Scala analysis: xen09-wilson-marwa-16b-04
Marwa permutation 4 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: 18/13 563.382340 tridecimal augmented 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: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole 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: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 1 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 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: 1 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 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: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 117/64 1044.438 cents 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 155.6 359.5 563.4 745.8 857.5 1061.4 1200.0 155.6 : 203.9 407.8 590.2 702.0 905.9 1044.4 1200.0 359.5 : 203.9 386.3 498.0 702.0 840.5 996.1 1200.0 563.4 : 182.4 294.1 498.0 636.6 792.2 996.1 1200.0 745.8 : 111.7 315.6 454.2 609.8 813.7 1017.6 1200.0 857.5 : 203.9 342.5 498.0 702.0 905.9 1088.3 1200.0 1061.4: 138.6 294.1 498.0 702.0 884.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 416/405, 46.3939 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 416/405, 46.3939 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 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 : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 175.74249 cents, oct.: 1230.19745 cents Scale is strictly proper Step pattern alph. order: ABBCDBE Step pattern size order : CEEDAEB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.558029 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.430211 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 2 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 class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 136.0098 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 117 Scale harmonicity : 0.021635 Average absolute harmonicity : 0.171922 Specific harmonicity : 0.129037 Fundamental : 1/117, -6.8704 octaves, 2.2361 Hz. Guide tone : 5760, 12.4919 octaves, 1506963.256 Hz. Exponens Consonantiae : 6.739200E+05, 19.36222 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 240.5, average 34.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.11502, average 1.15929 Sum of Tenney's harmonic distance : 17.47008, average 2.49573 Vogel's harmonic complexity : 12.00000 Wille's k value : 58 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 100.32750, average 3.58313 Lattice compactness (without 2's) : 47.73012, average 1.70465 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.42857 24 1 3: -2 .. 2 0.00000 6 5: 0 .. 1 0.14286 1 13: -1 .. 0 -0.85714 6 6 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 16 26| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.0077 c. M: 60.0718 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 31.3092 c. M: 59.4723 c. 9: 1 2 1 2 0 2 1 N D3 SD: 36.4778 c. M: 57.5173 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 23.6720 c. M:-36.6177 c. 13: 2 2 2 2 1 2 2 SP M ME S SD: 23.6622 c. M: 46.0427 c. Glacial-7, Lobonian 14: 2 2 3 2 1 2 2 P T3 SD: 22.6963 c. M:-36.6177 c. 15: 2 2 3 2 2 2 2 SP M ME S SD: 21.4433 c. M: 39.4723 c. 16: 2 3 3 2 1 3 2 P SD: 20.0664 c. M:-36.6177 c. 17: 2 3 3 3 1 3 2 N SD: 13.6751 c. M:-30.6845 c. 18: 2 3 3 3 2 3 2 P D3 SD: 18.3091 c. M: 30.0490 c. 19: 3 3 3 3 2 3 2 SP D3 S SD: 19.1387 c. M:-33.9113 c. 20: 3 3 3 3 2 4 2 SP D3 S SD: 18.7500 c. M: 25.7861 c. 21: 3 3 4 3 2 4 2 SP T3 SD: 13.0445 c. M:-24.2869 c. 23: 3 4 4 3 2 4 3 SP SD: 13.1991 c. M: 22.7347 c. 24: 3 4 4 4 2 4 3 P SD: 8.4904 c. M: 13.3823 c. 32: 4 6 5 5 3 5 4 P SD: 7.9821 c. M:-15.5277 c. 34: 4 6 6 5 3 6 4 P SD: 7.4524 c. M: 14.3859 c. 36: 5 6 6 5 4 6 4 SP S SD: 8.0364 c. M: 12.4527 c. 38: 5 6 7 6 3 7 4 P SD: 8.4351 c. M:-12.2569 c. 39: 5 7 6 6 4 6 5 SP SD: 8.3854 c. M: 15.2735 c. 40: 5 7 7 6 4 6 5 P SD: 7.3598 c. M:-12.4827 c. 41: 5 7 7 6 4 7 5 SP SD: 8.7920 c. M: 14.0787 c. 42: 5 8 7 6 4 7 5 P SD: 7.5232 c. M: 12.7052 c. 43: 6 7 7 7 4 7 5 SP SD: 6.5205 c. M:-11.8795 c. 45: 6 7 8 7 4 8 5 SP SD: 5.8658 c. M: 12.8057 c. 46: 6 8 8 7 4 8 5 P SD: 6.9441 c. M:-10.7357 c. 47: 6 8 8 7 5 8 5 SP SD: 6.2342 c. M:-10.9131 c. 51: 7 8 9 8 4 9 6 SP SD: 6.4958 c. M: 10.4585 c. 53: 7 9 9 8 5 9 6 SP SD: 2.4182 c. M:-2.9282 c. 77: 10 13 13 12 7 13 9 SP SD: 1.4518 c. M: 2.3434 c. 130: 17 22 22 20 12 22 15 SP SD: 0.9828 c. M:-1.9063 c. 164: 21 28 28 25 15 28 19 SP SD: 1.0021 c. M: 1.9038 c. 183: 24 31 31 28 17 31 21 SP SD: 1.2580 c. M:-1.8147 c. 190: 25 32 32 29 18 32 22 SP SD: 1.1837 c. M:-2.3324 c. 200: 26 34 34 30 19 34 23 SP SD: 0.8109 c. M: 1.7861 c. 206: 27 35 35 31 19 35 24 SP SD: 1.2872 c. M:-1.7192 c. 207: 27 35 35 32 19 35 24 SP SD: 0.9807 c. M:-2.0400 c. 217: 28 37 37 33 20 37 25 SP SD: 0.5066 c. M:-0.7577 c. 277: 36 47 47 42 26 47 32 SP SD: 0.3173 c. M: 0.6597 c. 417: 54 71 71 63 39 71 48 SP SD: 0.3615 c. M:-0.6464 c. 441: 57 75 75 67 41 75 51 SP SD: 0.2761 c. M: 0.4603 c. 494: 64 84 84 75 46 84 57 SP SD: 0.0911 c. M:-0.1804 c. 848: 110 144 144 129 79 144 98 SP SD: 0.0885 c. M: 0.1748 c. 1065: 138 181 181 162 99 181 123 SP SD: 0.0609 c. M:-0.1294 c. 1342: 174 228 228 204 125 228 155 SP SD: 0.0257 c. M: 0.0440 c. 1836: 238 312 312 279 171 312 212 SP SD: 0.0153 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: 23.5453 cents 4 x 5 x 6 x 7:8 S SD: 26.4772 cents 5 x 6:7 x 8:9:10 S SD: 15.6581 cents 6 x 7:8:9:10:11:12 S SD: 20.8374 cents 7:8:9:10:11 x 13:14 SD: 20.9593 cents 8:9:10:11:12:13:15:16 SD: 11.1883 cents 11:12:14:15:17:18:20:22 SD: 9.9750 cents 13:14:16:18:20:21:24:26 S SD: 5.5082 cents 20:22:25:28:31:33:37:40 SD: 5.4305 cents 21:23:26:29:32:34:39:42 SD: 4.6406 cents 26:28:32:36:40:43:48:52 SD: 4.3445 cents 30:33:37:42:46:49:55:60 SD: 3.8151 cents 31:34:38:43:48:51:57:62 SD: 2.3447 cents 39:43:48:54:60:64:72:78 SD: 1.9247 cents 44:48:54:61:68:72:81:88 SD: 1.8264 cents 52:57:64:72:80:85:96:104 SD: 1.0816 cents 65:71:80:90:100:107:120:130 SD: 0.8632 cents 86:94:106:119:132:141:159:172 SD: 0.8463 cents 104:114:128:144:160:171:192:208 SD: 0.6825 cents 117:128:144:162:180:192:216:234 SD: 0.0000 cents