Scala analysis: xen09-wilson-marwa-17b-01
Marwa permutation 1 from Figure 17b, Archytas 36/35 28/27 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 45/32 590.223716 diatonic tritone 3: 81/56 638.994097 4: 5/3 884.358713 major sixth, BP sixth 5: 15/8 1088.268715 classic major seventh 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 5/4 386.3137 major third 2: 9/8 203.9100 major whole tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 280/243 245.3646 5: 9/8 203.9100 major whole tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 64/45 609.776 cents 2nd tritone 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 243/140 954.635 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave 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 : 386.3 590.2 639.0 884.4 1088.3 1137.0 1200.0 386.3 : 203.9 252.7 498.0 702.0 750.7 813.7 1200.0 590.2 : 48.8 294.1 498.0 546.8 609.8 996.1 1200.0 639.0 : 245.4 449.3 498.0 561.0 947.3 1151.2 1200.0 884.4 : 203.9 252.7 315.6 702.0 905.9 954.6 1200.0 1088.3: 48.8 111.7 498.0 702.0 750.7 996.1 1200.0 1137.0: 63.0 449.3 653.2 702.0 947.3 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 197.74826 cents, oct.: 1384.23782 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : ECADCAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.594117 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 19683/19600, 7.3158 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.027763 Average absolute harmonicity : 0.209368 Specific harmonicity : 0.143875 Fundamental : 1/672, -9.3923 octaves, 0.3893 Hz. Guide tone : 810, 9.6618 octaves, 211916.708 Hz. Exponens Consonantiae : 5.443200E+05, 19.05410 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 149.0, average 21.28571 Mersenne's string divisions : 716234904 Sum of van Prooijen's expressibility: 7.56709, average 1.08101 Sum of Tenney's harmonic distance : 14.24986, average 2.03569 Vogel's harmonic complexity : 17.85714 Wille's k value : 472 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 100.23254, average 3.57973 Lattice compactness (without 2's) : 64.64547, average 2.30877 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.85714 15 1 3: -1 .. 4 1.28571 11 5: 0 .. 1 0.57143 4 4 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 11 / 7 = 1.57143 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 1 0 2 1 0 1 N T3 SD: 74.9065 c. M: 124.7084 c. 8: 3 1 0 2 1 1 0 N SD: 40.2586 c. M:-63.6863 c. 9: 3 2 0 2 1 1 0 N SD: 44.1197 c. M:-76.4430 c. 10: 3 2 0 2 2 0 1 N SD: 32.9460 c. M: 57.0391 c. 12: 4 2 0 3 2 0 1 N SD: 22.5439 c. M: 38.9941 c. 15: 5 2 1 3 3 0 1 N SD: 18.5857 c. M:-31.7313 c. 18: 6 3 1 3 3 1 1 N SD: 16.2219 c. M:-27.6726 c. 19: 6 3 1 4 3 1 1 N SD: 10.6729 c. M: 21.8027 c. 22: 7 4 1 4 4 1 1 N SD: 9.0294 c. M:-15.5514 c. 34: 11 6 1 7 6 1 2 N SD: 5.4690 c. M:-9.7763 c. 41: 13 7 2 8 7 2 2 N SD: 4.9216 c. M: 6.3099 c. 43: 14 7 2 9 7 2 2 N SD: 4.9432 c. M:-8.6645 c. 53: 17 9 2 11 9 2 3 N SD: 2.8859 c. M: 5.0318 c. 75: 24 13 3 15 13 3 4 N SD: 2.0588 c. M: 4.3587 c. 77: 25 13 3 16 13 3 4 N SD: 2.3235 c. M:-3.9530 c. 94: 30 16 4 19 16 4 5 N SD: 2.4958 c. M: 3.5076 c. 96: 31 16 4 20 16 4 5 N SD: 1.7619 c. M:-3.1413 c. 118: 38 20 5 24 20 5 6 N SD: 0.9966 c. M:-1.9440 c. 152: 49 26 6 31 26 6 8 N SD: 0.8914 c. M:-1.8815 c. 171: 55 29 7 35 29 7 9 N SD: 0.4149 c. M: 0.7500 c. 289: 93 49 12 59 49 12 15 N SD: 0.4142 c. M:-0.6772 c. 323: 104 55 13 66 55 13 17 N SD: 0.2329 c. M:-0.4884 c. 441: 142 75 18 90 75 18 23 N SD: 0.2543 c. M:-0.4617 c. 494: 159 84 20 101 84 20 26 N SD: 0.1115 c. M: 0.1970 c. 783: 252 133 32 160 133 32 41 N SD: 0.1165 c. M: 0.1854 c. 935: 301 159 38 191 159 38 49 N SD: 0.0945 c. M:-0.1506 c. 1106: 356 188 45 226 188 45 58 N SD: 0.0500 c. M: 0.0911 c. 1600: 515 272 65 327 272 65 84 N SD: 0.0514 c. M: 0.1087 c. 1848: 595 314 75 378 314 75 97 N SD: 0.0390 c. M:-0.0569 c. 2019: 650 343 82 413 343 82 106 N SD: 0.0349 c. M: 0.0639 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 31.4805 cents 3 x 4 x 5 x x 6 S SD: 30.7262 cents 4:5 x 6:7 x x 8 S SD: 26.3377 cents 5:6:7 x 8:9 x 10 S SD: 24.5302 cents 6 x 8:9:10:11 x 12 S SD: 23.6429 cents 7:9 x 10:12:13 x 14 SD: 14.8244 cents 8:10:11:12:13:15 x 16 SD: 14.3361 cents 9:11 x 13:15:17 x 18 SD: 8.2038 cents 10:13:14 x 17:19 x 20 SD: 15.9638 cents 11:14:15:16:18 x 21:22 SD: 12.0450 cents 12:15:17 x 20 x 23:24 SD: 3.3356 cents 14:18 x 20:23:26:27:28 SD: 10.1872 cents 15:19:21:22:25:28:29:30 SD: 5.0338 cents 16:20 x 23:27:30:31:32 SD: 4.2209 cents 19:24:27 x 32:36:37:38 SD: 6.6594 cents 20:25:28:29:33:38:39:40 SD: 5.0954 cents 21:26 x 30:35:39:41:42 SD: 6.3742 cents 22:28:31:32:37:41:42:44 SD: 5.9664 cents 23:29:32:33:38:43:44:46 SD: 4.9744 cents 24:30:34:35:40:45:46:48 SD: 3.1283 cents 27:34:38:39:45:51:52:54 SD: 2.6334 cents 32:40:45:46:53:60:62:64 SD: 2.4606 cents 39:49:55:56:65:73:75:78 SD: 2.4574 cents 40:50:56:58:67:75:77:80 SD: 1.8214 cents 56:70:79:81:93:105:108:112 SD: 1.1821 cents 69:86:97:100:115:129:133:138 SD: 1.1363 cents 72:90:101:104:120:135:139:144 SD: 0.7442 cents 96:120:135:139:160:180:185:192 SD: 0.3180 cents 168:210:236:243:280:315:324:336 SD: 0.2619 cents 224:280:315:324:373:420:432:448 SD: 0.2209 cents 264:330:371:382:440:495:509:528 SD: 0.2028 cents 320:400:450:463:533:600:617:640 SD: 0.1817 cents 352:440:495:509:587:660:679:704 SD: 0.1651 cents 408:510:574:590:680:765:787:816 SD: 0.1312 cents 448:560:630:648:747:840:864:896 SD: 0.1104 cents 504:630:709:729:840:945:972:1008 SD: 0.0872 cents 576:720:810:833:960:1080:1111:1152 SD: 0.0530 cents