Scala analysis: xen09-wilson-marwa-13-03
Marwa permutation 3 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: 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: 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: 10/9 182.4037 minor whole 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 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: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major 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 : 133.2 315.6 519.6 631.3 813.7 1017.6 1200.0 133.2 : 182.4 386.3 498.0 680.4 884.4 1066.8 1200.0 315.6 : 203.9 315.6 498.0 702.0 884.4 1017.6 1200.0 519.6 : 111.7 294.1 498.0 680.4 813.7 996.1 1200.0 631.3 : 182.4 386.3 568.7 702.0 884.4 1088.3 1200.0 813.7 : 203.9 386.3 519.6 702.0 905.9 1017.6 1200.0 1017.6: 182.4 315.6 498.0 702.0 813.7 996.1 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 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 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 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 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: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 167.30224 cents, oct.: 1171.11567 cents Scale is strictly proper Step pattern alph. order: ABCDBCB Step pattern size order : BCDACDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.405280 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.574950 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 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 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 Scale is fully connected 5-limit major-minor triadic Length of longest harmonic part : 2 at degree 5 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 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 92.1787 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 27 Scale harmonicity : 0.038760 Average absolute harmonicity : 0.207095 Specific harmonicity : 0.201723 Fundamental : 1/100, -6.6439 octaves, 2.6163 Hz. Guide tone : 216, 7.7549 octaves, 56511.122 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 100.5, average 14.35714 Mersenne's string divisions : 34438404 Sum of van Prooijen's expressibility: 6.61285, average 0.94469 Sum of Tenney's harmonic distance : 13.54936, average 1.93562 Vogel's harmonic complexity : 11.71429 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 78.42543, average 2.80091 Lattice compactness (without 2's) : 53.37013, average 1.90608 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.71429 9 1 3: 0 .. 3 1.57143 11 5: -2 .. 0 -1.14286 8 6 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 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: 32.0685 c. M:-54.4317 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 30.3214 c. M:-49.0704 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 28.5746 c. M: 50.0499 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 21.4049 c. M: 33.2376 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 15: 2 2 3 1 2 3 2 P D3 SD: 21.1679 c. M:-40.4487 c. 16: 2 2 3 1 3 3 2 P T3 SD: 19.6829 c. M:-32.4037 c. 18: 2 3 3 1 3 3 3 P T3 SD: 16.8120 c. M: 31.2826 c. 19: 2 3 3 2 3 3 3 SP M ME S SD: 7.1356 c. M: 14.2881 c. Nineteen-tone Locrian 27: 3 4 5 2 4 5 4 SP SD: 8.4624 c. M:-13.7820 c. 34: 4 5 6 3 5 6 5 SP SD: 5.5967 c. M:-9.8605 c. 46: 5 7 8 4 7 8 7 SP SD: 3.1923 c. M: 5.1956 c. 53: 6 8 9 5 8 9 8 SP SD: 1.7256 c. M:-2.6797 c. 99: 11 15 17 9 15 17 15 SP SD: 0.9827 c. M:-1.6608 c. 118: 13 18 20 11 18 20 18 SP SD: 0.6630 c. M: 1.0342 c. 171: 19 26 29 16 26 29 26 SP SD: 0.2096 c. M:-0.3488 c. 388: 43 59 66 36 59 66 59 SP SD: 0.2090 c. M: 0.3547 c. 441: 49 67 75 41 67 75 67 SP SD: 0.0888 c. M:-0.1766 c. 559: 62 85 95 52 85 95 85 SP SD: 0.0969 c. M: 0.1556 c. 612: 68 93 104 57 93 104 93 SP SD: 0.0616 c. M:-0.0958 c. 730: 81 111 124 68 111 124 111 SP SD: 0.0591 c. M: 0.0992 c. 1000: 111 152 170 93 152 170 152 SP SD: 0.0531 c. M: 0.0863 c. 1171: 130 178 199 109 178 199 178 SP SD: 0.0161 c. M: 0.0272 c. 1342: 149 204 228 125 204 228 204 SP SD: 0.0159 c. M: 0.0282 c. 1783: 198 271 303 166 271 303 271 SP SD: 0.0140 c. M:-0.0225 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: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 27.8026 cents 5 x 6 x 7:8:9:10 S SD: 9.7541 cents 6 x 7:8:9:10:11:12 S SD: 19.6068 cents 7 x 8:9:10:11:13:14 SD: 22.5833 cents 8:9:10:11:12:13:14:16 S SD: 19.7391 cents 9:10:11:12:13:14:16:18 S SD: 11.7443 cents 10:11:12 x 14:16:18:20 S SD: 9.7006 cents 11:12:13:15:16:18:20:22 SD: 8.3584 cents 14:15:17:19:20:22:25:28 SD: 6.4637 cents 15:16:18:20:22:24:27:30 S SD: 6.2827 cents 20:22:24:27:29:32:36:40 SD: 4.8501 cents 25:27:30:34:36:40:45:50 SD: 1.8252 cents 60:65:72:81:86:96:108:120 SD: 1.3777 cents 75:81:90:101:108:120:135:150 SD: 0.6114 cents 100:108:120:135:144:160:180:200 SD: 0.0000 cents