Scala analysis: smalldi19a
Small diesic 19-note block, <16/15, 126/125, 1728/1715> commas
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: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 8/7 231.174094 septimal whole tone 4: 7/6 266.870906 septimal minor third 5: 6/5 315.641287 minor third 6: 175/144 337.543332 7: 5/4 386.313714 major third 8: 48/35 546.815381 septimal semi-augmented fourth 9: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 10: 10/7 617.487807 Euler's tritone 11: 35/24 653.184619 septimal semi-diminished fifth 12: 8/5 813.686286 minor sixth 13: 288/175 862.456668 14: 5/3 884.358713 major sixth, BP sixth 15: 12/7 933.129094 septimal major sixth 16: 7/4 968.825906 harmonic seventh 17: 48/25 1129.327573 classic diminished octave 18: 35/18 1151.229619 septimal semi-diminished octave 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 875/864 21.9020 keema 3: 192/175 160.5017 septimal 4/5-tone 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 875/864 21.9020 keema 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 192/175 160.5017 septimal 4/5-tone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 11: 49/48 35.6968 slendro diesis, septimal 1/6-tone 12: 192/175 160.5017 septimal 4/5-tone 13: 36/35 48.7704 septimal diesis, 1/4-tone 14: 875/864 21.9020 keema 15: 36/35 48.7704 septimal diesis, 1/4-tone 16: 49/48 35.6968 slendro diesis, septimal 1/6-tone 17: 192/175 160.5017 septimal 4/5-tone 18: 875/864 21.9020 keema 19: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 875/864 21.902 cents keema 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 4 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 6 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 192/175 160.502 cents septimal 4/5-tone 2: 8 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 2 21/20 84.467 cents minor semitone 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 10/9 182.404 cents minor whole tone 2: 4 28/25 196.198 cents middle second 2: 2 6912/6125 209.272 cents 3: 3 1225/1152 106.369 cents 3: 4 15/14 119.443 cents major diatonic semitone 3: 2 245/216 218.101 cents 3: 6 8/7 231.174 cents septimal whole tone 3: 4 144/125 244.969 cents classic diminished third 4: 1 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 4: 2 35/32 155.140 cents septimal neutral second 4: 10 7/6 266.871 cents septimal minor third 4: 6 288/245 279.944 cents 5: 2 6125/5184 288.773 cents 5: 4 25/21 301.847 cents BP second, quasi-equal minor third 5: 12 6/5 315.641 cents minor third 5: 1 32/25 427.373 cents classic diminished fourth 6: 8 175/144 337.543 cents 6: 2 60/49 350.617 cents smaller approximation to neutral third 6: 2 49/40 351.338 cents larger approximation to neutral third 6: 2 216/175 364.412 cents 6: 1 64/49 462.348 cents 2 septatones or septatonic major third 6: 4 1152/875 476.143 cents 7: 10 5/4 386.314 cents major third 7: 6 4/3 498.045 cents perfect fourth 7: 2 168/125 511.840 cents 7: 1 41472/30625 524.913 cents 8: 2 4375/3456 408.216 cents 8: 2 245/192 422.011 cents 8: 2 9/7 435.084 cents septimal major third, BP third 8: 3 49/36 533.742 cents Arabic lute acute fourth 8: 10 48/35 546.815 cents septimal semi-augmented fourth 9: 2 125/96 456.986 cents classic augmented third 9: 5 25/18 568.717 cents classic augmented fourth 9: 8 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 4 1728/1225 595.586 cents 10: 4 1225/864 604.414 cents 10: 8 10/7 617.488 cents Euler's tritone 10: 5 36/25 631.283 cents classic diminished fifth 10: 2 192/125 743.014 cents classic diminished sixth 11: 10 35/24 653.185 cents septimal semi-diminished fifth 11: 3 72/49 666.258 cents Arabic lute grave fifth 11: 2 14/9 764.916 cents septimal minor sixth 11: 2 384/245 777.989 cents 11: 2 6912/4375 791.784 cents 12: 1 30625/20736 675.087 cents 12: 2 125/84 688.160 cents 12: 6 3/2 701.955 cents perfect fifth 12: 10 8/5 813.686 cents minor sixth 13: 4 875/576 723.857 cents 13: 1 49/32 737.652 cents 13: 2 175/108 835.588 cents 13: 2 80/49 848.662 cents smaller approximation to neutral sixth 13: 2 49/30 849.383 cents larger approximation to neutral sixth 13: 8 288/175 862.457 cents 14: 1 25/16 772.627 cents classic augmented fifth 14: 12 5/3 884.359 cents major sixth, BP sixth 14: 4 42/25 898.153 cents quasi-equal major sixth 14: 2 10368/6125 911.227 cents 15: 6 245/144 920.056 cents 15: 10 12/7 933.129 cents septimal major sixth 15: 2 64/35 1044.860 cents septimal neutral seventh 15: 1 1152/625 1058.655 cents 16: 4 125/72 955.031 cents classic augmented sixth 16: 6 7/4 968.826 cents harmonic seventh 16: 2 432/245 981.899 cents 16: 4 28/15 1080.557 cents grave major seventh 16: 3 2304/1225 1093.631 cents two (septimal semi-augmented fourth) 17: 2 6125/3456 990.728 cents 17: 4 25/14 1003.802 cents middle minor seventh 17: 2 9/5 1017.596 cents just minor seventh, BP seventh 17: 1 1225/648 1102.459 cents 17: 2 40/21 1115.533 cents acute major seventh 17: 8 48/25 1129.328 cents classic diminished octave 18: 4 175/96 1039.498 cents 18: 6 35/18 1151.230 cents septimal semi-diminished octave 18: 4 96/49 1164.303 cents 18: 1 49/25 1165.024 cents BP eighth 18: 4 1728/875 1178.098 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.77778 = 43/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 48.8 70.7 231.2 266.9 315.6 337.5 386.3 546.8 582.5 617.5 653.2 813.7 862.5 884.4 933.1 968.8 1129.3 1151.2 1200.0 48.8 : 21.9 182.4 218.1 266.9 288.8 337.5 498.0 533.7 568.7 604.4 764.9 813.7 835.6 884.4 920.1 1080.6 1102.5 1151.2 1200.0 70.7 : 160.5 196.2 245.0 266.9 315.6 476.1 511.8 546.8 582.5 743.0 791.8 813.7 862.5 898.2 1058.7 1080.6 1129.3 1178.1 1200.0 231.2 : 35.7 84.5 106.4 155.1 315.6 351.3 386.3 422.0 582.5 631.3 653.2 702.0 737.7 898.2 920.1 968.8 1017.6 1039.5 1200.0 266.9 : 48.8 70.7 119.4 279.9 315.6 350.6 386.3 546.8 595.6 617.5 666.3 702.0 862.5 884.4 933.1 981.9 1003.8 1164.3 1200.0 315.6 : 21.9 70.7 231.2 266.9 301.8 337.5 498.0 546.8 568.7 617.5 653.2 813.7 835.6 884.4 933.1 955.0 1115.5 1151.2 1200.0 337.5 : 48.8 209.3 245.0 279.9 315.6 476.1 524.9 546.8 595.6 631.3 791.8 813.7 862.5 911.2 933.1 1093.6 1129.3 1178.1 1200.0 386.3 : 160.5 196.2 231.2 266.9 427.4 476.1 498.0 546.8 582.5 743.0 764.9 813.7 862.5 884.4 1044.9 1080.6 1129.3 1151.2 1200.0 546.8 : 35.7 70.7 106.4 266.9 315.6 337.5 386.3 422.0 582.5 604.4 653.2 702.0 723.9 884.4 920.1 968.8 990.7 1039.5 1200.0 582.5 : 35.0 70.7 231.2 279.9 301.8 350.6 386.3 546.8 568.7 617.5 666.3 688.2 848.7 884.4 933.1 955.0 1003.8 1164.3 1200.0 617.5 : 35.7 196.2 245.0 266.9 315.6 351.3 511.8 533.7 582.5 631.3 653.2 813.7 849.4 898.2 920.1 968.8 1129.3 1165.0 1200.0 653.2 : 160.5 209.3 231.2 279.9 315.6 476.1 498.0 546.8 595.6 617.5 778.0 813.7 862.5 884.4 933.1 1093.6 1129.3 1164.3 1200.0 813.7 : 48.8 70.7 119.4 155.1 315.6 337.5 386.3 435.1 457.0 617.5 653.2 702.0 723.9 772.6 933.1 968.8 1003.8 1039.5 1200.0 862.5 : 21.9 70.7 106.4 266.9 288.8 337.5 386.3 408.2 568.7 604.4 653.2 675.1 723.9 884.4 920.1 955.0 990.7 1151.2 1200.0 884.4 : 48.8 84.5 245.0 266.9 315.6 364.4 386.3 546.8 582.5 631.3 653.2 702.0 862.5 898.2 933.1 968.8 1129.3 1178.1 1200.0 933.1 : 35.7 196.2 218.1 266.9 315.6 337.5 498.0 533.7 582.5 604.4 653.2 813.7 849.4 884.4 920.1 1080.6 1129.3 1151.2 1200.0 968.8 : 160.5 182.4 231.2 279.9 301.8 462.3 498.0 546.8 568.7 617.5 778.0 813.7 848.7 884.4 1044.9 1093.6 1115.5 1164.3 1200.0 1129.3: 21.9 70.7 119.4 141.3 301.8 337.5 386.3 408.2 457.0 617.5 653.2 688.2 723.9 884.4 933.1 955.0 1003.8 1039.5 1200.0 1151.2: 48.8 97.5 119.4 279.9 315.6 364.4 386.3 435.1 595.6 631.3 666.3 702.0 862.5 911.2 933.1 981.9 1017.6 1178.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.9020 .. 160.5017 cents 165888/153125, 138.5996 cents 875/864, 21.9020 cents 2: 70.6724 .. 209.2720 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 3: 106.3692 .. 244.9689 cents 165888/153125, 138.5996 cents 7503125/7962624,-102.9028 cents 4: 141.3449 .. 279.9445 cents 165888/153125, 138.5996 cents 78125/82944,-103.6240 cents 5: 288.7730 .. 427.3726 cents 165888/153125, 138.5996 cents 1500625/1492992, 8.8285 cents 6: 337.5433 .. 476.1430 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 7: 386.3137 .. 524.9133 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 8: 408.2158 .. 546.8154 cents 165888/153125, 138.5996 cents 133984375/143327232,-116.6976 cents 9: 456.9861 .. 595.5858 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 10: 604.4142 .. 743.0139 cents 165888/153125, 138.5996 cents 1500625/1492992, 8.8285 cents 11: 653.1846 .. 791.7842 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 12: 675.0867 .. 813.6863 cents 165888/153125, 138.5996 cents 133984375/143327232,-116.6976 cents 13: 723.8570 .. 862.4567 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 14: 772.6274 .. 911.2270 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents 15: 920.0555 .. 1058.6551 cents 165888/153125, 138.5996 cents 1500625/1492992, 8.8285 cents 16: 955.0311 .. 1093.6308 cents 165888/153125, 138.5996 cents 78125/82944,-103.6240 cents 17: 990.7280 .. 1129.3276 cents 165888/153125, 138.5996 cents 7503125/7962624,-102.9028 cents 18: 1039.4983 .. 1178.0980 cents 165888/153125, 138.5996 cents 4375/4608,-89.8292 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 875/864, 21.9020 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 192/175, 160.5017 cents Average / Smallest step : 2.883653 Largest / Average step : 2.541276 Largest / Smallest step : 7.328159 Median interval of one step : 36/35, 48.7704 cents, amount: 6 Most common interval of one step : 36/35, 48.7704 cents, amount: 6 Least squares average step : 63.48659 cents, oct.: 1206.24517 cents Scale is not proper Step pattern alph. order: ABCDABACDEDCABADCBA Step pattern size order : DAECDADECBCEDADCEAD Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.462492 Lumma stability : 0.058575 Lumma impropriety factor : 0.639281 Number of different interval sizes : 86 = 4.77778 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.77778 = 43/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 12 Most common triad is 0.0 315.641 884.359 cents, amount: 5 Number of recognisable fifths : 8, average 698.5063 cents Number of appreciable fifths : 6, average 701.9550 cents Scale contains a complete diamond : 3 5 7 35 Length of longest harmonic part : 2 at degree 8 Length of longest subharmonic part : 2 at degree 9 Formal octave complements present : 19 = 100.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 7 Odd number limit : 30625 (O: 30625 U: 30625) Highest odd numerator or denominator: 175 Scale harmonicity : 0.015189 Average absolute harmonicity : 0.115035 Specific harmonicity : 0.087611 Fundamental : 1/25200, -14.6211 octaves, 0.0104 Hz. Guide tone : 50400, 15.6211 octaves, 13185928.491 Hz. Exponens Consonantiae : 1.270080E+09, 30.24227 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 650.5, average 34.23684 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 21.32470, average 1.12235 Sum of Tenney's harmonic distance : 42.99984, average 2.26315 Vogel's harmonic complexity : 27.52632 Wille's k value : 15312 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 746.56817, average 3.92931 Lattice compactness (without 2's) : 438.38221, average 2.30727 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.52632 42 1 3: -2 .. 2 0.00000 16 5: -2 .. 2 0.00000 18 6 7: -1 .. 1 0.00000 12 12 Average exponent except 2's : 0 / 19 = 0.00000 Average absolute exponent except 2's: 46 / 19 = 2.42105 Scale is weakly epimorphic with val: <19 27 44 56| Scale is weakly epimorphic with val: <19 30 46 50| Scale is JI-epimorphic with val: <19 31 45 54| Scale is weakly epimorphic with val: <19 32 43 53| Scale is weakly epimorphic with val: <19 33 43 55| Scale is weakly epimorphic with val: <19 33 46 53|
FIT/MODE
19: 1 0 3 0 1 0 1 3 0 1 0 3 1 0 1 0 3 0 1 N I SD: 14.9368 c. M:-21.7539 c. 22: 1 0 3 1 1 0 1 3 1 0 1 3 1 0 1 1 3 0 1 N I SD: 10.5889 c. M:-17.4878 c. 31: 1 1 4 1 1 1 1 4 1 1 1 4 1 1 1 1 4 1 1 N M DE I SD: 6.0329 c. M:-10.8438 c. 46: 2 1 6 1 2 1 2 6 1 2 1 6 2 1 2 1 6 1 2 N I SD: 4.8920 c. M:-8.5991 c. 50: 2 1 7 1 2 1 2 7 1 2 1 7 2 1 2 1 7 1 2 N I SD: 4.3381 c. M:-8.8259 c. 53: 2 1 7 2 2 1 2 7 2 1 2 7 2 1 2 2 7 1 2 N I SD: 3.6054 c. M:-6.1671 c. 68: 3 1 9 2 3 1 3 9 2 2 2 9 3 1 3 2 9 1 3 N I SD: 2.0014 c. M:-4.1708 c. 99: 4 2 13 3 4 2 4 13 3 3 3 13 4 2 4 3 13 2 4 N I SD: 1.1944 c. M:-2.0548 c. 167: 7 3 22 5 7 3 7 22 5 5 5 22 7 3 7 5 22 3 7 N I SD: 1.0377 c. M: 1.7102 c. 171: 7 3 23 5 7 3 7 23 5 5 5 23 7 3 7 5 23 3 7 N I SD: 0.4002 c. M:-0.7012 c. 270: 11 5 36 8 11 5 11 36 8 8 8 36 11 5 11 8 36 5 11 N I SD: 0.2396 c. M:-0.4387 c. 441: 18 8 59 13 18 8 18 59 13 13 13 59 18 8 18 13 59 8 18 N I SD: 0.1389 c. M:-0.2092 c. 935: 38 17 125 28 38 17 38 125 28 27 28 125 38 17 38 28 125 17 38 N I SD: 0.0902 c. M:-0.1616 c. 1106: 45 20 148 33 45 20 45 148 33 32 33 148 45 20 45 33 148 20 45 N I SD: 0.0870 c. M: 0.1480 c. 1205: 49 22 161 36 49 22 49 161 36 35 36 161 49 22 49 36 161 22 49 N I SD: 0.0676 c. M:-0.1367 c. 1376: 56 25 184 41 56 25 56 184 41 40 41 184 56 25 56 41 184 25 56 N I SD: 0.0440 c. M:-0.0694 c. 1749: 71 32 234 52 71 32 71 234 52 51 52 234 71 32 71 52 234 32 71 N I SD: 0.0303 c. M:-0.0568 c. 2019: 82 37 270 60 82 37 82 270 60 59 60 270 82 37 82 60 270 37 82 N I SD: 0.0349 c. M: 0.0557 c. 2190: 89 40 293 65 89 40 89 293 65 64 65 293 89 40 89 65 293 40 89 N I SD: 0.0295 c. M:-0.0588 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 24.3852 cents 3 .. 6 match: 3 H SD: 16.2568 cents 4 .. 8 match: 4 H SD: 12.1926 cents 5 .. 10 match: 5 H SD: 9.7541 cents 6 .. 12 match: 5 S SD: 13.7943 cents 7 .. 14 match: 7 H SD: 11.6692 cents 8 .. 16 match: 8 H SD: 9.1077 cents 9 .. 18 match: 9 H SD: 10.5705 cents 10 .. 20 match: 10 H SD: 11.9518 cents 11 .. 22 match: 9 SD: 10.1528 cents 12 .. 24 match: 11 SD: 9.0522 cents 13 .. 26 match: 10 SD: 7.4190 cents 14 .. 28 match: 12 SD: 7.1456 cents 15 .. 30 match: 11 SD: 4.8886 cents 16 .. 32 match: 11 SD: 5.2740 cents 17 .. 34 match: 13 SD: 5.0726 cents 18 .. 36 match: 12 SD: 4.9206 cents 19 .. 38 match: 14 S SD: 3.9650 cents 20 .. 40 match: 14 SD: 2.9723 cents 21 .. 42 match: 14 SD: 3.1519 cents 22 .. 44 match: 16 SD: 3.6597 cents 23 .. 46 match: 15 SD: 3.1293 cents 24 .. 48 match: 15 SD: 2.6647 cents 25 .. 50 match: 15 SD: 2.3542 cents 26 .. 52 match: 15 SD: 3.7457 cents 27 .. 54 match: 16 SD: 2.8346 cents 28 .. 56 match: 16 SD: 2.1157 cents 29 .. 58 match: 14 SD: 2.8492 cents 30 .. 60 match: 16 SD: 2.5882 cents 31 .. 62 match: 16 SD: 2.7201 cents 32 .. 64 match: 16 SD: 2.2874 cents 33 .. 66 match: 17 SD: 2.2746 cents 34 .. 68 match: 17 SD: 2.7516 cents 35 .. 70 match: 17 SD: 1.5350 cents 38 .. 76 match: 17 SD: 2.4960 cents 39 .. 78 match: 18 SD: 2.3368 cents 40 .. 80 match: 19 SD: 1.7283 cents 43 .. 86 match: 18 SD: 1.6998 cents 44 .. 88 match: 18 SD: 1.9202 cents 45 .. 90 match: 19 SD: 1.8208 cents 47 .. 94 match: 19 SD: 1.7736 cents 48 .. 96 match: 18 SD: 1.3110 cents 53 .. 106 match: 17 SD: 1.5145 cents 54 .. 108 match: 18 SD: 1.5566 cents 55 .. 110 match: 18 SD: 1.3534 cents 56 .. 112 match: 18 SD: 1.2710 cents 57 .. 114 match: 18 SD: 1.5100 cents 58 .. 116 match: 17 SD: 1.8157 cents 59 .. 118 match: 18 SD: 1.3482 cents 60 .. 120 match: 19 SD: 1.2900 cents 64 .. 128 match: 19 SD: 1.2455 cents 65 .. 130 match: 19 SD: 0.9259 cents 70 .. 140 match: 19 SD: 0.8596 cents 91 .. 182 match: 19 SD: 0.8383 cents 92 .. 184 match: 19 SD: 0.8358 cents 96 .. 192 match: 19 SD: 0.7126 cents 100 .. 200 match: 19 SD: 0.7033 cents 105 .. 210 match: 19 SD: 0.6447 cents 112 .. 224 match: 19 SD: 0.6332 cents 115 .. 230 match: 19 SD: 0.6261 cents 120 .. 240 match: 19 SD: 0.5804 cents 135 .. 270 match: 19 SD: 0.5382 cents 139 .. 278 match: 19 SD: 0.5204 cents 140 .. 280 match: 19 SD: 0.3297 cents 175 .. 350 match: 19 SD: 0.2909 cents 215 .. 430 match: 19 SD: 0.2885 cents 240 .. 480 match: 19 SD: 0.2012 cents 288 .. 576 match: 19 SD: 0.1821 cents 380 .. 760 match: 19 SD: 0.1606 cents 385 .. 770 match: 19 SD: 0.1381 cents 455 .. 910 match: 19 SD: 0.1099 cents 525 .. 1050 match: 19 SD: 0.1000 cents 595 .. 1190 match: 19 SD: 0.0789 cents