Scala analysis: xen09-wilson-marwa-16a-06
Marwa permutation 6 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: 4/3 498.044999 perfect fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 5/3 884.358713 major sixth, BP sixth 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: 16/15 111.7313 minor diatonic semitone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 2 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: 1 45/26 949.696 cents 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 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 : 247.7 386.3 498.0 745.8 884.4 1088.3 1200.0 247.7 : 138.6 250.3 498.0 636.6 840.5 952.3 1200.0 386.3 : 111.7 359.5 498.0 702.0 813.7 1061.4 1200.0 498.0 : 247.7 386.3 590.2 702.0 949.7 1088.3 1200.0 745.8 : 138.6 342.5 454.2 702.0 840.5 952.3 1200.0 884.4 : 203.9 315.6 563.4 702.0 813.7 1061.4 1200.0 1088.3: 111.7 359.5 498.0 609.8 857.5 996.1 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: 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 177.49324 cents, oct.: 1242.45268 cents Scale is strictly proper Step pattern alph. order: ABCABDC Step pattern size order : DBADBCA Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.523872 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 136.0098 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.025715 Average absolute harmonicity : 0.227322 Specific harmonicity : 0.132273 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.872000E+04, 14.19229 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 55.5, average 7.92857 Mersenne's string divisions : 127512 Sum of van Prooijen's expressibility: 5.34119, average 0.76303 Sum of Tenney's harmonic distance : 10.64152, average 1.52022 Vogel's harmonic complexity : 18.85714 Wille's k value : 292 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 74.62650, average 2.66523 Lattice compactness (without 2's) : 38.25991, average 1.36643 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 10 1 3: -1 .. 1 0.00000 4 1 5: 0 .. 1 0.71429 5 3 13: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 47.6429 c. M: 76.3125 c. Lebeng 8: 2 1 0 2 1 1 1 N D3 SD: 39.3195 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 32.9395 c. M:-54.2139 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 23.2347 c. M: 44.3587 c. Sethares Neutral, Beatles-7, Dichotic-7 13: 3 1 1 3 2 2 1 N SD: 25.0889 c. M:-38.7182 c. 14: 3 2 1 3 1 3 1 P T3 SD: 24.5328 c. M:-42.2577 c. 15: 3 2 1 3 2 3 1 N T3 SD: 17.9827 c. M:-31.7313 c. Fifteen-tone "Major" 18: 4 2 1 4 2 3 2 N SD: 18.7648 c. M: 31.3783 c. 19: 4 2 2 4 2 3 2 P T3 S SD: 8.3635 c. M: 14.5845 c. 24: 5 3 2 5 3 4 2 P SD: 9.2294 c. M:-15.6413 c. 29: 6 3 3 6 3 5 3 P T3 S SD: 9.1614 c. M: 15.3932 c. 31: 6 4 3 6 4 5 3 SP SD: 7.8214 c. M: 15.4830 c. 34: 7 4 3 7 4 6 3 P SD: 3.3608 c. M:-5.8489 c. 53: 11 6 5 11 6 9 5 P SD: 1.1715 c. M: 1.4763 c. 87: 18 10 8 18 10 15 8 P SD: 1.0643 c. M: 1.6001 c. 140: 29 16 13 29 16 24 13 P SD: 0.7759 c. M: 1.5016 c. 193: 40 22 18 40 22 33 18 P SD: 0.7813 c. M: 1.4572 c. 217: 45 25 20 45 25 37 20 P SD: 0.7564 c. M:-1.1322 c. 224: 46 26 21 46 26 38 21 SP SD: 0.7740 c. M: 1.3125 c. 248: 51 29 23 51 29 42 23 SP SD: 0.7087 c. M:-1.1252 c. 267: 55 31 25 55 31 45 25 SP SD: 0.6070 c. M:-1.0345 c. 270: 56 31 25 56 31 46 25 P SD: 0.6189 c. M:-1.1478 c. 277: 57 32 26 57 32 47 26 SP SD: 0.6397 c. M: 0.9041 c. 301: 62 35 28 62 35 51 28 SP SD: 0.4009 c. M:-0.6911 c. 354: 73 41 33 73 41 60 33 SP SD: 0.2178 c. M:-0.3870 c. 407: 84 47 38 84 47 69 38 SP SD: 0.1744 c. M: 0.3080 c. 441: 91 51 41 91 51 75 41 SP SD: 0.1194 c. M: 0.2078 c. 494: 102 57 46 102 57 84 46 SP SD: 0.0712 c. M: 0.1482 c. 848: 175 98 79 175 98 144 79 SP SD: 0.0598 c. M: 0.0995 c. 1289: 266 149 120 266 149 219 120 SP SD: 0.0583 c. M: 0.1072 c. 1342: 277 155 125 277 155 228 125 SP SD: 0.0304 c. M: 0.0510 c. 1836: 379 212 171 379 212 312 171 SP SD: 0.0310 c. M: 0.0450 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: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 23.7906 cents 5:6 x 7:8 x 9:10 S SD: 29.2234 cents 6:7 x 8:9:10:11:12 S SD: 10.2751 cents 7:8:9 x 11:12:13:14 SD: 13.5947 cents 8:9:10:11:12:13:15:16 SD: 13.2492 cents 9:10:11:12:14:15:17:18 SD: 11.3496 cents 10:12 x 13:15:17:19:20 SD: 16.7944 cents 11:13:14:15:17:18:21:22 SD: 11.2941 cents 12:14:15:16:18:20:23:24 SD: 8.7306 cents 13:15:16:17:20:22:24:26 SD: 8.1687 cents 15:17:19:20:23:25:28:30 SD: 5.6840 cents 20:23:25:27:31:33:38:40 SD: 5.5177 cents 21:24:26:28:32:35:39:42 SD: 4.7334 cents 24:28:30:32:37:40:45:48 SD: 2.7809 cents 32:37:40:43:49:53:60:64 SD: 2.7792 cents 33:38:41:44:51:55:62:66 SD: 2.0044 cents 39:45:49:52:60:65:73:78 SD: 1.3339 cents 72:83:90:96:111:120:135:144 SD: 0.5634 cents 156:180:195:208:240:260:293:312 SD: 0.4224 cents 195:225:244:260:300:325:366:390 SD: 0.3585 cents 201:232:251:268:309:335:377:402 SD: 0.3289 cents 216:249:270:288:332:360:405:432 SD: 0.3240 cents 240:277:300:320:369:400:450:480 SD: 0.1692 cents 312:360:390:416:480:520:585:624 SD: 0.0000 cents