Scala analysis: xen09-wilson-marwa-16b-09
Marwa permutation 9 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole 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: 13/12 138.5727 tridecimal 2/3-tone 7: 9/8 203.9100 major whole 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 52/45 250.304 cents 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 3 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: 3 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 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: 1 117/64 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 155.6 359.5 498.0 745.8 857.5 996.1 1200.0 155.6 : 203.9 342.5 590.2 702.0 840.5 1044.4 1200.0 359.5 : 138.6 386.3 498.0 636.6 840.5 996.1 1200.0 498.0 : 247.7 359.5 498.0 702.0 857.5 1061.4 1200.0 745.8 : 111.7 250.3 454.2 609.8 813.7 952.3 1200.0 857.5 : 138.6 342.5 498.0 702.0 840.5 1088.3 1200.0 996.1 : 203.9 359.5 563.4 702.0 949.7 1061.4 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 : 128/117, 155.5623 cents, amount: 1 Least squares average step : 171.54223 cents, oct.: 1200.79564 cents Scale is strictly proper Step pattern alph. order: ABCDECB Step pattern size order : CDBEABD Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.498679 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 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 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 n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 117 Scale harmonicity : 0.024458 Average absolute harmonicity : 0.207690 Specific harmonicity : 0.115122 Fundamental : 1/117, -6.8704 octaves, 2.2361 Hz. Guide tone : 640, 9.3219 octaves, 167440.362 Hz. Exponens Consonantiae : 7.488000E+04, 16.19229 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 222.5, average 31.78571 Mersenne's string divisions : 120749475 Sum of van Prooijen's expressibility: 7.31850, average 1.04550 Sum of Tenney's harmonic distance : 15.84425, average 2.26346 Vogel's harmonic complexity : 13.42857 Wille's k value : 58 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 95.26580, average 3.40235 Lattice compactness (without 2's) : 40.43952, average 1.44427 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.71429 26 1 3: -2 .. 0 -0.85714 6 2 5: 0 .. 1 0.14286 1 13: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 17 26| Scale is JI-epimorphic with val: <7 11 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.9166 c. M: 60.0718 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 38.9231 c. M: 59.4723 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 23.4973 c. M: 36.0900 c. 13: 2 2 1 3 1 2 2 P D3 I SD: 22.0824 c. M: 36.5065 c. Diatronic 14: 2 2 2 3 1 2 2 P T3 SD: 18.9144 c. M:-32.4814 c. 17: 2 3 2 3 2 2 3 SP M ME S SD: 17.0227 c. M: 39.9037 c. 18: 2 3 2 4 2 2 3 P T3 SD: 18.5782 c. M: 31.3783 c. 21: 3 3 3 4 2 2 4 P T3 S SD: 14.1848 c. M: 24.6614 c. 22: 3 4 2 5 2 2 4 N SD: 13.9852 c. M:-22.3458 c. 23: 3 4 2 5 2 3 4 P SD: 15.2149 c. M: 28.4798 c. 24: 3 4 3 5 2 3 4 P SD: 5.5297 c. M: 9.4723 c. 46: 6 8 5 10 4 5 8 N SD: 5.1968 c. M:-10.7357 c. 53: 7 9 6 11 5 6 9 P SD: 1.9452 c. M:-2.9282 c. 77: 10 13 9 16 7 9 13 P SD: 1.1065 c. M:-2.2659 c. 130: 17 22 15 27 12 15 22 P SD: 1.0367 c. M:-1.9063 c. 140: 18 24 16 29 13 16 24 P SD: 0.9353 c. M: 1.8043 c. 193: 25 33 22 40 18 22 33 P SD: 0.7298 c. M: 1.2713 c. 217: 28 37 25 45 20 25 37 P SD: 0.5138 c. M:-0.7577 c. 224: 29 38 26 46 21 26 38 SP SD: 0.5248 c. M: 1.1432 c. 270: 35 46 31 56 25 31 46 P SD: 0.4596 c. M:-0.8806 c. 277: 36 47 32 57 26 32 47 SP SD: 0.3320 c. M: 0.6597 c. 354: 46 60 41 73 33 41 60 SP SD: 0.2700 c. M:-0.5202 c. 417: 54 71 48 86 39 48 71 SP SD: 0.2691 c. M: 0.4623 c. 441: 57 75 51 91 41 51 75 SP SD: 0.2714 c. M: 0.4603 c. 494: 64 84 57 102 46 57 84 SP SD: 0.0729 c. M: 0.1386 c. 848: 110 144 98 175 79 98 144 SP SD: 0.0719 c. M:-0.1364 c. 1065: 138 181 123 220 99 123 181 SP SD: 0.0621 c. M:-0.1294 c. 1289: 167 219 149 266 120 149 219 SP SD: 0.0805 c. M: 0.1240 c. 1342: 174 228 155 277 125 155 228 SP SD: 0.0224 c. M:-0.0352 c. 1836: 238 312 212 379 171 212 312 SP SD: 0.0143 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: 14.5451 cents 5 x 6:7 x 8:9:10 S SD: 21.3912 cents 6 x 7:8:9:10:11:12 S SD: 19.7587 cents 7:8 x 9:11 x 12:14 SD: 24.4889 cents 8:9:10:11:12:13:14:16 S SD: 13.4385 cents 9:10:11:12:14:15:16:18 S SD: 6.3123 cents 21:23:26:28:32:34:37:42 SD: 4.8859 cents 22:24:27:29:34:36:39:44 SD: 3.3508 cents 30:33:37:40:46:49:53:60 SD: 2.5536 cents 39:43:48:52:60:64:69:78 SD: 2.2638 cents 52:57:64:69:80:85:92:104 SD: 2.0028 cents 56:61:69:75:86:92:100:112 SD: 1.9809 cents 61:67:75:81:94:100:108:122 SD: 1.8211 cents 63:69:78:84:97:103:112:126 SD: 1.7660 cents 64:70:79:85:98:105:114:128 SD: 1.7467 cents 65:71:80:87:100:107:116:130 SD: 1.5962 cents 72:79:89:96:111:118:128:144 SD: 1.4281 cents 73:80:90:97:112:120:130:146 SD: 1.3771 cents 75:82:92:100:115:123:133:150 SD: 1.3397 cents 78:85:96:104:120:128:139:156 SD: 1.1356 cents 86:94:106:115:132:141:153:172 SD: 1.0533 cents 87:95:107:116:134:143:155:174 SD: 0.8794 cents 95:104:117:127:146:156:169:190 SD: 0.7721 cents 108:118:133:144:166:177:192:216 SD: 0.5298 cents 117:128:144:156:180:192:208:234 SD: 0.0000 cents