Scala analysis: xen09-wilson-marwa-11b-06
Marwa permutation 6 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: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean minor sixth 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: 32/27 294.1350 Pythagorean minor third 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 32/27 294.1350 Pythagorean minor third 5: 135/128 92.1787 major chroma, major limma 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: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 512/405 405.866 cents narrow diminished 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: 2 405/256 794.134 cents wide augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 294.1 386.3 498.0 792.2 884.4 1088.3 1200.0 294.1 : 92.2 203.9 498.0 590.2 794.1 905.9 1200.0 386.3 : 111.7 405.9 498.0 702.0 813.7 1107.8 1200.0 498.0 : 294.1 386.3 590.2 702.0 996.1 1088.3 1200.0 792.2 : 92.2 296.1 407.8 702.0 794.1 905.9 1200.0 884.4 : 203.9 315.6 609.8 702.0 813.7 1107.8 1200.0 1088.3: 111.7 405.9 498.0 609.8 903.9 996.1 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 .. 405.8663 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 794.1337 .. 996.0900 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 179.15017 cents, oct.: 1254.05116 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DABDACB Scale is not a Constant Structure Scale diversity : 1.390463 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.448980 redundancy: 0.551020 Efficiency x scale size : 3.142857 Number of different interval sizes : 22 = 3.66667 / 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 : 32805/32768, 1.9537 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 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 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 201.9563 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 81 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.237146 Specific harmonicity : 0.181818 Fundamental : 1/648, -9.3399 octaves, 0.4037 Hz. Guide tone : 1920, 10.9069 octaves, 502321.085 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 159.0, average 22.71429 Mersenne's string divisions : 142940952 Sum of van Prooijen's expressibility: 6.39100, average 0.91300 Sum of Tenney's harmonic distance : 12.88872, average 1.84125 Vogel's harmonic complexity : 15.14286 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 128.70679, average 4.59667 Lattice compactness (without 2's) : 60.21299, average 2.15046 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 7 1.42857 20 1 3: -4 .. 1 -1.14286 10 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 43.1786 c. M:-64.9629 c. 8: 2 0 1 2 1 1 1 N D3 SD: 43.5580 c. M: 86.3137 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 27.0275 c. M:-48.9746 c. 12: 3 1 1 3 1 2 1 N T3 S SD: 9.7758 c. M:-15.6413 c. 29: 7 2 3 7 2 5 3 N SD: 9.5772 c. M: 15.3932 c. 32: 8 2 3 8 3 5 3 N SD: 8.7891 c. M:-15.6413 c. 33: 8 3 3 8 2 6 3 N SD: 8.6450 c. M:-13.6863 c. 34: 8 3 3 8 3 6 3 N T3 S SD: 7.9548 c. M: 15.7094 c. 38: 9 3 4 9 3 6 4 N SD: 7.7911 c. M: 14.5845 c. 41: 10 3 4 10 3 7 4 N SD: 3.9349 c. M: 6.3099 c. 53: 13 4 5 13 4 9 5 N SD: 0.9318 c. M: 1.4763 c. 118: 29 9 11 29 9 20 11 N SD: 0.5268 c. M:-1.0403 c. 171: 42 13 16 42 13 29 16 N SD: 0.4617 c. M:-0.8025 c. 224: 55 17 21 55 17 38 21 N SD: 0.5183 c. M: 0.7687 c. 289: 71 22 27 71 22 49 27 N SD: 0.4610 c. M:-0.8996 c. 323: 79 25 30 79 25 55 30 N SD: 0.4264 c. M: 0.8487 c. 335: 82 26 31 82 26 57 31 N SD: 0.4505 c. M:-0.6865 c. 376: 92 29 35 92 29 64 35 N SD: 0.3579 c. M: 0.6906 c. 388: 95 30 36 95 30 66 36 N SD: 0.2834 c. M: 0.4274 c. 441: 108 34 41 108 34 75 41 N SD: 0.1796 c. M: 0.3433 c. 494: 121 38 46 121 38 84 46 N SD: 0.1479 c. M: 0.2772 c. 506: 124 39 47 124 39 86 47 N SD: 0.1676 c. M:-0.2688 c. 547: 134 42 51 134 42 93 51 N SD: 0.1761 c. M: 0.2636 c. 559: 137 43 52 137 43 95 52 N SD: 0.0646 c. M:-0.1034 c. 612: 150 47 57 150 47 104 57 N SD: 0.0282 c. M: 0.0450 c. 1171: 287 90 109 287 90 199 109 N SD: 0.0236 c. M: 0.0365 c. 1783: 437 137 166 437 137 303 166 N SD: 0.0160 c. M: 0.0319 c. 1901: 466 146 177 466 146 323 177 N SD: 0.0183 c. M:-0.0346 c. 2395: 587 184 223 587 184 407 223 N SD: 0.0159 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 x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 30.8983 cents 5:6 x 7:8 x 9:10 S SD: 22.8511 cents 6:7 x 8:9:10:11:12 S SD: 16.9947 cents 7:8:9 x 11:12:13:14 SD: 15.8898 cents 8:9:10:11 x 13:15:16 SD: 18.9295 cents 9 x 11:12:14:15:17:18 SD: 8.1993 cents 10:12 x 13:16:17:19:20 SD: 11.2390 cents 11:13:14:15:17:18:21:22 SD: 11.0460 cents 12:14:15:16:19:20:23:24 SD: 6.7045 cents 15:18:19:20:24:25:28:30 SD: 5.5518 cents 21:25:26:28:33:35:39:42 SD: 3.7857 cents 27:32:34:36:43:45:51:54 SD: 3.2198 cents 33:39:41:44:52:55:62:66 SD: 1.8707 cents 48:57:60:64:76:80:90:96 SD: 0.6825 cents 81:96:101:108:128:135:152:162 SD: 0.6444 cents 120:142:150:160:190:200:225:240 SD: 0.6184 cents 129:153:161:172:204:215:242:258 SD: 0.4776 cents 168:199:210:224:265:280:315:336 SD: 0.4697 cents 183:217:229:244:289:305:343:366 SD: 0.3496 cents 216:256:270:288:341:360:405:432 SD: 0.2416 cents 264:313:330:352:417:440:495:528 SD: 0.1406 cents 336:398:420:448:531:560:630:672 SD: 0.1391 cents 384:455:480:512:607:640:720:768 SD: 0.0967 cents 567:672:709:756:896:945:1063:1134 SD: 0.0919 cents 600:711:750:800:948:1000:1125:1200 SD: 0.0547 cents