Scala analysis: xen09-wilson-marwa-18b-02
Marwa permutation 2 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: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 33/20 866.959229 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 88/81 143.4979 2nd undecimal neutral second 5: 9/8 203.9100 major whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 3 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 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: 2 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 165.0 315.6 519.6 663.0 867.0 1017.6 1200.0 165.0 : 150.6 354.5 498.0 702.0 852.6 1035.0 1200.0 315.6 : 203.9 347.4 551.3 702.0 884.4 1049.4 1200.0 519.6 : 143.5 347.4 498.0 680.4 845.5 996.1 1200.0 663.0 : 203.9 354.5 537.0 702.0 852.6 1056.5 1200.0 867.0 : 150.6 333.0 498.0 648.7 852.6 996.1 1200.0 1017.6: 182.4 347.4 498.0 702.0 845.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 315.6413 .. 354.5471 cents 45/44, 38.9058 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 88/81, 143.4979 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 845.4529 .. 884.3587 cents 45/44, 38.9058 cents 88/81, 143.4979 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 170.33937 cents, oct.: 1192.37557 cents Scale is strictly proper Step pattern alph. order: ABCDCBE Step pattern size order : CBEAEBD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.268819 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.745682 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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: 2 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 : 3 at degree 6 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 n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited transpositions with margin 38.9058 cents: 5 Limited inverse transpositions with margin 38.9058 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 33 Scale harmonicity : 0.026145 Average absolute harmonicity : 0.193460 Specific harmonicity : 0.127103 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 594, 9.2143 octaves, 155405.586 Hz. Exponens Consonantiae : 3.564000E+04, 15.12121 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 93.0, average 13.28571 Mersenne's string divisions : 42581154 Sum of van Prooijen's expressibility: 6.82057, average 0.97437 Sum of Tenney's harmonic distance : 13.54321, average 1.93474 Vogel's harmonic complexity : 12.71429 Wille's k value : 49 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 72.18264, average 2.57795 Lattice compactness (without 2's) : 52.36604, average 1.87022 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.28571 8 1 3: -1 .. 3 0.85714 8 5: -1 .. 0 -0.85714 6 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is JI-epimorphic with val: <7 11 16 24| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 14.8335 c. M:-27.2159 c. Lebeng 20: 3 2 4 2 3 3 3 SP D3 S SD: 15.2575 c. M: 26.9592 c. 22: 3 3 4 2 4 3 3 SP D3 I SD: 13.4480 c. M:-25.9033 c. Symmetric Diminished Porcupine 23: 3 3 4 3 4 3 3 SP D3 I SD: 14.0644 c. M:-25.8820 c. 24: 3 3 4 3 4 3 4 SP M ME S SD: 15.2107 c. M: 19.5513 c. Neutral Phrygian, Iced Locrian 25: 3 4 4 3 4 3 4 SP M ME S SD: 12.5812 c. M: 21.0042 c. Dicot-7 26: 4 3 4 3 5 3 4 SP D3 SD: 11.7725 c. M:-19.6112 c. 27: 4 3 5 3 5 3 4 SP D3 I SD: 11.2696 c. M:-21.9297 c. 29: 4 4 5 3 5 4 4 SP D3 I SD: 11.1173 c. M:-18.3797 c. 30: 4 4 5 4 5 3 5 SP D3 SD: 10.7654 c. M: 17.5963 c. 31: 4 4 5 4 5 4 5 SP M ME S SD: 10.6233 c. M: 16.3255 c. Neutral Phrygian 32: 4 4 6 4 5 4 5 SP T3 SD: 9.9149 c. M: 15.6413 c. 33: 5 4 5 4 6 4 5 SP D3 SD: 9.5120 c. M:-16.8140 c. 34: 5 4 6 4 6 4 5 SP D3 I SD: 8.9581 c. M:-15.3937 c. 35: 5 4 6 4 6 5 5 SP T3 SD: 8.2014 c. M: 11.6207 c. 42: 6 5 7 5 7 6 6 SP T3 SD: 6.7880 c. M:-10.9751 c. 44: 6 6 7 5 8 5 7 SP S SD: 6.7291 c. M:-11.6314 c. 46: 6 6 8 5 8 6 7 SP SD: 5.8418 c. M: 10.8753 c. 50: 7 6 9 6 8 6 8 SP SD: 6.2630 c. M: 9.5963 c. 51: 7 6 9 6 9 6 8 SP SD: 4.8401 c. M: 9.7589 c. 53: 7 7 9 6 9 7 8 SP SD: 4.3450 c. M: 6.5819 c. 58: 8 7 10 7 10 7 9 SP SD: 2.7543 c. M: 5.2965 c. 65: 9 8 11 8 11 8 10 SP SD: 1.6619 c. M: 2.6282 c. 118: 16 15 20 14 20 15 18 SP SD: 1.5717 c. M: 2.5524 c. 125: 17 16 21 15 21 16 19 SP SD: 1.4688 c. M: 2.9592 c. 145: 20 18 25 17 25 18 22 SP SD: 1.1979 c. M:-2.0063 c. 152: 21 19 26 18 26 19 23 SP SD: 0.9041 c. M:-1.5013 c. 159: 22 20 27 19 27 20 24 SP SD: 1.0740 c. M:-1.3398 c. 190: 26 24 32 23 32 24 29 SP SD: 0.9895 c. M: 1.6961 c. 210: 29 26 36 25 36 26 32 SP SD: 0.8771 c. M:-1.6122 c. 217: 30 27 37 26 37 27 33 SP SD: 0.6446 c. M:-1.2435 c. 224: 31 28 38 27 38 28 34 SP SD: 0.7305 c. M:-1.2365 c. 263: 36 33 45 31 45 33 40 SP SD: 0.7269 c. M: 1.4523 c. 270: 37 34 46 32 46 34 41 SP SD: 0.4350 c. M: 0.8270 c. 277: 38 35 47 33 47 35 42 SP SD: 0.4053 c. M:-0.6042 c. 335: 46 42 57 40 57 42 51 SP SD: 0.2587 c. M: 0.4174 c. 342: 47 43 58 41 58 43 52 SP SD: 0.1667 c. M: 0.2926 c. 494: 68 62 84 59 84 62 75 SP SD: 0.1913 c. M:-0.2868 c. 677: 93 85 115 81 115 85 103 SP SD: 0.1531 c. M: 0.2012 c. 829: 114 104 141 99 141 104 126 SP SD: 0.0736 c. M:-0.1110 c. 1171: 161 147 199 140 199 147 178 SP SD: 0.0134 c. M: 0.0262 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: 9.2211 cents 4 x 5 x 6 x 7:8 S SD: 23.5675 cents 5 x 6:7 x 8:9:10 S SD: 16.4949 cents 6 x 7:8:9:10:11:12 S SD: 12.5461 cents 7:8 x 9:10:12:13:14 S SD: 24.0918 cents 8:9:10:11:12:13:14:16 S SD: 15.7196 cents 9:10:11:12:13:15:16:18 SD: 8.1294 cents 11:12:13:15:16:18:20:22 SD: 6.2652 cents 19:21:23:26:28:31:34:38 SD: 5.3387 cents 20:22:24:27:29:33:36:40 SD: 2.8265 cents 39:43:47:53:57:64:70:78 SD: 2.6827 cents 40:44:48:54:59:66:72:80 SD: 1.4012 cents 60:66:72:81:88:99:108:120 SD: 0.0000 cents