Scala analysis: xen09-wilson-marwa-18b-04
Marwa permutation 4 from Figure 18b, Ptolemy 10/9 11/10 12/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 88/81 143.4979 2nd undecimal neutral second 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 315.6 519.6 663.0 813.7 1017.6 1200.0 111.7 : 203.9 407.8 551.3 702.0 905.9 1088.3 1200.0 315.6 : 203.9 347.4 498.0 702.0 884.4 996.1 1200.0 519.6 : 143.5 294.1 498.0 680.4 792.2 996.1 1200.0 663.0 : 150.6 354.5 537.0 648.7 852.6 1056.5 1200.0 813.7 : 203.9 386.3 498.0 702.0 905.9 1049.4 1200.0 1017.6: 182.4 294.1 498.0 702.0 845.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 256/243, 90.2250 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 168.05624 cents, oct.: 1176.39369 cents Scale is strictly proper Step pattern alph. order: ABBCDBE Step pattern size order : AEEBCED Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.485325 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.568106 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions with margin 92.1787 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.024243 Average absolute harmonicity : 0.209122 Specific harmonicity : 0.165486 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 4752, 12.2143 octaves, 1243244.686 Hz. Exponens Consonantiae : 2.851200E+05, 18.12121 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 78.0, average 11.14286 Mersenne's string divisions : 323777454 Sum of van Prooijen's expressibility: 6.13573, average 0.87653 Sum of Tenney's harmonic distance : 12.66454, average 1.80922 Vogel's harmonic complexity : 10.14286 Wille's k value : 40 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 86.04479, average 3.07303 Lattice compactness (without 2's) : 53.85331, average 1.92333 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.14286 12 1 3: -1 .. 3 0.57143 8 5: -1 .. 0 -0.85714 6 5 11: 0 .. 1 0.14286 1 1 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 15 22| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 18 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.2931 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 28.4440 c. M:-49.0704 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 25.8308 c. M: 50.0499 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 27.3514 c. M: 63.0492 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 2 3 1 2 2 2 P D3 SD: 22.7869 c. M: 38.7182 c. 16: 2 2 3 2 2 3 2 SP M ME S SD: 20.9068 c. M:-38.2687 c. Antimixolydian 18: 2 3 3 2 2 3 3 SP D3 S SD: 14.5388 c. M:-21.6020 c. 20: 2 3 4 2 3 3 3 SP D3 SD: 14.3361 c. M:-26.3137 c. 22: 2 4 4 2 3 4 3 SP S SD: 13.4056 c. M:-25.9033 c. 24: 2 4 4 3 3 4 4 SP D3 S SD: 14.3016 c. M: 19.5513 c. 25: 2 5 4 3 3 4 4 SP SD: 11.4073 c. M:-20.3587 c. 27: 3 4 5 3 3 5 4 SP S SD: 11.3321 c. M:-21.6020 c. 30: 3 5 5 4 3 5 5 SP SD: 11.1602 c. M: 17.5963 c. 31: 3 5 5 4 4 5 5 SP D3 S SD: 8.2036 c. M: 16.3255 c. 32: 3 5 6 4 4 5 5 SP SD: 9.0374 c. M: 15.6413 c. 33: 3 6 5 4 4 6 5 SP SD: 8.5495 c. M: 13.6863 c. 34: 3 6 6 4 4 6 5 SP SD: 5.7470 c. M:-9.8605 c. 41: 4 7 7 5 5 7 6 SP SD: 6.5886 c. M:-10.1215 c. 46: 4 8 8 5 6 8 7 SP SD: 5.4677 c. M: 10.8753 c. 47: 4 8 8 6 6 8 7 SP SD: 6.3546 c. M: 9.6036 c. 50: 5 8 9 6 6 8 8 SP SD: 6.8720 c. M: 9.5963 c. 52: 5 9 9 6 6 9 8 SP SD: 6.2508 c. M:-11.2179 c. 53: 5 9 9 6 7 9 8 SP SD: 2.6877 c. M: 6.4455 c. 65: 6 11 11 8 8 11 10 SP SD: 1.7030 c. M: 2.6282 c. 118: 11 20 20 14 15 20 18 SP SD: 0.8909 c. M: 2.0323 c. 152: 14 26 26 18 19 26 23 SP SD: 0.8193 c. M:-1.5013 c. 159: 15 27 27 19 20 27 24 SP SD: 1.2093 c. M:-1.4763 c. 183: 17 31 31 22 23 31 28 SP SD: 0.8865 c. M: 1.5185 c. 212: 20 36 36 25 27 36 32 SP SD: 1.1734 c. M:-1.4763 c. 217: 20 37 37 26 27 37 33 SP SD: 0.5925 c. M: 1.1322 c. 224: 21 38 38 27 28 38 34 SP SD: 0.6257 c. M:-1.2365 c. 270: 25 46 46 32 34 46 41 SP SD: 0.4527 c. M: 0.8270 c. 335: 31 57 57 40 42 57 51 SP SD: 0.4112 c. M: 0.6865 c. 342: 32 58 58 41 43 58 52 SP SD: 0.2736 c. M:-0.5494 c. 460: 43 78 78 55 58 78 70 SP SD: 0.3072 c. M:-0.4426 c. 494: 46 84 84 59 62 84 75 SP SD: 0.1557 c. M:-0.2868 c. 559: 52 95 95 67 70 95 85 SP SD: 0.1249 c. M:-0.2781 c. 612: 57 104 104 73 77 104 93 SP SD: 0.1213 c. M: 0.3041 c. 677: 63 115 115 81 85 115 103 SP SD: 0.1278 c. M: 0.2012 c. 901: 84 153 153 108 113 153 137 SP SD: 0.1150 c. M:-0.2138 c. 1019: 95 173 173 122 128 173 155 SP SD: 0.1140 c. M: 0.2186 c. 1053: 98 179 179 126 132 179 160 SP SD: 0.0917 c. M:-0.1986 c. 1106: 103 188 188 132 139 188 168 SP SD: 0.0982 c. M:-0.1594 c. 1171: 109 199 199 140 147 199 178 SP SD: 0.0187 c. M: 0.0319 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 23.5675 cents 5 x 6:7 x 8:9:10 S SD: 12.5922 cents 6 x 7:8:9:10:11:12 S SD: 16.9627 cents 7 x 8:9:10:11:13:14 SD: 23.7146 cents 8:9:10:11:12:13:14:16 S SD: 19.7501 cents 9:10:11:12:13:14:16:18 S SD: 14.2900 cents 10:11:12:14:15:16:18:20 S SD: 13.0272 cents 11:12:13:15:16:18:20:22 SD: 9.6234 cents 14:15:17:19:21:22:25:28 SD: 8.1312 cents 15:16:18:20:22:24:27:30 S SD: 3.0723 cents 30:32:36:41:44:48:54:60 SD: 3.0346 cents 40:43:48:54:59:64:72:80 SD: 2.3807 cents 45:48:54:61:66:72:81:90 SD: 1.0157 cents 60:64:72:81:88:96:108:120 SD: 0.0000 cents