Scala analysis: xen09-wilson-marwa-04-04
Marwa permutation 4 from Figure 4, Didymus 16/15 10/9 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute fourth 4: 3/2 701.955001 perfect 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: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 16/15 111.7313 minor diatonic semitone 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: 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: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 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: 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: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 315.6 519.6 702.0 813.7 1017.6 1200.0 203.9 : 111.7 315.6 498.0 609.8 813.7 996.1 1200.0 315.6 : 203.9 386.3 498.0 702.0 884.4 1088.3 1200.0 519.6 : 182.4 294.1 498.0 680.4 884.4 996.1 1200.0 702.0 : 111.7 315.6 498.0 702.0 813.7 1017.6 1200.0 813.7 : 203.9 386.3 590.2 702.0 905.9 1088.3 1200.0 1017.6: 182.4 386.3 498.0 702.0 884.4 996.1 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 .. 590.2237 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 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: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 169.82625 cents, oct.: 1188.78378 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAC Step pattern size order : LSLMSLM Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.374079 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.539106 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Hypodorian octave species of abstract tetrachord 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Limited inverse transpositions with margin 92.1787 cents: 6 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 27 Scale harmonicity : 0.049020 Average absolute harmonicity : 0.249235 Specific harmonicity : 0.242363 Fundamental : 1/40, -5.3219 octaves, 6.5406 Hz. Guide tone : 216, 7.7549 octaves, 56511.122 Hz. Exponens Consonantiae : 8.640000E+03, 13.07682 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 55.0, average 7.85714 Mersenne's string divisions : 23993970 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 10.40130, average 1.48590 Vogel's harmonic complexity : 8.85714 Wille's k value : 22 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 81.42351, average 2.90798 Lattice compactness (without 2's) : 44.75411, average 1.59836 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.14286 11 1 3: 0 .. 3 1.28571 9 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 5 / 7 = 0.71429 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: 24.1902 c. M:-43.4566 c. Lebeng 12: 2 1 2 2 1 2 2 P M ME S SD: 12.7781 c. M: 19.5513 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 19: 3 2 3 3 2 3 3 SP M ME S SD: 9.0153 c. M: 14.4363 c. Nineteen-tone Natural Minor, Aeolian 31: 5 3 5 5 3 5 5 SP M DE S SD: 8.9531 c. M: 16.3255 c. Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian 34: 6 3 6 5 3 6 5 P T3 SD: 5.5712 c. M:-9.8605 c. 41: 7 4 7 6 4 7 6 SP T3 SD: 4.9865 c. M:-7.2780 c. 46: 8 4 8 7 4 8 7 P T3 SD: 3.0499 c. M: 4.9906 c. 53: 9 5 9 8 5 9 8 SP T3 SD: 0.9904 c. M:-1.4081 c. 118: 20 11 20 18 11 20 18 SP T3 SD: 0.4994 c. M: 0.9072 c. 171: 29 16 29 26 16 29 26 SP T3 SD: 0.2425 c. M: 0.4012 c. 388: 66 36 66 59 36 66 59 SP T3 SD: 0.1584 c. M: 0.2842 c. 441: 75 41 75 67 41 75 67 SP T3 SD: 0.1088 c. M:-0.1766 c. 559: 95 52 95 85 52 95 85 SP T3 SD: 0.0561 c. M: 0.0906 c. 612: 104 57 104 93 57 104 93 SP T3 SD: 0.0368 c. M:-0.0566 c. 1171: 199 109 199 178 109 199 178 SP T3 SD: 0.0129 c. M: 0.0228 c. 1783: 303 166 303 271 166 303 271 SP T3 SD: 0.0124 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 24.6241 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 12.5922 cents 6 x 7:8:9:10:11:12 S SD: 15.6745 cents 7:8 x 9 x 11:13:14 SD: 21.7058 cents 8:9:10:11:12:13:14:16 S SD: 13.6297 cents 9:10:11:12 x 14:16:18 S SD: 11.5172 cents 10:11:12:14:15:16:18:20 S SD: 10.5731 cents 12 x 14:16:18:19:22:24 SD: 10.7740 cents 14:16:17:19:21:22:25:28 SD: 7.0130 cents 15:17:18:20:23:24:27:30 SD: 6.5053 cents 20:23:24:27:30:32:36:40 SD: 5.4358 cents 24:27:29:32:36:38:43:48 SD: 4.5158 cents 25:28:30:34:38:40:45:50 SD: 3.9085 cents 26:29:31:35:39:42:47:52 SD: 3.7746 cents 30:34:36:41:45:48:54:60 SD: 3.5413 cents 32:36:38:43:48:51:58:64 SD: 3.4482 cents 34:38:41:46:51:54:61:68 SD: 2.8930 cents 40:45:48:54:60:64:72:80 S SD: 0.0000 cents