Scala analysis: xen09-wilson-marwa-03-04
Marwa permutation 4 from Figure 3, Ptolemy 16/15 9/8 10/9
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: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 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: 16/15 111.7313 minor diatonic semitone
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 : 203.9 386.3 590.2 702.0 884.4 1088.3 1200.0 203.9 : 182.4 386.3 498.0 680.4 884.4 996.1 1200.0 386.3 : 203.9 315.6 498.0 702.0 813.7 1017.6 1200.0 590.2 : 111.7 294.1 498.0 609.8 813.7 996.1 1200.0 702.0 : 182.4 386.3 498.0 702.0 884.4 1088.3 1200.0 884.4 : 203.9 315.6 519.6 702.0 905.9 1017.6 1200.0 1088.3: 111.7 315.6 498.0 702.0 813.7 996.1 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 .. 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 : 177.90310 cents, oct.: 1245.32172 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAC Step pattern size order : LMLSMLS 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 0.0 315.641 701.955 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 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is 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: 3 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.049020 Average absolute harmonicity : 0.252100 Specific harmonicity : 0.243593 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 8.640000E+03, 13.07682 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 71.0, average 10.14286 Mersenne's string divisions : 10838520 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 10.65118, average 1.52160 Vogel's harmonic complexity : 11.14286 Wille's k value : 67 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 82.99559, average 2.96413 Lattice compactness (without 2's) : 43.00604, average 1.53593 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.85714 15 1 3: -1 .. 2 0.71429 7 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 43.5535 c. M: 75.9380 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 39.7767 c. M:-63.6863 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 25.2195 c. M: 44.3587 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 9.8870 c. M:-15.6413 c. G.Hypolydian, M.Lydian, G.M.Hypolocrian, Rut biscale ascending, Kalyan That (Yaman), Mela Mecakalyani, Raga Chandrakant, Malarani, Shuddh Kalyan, Ping, Kung, Gu: China 22: 4 3 4 2 3 4 2 P T3 SD: 8.5578 c. M:-14.2718 c. 29: 5 4 5 3 4 5 3 SP T3 SD: 10.1019 c. M: 15.3932 c. 30: 5 5 5 3 4 5 3 P SD: 10.0795 c. M:-18.0450 c. 31: 5 5 5 3 5 5 3 SP M DE S SD: 6.3412 c. M: 10.3616 c. Intense Diatonic Hypolydian, M.Lydian 34: 6 5 6 3 5 6 3 P T3 SD: 5.5372 c. M:-9.7763 c. 41: 7 6 7 4 6 7 4 SP T3 SD: 4.2605 c. M: 6.3099 c. 53: 9 8 9 5 8 9 5 SP T3 SD: 1.0932 c. M: 1.5445 c. 65: 11 10 11 6 10 11 6 SP T3 SD: 1.0151 c. M:-1.7951 c. 118: 20 18 20 11 18 20 11 SP T3 SD: 0.3109 c. M: 0.5202 c. 289: 49 44 49 27 44 49 27 SP T3 SD: 0.3361 c. M: 0.6043 c. 323: 55 49 55 30 49 55 30 SP T3 SD: 0.2843 c. M:-0.4884 c. 376: 64 57 64 35 57 64 35 SP T3 SD: 0.2108 c. M:-0.3453 c. 441: 75 67 75 41 67 75 41 SP T3 SD: 0.1388 c. M:-0.2525 c. 494: 84 75 84 46 75 84 46 SP T3 SD: 0.0893 c. M: 0.1482 c. 559: 95 85 95 52 85 95 52 SP T3 SD: 0.0749 c. M:-0.1162 c. 612: 104 93 104 57 93 104 57 SP T3 SD: 0.0283 c. M: 0.0450 c. 1171: 199 178 199 109 178 199 109 SP T3 SD: 0.0234 c. M:-0.0410 c. 1783: 303 271 303 166 271 303 166 SP T3 SD: 0.0104 c. M:-0.0175 c. 2395: 407 364 407 223 364 407 223 SP T3 SD: 0.0097 c. M: 0.0163 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: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 24.5302 cents 6:7 x 8:9:10:11:12 S SD: 19.7024 cents 7:8:9:10:11:12:13:14 H SD: 16.2910 cents 8:9:10:11:12:13:15:16 SD: 8.3725 cents 15:17:19:21:23:25:28:30 SD: 6.7851 cents 16:18:20:23:24:27:30:32 SD: 6.2440 cents 22:25:28:31:33:37:41:44 SD: 5.7928 cents 23:26:29:32:35:38:43:46 SD: 5.5528 cents 24:27:30:34:36:40:45:48 SD: 1.8252 cents 32:36:40:45:48:53:60:64 SD: 1.5506 cents 56:63:70:79:84:93:105:112 SD: 1.1821 cents 64:72:80:90:96:107:120:128 SD: 0.7717 cents 72:81:90:101:108:120:135:144 SD: 0.6114 cents 96:108:120:135:144:160:180:192 S SD: 0.0000 cents