Scala analysis: xen09-wilson-marwa-16b-07
Marwa permutation 7 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: 128/117 155.562336 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: 128/117 155.5623 2: 9/8 203.9100 major whole tone 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: 1 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 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: 1 6/5 315.641 cents minor third 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 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: 1 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 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 : 155.6 359.5 498.0 745.8 857.5 1061.4 1200.0 155.6 : 203.9 342.5 590.2 702.0 905.9 1044.4 1200.0 359.5 : 138.6 386.3 498.0 702.0 840.5 996.1 1200.0 498.0 : 247.7 359.5 563.4 702.0 857.5 1061.4 1200.0 745.8 : 111.7 315.6 454.2 609.8 813.7 952.3 1200.0 857.5 : 203.9 342.5 498.0 702.0 840.5 1088.3 1200.0 1061.4: 138.6 294.1 498.0 636.6 884.4 996.1 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: 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 : 128/117, 155.5623 cents, amount: 1 Least squares average step : 174.34241 cents, oct.: 1220.39685 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : CDBEADB Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.571781 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 minor thirds form a closed circle 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 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 : 117 (O: 117 U: 117) Highest odd numerator or denominator: 117 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.197519 Specific harmonicity : 0.119527 Fundamental : 1/117, -6.8704 octaves, 2.2361 Hz. Guide tone : 1920, 10.9069 octaves, 502321.085 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 228.5, average 32.64286 Mersenne's string divisions : 893546115 Sum of van Prooijen's expressibility: 7.47820, average 1.06831 Sum of Tenney's harmonic distance : 16.18004, average 2.31143 Vogel's harmonic complexity : 12.71429 Wille's k value : 58 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 93.90935, average 3.35391 Lattice compactness (without 2's) : 40.81846, average 1.45780 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.57143 25 1 3: -2 .. 1 -0.42857 5 1 5: 0 .. 1 0.14286 1 13: -1 .. 0 -0.71429 5 5 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.9792 c. M: 60.0718 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 33.4436 c. M: 59.4723 c. 9: 1 2 1 2 0 2 1 N D3 SD: 37.1421 c. M: 57.5173 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 20.3796 c. M: 35.5623 c. 14: 2 2 2 3 1 2 2 P T3 SD: 19.0066 c. M: 32.8559 c. 16: 2 3 2 3 1 3 2 P D3 SD: 17.7456 c. M: 32.5173 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 16.7907 c. M: 39.9037 c. Neutral Dorian, Maqamic-7 18: 2 3 2 4 2 3 2 P T3 I SD: 18.6249 c. M: 31.3783 c. 19: 3 3 2 4 2 3 2 SP D3 SD: 19.2381 c. M:-33.9113 c. 21: 3 3 3 4 2 4 2 SP T3 SD: 14.0922 c. M:-24.2869 c. 24: 3 4 3 5 2 4 3 P SD: 6.8592 c. M: 11.4273 c. 34: 4 6 4 7 3 6 4 P SD: 7.5823 c. M: 14.3859 c. 43: 6 7 5 9 4 7 5 SP SD: 6.4193 c. M:-11.8795 c. 46: 6 8 5 10 4 8 5 P SD: 5.7616 c. M:-10.7357 c. 52: 7 9 6 10 5 9 6 SP SD: 6.4493 c. M:-9.7584 c. 53: 7 9 6 11 5 9 6 SP SD: 2.2002 c. M:-2.9282 c. 77: 10 13 9 16 7 13 9 SP SD: 1.1768 c. M:-2.2659 c. 130: 17 22 15 27 12 22 15 SP SD: 0.9886 c. M:-1.9063 c. 140: 18 24 16 29 13 24 16 SP SD: 0.8377 c. M:-1.4298 c. 200: 26 34 23 41 19 34 23 SP SD: 0.7767 c. M: 1.7861 c. 217: 28 37 25 45 20 37 25 SP SD: 0.4575 c. M:-0.7577 c. 270: 35 46 31 56 25 46 31 SP SD: 0.5106 c. M:-0.8806 c. 277: 36 47 32 57 26 47 32 SP SD: 0.3128 c. M: 0.6597 c. 354: 46 60 41 73 33 60 41 SP SD: 0.2414 c. M: 0.4104 c. 441: 57 75 51 91 41 75 51 SP SD: 0.2744 c. M: 0.4603 c. 494: 64 84 57 102 46 84 57 SP SD: 0.0659 c. M:-0.1111 c. 848: 110 144 98 175 79 144 98 SP SD: 0.0643 c. M: 0.1066 c. 1065: 138 181 123 220 99 181 123 SP SD: 0.0612 c. M:-0.1294 c. 1342: 174 228 155 277 125 228 155 SP SD: 0.0206 c. M: 0.0334 c. 1836: 238 312 212 379 171 312 212 SP SD: 0.0141 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 x 7:8:9:10:11:12 S SD: 17.7656 cents 7:8 x 9:11 x 13:14 SD: 21.1037 cents 8:9:10:11:12:13:15:16 SD: 13.4211 cents 9:10:11:12:14:15:17:18 SD: 8.4781 cents 13:14:16:17:20:21:24:26 SD: 7.3078 cents 18:20:22:24:28:30:33:36 S SD: 6.5434 cents 19:21:23:25:29:31:35:38 SD: 6.3346 cents 20:22:25:27:31:33:37:40 SD: 5.6090 cents 21:23:26:28:32:34:39:42 SD: 4.5942 cents 22:24:27:29:34:36:41:44 SD: 4.0207 cents 30:33:37:40:46:49:55:60 SD: 2.6621 cents 39:43:48:52:60:64:72:78 SD: 1.9247 cents 52:57:64:69:80:85:96:104 SD: 1.6095 cents 65:71:80:87:100:107:120:130 SD: 1.2831 cents 78:85:96:104:120:128:144:156 SD: 0.9680 cents 87:95:107:116:134:143:161:174 SD: 0.9164 cents 104:114:128:139:160:171:192:208 SD: 0.9046 cents 108:118:133:144:166:177:199:216 SD: 0.7132 cents 117:128:144:156:180:192:216:234 SD: 0.0000 cents