Scala analysis: xen09-wilson-marwa-13-09
Marwa permutation 9 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: 4/3 498.044999 perfect fourth 4: 36/25 631.282574 classic diminished fifth 5: 8/5 813.686286 minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major 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 : 111.7 315.6 498.0 631.3 813.7 996.1 1200.0 111.7 : 203.9 386.3 519.6 702.0 884.4 1088.3 1200.0 315.6 : 182.4 315.6 498.0 680.4 884.4 996.1 1200.0 498.0 : 133.2 315.6 498.0 702.0 813.7 1017.6 1200.0 631.3 : 182.4 364.8 568.7 680.4 884.4 1066.8 1200.0 813.7 : 182.4 386.3 498.0 702.0 884.4 1017.6 1200.0 996.1 : 203.9 315.6 519.6 702.0 835.2 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 : 165.76608 cents, oct.: 1160.36253 cents Scale is strictly proper Step pattern alph. order: ABCDCCB Step pattern size order : ADCBCCD 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 Most common triad is 0.0 315.641 498.045 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 1 Length of longest subharmonic part : 2 at degree 5 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 92.1787 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 25 Scale harmonicity : 0.036408 Average absolute harmonicity : 0.236192 Specific harmonicity : 0.209469 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 3.240000E+04, 14.98371 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 75.5, average 10.78571 Mersenne's string divisions : 141966825 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 11.95221, average 1.70746 Vogel's harmonic complexity : 14.42857 Wille's k value : 112 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 75.85579, average 2.70914 Lattice compactness (without 2's) : 50.66680, average 1.80953 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.42857 17 1 3: -2 .. 2 -0.14286 7 2 5: -2 .. 0 -0.71429 5 4 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 38.6829 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 36.8165 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 2 1 1 2 1 2 P M ME S SD: 27.6074 c. M:-44.3587 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 14.9633 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: 8.6816 c. M:-14.5845 c. Nineteen-tone Locrian 31: 3 5 5 3 5 5 5 SP M DE S SD: 6.8868 c. M: 11.9277 c. Intense Diatonic Mixolydian, M.Locrian 34: 3 6 5 4 5 5 6 SP SD: 4.3938 c. M: 7.8547 c. 46: 4 8 7 5 7 7 8 SP SD: 4.5007 c. M: 7.3835 c. 53: 5 9 8 6 8 8 9 SP SD: 1.3712 c. M:-2.6797 c. 99: 9 17 15 11 15 15 17 SP SD: 1.5307 c. M: 2.6404 c. 118: 11 20 18 13 18 18 20 SP SD: 0.4002 c. M: 0.7741 c. 171: 16 29 26 19 26 26 29 SP SD: 0.3239 c. M:-0.5494 c. 289: 27 49 44 32 44 44 49 SP SD: 0.2523 c. M:-0.4498 c. 323: 30 55 49 36 49 49 55 SP SD: 0.2436 c. M: 0.4244 c. 388: 36 66 59 43 59 59 66 SP SD: 0.2530 c. M: 0.3911 c. 441: 41 75 67 49 67 67 75 SP SD: 0.1009 c. M: 0.1716 c. 559: 52 95 85 62 85 85 95 SP SD: 0.0845 c. M: 0.1556 c. 612: 57 104 93 68 93 93 104 SP SD: 0.0430 c. M:-0.0900 c. 730: 68 124 111 81 111 111 124 SP SD: 0.0424 c. M:-0.0744 c. 1171: 109 199 178 130 178 178 199 SP SD: 0.0203 c. M: 0.0319 c. 1783: 166 303 271 198 271 271 303 SP SD: 0.0094 c. M: 0.0160 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 25.8995 cents 5 x 6 x 7:8:9:10 S SD: 10.6603 cents 6 x 7:8:9:10:11:12 S SD: 20.5519 cents 7 x 8:9:10:11:12:14 S SD: 21.2304 cents 9:10:11:12:13:14:16:18 S SD: 13.1014 cents 10:11:12:13:14:16:18:20 S SD: 12.4542 cents 11:12:13:15:16:18:20:22 SD: 12.0000 cents 12:13:14:16:17:19:21:24 SD: 10.0720 cents 13:14:16:17:19:21:23:26 SD: 9.4009 cents 14:15:17:19:20:22:25:28 SD: 7.3415 cents 15:16:18:20:22:24:27:30 S SD: 5.4803 cents 25:27:30:33:36:40:44:50 SD: 4.6686 cents 27:29:32:36:39:43:48:54 SD: 3.7771 cents 30:32:36:40:43:48:53:60 SD: 1.9291 cents 45:48:54:60:65:72:80:90 SD: 0.7622 cents 75:80:90:100:108:120:133:150 SD: 0.6191 cents 105:112:126:140:151:168:187:210 SD: 0.5494 cents 120:128:144:160:173:192:213:240 SD: 0.4811 cents 150:160:180:200:216:240:267:300 SD: 0.3090 cents 180:192:216:240:259:288:320:360 SD: 0.1909 cents 225:240:270:300:324:360:400:450 SD: 0.0000 cents