Scala analysis: xen09-wilson-marwa-06-02
Marwa permutation 2 from Figure 6, Didymus/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: 16/15 111.731285 minor diatonic semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 64/45 609.776284 2nd tritone 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: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major 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: 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 : 111.7 315.6 498.0 609.8 813.7 1017.6 1200.0 111.7 : 203.9 386.3 498.0 702.0 905.9 1088.3 1200.0 315.6 : 182.4 294.1 498.0 702.0 884.4 996.1 1200.0 498.0 : 111.7 315.6 519.6 702.0 813.7 1017.6 1200.0 609.8 : 203.9 407.8 590.2 702.0 905.9 1088.3 1200.0 813.7 : 203.9 386.3 498.0 702.0 884.4 996.1 1200.0 1017.6: 182.4 294.1 498.0 680.4 792.2 996.1 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 : 166.07331 cents, oct.: 1162.51316 cents Scale is strictly proper Step pattern alph. order: ABCABBC Step pattern size order : SLMSLLM 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 Lydian octave species of abstract tetrachord Scale is Phrygian 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 92.1787 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 45 Scale harmonicity : 0.043353 Average absolute harmonicity : 0.234022 Specific harmonicity : 0.233292 Fundamental : 1/45, -5.4919 octaves, 5.8139 Hz. Guide tone : 576, 9.1699 octaves, 150696.326 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 94.0, average 13.42857 Mersenne's string divisions : 20294274 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 11.95221, average 1.70746 Vogel's harmonic complexity : 9.42857 Wille's k value : 40 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 87.88124, average 3.13862 Lattice compactness (without 2's) : 47.82790, average 1.70814 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 6 2.42857 17 1 3: -2 .. 2 -0.14286 7 1 5: -1 .. 0 -0.71429 5 5 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 41.9927 c. M:-75.9380 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 36.2905 c. M: 63.6863 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 37.6870 c. M:-56.8904 c. 10: 1 2 1 1 2 1 2 P M ME S SD: 30.3950 c. M: 57.5963 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 11.8238 c. M: 17.5963 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: 10.9833 c. M:-21.8027 c. Nineteen-tone Locrian 22: 2 4 3 2 4 4 3 P SD: 9.7188 c. M:-18.7673 c. 28: 3 4 5 2 5 5 4 P SD: 12.0023 c. M:-16.8401 c. 29: 3 5 4 3 5 5 4 SP SD: 11.8958 c. M:-16.8865 c. 31: 3 5 5 3 5 5 5 SP M DE S SD: 6.5281 c. M: 11.1447 c. Intense Diatonic Mixolydian, M.Locrian 34: 3 6 5 3 6 6 5 P SD: 5.1841 c. M: 9.7763 c. 41: 4 7 6 4 7 7 6 SP SD: 4.9610 c. M:-6.7940 c. 53: 5 9 8 5 9 9 8 SP SD: 1.1931 c. M:-1.5445 c. Makam Arak 118: 11 20 18 11 20 20 18 SP SD: 0.3432 c. M: 0.6471 c. 171: 16 29 26 16 29 29 26 SP SD: 0.3875 c. M:-0.7500 c. 289: 27 49 44 27 49 49 44 SP SD: 0.3107 c. M:-0.6043 c. 323: 30 55 49 30 55 55 49 SP SD: 0.2714 c. M: 0.4884 c. 376: 35 64 57 35 64 64 57 SP SD: 0.2481 c. M:-0.4888 c. 388: 36 66 59 36 66 66 59 SP SD: 0.2750 c. M: 0.4979 c. 441: 41 75 67 41 75 75 67 SP SD: 0.1274 c. M: 0.2525 c. 494: 46 84 75 46 84 84 75 SP SD: 0.1095 c. M:-0.2175 c. 559: 52 95 85 52 95 95 85 SP SD: 0.0782 c. M: 0.1162 c. 612: 57 104 93 57 104 104 93 SP SD: 0.0339 c. M:-0.0508 c. 1171: 109 199 178 109 199 199 178 SP SD: 0.0224 c. M: 0.0410 c. 1783: 166 303 271 166 303 303 271 SP SD: 0.0101 c. M: 0.0175 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: 46.0894 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 31.4941 cents 5 x 6 x 7:8:9:10 S SD: 5.4528 cents 6 x 7:8:9:10:11:12 S SD: 21.6533 cents 7 x 8:9:10:11:13:14 SD: 20.4523 cents 8:9:10:11 x 13:14:16 SD: 23.2310 cents 9:10:11:12:13:14:16:18 S SD: 13.9717 cents 10:11:12:13:14:16:18:20 S SD: 10.5970 cents 12:13:14:16:17:19:22:24 SD: 9.5647 cents 14:15:17:19:20:22:25:28 SD: 7.3415 cents 15:16:18:20:21:24:27:30 S SD: 3.8949 cents 29:31:35:39:41:46:52:58 SD: 3.8009 cents 30:32:36:40:43:48:54:60 SD: 1.9247 cents 45:48:54:60:64:72:81:90 S SD: 0.0000 cents