: 27 35 179 35 27 362 N SD: 0.1045 c. M: 0.1969 c. 858: 35 45 231 45 35 467 N SD: 0.1247 c. M:-0.1807 c. 913: 37 48 246 48 37 497 N SD: 0.0726 c. M: 0.1395 c. 935: 38 49 252 49 38 509 N SD: 0.0538 c. M: 0.0774 c. 1106: 45 58 298 58 45 602 N SD: 0.0290 c. M:-0.0542 c. 2019: 82 106 544 106 82 1099 N SD: 0.0187 c. M: 0.0334 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x x 3:4 S SD: 77.5698 cents 3 x x x 4 x 6 S SD: 0.0000 cents 4 x x 5 x 6:8 S SD: 54.2083 cents 5 x x 6 x 7:10 SD: 41.5543 cents 6 x 7 x 8 x 12 S SD: 51.7132 cents 7 x 8:9 x 10:14 SD: 34.6962 cents 8 x 9:10 x 11:16 SD: 26.0957 cents 9 x 10 x 12 x 18 S SD: 23.5575 cents 10 x 11:13 x 14:20 SD: 16.7299 cents 11 x 12:14 x 15:22 SD: 10.9541 cents 12 x 13:15:16 x 24 SD: 13.9172 cents 13 x 14:17 x 18:26 SD: 9.3874 cents 14 x 15:18 x 19:28 SD: 4.9251 cents 15 x 16:19:20:21:30 SD: 8.8135 cents 16 x 17 x 21:22:32 SD: 7.1130 cents 17 x 18:22 x 23:34 SD: 7.2566 cents 18 x 19:23:24:25:36 SD: 6.0770 cents 19 x 20:24:25:26:38 SD: 8.9555 cents 20 x 21:26:27 x 40 SD: 9.9115 cents 21 x 22:27:28:29:42 SD: 6.6832 cents 22:23 x 28:29:30:44 SD: 7.9804 cents 24:25:26:31:32:33:48 SD: 5.9730 cents 27:28:29:35:36:37:54 SD: 3.9018 cents 30:31:32:39:40:41:60 SD: 3.5984 cents 32:33:34:41:43:44:64 SD: 2.9070 cents 42:43:45:54:56:58:84 SD: 2.7261 cents 45:46:48:58:60:62:90 SD: 2.3398 cents 59:61:63:76:79:81:118 SD: 2.0473 cents 60:62:64:77:80:82:120 SD: 1.7520 cents 70:72:75:90:93:96:140 SD: 1.6485 cents 73:75:78:94:97:100:146 SD: 1.2780 cents 102:105:109:131:136:140:204 SD: 0.7005 cents 105:108:112:135:140:144:210 SD: 0.0000 cents