Scala analysis: xen02-wilson-arabic
Classic Arabic System of 17 tones (for Gary)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 10/9 182.403712 minor whole tone 3: 9/8 203.910002 major whole tone 4: 32/27 294.134997 Pythagorean minor third 5: 5/4 386.313714 major third 6: 81/64 407.820003 Pythagorean major third 7: 4/3 498.044999 perfect fourth 8: 45/32 590.223716 diatonic tritone 9: 40/27 680.448711 grave fifth 10: 3/2 701.955001 perfect fifth 11: 128/81 792.179997 Pythagorean minor sixth 12: 5/3 884.358713 major sixth, BP sixth 13: 27/16 905.865003 Pythagorean major sixth 14: 16/9 996.089998 Pythagorean minor seventh 15: 15/8 1088.268715 classic major seventh 16: 160/81 1178.493710 octave - syntonic comma 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/80 21.5063 syntonic comma, Didymus comma 1: 135/128 92.1787 major chroma, major limma 2: 256/243 90.2250 limma, Pythagorean minor second 3: 81/80 21.5063 syntonic comma, Didymus comma 4: 256/243 90.2250 limma, Pythagorean minor second 5: 135/128 92.1787 major chroma, major limma 6: 81/80 21.5063 syntonic comma, Didymus comma 7: 256/243 90.2250 limma, Pythagorean minor second 8: 135/128 92.1787 major chroma, major limma 9: 256/243 90.2250 limma, Pythagorean minor second 10: 81/80 21.5063 syntonic comma, Didymus comma 11: 256/243 90.2250 limma, Pythagorean minor second 12: 135/128 92.1787 major chroma, major limma 13: 81/80 21.5063 syntonic comma, Didymus comma 14: 256/243 90.2250 limma, Pythagorean minor second 15: 135/128 92.1787 major chroma, major limma 16: 256/243 90.2250 limma, Pythagorean minor second 17: 81/80 21.5063 syntonic comma, Didymus comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 81/80 21.506 cents syntonic comma, Didymus comma 1: 7 256/243 90.225 cents limma, Pythagorean minor second 1: 5 135/128 92.179 cents major chroma, major limma 2: 7 16/15 111.731 cents minor diatonic semitone 2: 3 2187/2048 113.685 cents apotome 2: 7 10/9 182.404 cents minor whole tone 3: 2 4096/3645 201.956 cents narrow diminished third 3: 13 9/8 203.910 cents major whole tone 3: 2 2560/2187 272.629 cents grave minor third 4: 3 729/640 225.416 cents acute major second 4: 11 32/27 294.135 cents Pythagorean minor third 4: 3 1215/1024 296.089 cents wide augmented second 5: 8 6/5 315.641 cents minor third 5: 1 8192/6561 384.360 cents Pythagorean diminished fourth 5: 8 5/4 386.314 cents major third 6: 4 512/405 405.866 cents narrow diminished fourth 6: 9 81/64 407.820 cents Pythagorean major third 6: 4 320/243 476.539 cents grave fourth 7: 1 6561/5120 429.326 cents acute major third 7: 15 4/3 498.045 cents perfect fourth 7: 1 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 8: 6 27/20 519.551 cents acute fourth 8: 5 1024/729 588.270 cents Pythagorean diminished fifth 8: 6 45/32 590.224 cents diatonic tritone 9: 6 64/45 609.776 cents 2nd tritone 9: 5 729/512 611.730 cents Pythagorean tritone 9: 6 40/27 680.449 cents grave fifth 10: 1 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 10: 15 3/2 701.955 cents perfect fifth 10: 1 10240/6561 770.674 cents grave minor sixth 11: 4 243/160 723.461 cents acute fifth 11: 9 128/81 792.180 cents Pythagorean minor sixth 11: 4 405/256 794.134 cents wide augmented fifth 12: 8 8/5 813.686 cents minor sixth 12: 1 6561/4096 815.640 cents Pythagorean augmented fifth 12: 8 5/3 884.359 cents major sixth, BP sixth 13: 3 2048/1215 903.911 cents narrow diminished seventh 13: 11 27/16 905.865 cents Pythagorean major sixth 13: 3 1280/729 974.584 cents grave minor seventh 14: 2 2187/1280 927.371 cents acute major sixth 14: 13 16/9 996.090 cents Pythagorean minor seventh 14: 2 3645/2048 998.044 cents wide augmented sixth 15: 7 9/5 1017.596 cents just minor seventh, BP seventh 15: 3 4096/2187 1086.315 cents Pythagorean diminished octave 15: 7 15/8 1088.269 cents classic major seventh 16: 5 256/135 1107.821 cents octave - major chroma 16: 7 243/128 1109.775 cents Pythagorean major seventh 16: 5 160/81 1178.494 cents octave - syntonic comma 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 8 9 10 11 12 13 14 15 16 17 0.0 : 92.2 182.4 203.9 294.1 386.3 407.8 498.0 590.2 680.4 702.0 792.2 884.4 905.9 996.1 1088.3 1178.5 1200.0 92.2 : 90.2 111.7 202.0 294.1 315.6 405.9 498.0 588.3 609.8 700.0 792.2 813.7 903.9 996.1 1086.3 1107.8 1200.0 182.4 : 21.5 111.7 203.9 225.4 315.6 407.8 498.0 519.6 609.8 702.0 723.5 813.7 905.9 996.1 1017.6 1109.8 1200.0 203.9 : 90.2 182.4 203.9 294.1 386.3 476.5 498.0 588.3 680.4 702.0 792.2 884.4 974.6 996.1 1088.3 1178.5 1200.0 294.1 : 92.2 113.7 203.9 296.1 386.3 407.8 498.0 590.2 611.7 702.0 794.1 884.4 905.9 998.0 1088.3 1109.8 1200.0 386.3 : 21.5 111.7 203.9 294.1 315.6 405.9 498.0 519.6 609.8 702.0 792.2 813.7 905.9 996.1 1017.6 1107.8 1200.0 407.8 : 90.2 182.4 272.6 294.1 384.4 476.5 498.0 588.3 680.4 770.7 792.2 884.4 974.6 996.1 1086.3 1178.5 1200.0 498.0 : 92.2 182.4 203.9 294.1 386.3 407.8 498.0 590.2 680.4 702.0 794.1 884.4 905.9 996.1 1088.3 1109.8 1200.0 590.2 : 90.2 111.7 202.0 294.1 315.6 405.9 498.0 588.3 609.8 702.0 792.2 813.7 903.9 996.1 1017.6 1107.8 1200.0 680.4 : 21.5 111.7 203.9 225.4 315.6 407.8 498.0 519.6 611.7 702.0 723.5 813.7 905.9 927.4 1017.6 1109.8 1200.0 702.0 : 90.2 182.4 203.9 294.1 386.3 476.5 498.0 590.2 680.4 702.0 792.2 884.4 905.9 996.1 1088.3 1178.5 1200.0 792.2 : 92.2 113.7 203.9 296.1 386.3 407.8 500.0 590.2 611.7 702.0 794.1 815.6 905.9 998.0 1088.3 1109.8 1200.0 884.4 : 21.5 111.7 203.9 294.1 315.6 407.8 498.0 519.6 609.8 702.0 723.5 813.7 905.9 996.1 1017.6 1107.8 1200.0 905.9 : 90.2 182.4 272.6 294.1 386.3 476.5 498.0 588.3 680.4 702.0 792.2 884.4 974.6 996.1 1086.3 1178.5 1200.0 996.1 : 92.2 182.4 203.9 296.1 386.3 407.8 498.0 590.2 611.7 702.0 794.1 884.4 905.9 996.1 1088.3 1109.8 1200.0 1088.3: 90.2 111.7 203.9 294.1 315.6 405.9 498.0 519.6 609.8 702.0 792.2 813.7 903.9 996.1 1017.6 1107.8 1200.0 1178.5: 21.5 113.7 203.9 225.4 315.6 407.8 429.3 519.6 611.7 702.0 723.5 813.7 905.9 927.4 1017.6 1109.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 92.1787 cents 25/24, 70.6724 cents 81/80, 21.5063 cents 2: 111.7313 .. 182.4037 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 3: 201.9563 .. 272.6287 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 4: 225.4163 .. 296.0887 cents 25/24, 70.6724 cents 1594323/1638400,-47.2124 cents 5: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 6: 405.8663 .. 476.5387 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 7: 429.3263 .. 499.9987 cents 25/24, 70.6724 cents 1594323/1638400,-47.2124 cents 8: 519.5513 .. 590.2237 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 9: 609.7763 .. 680.4487 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 10: 700.0013 .. 770.6737 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 11: 723.4613 .. 794.1337 cents 25/24, 70.6724 cents 1594323/1638400,-47.2124 cents 12: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 13: 903.9113 .. 974.5837 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 14: 927.3713 .. 998.0437 cents 25/24, 70.6724 cents 1594323/1638400,-47.2124 cents 15: 1017.5963 .. 1088.2687 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents 16: 1107.8213 .. 1178.4937 cents 25/24, 70.6724 cents 2048/2025, 19.5526 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 135/128, 92.1787 cents Average / Smallest step : 3.282214 Largest / Average step : 1.305865 Largest / Smallest step : 4.286128 Median interval of one step : 256/243, 90.2250 cents, amount: 7 Most common interval of one step : 256/243, 90.2250 cents, amount: 7 Least squares average step : 72.04659 cents, oct.: 1224.79198 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACBABCBACBABC Step pattern size order : LMSMLSMLMSMLSMLMS Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.148686 Lumma stability : 0.215076 Lumma impropriety factor : 0.157375 Number of different interval sizes : 48 = 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 : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 386.314 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 13 Number of recognisable fifths : 16, average 701.8329 cents Scale contains two identical conjunct "tetrachords" of 8 notes Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 9 27 81 Formal octave complements present : 9 = 52.9412% Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Scale is n-1 differentially coherent in interval classes 11 and 12 combined Scale is n-1 differentially coherent in interval class 12 Limited inverse transpositions with margin 70.6724 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 10935 (O: 10935 U: 10935) Highest odd numerator or denominator: 135 Scale harmonicity : 0.023962 Average absolute harmonicity : 0.152414 Specific harmonicity : 0.133498 Fundamental : 1/10368, -13.3399 octaves, 0.0252 Hz. Guide tone : 51840, 15.6618 octaves, 13562669.305 Hz. Exponens Consonantiae : 5.374771E+08, 29.00163 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 610.0, average 35.88235 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.19409, average 1.18789 Sum of Tenney's harmonic distance : 40.52889, average 2.38405 Vogel's harmonic complexity : 20.47059 Wille's k value : 5467 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 9 Triangular lattice diameter : 8 Lattice compactness : 881.86114, average 5.76380 Lattice compactness (without 2's) : 468.30573, average 3.06082 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 7 -0.17647 59 1 3: -4 .. 4 -0.23529 36 8 5: 0 .. 1 0.47059 8 8 Average exponent except 2's : 4 / 17 = 0.23529 Average absolute exponent except 2's: 44 / 17 = 2.58824 Scale is weakly epimorphic with val: <17 25 38| Scale is JI-epimorphic with val: <17 27 39| = patent Scale is weakly epimorphic with val: <17 29 40|
FIT/MODE
17: 1 2 0 1 1 1 1 1 2 0 1 2 0 1 1 2 0 N T3 SD: 20.4408 c. M: 33.3725 c. 18: 1 2 0 1 2 0 1 2 1 1 1 1 1 1 1 2 0 N D3 SD: 19.2608 c. M: 31.3783 c. 19: 1 2 0 2 1 0 2 1 2 0 2 1 0 2 1 2 0 N T3 SD: 17.8677 c. M: 29.0208 c. 20: 2 1 0 2 1 1 1 2 1 1 1 2 0 2 1 2 0 N T3 SD: 17.0149 c. M:-27.8213 c. 21: 2 1 1 1 2 0 2 1 2 0 2 1 1 1 2 2 0 N T3 SD: 16.0793 c. M: 27.2159 c. 22: 2 1 1 1 2 0 2 2 1 1 2 1 1 1 2 2 0 N SD: 16.8169 c. M:-26.0018 c. 23: 2 1 1 1 2 1 1 2 2 0 2 2 0 2 2 1 1 N D3 S SD: 18.1518 c. M: 33.2654 c. 24: 2 2 0 2 2 0 2 2 2 0 2 2 0 2 2 2 0 N M DE S SD: 11.1410 c. M:-21.5063 c. 29: 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 P M ME S SD: 10.6925 c. M: 19.8730 c. 31: 2 3 0 3 2 1 2 2 3 0 2 3 0 3 2 2 1 N SD: 12.0058 c. M:-17.9864 c. 32: 2 3 0 3 2 1 2 3 2 1 2 3 0 3 2 2 1 N SD: 10.7072 c. M: 17.1787 c. 33: 3 2 1 2 3 0 3 2 3 0 3 2 1 2 3 2 1 N SD: 10.3221 c. M:-16.9122 c. 34: 3 2 1 2 3 1 2 3 2 1 2 3 1 2 3 2 1 P T3 SD: 9.6201 c. M:-15.7094 c. 37: 3 3 0 3 3 1 2 3 3 1 2 3 1 3 3 2 1 N SD: 9.2668 c. M:-14.4340 c. 41: 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 N M DE S SD: 4.3281 c. M: 7.7620 c. 53: 4 4 1 4 4 1 4 4 4 1 4 4 1 4 4 4 1 N M DE S SD: 0.9572 c. M: 1.6127 c. 118: 9 9 2 9 9 2 9 9 9 2 9 9 2 9 9 9 2 N M DE S SD: 0.6610 c. M:-1.1673 c. 171: 13 13 3 13 13 3 13 13 13 3 13 13 3 13 13 13 3 N M DE S SD: 0.5201 c. M: 0.9506 c. 224: 17 17 4 17 17 4 17 17 17 4 17 17 4 17 17 17 4 N M DE S SD: 0.5447 c. M: 1.1073 c. 289: 22 22 5 22 22 5 22 22 22 5 22 22 5 22 22 22 5 N M DE S SD: 0.5516 c. M:-0.8996 c. 323: 25 24 6 24 25 6 24 25 24 6 24 25 6 24 25 24 6 N T3 SD: 0.5205 c. M:-0.8487 c. 335: 26 25 6 25 26 6 25 26 25 6 25 26 6 25 26 25 6 N T3 SD: 0.4682 c. M:-0.9556 c. 376: 29 28 7 28 29 7 28 29 28 7 28 29 7 28 29 28 7 N T3 SD: 0.4514 c. M: 0.8341 c. 388: 30 29 7 29 30 7 29 30 29 7 29 30 7 29 30 29 7 N T3 SD: 0.3059 c. M:-0.6048 c. 441: 34 33 8 33 34 8 33 34 33 8 33 34 8 33 34 33 8 N T3 SD: 0.2118 c. M:-0.3433 c. 494: 38 37 9 37 38 9 37 38 37 9 37 38 9 37 38 37 9 N T3 SD: 0.1867 c. M: 0.3561 c. 506: 39 38 9 38 39 9 38 39 38 9 38 39 9 38 39 38 9 N T3 SD: 0.1707 c. M:-0.3114 c. 559: 43 42 10 42 43 10 42 43 42 10 42 43 10 42 43 42 10 N T3 SD: 0.0657 c. M:-0.1290 c. 612: 47 46 11 46 47 11 46 47 46 11 46 47 11 46 47 46 11 N T3 SD: 0.0322 c. M: 0.0623 c. 1171: 90 88 21 88 90 21 88 90 88 21 88 90 21 88 90 88 21 N T3 SD: 0.0256 c. M:-0.0501 c. 1783: 137 134 32 134 137 32 134 137 134 32 134 137 32 134 137 134 32 N T3 SD: 0.0196 c. M:-0.0319 c. 2395: 184 180 43 180 184 43 180 184 180 43 180 184 43 180 184 180 43 N T3 SD: 0.0201 c. M: 0.0386 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: 0.0000 cents 4 .. 8 match: 4 H SD: 6.8160 cents 5 .. 10 match: 5 H SD: 7.6080 cents 6 .. 12 match: 6 H SD: 7.9180 cents 7 .. 14 match: 7 H SD: 8.2581 cents 8 .. 16 match: 8 H SD: 8.0798 cents 9 .. 18 match: 9 H SD: 7.3210 cents 10 .. 20 match: 10 H SD: 6.6030 cents 11 .. 22 match: 11 H SD: 9.2074 cents 12 .. 24 match: 11 SD: 6.4477 cents 13 .. 26 match: 12 S SD: 8.5523 cents 14 .. 28 match: 13 S SD: 6.6473 cents 15 .. 30 match: 13 SD: 4.7448 cents 16 .. 32 match: 12 SD: 4.9241 cents 17 .. 34 match: 15 S SD: 4.8316 cents 18 .. 36 match: 12 SD: 4.0724 cents 19 .. 38 match: 13 SD: 4.7188 cents 20 .. 40 match: 14 SD: 4.9028 cents 21 .. 42 match: 16 SD: 4.4720 cents 22 .. 44 match: 14 SD: 3.7148 cents 23 .. 46 match: 15 SD: 3.6198 cents 24 .. 48 match: 14 SD: 3.3780 cents 25 .. 50 match: 15 SD: 4.0031 cents 26 .. 52 match: 14 SD: 3.2779 cents 27 .. 54 match: 15 SD: 3.0692 cents 28 .. 56 match: 15 SD: 3.7380 cents 29 .. 58 match: 17 SD: 3.2733 cents 30 .. 60 match: 16 SD: 2.9951 cents 31 .. 62 match: 15 SD: 3.0115 cents 32 .. 64 match: 16 SD: 2.3469 cents 33 .. 66 match: 16 SD: 2.1264 cents 34 .. 68 match: 14 SD: 2.3602 cents 35 .. 70 match: 15 SD: 2.4894 cents 36 .. 72 match: 17 SD: 2.2183 cents 37 .. 74 match: 16 SD: 2.2083 cents 38 .. 76 match: 16 SD: 1.8645 cents 39 .. 78 match: 16 SD: 1.8528 cents 41 .. 82 match: 16 SD: 1.9942 cents 42 .. 84 match: 15 SD: 1.5497 cents 43 .. 86 match: 15 SD: 2.2913 cents 44 .. 88 match: 17 SD: 2.0114 cents 45 .. 90 match: 17 SD: 1.8590 cents 46 .. 92 match: 16 SD: 2.0353 cents 47 .. 94 match: 16 SD: 1.9745 cents 48 .. 96 match: 17 SD: 1.4195 cents 50 .. 100 match: 15 SD: 1.5488 cents 51 .. 102 match: 16 SD: 1.9415 cents 52 .. 104 match: 17 SD: 1.6099 cents 54 .. 108 match: 16 SD: 0.9476 cents 58 .. 116 match: 16 SD: 1.5747 cents 59 .. 118 match: 16 SD: 1.5820 cents 60 .. 120 match: 17 SD: 1.3643 cents 62 .. 124 match: 16 SD: 1.5324 cents 63 .. 126 match: 17 SD: 1.4158 cents 64 .. 128 match: 17 SD: 1.0497 cents 71 .. 142 match: 17 SD: 0.9153 cents 72 .. 144 match: 17 SD: 0.7678 cents 96 .. 192 match: 17 SD: 0.7229 cents 108 .. 216 match: 17 SD: 0.6249 cents 120 .. 240 match: 17 SD: 0.6228 cents 126 .. 252 match: 17 SD: 0.6155 cents 128 .. 256 match: 17 SD: 0.4812 cents 144 .. 288 match: 17 SD: 0.4683 cents 152 .. 304 match: 17 SD: 0.4669 cents 160 .. 320 match: 17 SD: 0.4616 cents 162 .. 324 match: 17 SD: 0.3514 cents 199 .. 398 match: 17 SD: 0.3496 cents 200 .. 400 match: 17 SD: 0.3141 cents 216 .. 432 match: 17 SD: 0.2632 cents 279 .. 558 match: 17 SD: 0.2435 cents 288 .. 576 match: 17 SD: 0.2092 cents 312 .. 624 match: 17 SD: 0.1899 cents 351 .. 702 match: 17 SD: 0.1896 cents 360 .. 720 match: 17 SD: 0.1861 cents 368 .. 736 match: 17 SD: 0.1812 cents 369 .. 738 match: 17 SD: 0.1687 cents 384 .. 768 match: 17 SD: 0.1223 cents 512 .. 1024 match: 17 SD: 0.1078 cents 567 .. 1134 match: 17 SD: 0.1040 cents 584 .. 1168 match: 17 SD: 0.1024 cents