Scala analysis: xen09-wilson-marwa-16a-02
Marwa permutation 2 from Figure 16a, Schlesinger 16/15 15/13 13/12
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: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 45/26 949.696054 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/13 247.7411 tridecimal 5/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 9/8 203.9100 major whole tone 4: 128/117 155.5623 5: 9/8 203.9100 major whole tone 6: 13/12 138.5727 tridecimal 2/3-tone 7: 16/15 111.7313 minor diatonic semitone
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 : 247.7 386.3 590.2 745.8 949.7 1088.3 1200.0 247.7 : 138.6 342.5 498.0 702.0 840.5 952.3 1200.0 386.3 : 203.9 359.5 563.4 702.0 813.7 1061.4 1200.0 590.2 : 155.6 359.5 498.0 609.8 857.5 996.1 1200.0 745.8 : 203.9 342.5 454.2 702.0 840.5 1044.4 1200.0 949.7 : 138.6 250.3 498.0 636.6 840.5 996.1 1200.0 1088.3: 111.7 359.5 498.0 702.0 857.5 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 : 181.80197 cents, oct.: 1272.61382 cents Scale is strictly proper Step pattern alph. order: ABCDCBE Step pattern size order : EBDCDBA Scale is sum-free (all different intervals) 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 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined 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: 45 Scale harmonicity : 0.024458 Average absolute harmonicity : 0.193586 Specific harmonicity : 0.114331 Fundamental : 1/416, -8.7004 octaves, 0.6289 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 7.488000E+04, 16.19229 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 122.0, average 17.42857 Mersenne's string divisions : 4526676 Sum of van Prooijen's expressibility: 7.47152, average 1.06736 Sum of Tenney's harmonic distance : 14.61280, average 2.08754 Vogel's harmonic complexity : 18.14286 Wille's k value : 292 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 90.56898, average 3.23461 Lattice compactness (without 2's) : 41.62106, average 1.48647 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.14286 14 1 3: 0 .. 2 0.85714 6 5: 0 .. 1 0.85714 6 3 13: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 64.6055 c. M: 92.5532 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 39.3418 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 32.6355 c. M: 56.8904 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 15.5259 c. M: 26.3137 c. 18: 4 2 3 2 3 2 2 P T3 SD: 14.7867 c. M: 21.6020 c. 19: 4 2 3 3 3 2 2 P T3 SD: 11.4535 c. M: 21.8027 c. 23: 5 2 4 3 4 3 2 P SD: 13.5502 c. M: 21.0963 c. 24: 5 3 4 3 4 3 2 P SD: 7.9594 c. M:-13.6863 c. 34: 7 4 6 4 6 4 3 P SD: 4.8657 c. M:-9.7763 c. 43: 9 5 7 6 7 5 4 P SD: 3.9361 c. M:-7.7023 c. 53: 11 6 9 7 9 6 5 P SD: 1.2955 c. M: 1.5445 c. 130: 27 15 22 17 22 15 12 P SD: 1.2029 c. M:-1.9063 c. 140: 29 16 24 18 24 16 13 P SD: 0.8943 c. M:-1.7325 c. 193: 40 22 33 25 33 22 18 P SD: 0.8023 c. M:-1.5993 c. 217: 45 25 37 28 37 25 20 P SD: 1.0696 c. M:-1.4814 c. 224: 46 26 38 29 38 26 21 SP SD: 1.0039 c. M: 1.4818 c. 236: 49 27 40 31 40 27 22 P SD: 0.9487 c. M:-1.6716 c. 246: 51 28 42 32 42 28 23 P SD: 0.8301 c. M:-1.5235 c. 248: 51 29 42 32 42 29 23 SP SD: 0.7422 c. M: 1.3090 c. 270: 56 31 46 35 46 31 25 P SD: 0.8777 c. M:-1.4151 c. 277: 57 32 47 36 47 32 26 SP SD: 0.8026 c. M: 1.0540 c. 291: 60 34 49 38 49 34 27 SP SD: 0.7726 c. M:-1.3152 c. 301: 62 35 51 39 51 35 28 SP SD: 0.4367 c. M: 0.8588 c. 335: 69 39 57 43 57 39 31 SP SD: 0.5958 c. M:-0.8211 c. 354: 73 41 60 46 60 41 33 SP SD: 0.2840 c. M: 0.5435 c. 388: 80 45 66 50 66 45 36 SP SD: 0.3399 c. M:-0.4979 c. 407: 84 47 69 53 69 47 38 SP SD: 0.2733 c. M: 0.5431 c. 441: 91 51 75 57 75 51 41 SP SD: 0.1500 c. M:-0.2525 c. 494: 102 57 84 64 84 57 46 SP SD: 0.0568 c. M:-0.1015 c. 1342: 277 155 228 174 228 155 125 SP SD: 0.0453 c. M: 0.0686 c. 1836: 379 212 312 238 312 212 171 SP SD: 0.0291 c. M: 0.0392 c. 2330: 481 269 396 302 396 269 217 SP SD: 0.0257 c. M: 0.0476 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: 37.6621 cents 4 x 5 x 6:7 x 8 S SD: 11.9559 cents 5:6 x 7:8:9 x 10 S SD: 23.5718 cents 6:7 x 8:9:10:11:12 S SD: 21.4519 cents 7:8:9:10:11:12:13:14 H SD: 10.3929 cents 12:14:15:17:18:21:23:24 SD: 9.3286 cents 13:15:16:18:20:23:24:26 SD: 8.5824 cents 15:17:19:21:23:26:28:30 SD: 5.8013 cents 19:22:24:27:29:33:36:38 SD: 5.0462 cents 20:23:25:28:31:35:38:40 SD: 4.8487 cents 24:28:30:34:37:42:45:48 SD: 4.3050 cents 27:31:34:38:42:47:51:54 SD: 4.2060 cents 31:36:39:44:48:54:58:62 SD: 3.9579 cents 32:37:40:45:49:55:60:64 SD: 2.1414 cents 52:60:65:73:80:90:98:104 SD: 1.3339 cents 71:82:89:100:109:123:133:142 SD: 1.0339 cents 89:103:111:125:137:154:167:178 SD: 1.0049 cents 96:111:120:135:148:166:180:192 SD: 0.7631 cents 104:120:130:146:160:180:195:208 SD: 0.4231 cents 175:202:219:246:269:303:328:350 SD: 0.4004 cents 216:249:270:304:332:374:405:432 SD: 0.3959 cents 241:278:301:339:371:417:452:482 SD: 0.2908 cents 280:323:350:394:431:485:525:560 SD: 0.2901 cents 293:338:366:412:451:507:549:586 SD: 0.2824 cents 305:352:381:429:469:528:572:610 SD: 0.2298 cents 312:360:390:439:480:540:585:624 SD: 0.1409 cents 416:480:520:585:640:720:780:832 SD: 0.0000 cents