Scala analysis: xen03-wilson-acute-17
Acute, linear-mapped intonational system, 17 notes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 16/15 111.731285 minor diatonic semitone 3: 9/8 203.910002 major whole tone 4: 7/6 266.870906 septimal minor third 5: 6/5 315.641287 minor third 6: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 7: 4/3 498.044999 perfect fourth 8: 112/81 561.005903 9: 64/45 609.776284 2nd tritone 10: 3/2 701.955001 perfect fifth 11: 14/9 764.915905 septimal minor sixth 12: 8/5 813.686286 minor sixth 13: 27/16 905.865003 Pythagorean major sixth 14: 7/4 968.825906 harmonic seventh 15: 9/5 1017.596288 just minor seventh, BP seventh 16: 35/18 1151.229619 septimal semi-diminished octave 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 135/128 92.1787 major chroma, major limma 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 175/162 133.6333 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 135/128 92.1787 major chroma, major limma 11: 28/27 62.9609 Archytas' 1/3-tone 12: 36/35 48.7704 septimal diesis, 1/4-tone 13: 135/128 92.1787 major chroma, major limma 14: 28/27 62.9609 Archytas' 1/3-tone 15: 36/35 48.7704 septimal diesis, 1/4-tone 16: 175/162 133.6333 17: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 36/35 48.770 cents septimal diesis, 1/4-tone 1: 5 28/27 62.961 cents Archytas' 1/3-tone 1: 3 135/128 92.179 cents major chroma, major limma 1: 2 175/162 133.633 cents 2: 7 16/15 111.731 cents minor diatonic semitone 2: 3 243/224 140.949 cents Archytas' 2/3-tone 2: 3 35/32 155.140 cents septimal neutral second 2: 4 10/9 182.404 cents minor whole tone 3: 2 192/175 160.502 cents septimal 4/5-tone 3: 9 9/8 203.910 cents major whole tone 3: 2 8/7 231.174 cents septimal whole tone 3: 4 280/243 245.365 cents 4: 5 81/70 252.680 cents Al-Hwarizmi's lute middle finger 4: 3 7/6 266.871 cents septimal minor third 4: 6 32/27 294.135 cents Pythagorean minor third 4: 1 1215/1024 296.089 cents wide augmented second 4: 2 175/144 337.543 cents 5: 5 6/5 315.641 cents minor third 5: 2 128/105 342.905 cents septimal neutral third 5: 1 2187/1792 344.859 cents 5: 2 896/729 357.096 cents 5: 1 315/256 359.050 cents 5: 6 5/4 386.314 cents major third 6: 2 216/175 364.412 cents 6: 2 512/405 405.866 cents narrow diminished fourth 6: 3 81/64 407.820 cents Pythagorean major third 6: 4 9/7 435.084 cents septimal major third, BP third 6: 6 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 7: 2 729/560 456.590 cents 7: 1 21/16 470.781 cents narrow fourth 7: 13 4/3 498.045 cents perfect fourth 7: 1 175/128 541.453 cents 8: 2 27/20 519.551 cents acute fourth 8: 5 48/35 546.815 cents septimal semi-augmented fourth 8: 4 112/81 561.006 cents 8: 5 45/32 590.224 cents diatonic tritone 8: 1 350/243 631.678 cents 9: 1 243/175 568.322 cents 9: 5 64/45 609.776 cents 2nd tritone 9: 4 81/56 638.994 cents 9: 5 35/24 653.185 cents septimal semi-diminished fifth 9: 2 40/27 680.449 cents grave fifth 10: 1 256/175 658.547 cents 10: 13 3/2 701.955 cents perfect fifth 10: 1 32/21 729.219 cents wide fifth 10: 2 1120/729 743.410 cents 11: 6 54/35 750.725 cents septimal semi-augmented fifth 11: 4 14/9 764.916 cents septimal minor sixth 11: 3 128/81 792.180 cents Pythagorean minor sixth 11: 2 405/256 794.134 cents wide augmented fifth 11: 2 175/108 835.588 cents 12: 6 8/5 813.686 cents minor sixth 12: 1 512/315 840.950 cents 12: 2 729/448 842.904 cents 12: 1 3584/2187 855.141 cents 12: 2 105/64 857.095 cents septimal neutral sixth 12: 5 5/3 884.359 cents major sixth, BP sixth 13: 2 288/175 862.457 cents 13: 1 2048/1215 903.911 cents narrow diminished seventh 13: 6 27/16 905.865 cents Pythagorean major sixth 13: 3 12/7 933.129 cents septimal major sixth 13: 5 140/81 947.320 cents 14: 4 243/140 954.635 cents 14: 2 7/4 968.826 cents harmonic seventh 14: 9 16/9 996.090 cents Pythagorean minor seventh 14: 2 175/96 1039.498 cents 15: 4 9/5 1017.596 cents just minor seventh, BP seventh 15: 3 64/35 1044.860 cents septimal neutral seventh 15: 3 448/243 1059.051 cents 15: 7 15/8 1088.269 cents classic major seventh 16: 2 324/175 1066.367 cents 16: 3 256/135 1107.821 cents octave - major chroma 16: 5 27/14 1137.039 cents septimal major seventh 16: 7 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.62500 = 37/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 63.0 111.7 203.9 266.9 315.6 449.3 498.0 561.0 609.8 702.0 764.9 813.7 905.9 968.8 1017.6 1151.2 1200.0 63.0 : 48.8 140.9 203.9 252.7 386.3 435.1 498.0 546.8 639.0 702.0 750.7 842.9 905.9 954.6 1088.3 1137.0 1200.0 111.7 : 92.2 155.1 203.9 337.5 386.3 449.3 498.0 590.2 653.2 702.0 794.1 857.1 905.9 1039.5 1088.3 1151.2 1200.0 203.9 : 63.0 111.7 245.4 294.1 357.1 405.9 498.0 561.0 609.8 702.0 764.9 813.7 947.3 996.1 1059.1 1107.8 1200.0 266.9 : 48.8 182.4 231.2 294.1 342.9 435.1 498.0 546.8 639.0 702.0 750.7 884.4 933.1 996.1 1044.9 1137.0 1200.0 315.6 : 133.6 182.4 245.4 294.1 386.3 449.3 498.0 590.2 653.2 702.0 835.6 884.4 947.3 996.1 1088.3 1151.2 1200.0 449.3 : 48.8 111.7 160.5 252.7 315.6 364.4 456.6 519.6 568.3 702.0 750.7 813.7 862.5 954.6 1017.6 1066.4 1200.0 498.0 : 63.0 111.7 203.9 266.9 315.6 407.8 470.8 519.6 653.2 702.0 764.9 813.7 905.9 968.8 1017.6 1151.2 1200.0 561.0 : 48.8 140.9 203.9 252.7 344.9 407.8 456.6 590.2 639.0 702.0 750.7 842.9 905.9 954.6 1088.3 1137.0 1200.0 609.8 : 92.2 155.1 203.9 296.1 359.0 407.8 541.5 590.2 653.2 702.0 794.1 857.1 905.9 1039.5 1088.3 1151.2 1200.0 702.0 : 63.0 111.7 203.9 266.9 315.6 449.3 498.0 561.0 609.8 702.0 764.9 813.7 947.3 996.1 1059.1 1107.8 1200.0 764.9 : 48.8 140.9 203.9 252.7 386.3 435.1 498.0 546.8 639.0 702.0 750.7 884.4 933.1 996.1 1044.9 1137.0 1200.0 813.7 : 92.2 155.1 203.9 337.5 386.3 449.3 498.0 590.2 653.2 702.0 835.6 884.4 947.3 996.1 1088.3 1151.2 1200.0 905.9 : 63.0 111.7 245.4 294.1 357.1 405.9 498.0 561.0 609.8 743.4 792.2 855.1 903.9 996.1 1059.1 1107.8 1200.0 968.8 : 48.8 182.4 231.2 294.1 342.9 435.1 498.0 546.8 680.4 729.2 792.2 841.0 933.1 996.1 1044.9 1137.0 1200.0 1017.6: 133.6 182.4 245.4 294.1 386.3 449.3 498.0 631.7 680.4 743.4 792.2 884.4 947.3 996.1 1088.3 1151.2 1200.0 1151.2: 48.8 111.7 160.5 252.7 315.6 364.4 498.0 546.8 609.8 658.5 750.7 813.7 862.5 954.6 1017.6 1066.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 133.6333 cents 6125/5832, 84.8629 cents 36/35, 48.7704 cents 2: 111.7313 .. 182.4037 cents 25/24, 70.6724 cents 864/875,-21.9020 cents 3: 160.5017 .. 245.3646 cents 6125/5832, 84.8629 cents 864/875,-21.9020 cents 4: 252.6804 .. 337.5433 cents 6125/5832, 84.8629 cents 19683/19600, 7.3158 cents 5: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 864/875,-21.9020 cents 6: 364.4117 .. 449.2746 cents 6125/5832, 84.8629 cents 864/875,-21.9020 cents 7: 456.5904 .. 541.4533 cents 6125/5832, 84.8629 cents 19683/19600, 7.3158 cents 8: 519.5513 .. 631.6783 cents 7000/6561, 112.1270 cents 864/875,-21.9020 cents 9: 568.3217 .. 680.4487 cents 7000/6561, 112.1270 cents 59049/61250,-63.3567 cents 10: 658.5467 .. 743.4096 cents 6125/5832, 84.8629 cents 864/875,-21.9020 cents 11: 750.7254 .. 835.5883 cents 6125/5832, 84.8629 cents 19683/19600, 7.3158 cents 12: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 864/875,-21.9020 cents 13: 862.4567 .. 947.3196 cents 6125/5832, 84.8629 cents 864/875,-21.9020 cents 14: 954.6354 .. 1039.4983 cents 6125/5832, 84.8629 cents 19683/19600, 7.3158 cents 15: 1017.5963 .. 1088.2687 cents 25/24, 70.6724 cents 864/875,-21.9020 cents 16: 1066.3667 .. 1151.2296 cents 6125/5832, 84.8629 cents 864/875,-21.9020 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 175/162, 133.6333 cents Average / Smallest step : 1.447359 Largest / Average step : 1.893139 Largest / Smallest step : 2.740051 Median interval of one step : 28/27, 62.9609 cents, amount: 5 Most common interval of one step : 36/35, 48.7704 cents, amount: 7 Least squares average step : 69.64881 cents, oct.: 1184.02977 cents Scale is not proper Step pattern alph. order: ABCABDBABCABCABDB Step pattern size order : BACBADABACBACBADA Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.410135 Lumma stability : 0.105670 Lumma impropriety factor : 0.235314 Number of different interval sizes : 74 = 4.62500 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.62500 = 37/8 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 13 Most common triad is 0.0 498.045 701.955 cents, amount: 9 Number of recognisable fifths : 13, average 701.9550 cents Scale contains two identical disjunct "tetrachords" of 8 notes 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 = 17.6471% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.019323 Average absolute harmonicity : 0.147104 Specific harmonicity : 0.116597 Fundamental : 1/6480, -12.6618 octaves, 0.0404 Hz. Guide tone : 60480, 15.8842 octaves, 15823114.189 Hz. Exponens Consonantiae : 3.919104E+08, 28.54595 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 331.5, average 19.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.59376, average 1.03493 Sum of Tenney's harmonic distance : 35.00495, average 2.05911 Vogel's harmonic complexity : 21.94118 Wille's k value : 5467 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 641.02856, average 4.18973 Lattice compactness (without 2's) : 395.14277, average 2.58263 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 6 0.70588 36 1 3: -4 .. 3 -0.58824 28 4 5: -1 .. 1 -0.17647 7 5 7: 0 .. 1 0.41176 7 7 Average exponent except 2's :-6 / 17 =-0.35294 Average absolute exponent except 2's: 42 / 17 = 2.47059 Scale is JI-epimorphic with val: <17 27 39 48| = patent Scale is weakly epimorphic with val: <17 27 40 46|
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.5773 c. M:-41.2272 c. 18: 1 1 1 1 1 2 0 1 1 2 0 1 2 1 0 2 1 N D3 SD: 20.9800 c. M: 31.5826 c. 19: 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 N D3 S SD: 12.3664 c. M:-21.8027 c. 22: 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 P M ME S SD: 11.0919 c. M:-21.4077 c. 24: 1 1 2 1 1 3 1 1 1 2 1 1 2 1 1 3 1 N SD: 11.3366 c. M: 18.8259 c. 30: 2 1 2 2 1 3 1 2 1 3 1 1 3 1 1 4 1 N SD: 11.5681 c. M:-18.0450 c. 31: 2 1 2 2 1 4 1 1 2 2 2 1 2 2 1 4 1 N SD: 9.9539 c. M: 19.0704 c. 32: 2 1 2 2 1 4 1 2 1 3 1 2 2 2 1 4 1 N SD: 9.6262 c. M: 16.4100 c. 33: 2 1 3 1 2 3 2 1 2 2 2 1 3 2 1 4 1 N SD: 10.4005 c. M: 15.5514 c. 34: 2 1 3 2 1 4 1 2 1 3 2 1 3 2 1 4 1 N SD: 9.3891 c. M:-19.4094 c. 39: 2 2 3 2 1 5 1 2 2 3 2 1 3 2 2 4 2 N SD: 9.4172 c. M: 14.9798 c. 41: 2 2 3 2 2 4 2 2 2 3 2 2 3 2 2 4 2 N SD: 5.1790 c. M: 10.2502 c. 53: 3 2 4 3 2 6 2 3 2 4 3 2 4 3 2 6 2 N SD: 3.0167 c. M:-5.0318 c. 77: 4 3 6 4 3 9 3 4 3 6 4 3 6 4 3 9 3 N SD: 2.2857 c. M: 4.6093 c. 94: 5 4 7 5 4 10 4 5 4 7 5 4 7 5 4 10 4 N SD: 2.0782 c. M:-3.6803 c. 99: 5 4 8 5 4 11 4 5 4 8 5 4 8 5 4 11 4 N SD: 1.9037 c. M: 3.7157 c. 118: 6 5 9 6 5 13 5 6 5 9 6 5 9 6 5 13 5 N SD: 1.4215 c. M: 2.7242 c. 152: 8 6 12 8 6 17 6 8 6 12 8 6 12 8 6 17 6 N SD: 1.1813 c. M:-2.2267 c. 171: 9 7 13 9 7 19 7 9 7 13 9 7 13 9 7 19 7 N SD: 0.3568 c. M:-0.7500 c. 323: 17 13 25 17 13 36 13 17 13 25 17 13 25 17 13 36 13 N SD: 0.4004 c. M:-0.8335 c. 441: 23 18 34 23 18 49 18 23 18 34 23 18 34 23 18 49 18 N SD: 0.2225 c. M: 0.4617 c. 494: 26 20 38 26 20 55 20 26 20 38 26 20 38 26 20 55 20 N SD: 0.1883 c. M:-0.4049 c. 612: 32 25 47 32 25 68 25 32 25 47 32 25 47 32 25 68 25 N SD: 0.1448 c. M: 0.2550 c. 665: 35 27 51 35 27 74 27 35 27 51 35 27 51 35 27 74 27 N SD: 0.1347 c. M:-0.1971 c. 935: 49 38 72 49 38 104 38 49 38 72 49 38 72 49 38 104 38 N SD: 0.1122 c. M:-0.2313 c. 1106: 58 45 85 58 45 123 45 58 45 85 58 45 85 58 45 123 45 N SD: 0.0632 c. M:-0.1252 c. 1277: 67 52 98 67 52 142 52 67 52 98 67 52 98 67 52 142 52 N SD: 0.0617 c. M:-0.1014 c. 1771: 93 72 136 93 72 197 72 93 72 136 93 72 136 93 72 197 72 N SD: 0.0718 c. M:-0.1338 c. 1848: 97 75 142 97 75 206 75 97 75 142 97 75 142 97 75 206 75 N SD: 0.0395 c. M:-0.0760 c. 2019: 106 82 155 106 82 225 82 106 82 155 106 82 155 106 82 225 82 N SD: 0.0393 c. M: 0.0701 c. 2289: 120 93 176 120 93 255 93 120 93 176 120 93 176 120 93 255 93 N SD: 0.0407 c. M: 0.0777 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 7.1688 cents 4 .. 8 match: 4 H SD: 15.7402 cents 5 .. 10 match: 5 H SD: 4.3013 cents 6 .. 12 match: 6 H SD: 6.3937 cents 7 .. 14 match: 7 H SD: 10.0852 cents 8 .. 16 match: 7 S SD: 9.8751 cents 9 .. 18 match: 8 S SD: 6.9789 cents 10 .. 20 match: 10 H SD: 6.1370 cents 11 .. 22 match: 11 H SD: 8.4203 cents 12 .. 24 match: 11 S SD: 5.1323 cents 13 .. 26 match: 11 SD: 5.8814 cents 14 .. 28 match: 12 SD: 5.1816 cents 15 .. 30 match: 13 SD: 4.6690 cents 16 .. 32 match: 14 SD: 3.3768 cents 17 .. 34 match: 13 SD: 4.4936 cents 18 .. 36 match: 15 SD: 4.3560 cents 19 .. 38 match: 14 SD: 4.7595 cents 20 .. 40 match: 14 SD: 3.3945 cents 21 .. 42 match: 15 SD: 4.0627 cents 22 .. 44 match: 14 SD: 4.1444 cents 23 .. 46 match: 17 SD: 3.8135 cents 24 .. 48 match: 17 SD: 2.8449 cents 27 .. 54 match: 16 SD: 3.4134 cents 28 .. 56 match: 17 SD: 3.2448 cents 29 .. 58 match: 17 SD: 2.7509 cents 30 .. 60 match: 17 SD: 2.2773 cents 31 .. 62 match: 17 SD: 2.2339 cents 40 .. 80 match: 17 SD: 2.0507 cents 45 .. 90 match: 17 SD: 1.8730 cents 47 .. 94 match: 17 SD: 1.6433 cents 48 .. 96 match: 17 SD: 1.4525 cents 54 .. 108 match: 17 SD: 1.2734 cents 60 .. 120 match: 17 SD: 1.1061 cents 74 .. 148 match: 17 SD: 1.0158 cents 78 .. 156 match: 17 SD: 0.9220 cents 88 .. 176 match: 17 SD: 0.8683 cents 90 .. 180 match: 17 SD: 0.7242 cents 102 .. 204 match: 17 SD: 0.7067 cents 104 .. 208 match: 17 SD: 0.6472 cents 120 .. 240 match: 17 SD: 0.6132 cents 128 .. 256 match: 17 SD: 0.6090 cents 135 .. 270 match: 17 SD: 0.5133 cents 144 .. 288 match: 17 SD: 0.4684 cents 160 .. 320 match: 17 SD: 0.4411 cents 162 .. 324 match: 17 SD: 0.4314 cents 168 .. 336 match: 17 SD: 0.4276 cents 180 .. 360 match: 17 SD: 0.3555 cents 192 .. 384 match: 17 SD: 0.3475 cents 209 .. 418 match: 17 SD: 0.3472 cents 210 .. 420 match: 17 SD: 0.3281 cents 216 .. 432 match: 17 SD: 0.3015 cents 240 .. 480 match: 17 SD: 0.1701 cents 360 .. 720 match: 17 SD: 0.1505 cents 432 .. 864 match: 17 SD: 0.1392 cents 450 .. 900 match: 17 SD: 0.1387 cents 480 .. 960 match: 17 SD: 0.1064 cents 540 .. 1080 match: 17 SD: 0.0993 cents 570 .. 1140 match: 17 SD: 0.0974 cents