Scala analysis: xen09-wilson-marwa-04-05
Marwa permutation 5 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: 16/15 111.731285 minor diatonic semitone 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: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 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: 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: 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: 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 : 111.7 315.6 519.6 702.0 813.7 1017.6 1200.0 111.7 : 203.9 407.8 590.2 702.0 905.9 1088.3 1200.0 315.6 : 203.9 386.3 498.0 702.0 884.4 996.1 1200.0 519.6 : 182.4 294.1 498.0 680.4 792.2 996.1 1200.0 702.0 : 111.7 315.6 498.0 609.8 813.7 1017.6 1200.0 813.7 : 203.9 386.3 498.0 702.0 905.9 1088.3 1200.0 1017.6: 182.4 294.1 498.0 702.0 884.4 996.1 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 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 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 : 169.16783 cents, oct.: 1184.17484 cents Scale is strictly proper Step pattern alph. order: ABBCABC Step pattern size order : SLLMSLM Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.415885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503263 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord Scale is Hypophrygian 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 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 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: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.043353 Average absolute harmonicity : 0.243025 Specific harmonicity : 0.233576 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 62.0, average 8.85714 Mersenne's string divisions : 43753710 Sum of van Prooijen's expressibility: 5.43676, average 0.77668 Sum of Tenney's harmonic distance : 10.92418, average 1.56060 Vogel's harmonic complexity : 9.85714 Wille's k value : 40 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 85.83702, average 3.06561 Lattice compactness (without 2's) : 48.75411, average 1.74122 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.85714 12 1 3: -1 .. 3 0.85714 8 1 5: -1 .. 0 -0.71429 5 5 Average exponent except 2's : 1 / 7 = 0.14286 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: 30.7173 c. M:-59.6973 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 31.3861 c. M:-49.0704 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 31.2729 c. M: 50.0499 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 13.4446 c. M: 19.5513 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 19: 2 3 3 3 2 3 3 SP M ME S SD: 9.0493 c. M:-14.5845 c. Nineteen-tone Phrygian 31: 3 5 5 5 3 5 5 SP M DE S SD: 8.2209 c. M: 16.3255 c. Intense Diatonic Dorian, M.Phrygian 33: 3 6 5 5 3 6 5 SP SD: 8.9551 c. M: 13.6863 c. 34: 3 6 6 5 3 6 5 P SD: 5.2069 c. M:-9.8605 c. 41: 4 7 7 6 4 7 6 SP SD: 5.3673 c. M:-7.2780 c. 46: 4 8 8 7 4 8 7 P SD: 3.7172 c. M: 7.3835 c. 53: 5 9 9 8 5 9 8 SP SD: 1.1356 c. M:-1.4763 c. 118: 11 20 20 18 11 20 18 SP SD: 0.4618 c. M: 0.9072 c. 171: 16 29 29 26 16 29 26 SP SD: 0.2809 c. M:-0.5494 c. 289: 27 49 49 44 27 49 44 SP SD: 0.2881 c. M: 0.5201 c. 323: 30 55 55 49 30 55 49 SP SD: 0.2940 c. M:-0.5726 c. 376: 35 64 64 57 35 64 57 SP SD: 0.3439 c. M:-0.6615 c. 388: 36 66 66 59 36 66 59 SP SD: 0.2010 c. M: 0.3911 c. 441: 41 75 75 67 41 75 67 SP SD: 0.1077 c. M:-0.1766 c. 559: 52 95 95 85 52 95 85 SP SD: 0.0677 c. M: 0.1034 c. 612: 57 104 104 93 57 104 93 SP SD: 0.0387 c. M:-0.0566 c. 1171: 109 199 199 178 109 199 178 SP SD: 0.0162 c. M: 0.0319 c. 1783: 166 303 303 271 166 303 271 SP SD: 0.0114 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 x 8:9 x 11:13:14 SD: 26.9592 cents 8:9:10:11:12:13:14:16 S SD: 18.9519 cents 9:10:11:12 x 14:16:18 S SD: 16.0791 cents 10:11:12:14:15:16:18:20 S SD: 11.7821 cents 12:13:14:16:18:19:22:24 SD: 9.9993 cents 14:15:17:19:21:22:25:28 SD: 5.9352 cents 20:21:24:27:30:32:36:40 S SD: 3.8949 cents 30:32:36:41:45:48:54:60 SD: 3.0346 cents 34:36:41:46:51:54:61:68 SD: 3.0118 cents 40:43:48:54:60:64:72:80 SD: 1.9247 cents 46:49:55:62:69:74:83:92 SD: 1.7974 cents 60:64:72:81:90:96:108:120 S SD: 0.0000 cents