Scala analysis: xen09-wilson-marwa-13-07
Marwa permutation 7 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: 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: 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: 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 : 111.7 315.6 498.0 631.3 813.7 1017.6 1200.0 111.7 : 203.9 386.3 519.6 702.0 905.9 1088.3 1200.0 315.6 : 182.4 315.6 498.0 702.0 884.4 996.1 1200.0 498.0 : 133.2 315.6 519.6 702.0 813.7 1017.6 1200.0 631.3 : 182.4 386.3 568.7 680.4 884.4 1066.8 1200.0 813.7 : 203.9 386.3 498.0 702.0 884.4 1017.6 1200.0 1017.6: 182.4 294.1 498.0 680.4 813.7 996.1 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 : 166.68777 cents, oct.: 1166.81442 cents Scale is strictly proper Step pattern alph. order: ABCDCBC Step pattern size order : ADCBCDC 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 1 Length of longest subharmonic part : 2 at degree 4 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 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: 25 Scale harmonicity : 0.040323 Average absolute harmonicity : 0.233061 Specific harmonicity : 0.219328 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 1.080000E+04, 13.39874 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 70.0, average 10.00000 Mersenne's string divisions : 11357346 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 11.44706, average 1.63529 Vogel's harmonic complexity : 11.85714 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 73.10350, average 2.61084 Lattice compactness (without 2's) : 49.01651, average 1.75059 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.85714 13 1 3: -1 .. 2 0.42857 7 1 5: -2 .. 0 -0.85714 6 5 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 36.9168 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 33.7166 c. M:-49.0704 c. 10: 1 2 1 1 2 1 2 P M ME S SD: 32.4038 c. M: 57.5963 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 16.3079 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: 7.2621 c. M:-14.5845 c. Nineteen-tone Locrian 31: 3 5 5 3 5 5 5 SP M DE S SD: 7.0593 c. M: 11.9277 c. Intense Diatonic Mixolydian, M.Locrian 34: 3 6 5 4 5 6 5 SP SD: 3.9396 c. M:-5.9331 c. 46: 4 8 7 5 7 8 7 SP SD: 4.1219 c. M: 7.3835 c. 53: 5 9 8 6 8 9 8 SP SD: 1.4521 c. M:-2.6797 c. 99: 9 17 15 11 15 17 15 SP SD: 1.3158 c. M: 2.6404 c. 118: 11 20 18 13 18 20 18 SP SD: 0.4258 c. M: 0.7741 c. 171: 16 29 26 19 26 29 26 SP SD: 0.2869 c. M:-0.5494 c. 289: 27 49 44 32 44 49 44 SP SD: 0.2172 c. M:-0.3794 c. 323: 30 55 49 36 49 55 49 SP SD: 0.2284 c. M:-0.3604 c. 388: 36 66 59 43 59 66 59 SP SD: 0.2413 c. M: 0.3911 c. 441: 41 75 67 49 67 75 67 SP SD: 0.0846 c. M: 0.1667 c. 559: 52 95 85 62 85 95 85 SP SD: 0.0874 c. M: 0.1556 c. 612: 57 104 93 68 93 104 93 SP SD: 0.0469 c. M:-0.0900 c. 730: 68 124 111 81 111 124 111 SP SD: 0.0395 c. M: 0.0620 c. 1171: 109 199 178 130 178 199 178 SP SD: 0.0191 c. M: 0.0319 c. 1783: 166 303 271 198 271 303 271 SP SD: 0.0091 c. M:-0.0145 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: 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: 19.2764 cents 7 x 8:9:10:11:13:14 SD: 20.5410 cents 9:10:11:12:13:14:16:18 S SD: 13.4568 cents 10:11:12:13:14:16:18:20 S SD: 12.0693 cents 11:12:13:15:16:18:20:22 SD: 10.9219 cents 12:13:14:16:17:19:22:24 SD: 10.3378 cents 13:14:16:17:19:21:23:26 SD: 10.2538 cents 14:15:17:19:20:22:25:28 SD: 7.5212 cents 15:16:18:20:22:24:27:30 S SD: 4.5381 cents 25:27:30:33:36:40:45:50 SD: 3.9519 cents 29:31:35:39:42:46:52:58 SD: 3.7808 cents 30:32:36:40:43:48:54:60 SD: 1.1477 cents 45:48:54:60:65:72:81:90 SD: 0.7622 cents 75:80:90:100:108:120:135:150 SD: 0.0000 cents