Scala analysis: xen09-wilson-marwa-13-02
Marwa permutation 2 from Figure 13, Al-Farabi 10/9 10/9 27/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute fourth 4: 36/25 631.282574 classic diminished fifth 5: 81/50 835.192576 acute 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor 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 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave major third 2: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 81/50 835.193 cents acute minor sixth 5: 4 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 6: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.2 315.6 519.6 631.3 835.2 1017.6 1200.0 133.2 : 182.4 386.3 498.0 702.0 884.4 1066.8 1200.0 315.6 : 203.9 315.6 519.6 702.0 884.4 1017.6 1200.0 519.6 : 111.7 315.6 498.0 680.4 813.7 996.1 1200.0 631.3 : 203.9 386.3 568.7 702.0 884.4 1088.3 1200.0 835.2 : 182.4 364.8 498.0 680.4 884.4 996.1 1200.0 1017.6: 182.4 315.6 498.0 702.0 813.7 1017.6 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: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 16/15, 111.7313 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: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 168.07032 cents, oct.: 1176.49225 cents Scale is strictly proper Step pattern alph. order: ABCDCBB Step pattern size order : BCDADCC Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.386222 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.610794 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents 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 4 Length of longest subharmonic part : 2 at degree 1 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 class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 70.6724 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.036408 Average absolute harmonicity : 0.197736 Specific harmonicity : 0.185794 Fundamental : 1/100, -6.6439 octaves, 2.6163 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 3.240000E+04, 14.98371 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 159.5, average 22.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.82237, average 1.11748 Sum of Tenney's harmonic distance : 15.55476, average 2.22211 Vogel's harmonic complexity : 12.14286 Wille's k value : 67 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 76.97064, average 2.74895 Lattice compactness (without 2's) : 58.72861, average 2.09745 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.14286 7 1 3: 0 .. 4 2.14286 15 5: -2 .. 0 -1.28571 9 6 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 24 / 7 = 3.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 28.7652 c. M:-54.4317 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 32.7041 c. M:-49.0704 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 25.6888 c. M:-37.5347 c. Orgone-7 12: 1 2 2 1 2 2 2 P M ME S SD: 24.6646 c. M: 35.1926 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 14: 2 2 2 1 3 2 2 P T3 SD: 23.3233 c. M:-38.1910 c. 16: 2 2 3 1 3 3 2 P T3 SD: 19.5952 c. M:-32.4037 c. 18: 2 3 3 1 4 2 3 P SD: 19.9349 c. M:-31.4741 c. 19: 2 3 3 2 3 3 3 SP M ME S SD: 8.4692 c. M: 14.2881 c. Nineteen-tone Locrian 26: 3 4 4 3 4 4 4 SP M ME S SD: 8.1838 c. M:-14.8713 c. 27: 3 4 5 2 5 4 4 SP SD: 7.5552 c. M:-13.7820 c. 33: 4 5 5 3 6 5 5 SP SD: 9.0024 c. M: 13.1008 c. 34: 4 5 6 3 6 5 5 SP SD: 7.1352 c. M:-11.8662 c. 42: 5 6 7 4 7 7 6 SP SD: 6.4779 c. M:-10.9751 c. 46: 5 7 8 4 8 7 7 SP SD: 2.5800 c. M: 5.1956 c. 53: 6 8 9 5 9 8 8 SP SD: 1.9022 c. M:-2.6797 c. 72: 8 11 12 7 12 11 11 SP SD: 1.5995 c. M: 2.8846 c. 99: 11 15 17 9 17 15 15 SP SD: 0.9009 c. M:-1.6608 c. 118: 13 18 20 11 20 18 18 SP SD: 0.8225 c. M: 1.2943 c. 171: 19 26 29 16 29 26 26 SP SD: 0.1676 c. M:-0.2964 c. 388: 43 59 66 36 66 59 59 SP SD: 0.1871 c. M: 0.3547 c. 441: 49 67 75 41 75 67 67 SP SD: 0.1080 c. M:-0.1816 c. 559: 62 85 95 52 95 85 85 SP SD: 0.1031 c. M: 0.1556 c. 612: 68 93 104 57 104 93 93 SP SD: 0.0711 c. M:-0.1015 c. 1000: 111 152 170 93 170 152 152 SP SD: 0.0420 c. M: 0.0826 c. 1171: 130 178 199 109 199 178 178 SP SD: 0.0140 c. M: 0.0272 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 17.8880 cents 4 x 5 x 6 x 7:8 S SD: 27.8026 cents 5 x 6 x 7:8:9:10 S SD: 10.6603 cents 6 x 7:8:9:10:11:12 S SD: 17.6872 cents 7 x 8:9:10:11:13:14 SD: 23.6669 cents 8:9:10:11:12:13:14:16 S SD: 19.3780 cents 9:10:11:12:13:15:16:18 SD: 11.7779 cents 10:11:12 x 14:16:18:20 S SD: 10.3417 cents 11:12:13:15:16:18:20:22 SD: 6.7194 cents 14:15:17:19:20:23:25:28 SD: 5.8248 cents 20:22:24:27:29:32:36:40 SD: 5.7413 cents 21:23:25:28:30:34:38:42 SD: 5.5622 cents 23:25:28:31:33:37:41:46 SD: 4.9915 cents 24:26:29:32:35:39:43:48 SD: 4.9636 cents 25:27:30:34:36:41:45:50 SD: 3.5413 cents 29:31:35:39:42:47:52:58 SD: 3.5046 cents 34:37:41:46:49:55:61:68 SD: 2.4713 cents 39:42:47:53:56:63:70:78 SD: 2.4061 cents 40:43:48:54:58:65:72:80 SD: 2.1971 cents 50:54:60:68:72:81:90:100 SD: 1.8252 cents 60:65:72:81:86:97:108:120 SD: 1.4688 cents 66:71:79:89:95:107:119:132 SD: 1.2782 cents 75:81:90:101:108:122:135:150 SD: 1.1855 cents 86:93:103:116:124:139:155:172 SD: 0.9513 cents 89:96:107:120:128:144:160:178 SD: 0.8315 cents 100:108:120:135:144:162:180:200 SD: 0.0000 cents