Scala analysis: xen09-wilson-marwa-11b-01
Marwa permutation 1 from Figure 11b, Hawkins 135/128 16/15 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 4/3 498.044999 perfect fourth 3: 45/32 590.223716 diatonic tritone 4: 128/81 792.179997 Pythagorean minor sixth 5: 16/9 996.089998 Pythagorean minor seventh 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: 32/27 294.1350 Pythagorean minor third 2: 9/8 203.9100 major whole tone 3: 135/128 92.1787 major chroma, major limma 4: 4096/3645 201.9563 narrow diminished third 5: 9/8 203.9100 major whole tone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 2 9/8 203.910 cents major whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 1215/1024 296.089 cents wide augmented second 2: 2 512/405 405.866 cents narrow diminished fourth 2: 1 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 2 405/256 794.134 cents wide augmented fifth 5: 2 2048/1215 903.911 cents narrow diminished seventh 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma 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 : 294.1 498.0 590.2 792.2 996.1 1088.3 1200.0 294.1 : 203.9 296.1 498.0 702.0 794.1 905.9 1200.0 498.0 : 92.2 294.1 498.0 590.2 702.0 996.1 1200.0 590.2 : 202.0 405.9 498.0 609.8 903.9 1107.8 1200.0 792.2 : 203.9 296.1 407.8 702.0 905.9 998.0 1200.0 996.1 : 92.2 203.9 498.0 702.0 794.1 996.1 1200.0 1088.3: 111.7 405.9 609.8 702.0 903.9 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 186.71199 cents, oct.: 1306.98392 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EDACDAB Scale is not a Constant Structure Scale diversity : 1.330644 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 81 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.228227 Specific harmonicity : 0.160884 Fundamental : 1/2592, -11.3399 octaves, 0.1009 Hz. Guide tone : 5760, 12.4919 octaves, 1506963.256 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 201.5, average 28.78571 Mersenne's string divisions : 148896825 Sum of van Prooijen's expressibility: 7.60052, average 1.08579 Sum of Tenney's harmonic distance : 15.72833, average 2.24690 Vogel's harmonic complexity : 17.00000 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 155.07895, average 5.53853 Lattice compactness (without 2's) : 71.38820, average 2.54958 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 7 1.57143 27 1 3: -4 .. 2 -1.00000 13 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 2 1 0 2 1 0 1 N T3 SD: 49.6317 c. M: 75.9380 c. 8: 2 1 1 1 2 0 1 N D3 SD: 35.0270 c. M:-53.9100 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 37.6689 c. M: 72.1800 c. 11: 3 2 0 2 2 1 1 N G SD: 30.1791 c. M:-47.4095 c. 12: 3 2 1 2 2 1 1 N SD: 7.0494 c. M:-11.7313 c. 29: 7 5 2 5 5 2 3 N SD: 6.9685 c. M: 12.4066 c. 41: 10 7 3 7 7 3 4 N SD: 2.9072 c. M: 5.3419 c. 53: 13 9 4 9 9 4 5 N SD: 0.8198 c. M: 1.5445 c. 65: 16 11 5 11 11 5 6 N SD: 0.9583 c. M:-1.6662 c. 118: 29 20 9 20 20 9 11 N SD: 0.5608 c. M:-1.0403 c. 171: 42 29 13 29 29 13 16 N SD: 0.5440 c. M:-0.8025 c. 289: 71 49 22 49 49 22 27 N SD: 0.5381 c. M:-0.8996 c. 311: 76 53 24 52 53 24 29 N SD: 0.6175 c. M: 1.1832 c. 323: 79 55 25 54 55 25 30 N SD: 0.4878 c. M: 0.8487 c. 364: 89 62 28 61 62 28 34 N SD: 0.5222 c. M: 0.9712 c. 376: 92 64 29 63 64 29 35 N SD: 0.3657 c. M: 0.6906 c. 388: 95 66 30 65 66 30 36 N SD: 0.3259 c. M:-0.4979 c. 429: 105 73 33 72 73 33 40 N SD: 0.3018 c. M: 0.5716 c. 441: 108 75 34 74 75 34 41 N SD: 0.2113 c. M: 0.3433 c. 494: 121 84 38 83 84 38 46 N SD: 0.1453 c. M: 0.2772 c. 547: 134 93 42 92 93 42 51 N SD: 0.1342 c. M: 0.2239 c. 559: 137 95 43 94 95 43 52 N SD: 0.0645 c. M:-0.1162 c. 612: 150 104 47 103 104 47 57 N SD: 0.0203 c. M: 0.0334 c. 1783: 437 303 137 300 303 137 166 N SD: 0.0182 c. M: 0.0319 c. 2395: 587 407 184 403 407 184 223 N SD: 0.0155 c. M: 0.0297 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: 45.1125 cents 3 x 4 x 5 x x 6 S SD: 30.7262 cents 4:5 x x 6:7 x 8 S SD: 32.9591 cents 5:6 x 7:8:9 x 10 S SD: 7.6080 cents 6:7:8 x 9 x 11:12 SD: 20.3937 cents 7:8:9:10:11:12:13:14 H SD: 16.2906 cents 8:9 x 11:13:14:15:16 SD: 18.8083 cents 9:11:12:13:14:16:17:18 SD: 10.9703 cents 10:12:13:14:16:18:19:20 S SD: 8.9146 cents 11:13:15 x 17:20:21:22 SD: 12.3718 cents 12:14:16:17:19:21:23:24 SD: 7.9657 cents 15:18:20:21:24:27:28:30 S SD: 5.5448 cents 17:20:23:24:27:30:32:34 SD: 4.8092 cents 22:26:29:31:35:39:41:44 SD: 3.7756 cents 27:32:36:38:43:48:51:54 SD: 2.6603 cents 39:46:52:55:62:69:73:78 SD: 2.3898 cents 42:50:56:59:66:75:79:84 SD: 2.2418 cents 45:53:60:63:71:80:84:90 SD: 2.2319 cents 48:57:64:68:76:85:90:96 SD: 2.1758 cents 49:58:65:69:77:87:92:98 SD: 1.9853 cents 54:64:72:76:85:96:101:108 SD: 1.1629 cents 81:96:108:114:128:144:152:162 SD: 0.2878 cents 264:313:352:371:417:469:495:528 SD: 0.2800 cents 288:341:384:405:455:512:540:576 SD: 0.2491 cents 303:359:404:426:479:539:568:606 SD: 0.2106 cents 345:409:460:485:545:613:647:690 SD: 0.1957 cents 384:455:512:540:607:683:720:768 SD: 0.1547 cents 438:519:584:616:692:779:821:876 SD: 0.1520 cents 465:551:620:654:735:827:872:930 SD: 0.1372 cents 519:615:692:730:820:923:973:1038 SD: 0.1256 cents 534:633:712:751:844:949:1001:1068 SD: 0.1247 cents 567:672:756:797:896:1008:1063:1134 SD: 0.1105 cents