Scala analysis: precata19
Cata[19] transversal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 13/12 138.572661 tridecimal 2/3-tone 3: 10/9 182.403712 minor whole tone 4: 52/45 250.303946 5: 6/5 315.641287 minor third 6: 5/4 386.313714 major third 7: 13/10 454.213948 tridecimal semi-diminished fourth 8: 4/3 498.044999 perfect fourth 9: 18/13 563.382340 tridecimal augmented fourth 10: 13/9 636.617660 tridecimal diminished fifth 11: 3/2 701.955001 perfect fifth 12: 20/13 745.786052 tridecimal semi-augmented fifth 13: 8/5 813.686286 minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 26/15 952.258947 tridecimal semi-augmented sixth 16: 9/5 1017.596288 just minor seventh, BP seventh 17: 24/13 1061.427339 tridecimal neutral seventh 18: 25/13 1132.099766 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 26/25 67.9002 tridecimal 1/3-tone 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 26/25 67.9002 tridecimal 1/3-tone 3: 40/39 43.8311 tridecimal minor diesis 4: 26/25 67.9002 tridecimal 1/3-tone 5: 27/26 65.3373 tridecimal comma 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 26/25 67.9002 tridecimal 1/3-tone 8: 40/39 43.8311 tridecimal minor diesis 9: 27/26 65.3373 tridecimal comma 10: 169/162 73.2353 11: 27/26 65.3373 tridecimal comma 12: 40/39 43.8311 tridecimal minor diesis 13: 26/25 67.9002 tridecimal 1/3-tone 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 26/25 67.9002 tridecimal 1/3-tone 16: 27/26 65.3373 tridecimal comma 17: 40/39 43.8311 tridecimal minor diesis 18: 25/24 70.6724 classic chromatic semitone, minor chroma 19: 26/25 67.9002 tridecimal 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 40/39 43.831 cents tridecimal minor diesis 1: 4 27/26 65.337 cents tridecimal comma 1: 6 26/25 67.900 cents tridecimal 1/3-tone 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 169/162 73.235 cents 2: 3 180/169 109.168 cents 2: 4 16/15 111.731 cents minor diatonic semitone 2: 1 125/117 114.503 cents 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 225/208 136.010 cents 2: 8 13/12 138.573 cents tridecimal 2/3-tone 3: 4 72/65 177.069 cents 3: 1 416/375 179.632 cents 3: 1 375/338 179.841 cents 3: 6 10/9 182.404 cents minor whole tone 3: 4 9/8 203.910 cents major whole tone 3: 2 169/150 206.473 cents 3: 1 325/288 209.245 cents 4: 1 144/125 244.969 cents classic diminished third 4: 9 15/13 247.741 cents tridecimal 5/4-tone 4: 5 52/45 250.304 cents 4: 1 125/108 253.076 cents semi-augmented whole tone 4: 2 117/100 271.810 cents 4: 1 169/144 277.145 cents two (tridecimal 2/3-tone) 5: 1 200/169 291.572 cents 5: 1 405/338 313.078 cents 5: 10 6/5 315.641 cents minor third 5: 1 1352/1125 318.204 cents 5: 2 125/104 318.413 cents 5: 4 65/54 320.976 cents 6: 4 16/13 359.472 cents tridecimal neutral third 6: 1 100/81 364.807 cents grave major third 6: 2 81/65 380.979 cents 6: 2 156/125 383.542 cents 6: 8 5/4 386.314 cents major third 6: 2 169/135 388.877 cents 7: 2 216/169 424.810 cents 7: 2 32/25 427.373 cents classic diminished fourth 7: 4 50/39 430.145 cents 7: 1 104/81 432.708 cents 7: 1 135/104 451.651 cents 7: 8 13/10 454.214 cents tridecimal semi-diminished fourth 7: 1 125/96 456.986 cents classic augmented third 8: 1 432/325 492.710 cents 8: 2 225/169 495.482 cents two (tridecimal 5/4-tone) 8: 10 4/3 498.045 cents perfect fourth 8: 2 27/20 519.551 cents acute fourth 8: 1 169/125 522.114 cents 8: 3 65/48 524.886 cents 9: 8 18/13 563.382 cents tridecimal augmented fourth 9: 4 104/75 565.945 cents 9: 5 25/18 568.717 cents classic augmented fourth 9: 2 169/120 592.787 cents 10: 2 240/169 607.213 cents 10: 5 36/25 631.283 cents classic diminished fifth 10: 4 75/52 634.055 cents 10: 8 13/9 636.618 cents tridecimal diminished fifth 11: 3 96/65 675.114 cents 11: 1 250/169 677.886 cents 11: 2 40/27 680.449 cents grave fifth 11: 10 3/2 701.955 cents perfect fifth 11: 2 338/225 704.518 cents 11: 1 325/216 707.290 cents 12: 1 192/125 743.014 cents classic diminished sixth 12: 8 20/13 745.786 cents tridecimal semi-augmented fifth 12: 1 208/135 748.349 cents 12: 1 81/52 767.292 cents 12: 4 39/25 769.855 cents 12: 2 25/16 772.627 cents classic augmented fifth 12: 2 169/108 775.190 cents 13: 2 270/169 811.123 cents 13: 8 8/5 813.686 cents minor sixth 13: 2 125/78 816.458 cents 13: 2 130/81 819.021 cents 13: 1 81/50 835.193 cents acute minor sixth 13: 4 13/8 840.528 cents tridecimal neutral sixth 14: 4 108/65 879.024 cents 14: 2 208/125 881.587 cents 14: 1 1125/676 881.796 cents 14: 10 5/3 884.359 cents major sixth, BP sixth 14: 1 676/405 886.922 cents 14: 1 169/100 908.428 cents two (tridecimal semi-diminished fourth) 15: 1 288/169 922.855 cents 15: 2 200/117 928.190 cents 15: 1 216/125 946.924 cents semi-augmented sixth 15: 5 45/26 949.696 cents 15: 9 26/15 952.259 cents tridecimal semi-augmented sixth 15: 1 125/72 955.031 cents classic augmented sixth 16: 1 576/325 990.755 cents 16: 2 300/169 993.527 cents 16: 4 16/9 996.090 cents Pythagorean minor seventh 16: 6 9/5 1017.596 cents just minor seventh, BP seventh 16: 1 676/375 1020.159 cents 16: 1 375/208 1020.368 cents 16: 4 65/36 1022.931 cents 17: 8 24/13 1061.427 cents tridecimal neutral seventh 17: 1 416/225 1063.990 cents 17: 2 50/27 1066.762 cents grave major seventh 17: 1 234/125 1085.497 cents 17: 4 15/8 1088.269 cents classic major seventh 17: 3 169/90 1090.832 cents 18: 1 324/169 1126.765 cents two (tridecimal augmented fourth) 18: 4 48/25 1129.328 cents classic diminished octave 18: 6 25/13 1132.100 cents 18: 4 52/27 1134.663 cents 18: 4 39/20 1156.169 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.88889 = 53/9
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 : 70.7 138.6 182.4 250.3 315.6 386.3 454.2 498.0 563.4 636.6 702.0 745.8 813.7 884.4 952.3 1017.6 1061.4 1132.1 1200.0 70.7 : 67.9 111.7 179.6 245.0 315.6 383.5 427.4 492.7 565.9 631.3 675.1 743.0 813.7 881.6 946.9 990.8 1061.4 1129.3 1200.0 138.6 : 43.8 111.7 177.1 247.7 315.6 359.5 424.8 498.0 563.4 607.2 675.1 745.8 813.7 879.0 922.9 993.5 1061.4 1132.1 1200.0 182.4 : 67.9 133.2 203.9 271.8 315.6 381.0 454.2 519.6 563.4 631.3 702.0 769.9 835.2 879.0 949.7 1017.6 1088.3 1156.2 1200.0 250.3 : 65.3 136.0 203.9 247.7 313.1 386.3 451.7 495.5 563.4 634.1 702.0 767.3 811.1 881.8 949.7 1020.4 1088.3 1132.1 1200.0 315.6 : 70.7 138.6 182.4 247.7 321.0 386.3 430.1 498.0 568.7 636.6 702.0 745.8 816.5 884.4 955.0 1022.9 1066.8 1134.7 1200.0 386.3 : 67.9 111.7 177.1 250.3 315.6 359.5 427.4 498.0 565.9 631.3 675.1 745.8 813.7 884.4 952.3 996.1 1064.0 1129.3 1200.0 454.2 : 43.8 109.2 182.4 247.7 291.6 359.5 430.1 498.0 563.4 607.2 677.9 745.8 816.5 884.4 928.2 996.1 1061.4 1132.1 1200.0 498.0 : 65.3 138.6 203.9 247.7 315.6 386.3 454.2 519.6 563.4 634.1 702.0 772.6 840.5 884.4 952.3 1017.6 1088.3 1156.2 1200.0 563.4 : 73.2 138.6 182.4 250.3 321.0 388.9 454.2 498.0 568.7 636.6 707.3 775.2 819.0 886.9 952.3 1022.9 1090.8 1134.7 1200.0 636.6 : 65.3 109.2 177.1 247.7 315.6 381.0 424.8 495.5 563.4 634.1 702.0 745.8 813.7 879.0 949.7 1017.6 1061.4 1126.8 1200.0 702.0 : 43.8 111.7 182.4 250.3 315.6 359.5 430.1 498.0 568.7 636.6 680.4 748.3 813.7 884.4 952.3 996.1 1061.4 1134.7 1200.0 745.8 : 67.9 138.6 206.5 271.8 315.6 386.3 454.2 524.9 592.8 636.6 704.5 769.9 840.5 908.4 952.3 1017.6 1090.8 1156.2 1200.0 813.7 : 70.7 138.6 203.9 247.7 318.4 386.3 457.0 524.9 568.7 636.6 702.0 772.6 840.5 884.4 949.7 1022.9 1088.3 1132.1 1200.0 884.4 : 67.9 133.2 177.1 247.7 315.6 386.3 454.2 498.0 565.9 631.3 702.0 769.9 813.7 879.0 952.3 1017.6 1061.4 1129.3 1200.0 952.3 : 65.3 109.2 179.8 247.7 318.4 386.3 430.1 498.0 563.4 634.1 702.0 745.8 811.1 884.4 949.7 993.5 1061.4 1132.1 1200.0 1017.6: 43.8 114.5 182.4 253.1 321.0 364.8 432.7 498.0 568.7 636.6 680.4 745.8 819.0 884.4 928.2 996.1 1066.8 1134.7 1200.0 1061.4: 70.7 138.6 209.2 277.1 321.0 388.9 454.2 524.9 592.8 636.6 702.0 775.2 840.5 884.4 952.3 1022.9 1090.8 1156.2 1200.0 1132.1: 67.9 138.6 206.5 250.3 318.2 383.5 454.2 522.1 565.9 631.3 704.5 769.9 813.7 881.6 952.3 1020.2 1085.5 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 73.2353 cents 2197/2160, 29.4043 cents 40/39, 43.8311 cents 2: 109.1684 .. 138.5727 cents 2197/2160, 29.4043 cents 29160/28561, 35.9331 cents 3: 177.0686 .. 209.2451 cents 21125/20736, 32.1765 cents 864/845, 38.4960 cents 4: 244.9689 .. 277.1453 cents 21125/20736, 32.1765 cents 41472/40625, 35.7238 cents 5: 291.5721 .. 320.9764 cents 2197/2160, 29.4043 cents 28800/28561, 14.4268 cents 6: 359.4723 .. 388.8766 cents 2197/2160, 29.4043 cents 864/845, 38.4960 cents 7: 424.8097 .. 456.9861 cents 21125/20736, 32.1765 cents 29160/28561, 35.9331 cents 8: 492.7099 .. 524.8864 cents 21125/20736, 32.1765 cents 41472/40625, 35.7238 cents 9: 563.3823 .. 592.7866 cents 2197/2160, 29.4043 cents 864/845, 38.4960 cents 10: 607.2134 .. 636.6177 cents 2197/2160, 29.4043 cents 28800/28561, 14.4268 cents 11: 675.1136 .. 707.2901 cents 21125/20736, 32.1765 cents 864/845, 38.4960 cents 12: 743.0139 .. 775.1903 cents 21125/20736, 32.1765 cents 41472/40625, 35.7238 cents 13: 811.1234 .. 840.5277 cents 2197/2160, 29.4043 cents 29160/28561, 35.9331 cents 14: 879.0236 .. 908.4279 cents 2197/2160, 29.4043 cents 864/845, 38.4960 cents 15: 922.8547 .. 955.0311 cents 21125/20736, 32.1765 cents 28800/28561, 14.4268 cents 16: 990.7549 .. 1022.9314 cents 21125/20736, 32.1765 cents 41472/40625, 35.7238 cents 17: 1061.4273 .. 1090.8316 cents 2197/2160, 29.4043 cents 864/845, 38.4960 cents 18: 1126.7647 .. 1156.1689 cents 2197/2160, 29.4043 cents 29160/28561, 35.9331 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 169/162, 73.2353 cents Average / Smallest step : 1.440940 Largest / Average step : 1.159559 Largest / Smallest step : 1.670855 Median interval of one step : 26/25, 67.9002 cents, amount: 6 Most common interval of one step : 26/25, 67.9002 cents, amount: 6 Least squares average step : 63.08104 cents, oct.: 1198.53981 cents Scale is strictly proper Step pattern alph. order: ABCBDABCDEDCBABDCAB Step pattern size order : DCACBDCABEBACDCBADC Scale is a Constant Structure, by a margin of 14.42678 cents Scale diversity : 1.296252 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.540455 Number of different interval sizes : 106 = 5.88889 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.88889 = 53/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 140625/140608, 0.2093 cents Most common triad is 0.0 498.045 884.359 cents, amount: 7 Number of recognisable fifths : 13, average 702.7597 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 3 5 9 13 Length of longest harmonic part : 3 at degree 13 Length of longest subharmonic part : 2 at degree 12 Formal octave complements present : 15 = 78.9474% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 1125 (O: 1125 U: 1125) Highest odd numerator or denominator: 45 Scale harmonicity : 0.012473 Average absolute harmonicity : 0.128356 Specific harmonicity : 0.073678 Fundamental : 1/4680, -12.1923 octaves, 0.0559 Hz. Guide tone : 23400, 14.5142 octaves, 6122038.228 Hz. Exponens Consonantiae : 1.095120E+08, 26.70651 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 242.5, average 12.76316 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.96745, average 0.94566 Sum of Tenney's harmonic distance : 36.22603, average 1.90663 Vogel's harmonic complexity : 28.00000 Wille's k value : 2437 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 592.98629, average 3.12098 Lattice compactness (without 2's) : 417.99165, average 2.19996 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42105 26 1 3: -2 .. 2 -0.21053 18 2 5: -1 .. 2 0.10526 14 7 13: -1 .. 1 0.05263 9 9 Average exponent except 2's :-1 / 19 =-0.05263 Average absolute exponent except 2's: 41 / 19 = 2.15789 Scale is JI-epimorphic with val: <19 30 44 70| = patent
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.4886 c. M: 12.2569 c. 34: 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 P M ME I SD: 3.1993 c. M: 5.9331 c. 53: 3 3 2 3 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 SP M ME I SD: 1.6922 c. M: 2.7479 c. 87: 5 5 3 5 5 5 5 3 5 5 5 3 5 5 5 5 3 5 5 SP M DE I SD: 1.6053 c. M: 3.0934 c. 140: 8 8 5 8 8 8 8 5 8 8 8 5 8 8 8 8 5 8 8 SP M DE I SD: 1.4858 c. M: 2.4037 c. 164: 10 9 6 9 9 10 9 6 9 10 9 6 9 10 9 9 6 10 9 SP SD: 1.0846 c. M:-2.4983 c. 171: 10 10 6 10 9 10 10 6 9 11 9 6 10 10 10 9 6 10 10 SP SD: 1.4014 c. M:-2.3276 c. 183: 11 10 7 10 10 11 10 7 10 11 10 7 10 11 10 10 7 11 10 SP SD: 1.1349 c. M:-2.3265 c. 190: 11 11 7 11 10 11 11 7 10 12 10 7 11 11 11 10 7 11 11 SP SD: 1.0379 c. M:-2.3276 c. 198: 12 11 7 11 11 12 11 7 11 12 11 7 11 12 11 11 7 12 11 SP SD: 1.0178 c. M:-2.0548 c. 217: 13 12 8 12 12 13 12 8 12 13 12 8 12 13 12 12 8 13 12 SP SD: 0.7720 c. M:-1.5408 c. 251: 15 14 9 14 14 15 14 9 14 15 14 9 14 15 14 14 9 15 14 SP SD: 0.7629 c. M: 1.6984 c. 270: 16 15 10 15 15 16 15 10 15 16 15 10 15 16 15 15 10 16 15 SP SD: 0.7461 c. M: 1.4151 c. 277: 16 16 10 16 15 16 16 10 15 17 15 10 16 16 16 15 10 16 16 SP SD: 0.6769 c. M: 1.4138 c. 301: 18 17 11 17 16 18 17 11 16 19 16 11 17 18 17 16 11 18 17 SP SD: 0.7538 c. M:-1.2561 c. 304: 18 17 11 17 17 18 17 11 17 18 17 11 17 18 17 17 11 18 17 SP SD: 0.7268 c. M: 1.6197 c. 320: 19 18 12 18 17 19 18 12 17 20 17 12 18 19 18 17 12 19 18 SP SD: 0.6862 c. M: 1.3463 c. 330: 19 19 12 19 18 19 19 12 18 20 18 12 19 19 19 18 12 19 19 SP SD: 0.6650 c. M: 1.5815 c. 335: 20 19 12 19 18 20 19 12 18 21 18 12 19 20 19 18 12 20 19 SP SD: 0.6564 c. M:-1.1288 c. 354: 21 20 13 20 19 21 20 13 19 22 19 13 20 21 20 19 13 21 20 SP SD: 0.4099 c. M: 0.6705 c. 388: 23 22 14 22 21 23 22 14 21 24 21 14 22 23 22 21 14 23 22 SP SD: 0.3415 c. M: 0.6026 c. 407: 24 23 15 23 22 24 23 15 22 25 22 15 23 24 23 22 15 24 23 SP SD: 0.2014 c. M: 0.3973 c. 441: 26 25 16 25 24 26 25 16 24 27 24 16 25 26 25 24 16 26 25 SP SD: 0.1211 c. M:-0.2078 c. 848: 50 48 31 48 46 50 48 31 46 52 46 31 48 50 48 46 31 50 48 SP SD: 0.1008 c. M: 0.1748 c. 901: 53 51 33 51 49 53 51 33 49 55 49 33 51 53 51 49 33 53 51 SP SD: 0.0543 c. M:-0.0845 c. 1342: 79 76 49 76 73 79 76 49 73 82 73 49 76 79 76 73 49 79 76 SP SD: 0.0335 c. M:-0.0686 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: 4.1417 cents 5 .. 10 match: 5 H SD: 3.8260 cents 6 .. 12 match: 6 H SD: 3.4157 cents 7 .. 14 match: 7 H SD: 7.2032 cents 8 .. 16 match: 8 H SD: 6.0253 cents 9 .. 18 match: 9 H SD: 5.8815 cents 10 .. 20 match: 10 H SD: 4.7283 cents 11 .. 22 match: 11 H SD: 5.9136 cents 12 .. 24 match: 12 H SD: 3.8968 cents 13 .. 26 match: 13 H SD: 4.3622 cents 14 .. 28 match: 14 H SD: 5.1022 cents 15 .. 30 match: 15 H SD: 4.1767 cents 16 .. 32 match: 16 H SD: 4.6855 cents 17 .. 34 match: 15 SD: 5.6772 cents 18 .. 36 match: 17 SD: 3.8736 cents 19 .. 38 match: 16 SD: 4.0874 cents 20 .. 40 match: 18 SD: 2.8489 cents 21 .. 42 match: 17 S SD: 3.5110 cents 22 .. 44 match: 17 SD: 4.2021 cents 23 .. 46 match: 18 SD: 3.7442 cents 24 .. 48 match: 19 SD: 2.5154 cents 25 .. 50 match: 17 SD: 2.6360 cents 26 .. 52 match: 19 SD: 2.5325 cents 30 .. 60 match: 18 SD: 2.5488 cents 31 .. 62 match: 18 SD: 2.7793 cents 33 .. 66 match: 19 SD: 2.4932 cents 34 .. 68 match: 19 SD: 2.3704 cents 36 .. 72 match: 19 SD: 2.0843 cents 39 .. 78 match: 19 SD: 1.9384 cents 44 .. 88 match: 19 SD: 1.5943 cents 45 .. 90 match: 19 SD: 1.4256 cents 52 .. 104 match: 19 SD: 1.3018 cents 60 .. 120 match: 19 SD: 1.1301 cents 70 .. 140 match: 19 SD: 0.9040 cents 72 .. 144 match: 19 SD: 0.8445 cents 90 .. 180 match: 19 SD: 0.7871 cents 96 .. 192 match: 19 SD: 0.6182 cents 117 .. 234 match: 19 SD: 0.5189 cents 120 .. 240 match: 19 SD: 0.4669 cents 144 .. 288 match: 19 SD: 0.4363 cents 160 .. 320 match: 19 SD: 0.4343 cents 168 .. 336 match: 19 SD: 0.4258 cents 169 .. 338 match: 19 SD: 0.3913 cents 180 .. 360 match: 19 SD: 0.2746 cents 216 .. 432 match: 19 SD: 0.2661 cents 240 .. 480 match: 19 SD: 0.2270 cents 288 .. 576 match: 19 SD: 0.1946 cents 336 .. 672 match: 19 SD: 0.1800 cents 340 .. 680 match: 19 SD: 0.1651 cents 360 .. 720 match: 19 SD: 0.1104 cents 520 .. 1040 match: 19 SD: 0.1097 cents 540 .. 1080 match: 19 SD: 0.1014 cents 600 .. 1200 match: 19 SD: 0.0819 cents