Scala analysis: xen09-wilson-marwa-16a-07
Marwa permutation 7 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: 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: 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: 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: 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 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 498.0 745.8 884.4 1088.3 1200.0 182.4 : 203.9 315.6 563.4 702.0 905.9 1017.6 1200.0 386.3 : 111.7 359.5 498.0 702.0 813.7 996.1 1200.0 498.0 : 247.7 386.3 590.2 702.0 884.4 1088.3 1200.0 745.8 : 138.6 342.5 454.2 636.6 840.5 952.3 1200.0 884.4 : 203.9 315.6 498.0 702.0 813.7 1061.4 1200.0 1088.3: 111.7 294.1 498.0 609.8 857.5 996.1 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: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 416/405, 46.3939 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 .. 905.8650 cents 135/128, 92.1787 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 416/405, 46.3939 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 : 177.02654 cents, oct.: 1239.18581 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : CDAEBDA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.575480 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393003 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 512/507, 16.9897 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle 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 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: 15 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.233966 Specific harmonicity : 0.165199 Fundamental : 1/936, -9.8704 octaves, 0.2795 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 51.0, average 7.28571 Mersenne's string divisions : 2422728 Sum of van Prooijen's expressibility: 5.11934, average 0.73133 Sum of Tenney's harmonic distance : 10.30573, average 1.47225 Vogel's harmonic complexity : 22.57143 Wille's k value : 877 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 76.53513, average 2.73340 Lattice compactness (without 2's) : 40.81846, average 1.45780 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.14286 11 1 3: -2 .. 1 -0.42857 5 1 5: 0 .. 1 0.71429 5 4 13: -1 .. 0 -0.14286 1 1 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 16 29| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 38.1459 c. M: 60.0718 c. Lebeng 9: 1 2 1 2 1 1 1 N D3 S SD: 37.1191 c. M:-54.2139 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 32.9789 c. M: 62.4037 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 30.4575 c. M:-50.0499 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 20.6308 c. M: 45.7861 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 13: 2 2 1 3 2 2 1 N T3 SD: 22.5498 c. M:-38.7182 c. 15: 2 3 1 3 2 3 1 N T3 SD: 19.6602 c. M:-31.7313 c. 18: 3 3 1 4 2 3 2 P SD: 18.5791 c. M: 31.3783 c. 19: 3 3 2 4 2 3 2 SP D3 SD: 8.5832 c. M: 14.5845 c. 31: 5 5 3 6 4 5 3 SP SD: 6.6837 c. M:-11.1447 c. 34: 5 6 3 7 4 6 3 P SD: 4.0320 c. M: 5.9331 c. 53: 8 9 5 11 6 9 5 SP SD: 1.1646 c. M: 1.4763 c. 140: 21 24 13 29 16 24 13 SP SD: 1.1528 c. M: 2.4037 c. 164: 25 28 15 34 19 28 15 SP SD: 1.0661 c. M:-1.9752 c. 171: 26 29 16 35 20 29 16 SP SD: 0.7746 c. M: 1.9264 c. 183: 28 31 17 38 21 31 17 SP SD: 0.9107 c. M:-1.7549 c. 217: 33 37 20 45 25 37 20 SP SD: 0.6309 c. M:-1.1322 c. 224: 34 38 21 46 26 38 21 SP SD: 0.6022 c. M: 1.1432 c. 270: 41 46 25 56 31 46 25 SP SD: 0.4466 c. M:-0.8806 c. 323: 49 55 30 67 37 55 30 SP SD: 0.4149 c. M:-0.9632 c. 335: 51 57 31 69 39 57 31 SP SD: 0.4712 c. M: 0.7114 c. 354: 54 60 33 73 41 60 33 SP SD: 0.3095 c. M:-0.6471 c. 388: 59 66 36 80 45 66 36 SP SD: 0.2570 c. M: 0.4252 c. 407: 62 69 38 84 47 69 38 SP SD: 0.2284 c. M:-0.3973 c. 441: 67 75 41 91 51 75 41 SP SD: 0.1153 c. M: 0.2078 c. 494: 75 84 46 102 57 84 46 SP SD: 0.1081 c. M: 0.2175 c. 848: 129 144 79 175 98 144 79 SP SD: 0.0714 c. M:-0.1435 c. 1289: 196 219 120 266 149 219 120 SP SD: 0.0482 c. M: 0.0917 c. 1342: 204 228 125 277 155 228 125 SP SD: 0.0238 c. M: 0.0422 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 6:7 x 8 S SD: 23.7906 cents 5 x 6:7:8 x 9:10 S SD: 29.4851 cents 6:7 x 8:9:10:11:12 S SD: 17.1347 cents 7:8:9 x 11:12:13:14 SD: 15.5969 cents 8:9:10:11:12:13:15:16 SD: 12.0736 cents 9:10:11:12:14:15:17:18 SD: 6.4568 cents 10:11 x 13:15:17:19:20 SD: 12.7434 cents 11:12:14:15:17:18:21:22 SD: 10.6327 cents 12:13:15:16:18:20:23:24 SD: 10.3905 cents 15:17:19:20:23:25:28:30 SD: 6.0508 cents 17:19:21:23:26:28:32:34 SD: 5.9447 cents 21:23:26:28:32:35:39:42 SD: 5.4284 cents 24:27:30:32:37:40:45:48 SD: 3.1151 cents 33:37:41:44:51:55:62:66 SD: 2.9626 cents 36:40:45:48:55:60:68:72 SD: 2.5104 cents 39:43:49:52:60:65:73:78 SD: 2.3295 cents 45:50:56:60:69:75:84:90 SD: 1.7633 cents 48:53:60:64:74:80:90:96 SD: 1.6338 cents 63:70:79:84:97:105:118:126 SD: 0.8494 cents 72:80:90:96:111:120:135:144 SD: 0.5147 cents 171:190:214:228:263:285:321:342 SD: 0.4152 cents 180:200:225:240:277:300:338:360 SD: 0.3725 cents 216:240:270:288:332:360:405:432 SD: 0.2291 cents 288:320:360:384:443:480:540:576 SD: 0.0429 cents