Scala analysis: xen09-wilson-marwa-03-02
Marwa permutation 2 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: 81/64 407.820003 Pythagorean major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major 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: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor 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: 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 : 203.9 407.8 590.2 702.0 905.9 1088.3 1200.0 203.9 : 203.9 386.3 498.0 702.0 884.4 996.1 1200.0 407.8 : 182.4 294.1 498.0 680.4 792.2 996.1 1200.0 590.2 : 111.7 315.6 498.0 609.8 813.7 1017.6 1200.0 702.0 : 203.9 386.3 498.0 702.0 905.9 1088.3 1200.0 905.9 : 182.4 294.1 498.0 702.0 884.4 996.1 1200.0 1088.3: 111.7 315.6 519.6 702.0 813.7 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: 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 : 178.97842 cents, oct.: 1252.84892 cents Scale is strictly proper Step pattern alph. order: AABCABC Step pattern size order : LLMSLMS Scale is sum-free (all different intervals) 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 Hypophrygian octave species of abstract tetrachord 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 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 113.6850 cents: 3 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.041551 Average absolute harmonicity : 0.239813 Specific harmonicity : 0.224456 Fundamental : 1/64, -6.0000 octaves, 4.0879 Hz. Guide tone : 810, 9.6618 octaves, 211916.708 Hz. Exponens Consonantiae : 5.184000E+04, 15.66178 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 156.5, average 22.35714 Mersenne's string divisions : 563151435 Sum of van Prooijen's expressibility: 7.60052, average 1.08579 Sum of Tenney's harmonic distance : 14.52421, average 2.07489 Vogel's harmonic complexity : 10.00000 Wille's k value : 40 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 100.55529, average 3.59126 Lattice compactness (without 2's) : 52.17762, average 1.86349 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -3.00000 23 1 3: 0 .. 4 1.85714 13 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 15 / 7 = 2.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 49.6317 c. M: 75.9380 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 35.0270 c. M: 53.9100 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 31.6440 c. M:-54.1350 c. 11: 2 2 1 1 2 2 1 P D3 S SD: 30.1791 c. M: 47.4095 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 7.0494 c. M:-11.7313 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 29: 5 5 4 3 5 4 3 SP SD: 6.9685 c. M: 12.4066 c. 41: 7 7 6 4 7 6 4 SP SD: 2.9072 c. M: 5.3419 c. 53: 9 9 8 5 9 8 5 SP SD: 0.8198 c. M: 1.5445 c. 118: 20 20 18 11 20 18 11 SP SD: 0.5608 c. M: 1.0403 c. 171: 29 29 26 16 29 26 16 SP SD: 0.5440 c. M: 0.8025 c. 289: 49 49 44 27 49 44 27 SP SD: 0.5381 c. M: 0.8996 c. 323: 55 55 49 30 55 49 30 SP SD: 0.4878 c. M:-0.8487 c. 376: 64 64 57 35 64 57 35 SP SD: 0.3657 c. M:-0.6906 c. 388: 66 66 59 36 66 59 36 SP SD: 0.3259 c. M:-0.4979 c. 429: 73 73 65 40 73 65 40 SP SD: 0.3018 c. M:-0.5716 c. 441: 75 75 67 41 75 67 41 SP SD: 0.2113 c. M:-0.3433 c. 494: 84 84 75 46 84 75 46 SP SD: 0.1453 c. M:-0.2772 c. 547: 93 93 83 51 93 83 51 SP SD: 0.1342 c. M:-0.2239 c. 559: 95 95 85 52 95 85 52 SP SD: 0.0645 c. M:-0.1162 c. 612: 104 104 93 57 104 93 57 SP SD: 0.0203 c. M: 0.0334 c. 1783: 303 303 271 166 303 271 166 SP SD: 0.0182 c. M:-0.0319 c. 2395: 407 407 364 223 407 364 223 SP SD: 0.0155 c. M:-0.0297 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 4 x x 5 x 6 S SD: 30.9176 cents 4 x 5 x 6:7 x 8 S SD: 16.6332 cents 5 x 6:7 x 8:9:10 S SD: 29.6971 cents 6:7:8 x 9:10:11:12 S SD: 19.7771 cents 7:8:9:10:11:12:13:14 H SD: 14.0944 cents 8:9:10:11:12:14:15:16 S SD: 11.0104 cents 10:11:13:14:15:17:19:20 SD: 9.4918 cents 14:16:18:20:21:24:26:28 S SD: 8.1413 cents 15:17:19:21:23:25:28:30 SD: 6.6923 cents 16:18:20:23:24:27:30:32 SD: 6.2440 cents 18:20:23:25:27:30:34:36 SD: 6.1021 cents 22:25:28:31:33:37:41:44 SD: 3.3614 cents 30:34:38:42:45:51:56:60 SD: 3.0219 cents 34:38:43:48:51:57:64:68 SD: 2.6770 cents 42:47:53:59:63:71:79:84 SD: 1.7676 cents 54:61:68:76:81:91:101:108 SD: 1.7656 cents 56:63:71:79:84:95:105:112 SD: 1.5836 cents 64:72:81:90:96:108:120:128 S SD: 0.0000 cents