Scala analysis: xen09-wilson-marwa-16a-09
Marwa permutation 9 from Figure 16a, Schlesinger 16/15 15/13 13/12
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: 4/3 498.044999 perfect fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 2 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 3 5/4 386.314 cents major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 45/26 949.696 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 24/13 1061.427 cents tridecimal neutral seventh 6: 2 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 498.0 745.8 884.4 996.1 1200.0 182.4 : 203.9 315.6 563.4 702.0 813.7 1017.6 1200.0 386.3 : 111.7 359.5 498.0 609.8 813.7 996.1 1200.0 498.0 : 247.7 386.3 498.0 702.0 884.4 1088.3 1200.0 745.8 : 138.6 250.3 454.2 636.6 840.5 952.3 1200.0 884.4 : 111.7 315.6 498.0 702.0 813.7 1061.4 1200.0 996.1 : 203.9 386.3 590.2 702.0 949.7 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 250.3039 .. 386.3137 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 949.6961 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 676/675, 2.5629 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 : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 173.07603 cents, oct.: 1211.53220 cents Scale is strictly proper Step pattern alph. order: ABCDECB Step pattern size order : CDAEBAD Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.537528 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 13 Scale harmonicity : 0.025071 Average absolute harmonicity : 0.237433 Specific harmonicity : 0.164042 Fundamental : 1/468, -8.8704 octaves, 0.5590 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 3.744000E+04, 15.19229 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 52.0, average 7.42857 Mersenne's string divisions : 2633400 Sum of van Prooijen's expressibility: 4.89749, average 0.69964 Sum of Tenney's harmonic distance : 10.38491, average 1.48356 Vogel's harmonic complexity : 20.57143 Wille's k value : 292 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 75.56679, average 2.69881 Lattice compactness (without 2's) : 40.43952, average 1.44427 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.14286 12 1 3: -2 .. 0 -0.85714 6 2 5: 0 .. 1 0.57143 4 3 13: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 16 25| Scale is JI-epimorphic with val: <7 11 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1168 c. M: 60.0718 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 35.5515 c. M: 62.4037 c. 11: 2 2 1 2 1 1 2 N D3 SD: 30.9154 c. M:-50.0499 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 20.2028 c. M: 45.7861 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 13: 2 2 1 3 2 1 2 P D3 SD: 22.5340 c. M:-38.7182 c. 15: 2 3 1 3 2 1 3 N T3 SD: 20.7063 c. M: 36.0900 c. 16: 2 3 2 3 2 1 3 P T3 SD: 19.3160 c. M: 32.4037 c. 18: 3 3 1 4 2 2 3 P SD: 16.7541 c. M: 31.3783 c. 19: 3 3 2 4 2 2 3 P T3 SD: 8.5473 c. M:-14.4363 c. 31: 5 5 3 6 4 3 5 SP SD: 7.5661 c. M:-11.1447 c. 34: 5 6 3 7 4 3 6 P SD: 4.4926 c. M: 7.8547 c. 53: 8 9 5 11 6 5 9 P SD: 1.0235 c. M: 1.4081 c. 164: 25 28 15 34 19 15 28 P SD: 0.8444 c. M:-1.4912 c. 171: 26 29 16 35 20 16 29 SP SD: 0.7614 c. M: 1.9264 c. 217: 33 37 20 45 25 20 37 P SD: 0.5335 c. M:-0.7831 c. 224: 34 38 21 46 26 21 38 SP SD: 0.5428 c. M: 1.1432 c. 270: 41 46 25 56 31 25 46 P SD: 0.4305 c. M:-0.8806 c. 277: 42 47 26 57 32 26 47 SP SD: 0.4910 c. M: 0.7541 c. 301: 46 51 28 62 35 28 51 SP SD: 0.5492 c. M:-0.9850 c. 323: 49 55 30 67 37 30 55 P SD: 0.4324 c. M:-0.9632 c. 335: 51 57 31 69 39 31 57 SP SD: 0.4063 c. M: 0.7114 c. 354: 54 60 33 73 41 33 60 SP SD: 0.3632 c. M:-0.6471 c. 388: 59 66 36 80 45 36 66 SP SD: 0.2252 c. M: 0.4252 c. 407: 62 69 38 84 47 38 69 SP SD: 0.2649 c. M:-0.4702 c. 441: 67 75 41 91 51 41 75 SP SD: 0.1164 c. M: 0.2078 c. 494: 75 84 46 102 57 46 84 SP SD: 0.1200 c. M: 0.2175 c. 848: 129 144 79 175 98 79 144 SP SD: 0.0850 c. M:-0.1435 c. 901: 137 153 84 186 104 84 153 SP SD: 0.0712 c. M:-0.1364 c. 1289: 196 219 120 266 149 120 219 SP SD: 0.0492 c. M: 0.0917 c. 1342: 204 228 125 277 155 125 228 SP SD: 0.0221 c. M:-0.0352 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 12.9047 cents 5 x 6:7:8 x 9:10 S SD: 26.2315 cents 6:7 x 8:9:10:11:12 S SD: 18.1765 cents 7:8:9 x 11:12 x 14 SD: 18.4206 cents 8:9:10:11:12:13:14:16 S SD: 12.6863 cents 9:10:11:12:14:15:16:18 S SD: 6.1935 cents 10:11 x 13:15:17:18:20 SD: 12.6742 cents 11:12:14:15:17:18:20:22 SD: 11.1395 cents 12:13:15:16:18:20:21:24 SD: 9.6739 cents 15:17:19:20:23:25:27:30 SD: 6.6961 cents 17:19:21:23:26:28:30:34 SD: 6.1428 cents 18:20:23:24:28:30:32:36 SD: 6.0841 cents 19:21:24:25:29:32:34:38 SD: 5.6851 cents 21:23:26:28:32:35:37:42 SD: 5.3653 cents 24:27:30:32:37:40:43:48 SD: 3.6618 cents 27:30:34:36:42:45:48:54 SD: 3.2863 cents 28:31:35:37:43:47:50:56 SD: 3.1954 cents 35:39:44:47:54:58:62:70 SD: 2.9786 cents 36:40:45:48:55:60:64:72 SD: 1.7235 cents 45:50:56:60:69:75:80:90 SD: 1.3768 cents 63:70:79:84:97:105:112:126 SD: 0.8081 cents 72:80:90:96:111:120:128:144 SD: 0.5147 cents 108:120:135:144:166:180:192:216 SD: 0.2291 cents 180:200:225:240:277:300:320:360 SD: 0.0687 cents 288:320:360:384:443:480:512:576 SD: 0.0429 cents 468:520:585:624:720:780:832:936 SD: 0.0000 cents