Scala analysis: xen09-wilson-marwa-16a-10
Marwa permutation 10 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: 32/27 294.134997 Pythagorean minor 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: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 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: 1 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: 1 135/104 451.651 cents 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: 1 208/135 748.349 cents 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 294.1 498.0 745.8 884.4 996.1 1200.0 182.4 : 111.7 315.6 563.4 702.0 813.7 1017.6 1200.0 294.1 : 203.9 451.7 590.2 702.0 905.9 1088.3 1200.0 498.0 : 247.7 386.3 498.0 702.0 884.4 996.1 1200.0 745.8 : 138.6 250.3 454.2 636.6 748.3 952.3 1200.0 884.4 : 111.7 315.6 498.0 609.8 813.7 1061.4 1200.0 996.1 : 203.9 386.3 498.0 702.0 949.7 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 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 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 : 171.75919 cents, oct.: 1202.31432 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : CADEBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.535644 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 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 : 676/675, 2.5629 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 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 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 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 27 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.231415 Specific harmonicity : 0.156577 Fundamental : 1/351, -8.4553 octaves, 0.7454 Hz. Guide tone : 160, 7.3219 octaves, 41860.090 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 77.0, average 11.00000 Mersenne's string divisions : 51790200 Sum of van Prooijen's expressibility: 5.62988, average 0.80427 Sum of Tenney's harmonic distance : 12.02039, average 1.71720 Vogel's harmonic complexity : 20.57143 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 79.60068, average 2.84288 Lattice compactness (without 2's) : 46.75615, average 1.66986 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 5 2.14286 15 1 3: -3 .. 0 -1.28571 9 3 5: 0 .. 1 0.42857 3 2 13: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 16 28| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.1476 c. M: 60.0718 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 30.6161 c. M:-53.9100 c. 11: 2 1 2 2 1 1 2 P D3 S SD: 27.4732 c. M:-47.4095 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 19.6547 c. M: 45.7861 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 13: 2 1 2 3 2 1 2 N G T3 I SD: 22.5480 c. M:-38.7182 c. 14: 2 1 3 3 1 2 2 N T3 S SD: 24.5121 c. M: 36.9921 c. 15: 2 1 3 3 2 1 3 N SD: 28.6470 c. M: 54.1350 c. 16: 2 2 3 3 2 1 3 P SD: 18.9668 c. M: 32.4037 c. 19: 3 2 3 4 2 2 3 P SD: 11.5019 c. M:-21.6545 c. 24: 4 2 4 5 3 2 4 P SD: 9.4532 c. M:-17.5963 c. 28: 4 3 5 5 4 2 5 P SD: 12.3477 c. M: 17.2146 c. 29: 4 3 5 6 3 3 5 P SD: 8.8982 c. M: 16.8865 c. 31: 5 3 5 6 4 3 5 SP SD: 9.5743 c. M:-15.5424 c. 34: 5 3 6 7 4 3 6 P SD: 6.2839 c. M: 11.7821 c. 45: 7 4 8 9 5 4 8 P SD: 5.3682 c. M: 9.4233 c. 48: 7 5 8 10 5 5 8 P SD: 5.5248 c. M: 9.3587 c. 53: 8 5 9 11 6 5 9 P SD: 0.8777 c. M:-1.3838 c. 164: 25 15 28 34 19 15 28 P SD: 0.8346 c. M: 1.4521 c. 171: 26 16 29 35 20 16 29 SP SD: 0.7837 c. M: 1.9264 c. 217: 33 20 37 45 25 20 37 P SD: 0.5948 c. M: 1.0474 c. 224: 34 21 38 46 26 21 38 SP SD: 0.5293 c. M: 1.1432 c. 270: 41 25 46 56 31 25 46 P SD: 0.5093 c. M:-0.8806 c. 277: 42 26 47 57 32 26 47 SP SD: 0.4345 c. M: 0.6597 c. 330: 50 31 56 68 38 31 56 SP SD: 0.4203 c. M: 0.7223 c. 335: 51 31 57 69 39 31 57 SP SD: 0.3806 c. M: 0.7114 c. 388: 59 36 66 80 45 36 66 SP SD: 0.2321 c. M: 0.4252 c. 441: 67 41 75 91 51 41 75 SP SD: 0.1486 c. M: 0.2574 c. 494: 75 46 84 102 57 46 84 SP SD: 0.1403 c. M: 0.2175 c. 848: 129 79 144 175 98 79 144 SP SD: 0.1149 c. M:-0.2046 c. 901: 137 84 153 186 104 84 153 SP SD: 0.1011 c. M:-0.2046 c. 1065: 162 99 181 220 123 99 181 SP SD: 0.0926 c. M:-0.1483 c. 1118: 170 104 190 231 129 104 190 SP SD: 0.0830 c. M:-0.1889 c. 1289: 196 120 219 266 149 120 219 SP SD: 0.0508 c. M: 0.0917 c. 1342: 204 125 228 277 155 125 228 SP SD: 0.0283 c. M:-0.0528 c. 1783: 271 166 303 368 206 166 303 SP SD: 0.0316 c. M: 0.0766 c. 1836: 279 171 312 379 212 171 312 SP SD: 0.0299 c. M: 0.0508 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: 26.4119 cents 5 x 6:7:8 x 9:10 S SD: 22.5124 cents 6 x 7:8:9:10:11:12 S SD: 12.3631 cents 7:8 x 9:11:12 x 14 SD: 20.0684 cents 8:9 x 11:12:13:14:16 SD: 14.8007 cents 9:10:11:12:14:15:16:18 S SD: 8.0862 cents 15:17:18:20:23:25:27:30 SD: 6.5990 cents 17:19:20:23:26:28:30:34 SD: 5.7008 cents 18:20:21:24:28:30:32:36 S SD: 4.7580 cents 26:29:31:35:40:43:46:52 SD: 3.7103 cents 27:30:32:36:42:45:48:54 S SD: 2.7328 cents 36:40:43:48:55:60:64:72 SD: 2.5836 cents 37:41:44:49:57:62:66:74 SD: 2.5574 cents 39:43:46:52:60:65:69:78 SD: 2.5473 cents 44:49:52:59:68:73:78:88 SD: 2.4076 cents 45:50:53:60:69:75:80:90 SD: 1.7568 cents 54:60:64:72:83:90:96:108 SD: 0.2291 cents 189:210:224:252:291:315:336:378 SD: 0.1962 cents 243:270:288:324:374:405:432:486 SD: 0.1018 cents 297:330:352:396:457:495:528:594 SD: 0.0416 cents 351:390:416:468:540:585:624:702 SD: 0.0000 cents