Scala analysis: xen09-wilson-marwa-13-04
Marwa permutation 4 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: 16/15 111.731285 minor diatonic 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: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major 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: 2 16/15 111.731 cents minor diatonic semitone 1: 2 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: 2 6/5 315.641 cents minor third 2: 2 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: 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 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: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 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 : 111.7 315.6 519.6 631.3 813.7 1017.6 1200.0 111.7 : 203.9 407.8 519.6 702.0 905.9 1088.3 1200.0 315.6 : 203.9 315.6 498.0 702.0 884.4 996.1 1200.0 519.6 : 111.7 294.1 498.0 680.4 792.2 996.1 1200.0 631.3 : 182.4 386.3 568.7 680.4 884.4 1088.3 1200.0 813.7 : 203.9 386.3 498.0 702.0 905.9 1017.6 1200.0 1017.6: 182.4 294.1 498.0 702.0 813.7 996.1 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 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 256/243, 90.2250 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 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: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 167.14862 cents, oct.: 1170.04036 cents Scale is strictly proper Step pattern alph. order: ABBACBC Step pattern size order : SLLSMLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.425071 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 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: 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033937 Average absolute harmonicity : 0.211160 Specific harmonicity : 0.210111 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 1.296000E+05, 16.98371 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 90.0, average 12.85714 Mersenne's string divisions : 533795262 Sum of van Prooijen's expressibility: 6.35758, average 0.90823 Sum of Tenney's harmonic distance : 13.10027, average 1.87147 Vogel's harmonic complexity : 14.28571 Wille's k value : 202 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 86.91527, average 3.10412 Lattice compactness (without 2's) : 53.33717, average 1.90490 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.28571 13 1 3: -1 .. 3 1.00000 9 5: -2 .. 0 -1.00000 7 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 15| Scale is JI-epimorphic with val: <7 11 16| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 36.4573 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 31.4014 c. M:-49.0704 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 27.0963 c. M: 50.0499 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 17.8888 c. M: 31.2826 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 19: 2 3 3 2 3 3 3 SP M ME S SD: 8.6290 c. M:-14.5845 c. Nineteen-tone Locrian 31: 3 5 5 3 5 5 5 SP M DE S SD: 9.1692 c. M: 16.3255 c. Intense Diatonic Mixolydian, M.Locrian 32: 3 5 6 3 5 5 5 SP SD: 8.1728 c. M: 15.6413 c. 34: 3 6 6 3 5 6 5 SP S SD: 5.2160 c. M:-9.8605 c. 46: 4 8 8 4 7 8 7 SP S SD: 4.1056 c. M: 7.3835 c. 53: 5 9 9 5 8 9 8 SP S SD: 1.5214 c. M:-2.6797 c. 99: 9 17 17 9 15 17 15 SP S SD: 1.4001 c. M: 2.6404 c. 118: 11 20 20 11 18 20 18 SP S SD: 0.5378 c. M: 0.9072 c. 171: 16 29 29 16 26 29 26 SP S SD: 0.2928 c. M:-0.5494 c. 289: 27 49 49 27 44 49 44 SP S SD: 0.2804 c. M: 0.5201 c. 388: 36 66 66 36 59 66 59 SP S SD: 0.2382 c. M: 0.3911 c. 441: 41 75 75 41 67 75 67 SP S SD: 0.1027 c. M:-0.1766 c. 559: 52 95 95 52 85 95 85 SP S SD: 0.0895 c. M: 0.1556 c. 612: 57 104 104 57 93 104 93 SP S SD: 0.0515 c. M:-0.0900 c. 1171: 109 199 199 109 178 199 178 SP S SD: 0.0189 c. M: 0.0319 c. 1783: 166 303 303 166 271 303 271 SP S SD: 0.0121 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: 21.4734 cents 9:10:11:12:13:14:16:18 S SD: 13.8031 cents 10:11:12 x 14:16:18:20 S SD: 12.0376 cents 11:12:13:15:16:18:20:22 SD: 9.7250 cents 14:15:17:19:20:22:25:28 SD: 6.2538 cents 15:16:18:20:22:24:27:30 S SD: 5.4803 cents 20:21:24:27:29:32:36:40 SD: 4.2543 cents 25:27:30:34:36:40:45:50 SD: 3.5736 cents 29:31:35:39:42:46:52:58 SD: 3.2694 cents 30:32:36:41:43:48:54:60 SD: 3.2444 cents 34:36:41:46:49:54:61:68 SD: 3.0185 cents 40:43:48:54:58:64:72:80 SD: 2.5756 cents 43:46:52:58:62:69:77:86 SD: 2.5432 cents 45:48:54:61:65:72:81:90 SD: 1.2698 cents 60:64:72:81:86:96:108:120 SD: 1.1477 cents 75:80:90:101:108:120:135:150 SD: 0.6114 cents 105:112:126:142:151:168:189:210 SD: 0.5451 cents 120:128:144:162:173:192:216:240 SD: 0.2861 cents 180:192:216:243:259:288:324:360 SD: 0.1909 cents 300:320:360:405:432:480:540:600 S SD: 0.0000 cents