Scala analysis: xen09-wilson-marwa-16b-10
Marwa permutation 10 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: 32/27 294.134997 Pythagorean minor 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: 13/12 138.5727 tridecimal 2/3-tone 3: 9/8 203.9100 major whole 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: 1 32/27 294.135 cents Pythagorean 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: 1 135/104 451.651 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 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 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: 1 117/64 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 : 155.6 294.1 498.0 745.8 857.5 996.1 1200.0 155.6 : 138.6 342.5 590.2 702.0 840.5 1044.4 1200.0 294.1 : 203.9 451.7 563.4 702.0 905.9 1061.4 1200.0 498.0 : 247.7 359.5 498.0 702.0 857.5 996.1 1200.0 745.8 : 111.7 250.3 454.2 609.8 748.3 952.3 1200.0 857.5 : 138.6 342.5 498.0 636.6 840.5 1088.3 1200.0 996.1 : 203.9 359.5 498.0 702.0 949.7 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 .. 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 : 128/117, 155.5623 cents, amount: 1 Least squares average step : 170.60884 cents, oct.: 1194.26191 cents Scale is strictly proper Step pattern alph. order: ABCDEBC Step pattern size order : CBDEABD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.512925 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 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 -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 117 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.213217 Specific harmonicity : 0.114127 Fundamental : 1/351, -8.4553 octaves, 0.7454 Hz. Guide tone : 640, 9.3219 octaves, 167440.362 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 237.5, average 33.92857 Mersenne's string divisions : 245662725 Sum of van Prooijen's expressibility: 7.63592, average 1.09085 Sum of Tenney's harmonic distance : 16.46270, average 2.35181 Vogel's harmonic complexity : 17.14286 Wille's k value : 175 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 100.43900, average 3.58711 Lattice compactness (without 2's) : 46.75615, average 1.66986 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.85714 27 1 3: -3 .. 0 -1.28571 9 3 5: 0 .. 1 0.14286 1 13: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-11 / 7 =-1.57143 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 32.8485 c. M: 60.0718 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 31.8534 c. M:-53.9100 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 31.1567 c. M: 54.1350 c. 11: 1 2 2 2 1 1 2 N D3 SD: 29.9023 c. M:-47.4095 c. 13: 2 1 2 3 1 2 2 P D3 SD: 22.7233 c. M: 36.5065 c. 15: 2 2 2 3 2 1 3 P D3 SD: 22.3197 c. M: 36.0900 c. 16: 2 2 3 3 1 2 3 P SD: 18.1731 c. M: 32.5173 c. 17: 2 2 3 3 2 2 3 SP D3 S SD: 17.4216 c. M: 39.9037 c. 18: 2 2 3 4 2 2 3 P SD: 18.8502 c. M: 31.3783 c. 20: 3 2 3 4 2 3 3 SP D3 SD: 18.9008 c. M: 25.7861 c. 21: 3 2 4 4 2 2 4 P SD: 13.1111 c. M: 24.6614 c. 22: 3 2 4 5 2 2 4 N SD: 13.7740 c. M: 21.4077 c. 24: 3 3 4 5 2 3 4 P SD: 4.7617 c. M: 7.5173 c. 53: 7 6 9 11 5 6 9 P SD: 1.6359 c. M:-2.9282 c. 77: 10 9 13 16 7 9 13 P SD: 1.2753 c. M:-2.2659 c. 130: 17 15 22 27 12 15 22 P SD: 1.1216 c. M:-1.9063 c. 164: 21 19 28 34 15 19 28 P SD: 1.1482 c. M: 1.9038 c. 171: 22 20 29 35 16 20 29 SP SD: 1.0388 c. M: 1.9264 c. 183: 24 21 31 38 17 21 31 P SD: 1.1961 c. M:-1.8147 c. 193: 25 22 33 40 18 22 33 P SD: 0.9292 c. M: 1.9070 c. 200: 26 23 34 41 19 23 34 SP SD: 0.7214 c. M: 1.7861 c. 217: 28 25 37 45 20 25 37 P SD: 0.6486 c. M: 1.0474 c. 224: 29 26 38 46 21 26 38 SP SD: 0.5197 c. M: 1.1432 c. 270: 35 31 46 56 25 31 46 P SD: 0.5131 c. M:-0.8806 c. 277: 36 32 47 57 26 32 47 SP SD: 0.3713 c. M: 0.6597 c. 354: 46 41 60 73 33 41 60 SP SD: 0.3958 c. M:-0.7803 c. 417: 54 48 71 86 39 48 71 SP SD: 0.3425 c. M: 0.6098 c. 441: 57 51 75 91 41 51 75 SP SD: 0.2668 c. M: 0.4603 c. 494: 64 57 84 102 46 57 84 SP SD: 0.1060 c. M: 0.2079 c. 795: 103 92 135 164 74 92 135 SP SD: 0.1278 c. M:-0.2046 c. 848: 110 98 144 175 79 98 144 SP SD: 0.1046 c. M:-0.2046 c. 1041: 135 120 177 215 97 120 177 SP SD: 0.1022 c. M: 0.1869 c. 1065: 138 123 181 220 99 123 181 SP SD: 0.0636 c. M:-0.1294 c. 1289: 167 149 219 266 120 149 219 SP SD: 0.0678 c. M: 0.1085 c. 1342: 174 155 228 277 125 155 228 SP SD: 0.0298 c. M:-0.0528 c. 1836: 238 212 312 379 171 212 312 SP SD: 0.0156 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: 26.4119 cents 5 x 6:7 x 8:9:10 S SD: 19.9809 cents 6 x 7:8:9:10:11:12 S SD: 13.1476 cents 7 x 8:9:11 x 12:14 SD: 23.0127 cents 8:9 x 11:12:13:14:16 SD: 15.0265 cents 9:10:11:12:14:15:16:18 S SD: 9.7362 cents 11:12:13:15:17:18:20:22 SD: 8.0328 cents 17:19:20:23:26:28:30:34 SD: 7.1122 cents 20:22:24:27:31:33:36:40 SD: 5.9474 cents 21:23:25:28:32:34:37:42 SD: 4.7887 cents 22:24:26:29:34:36:39:44 SD: 3.3508 cents 31:34:37:41:48:51:55:62 SD: 3.2540 cents 33:36:39:44:51:54:59:66 SD: 2.1695 cents 45:49:53:60:69:74:80:90 SD: 2.1683 cents 50:55:59:67:77:82:89:100 SD: 2.1673 cents 53:58:63:71:82:87:94:106 SD: 2.0457 cents 54:59:64:72:83:89:96:108 SD: 1.1418 cents 75:82:89:100:115:123:133:150 SD: 1.0993 cents 86:94:102:115:132:141:153:172 SD: 1.0063 cents 87:95:103:116:134:143:155:174 SD: 0.9016 cents 108:118:128:144:166:177:192:216 SD: 0.5101 cents 162:177:192:216:249:266:288:324 SD: 0.4205 cents 189:207:224:252:291:310:336:378 SD: 0.3601 cents 234:256:277:312:360:384:416:468 SD: 0.2974 cents 243:266:288:324:374:399:432:486 SD: 0.2265 cents 297:325:352:396:457:487:528:594 SD: 0.2080 cents 351:384:416:468:540:576:624:702 SD: 0.0000 cents