Scala analysis: xen09-wilson-marwa-03-05
Marwa permutation 5 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: 10/9 182.403712 minor 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major 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: 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 : 182.4 386.3 590.2 702.0 884.4 1088.3 1200.0 182.4 : 203.9 407.8 519.6 702.0 905.9 1017.6 1200.0 386.3 : 203.9 315.6 498.0 702.0 813.7 996.1 1200.0 590.2 : 111.7 294.1 498.0 609.8 792.2 996.1 1200.0 702.0 : 182.4 386.3 498.0 680.4 884.4 1088.3 1200.0 884.4 : 203.9 315.6 498.0 702.0 905.9 1017.6 1200.0 1088.3: 111.7 294.1 498.0 702.0 813.7 996.1 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 .. 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 : 177.74949 cents, oct.: 1244.24641 cents Scale is strictly proper Step pattern alph. order: ABBCABC Step pattern size order : MLLSMLS 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 major thirds form a closed circle Best minor thirds form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 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: 3 -- 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 : 0.246176 Specific harmonicity : 0.233292 Fundamental : 1/288, -8.1699 octaves, 0.9084 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 72.0, average 10.28571 Mersenne's string divisions : 12113640 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 10.74809, average 1.53544 Vogel's harmonic complexity : 13.71429 Wille's k value : 202 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: -5 .. 1 -1.28571 13 1 3: -2 .. 2 0.14286 7 1 5: 0 .. 1 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 2 1 1 1 1 1 P M ME S SD: 36.2905 c. M:-63.6863 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 30.3950 c. M:-57.5963 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 11.8238 c. M:-17.5963 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 19: 3 3 3 2 3 3 2 SP M ME S SD: 10.9833 c. M: 21.8027 c. Nineteen-tone Lydian 22: 3 4 4 2 3 4 2 P SD: 9.7188 c. M: 18.7673 c. 29: 4 5 5 3 4 5 3 SP SD: 11.8958 c. M: 16.8865 c. 31: 5 5 5 3 5 5 3 SP M DE S SD: 6.5281 c. M:-11.1447 c. Intense Diatonic Hypolydian, M.Lydian 34: 5 6 6 3 5 6 3 P SD: 5.1841 c. M:-9.7763 c. 41: 6 7 7 4 6 7 4 SP SD: 4.9610 c. M: 6.7940 c. 53: 8 9 9 5 8 9 5 SP SD: 1.1931 c. M: 1.5445 c. 118: 18 20 20 11 18 20 11 SP SD: 0.3432 c. M:-0.6471 c. 171: 26 29 29 16 26 29 16 SP SD: 0.3875 c. M: 0.7500 c. 289: 44 49 49 27 44 49 27 SP SD: 0.3107 c. M: 0.6043 c. 323: 49 55 55 30 49 55 30 SP SD: 0.2714 c. M:-0.4884 c. 376: 57 64 64 35 57 64 35 SP SD: 0.2481 c. M: 0.4888 c. 388: 59 66 66 36 59 66 36 SP SD: 0.2750 c. M:-0.4979 c. 441: 67 75 75 41 67 75 41 SP SD: 0.1274 c. M:-0.2525 c. 494: 75 84 84 46 75 84 46 SP SD: 0.1095 c. M: 0.2175 c. 559: 85 95 95 52 85 95 52 SP SD: 0.0782 c. M:-0.1162 c. 612: 93 104 104 57 93 104 57 SP SD: 0.0339 c. M: 0.0508 c. 1171: 178 199 199 109 178 199 109 SP SD: 0.0224 c. M:-0.0410 c. 1783: 271 303 303 166 271 303 166 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: 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: 21.8233 cents 7:8:9:10:11:12:13:14 H SD: 17.2849 cents 8:9:10:11:12:13:15:16 SD: 8.9184 cents 12:13:15:17:18:20:23:24 SD: 8.4904 cents 15:17:19:21:23:25:28:30 SD: 8.1665 cents 16:18:20:23:24:27:30:32 SD: 6.9589 cents 17:19:21:24:26:28:32:34 SD: 6.6464 cents 18:20:23:25:27:30:34:36 SD: 6.5053 cents 20:22:25:28:30:33:38:40 SD: 4.9296 cents 24:27:30:34:36:40:45:48 SD: 3.5736 cents 32:36:40:45:48:53:60:64 SD: 3.4414 cents 36:40:45:51:54:60:68:72 SD: 2.5813 cents 44:49:55:62:66:73:83:88 SD: 2.0167 cents 52:58:65:73:78:87:98:104 SD: 1.8927 cents 56:62:70:79:84:93:105:112 SD: 1.4766 cents 64:71:80:90:96:107:120:128 SD: 0.8632 cents 72:80:90:101:108:120:135:144 SD: 0.6114 cents 128:142:160:180:192:213:240:256 SD: 0.5469 cents 136:151:170:191:204:227:255:272 SD: 0.5195 cents 152:169:190:214:228:253:285:304 SD: 0.4648 cents 160:178:200:225:240:267:300:320 SD: 0.4369 cents 180:200:225:253:270:300:338:360 SD: 0.3860 cents 216:240:270:304:324:360:405:432 SD: 0.2035 cents 288:320:360:405:432:480:540:576 S SD: 0.0000 cents