Scala analysis: xen09-wilson-marwa-16b-06
Marwa permutation 6 from Figure 16b, Schlesinger 13/12 15/13 16/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/13 247.741053 tridecimal 5/4-tone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 64/39 857.517337 39th subharmonic 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 15/13 247.7411 tridecimal 5/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 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: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 45/26 949.696 cents 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 247.7 359.5 498.0 745.8 857.5 1061.4 1200.0 247.7 : 111.7 250.3 498.0 609.8 813.7 952.3 1200.0 359.5 : 138.6 386.3 498.0 702.0 840.5 1088.3 1200.0 498.0 : 247.7 359.5 563.4 702.0 949.7 1061.4 1200.0 745.8 : 111.7 315.6 454.2 702.0 813.7 952.3 1200.0 857.5 : 203.9 342.5 590.2 702.0 840.5 1088.3 1200.0 1061.4: 138.6 386.3 498.0 636.6 884.4 996.1 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: 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 175.00083 cents, oct.: 1225.00578 cents Scale is strictly proper Step pattern alph. order: ABCABDC Step pattern size order : DABDACB Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.523872 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 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 Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions with margin 136.0098 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 39 Scale harmonicity : 0.025071 Average absolute harmonicity : 0.197953 Specific harmonicity : 0.118275 Fundamental : 1/39, -5.2854 octaves, 6.7083 Hz. Guide tone : 960, 9.9069 octaves, 251160.543 Hz. Exponens Consonantiae : 3.744000E+04, 15.19229 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 120.0, average 17.14286 Mersenne's string divisions : 102119556 Sum of van Prooijen's expressibility: 6.58611, average 0.94087 Sum of Tenney's harmonic distance : 14.29468, average 2.04210 Vogel's harmonic complexity : 10.71429 Wille's k value : 22 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 82.40305, average 2.94297 Lattice compactness (without 2's) : 38.25991, average 1.36643 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 6 2.57143 18 1 3: -1 .. 1 0.00000 4 1 5: 0 .. 1 0.28571 2 13: -1 .. 0 -0.71429 5 5 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 11 15 27| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.7343 c. M: 76.3125 c. Lebeng 8: 2 0 1 2 1 1 1 N D3 SD: 38.7840 c. M: 59.4723 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 41.3359 c. M:-75.8160 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 15.5955 c. M: 25.7861 c. Sethares Neutral, Beatles-7, Dichotic-7 19: 4 2 2 4 2 3 2 P T3 S SD: 14.4651 c. M:-26.6932 c. 21: 4 2 3 4 2 4 2 SP T3 SD: 14.6671 c. M:-24.2869 c. 23: 5 2 3 4 2 4 3 N SD: 16.2194 c. M:-23.6941 c. 24: 5 2 3 5 2 4 3 P SD: 6.5846 c. M: 11.4273 c. 34: 7 3 4 7 3 6 4 P SD: 5.2909 c. M: 10.4585 c. 43: 9 4 5 9 4 7 5 P SD: 4.7665 c. M:-7.7023 c. 53: 11 5 6 11 5 9 6 P SD: 1.9655 c. M:-2.8600 c. 77: 16 7 9 16 7 13 9 P SD: 1.3204 c. M:-2.2659 c. 87: 18 8 10 18 8 15 10 P SD: 1.1994 c. M: 2.3449 c. 130: 27 12 15 27 12 22 15 P SD: 1.0148 c. M:-1.9063 c. 140: 29 13 16 29 13 24 16 P SD: 0.7532 c. M:-1.4298 c. 164: 34 15 19 34 15 28 19 P SD: 0.8210 c. M: 1.4198 c. 217: 45 20 25 45 20 37 25 P SD: 0.5564 c. M:-1.1069 c. 267: 55 25 31 55 25 45 31 SP SD: 0.5945 c. M:-0.9096 c. 270: 56 25 31 56 25 46 31 P SD: 0.6700 c. M:-1.1478 c. 277: 57 26 32 57 26 47 32 SP SD: 0.4114 c. M: 0.8096 c. 330: 68 31 38 68 31 56 38 SP SD: 0.4176 c. M:-0.6645 c. 354: 73 33 41 73 33 60 41 SP SD: 0.2241 c. M: 0.4104 c. 407: 84 38 47 84 38 69 47 SP SD: 0.2267 c. M:-0.4679 c. 441: 91 41 51 91 41 75 51 SP SD: 0.2172 c. M: 0.3745 c. 494: 102 46 57 102 46 84 57 SP SD: 0.0561 c. M:-0.1111 c. 848: 175 79 98 175 79 144 98 SP SD: 0.0647 c. M: 0.1066 c. 1342: 277 125 155 277 125 228 155 SP SD: 0.0264 c. M: 0.0510 c. 1836: 379 171 212 379 171 312 212 SP SD: 0.0176 c. M: 0.0344 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: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 26.4772 cents 5 x 6:7 x 8:9:10 S SD: 22.7140 cents 6:7 x 8:9:10:11:12 S SD: 9.3588 cents 7:8 x 9:11 x 13:14 SD: 15.0883 cents 8:9:10:11:12:13:15:16 SD: 13.1008 cents 9:10:11:12:14:15:17:18 SD: 12.0123 cents 10 x 12:13:15:16:18:20 SD: 16.3349 cents 11:13:14:15:17:18:20:22 SD: 12.2774 cents 12:14:15:16:18:20:22:24 S SD: 8.8912 cents 13:15:16:17:20:21:24:26 SD: 6.1833 cents 18:21:22:24:28:30:33:36 S SD: 5.9650 cents 19:22:23:25:29:31:35:38 SD: 5.8720 cents 20:23:25:27:31:33:37:40 SD: 5.5067 cents 21:24:26:28:32:34:39:42 SD: 5.1606 cents 25:29:31:33:38:41:46:50 SD: 4.5765 cents 26:30:32:35:40:43:48:52 SD: 3.0505 cents 33:38:41:44:51:54:61:66 SD: 2.7449 cents 39:45:48:52:60:64:72:78 SD: 0.0000 cents