Scala analysis: xen09-wilson-marwa-11b-08
Marwa permutation 8 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 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: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
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: 2 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 512/405 405.866 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: 1 405/256 794.134 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: 2 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 : 294.1 386.3 498.0 792.2 884.4 996.1 1200.0 294.1 : 92.2 203.9 498.0 590.2 702.0 905.9 1200.0 386.3 : 111.7 405.9 498.0 609.8 813.7 1107.8 1200.0 498.0 : 294.1 386.3 498.0 702.0 996.1 1088.3 1200.0 792.2 : 92.2 203.9 407.8 702.0 794.1 905.9 1200.0 884.4 : 111.7 315.6 609.8 702.0 813.7 1107.8 1200.0 996.1 : 203.9 498.0 590.2 702.0 996.1 1088.3 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 175.19965 cents, oct.: 1226.39755 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DABDABC Scale is not a Constant Structure Scale diversity : 1.389648 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 : 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: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords 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 class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.240613 Specific harmonicity : 0.207477 Fundamental : 1/324, -8.3399 octaves, 0.8075 Hz. Guide tone : 640, 9.3219 octaves, 167440.362 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 160.0, average 22.85714 Mersenne's string divisions : 155370600 Sum of van Prooijen's expressibility: 6.16915, average 0.88131 Sum of Tenney's harmonic distance : 12.96790, average 1.85256 Vogel's harmonic complexity : 13.14286 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 116.40485, average 4.15732 Lattice compactness (without 2's) : 54.57665, average 1.94917 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 7 2.42857 21 1 3: -4 .. 0 -1.57143 11 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 38.8072 c. M:-64.9629 c. 8: 2 1 0 2 1 1 1 N D3 SD: 40.2293 c. M:-63.6863 c. 9: 2 1 1 2 1 0 2 N SD: 35.0207 c. M: 62.7567 c. 12: 3 1 1 3 1 1 2 N SD: 8.8368 c. M:-15.6413 c. Chromatic Hypodorian inverse 29: 7 2 3 7 2 3 5 N SD: 8.4266 c. M: 15.3932 c. 33: 8 3 3 8 2 3 6 N SD: 10.1409 c. M: 14.2718 c. 34: 8 3 3 8 3 3 6 N SD: 8.1979 c. M: 15.7094 c. 37: 9 3 3 9 3 4 6 N SD: 8.4478 c. M: 13.8016 c. 38: 9 3 4 9 3 4 6 N SD: 7.7516 c. M:-14.4363 c. 41: 10 3 4 10 3 4 7 N SD: 3.3972 c. M: 6.3099 c. 53: 13 4 5 13 4 5 9 N SD: 0.7481 c. M: 1.4081 c. 118: 29 9 11 29 9 11 20 N SD: 0.5600 c. M:-1.0403 c. 171: 42 13 16 42 13 16 29 N SD: 0.4393 c. M:-0.8025 c. 224: 55 17 21 55 17 21 38 N SD: 0.4479 c. M:-0.6771 c. 323: 79 25 30 79 25 30 55 N SD: 0.4435 c. M: 0.8487 c. 335: 82 26 31 82 26 31 57 N SD: 0.3821 c. M:-0.5520 c. 376: 92 29 35 92 29 35 64 N SD: 0.3808 c. M: 0.6906 c. 388: 95 30 36 95 30 36 66 N SD: 0.2549 c. M: 0.4274 c. 441: 108 34 41 108 34 41 75 N SD: 0.1803 c. M: 0.3433 c. 494: 121 38 46 121 38 46 84 N SD: 0.1569 c. M: 0.2772 c. 506: 124 39 47 124 39 47 86 N SD: 0.1342 c. M:-0.2476 c. 559: 137 43 52 137 43 52 95 N SD: 0.0523 c. M:-0.0906 c. 612: 150 47 57 150 47 57 104 N SD: 0.0255 c. M: 0.0450 c. 1171: 287 90 109 287 90 109 199 N SD: 0.0214 c. M: 0.0365 c. 1783: 437 137 166 437 137 166 303 N SD: 0.0167 c. M: 0.0319 c. 1901: 466 146 177 466 146 177 323 N SD: 0.0195 c. M:-0.0346 c. 2395: 587 184 223 587 184 223 407 N SD: 0.0169 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 x 7:8 S SD: 23.5636 cents 5:6 x 7:8 x 9:10 S SD: 18.4632 cents 6:7 x 8:9:10:11:12 S SD: 18.0446 cents 7:8:9 x 11:12 x 14 SD: 18.7777 cents 8:9:10:11 x 13:14:16 SD: 19.4672 cents 9 x 11:12:14:15:16:18 SD: 7.9180 cents 10:12 x 13:16:17:18:20 SD: 11.1605 cents 12:14:15:16:19:20:21:24 SD: 5.5293 cents 21:25:26:28:33:35:37:42 SD: 3.6947 cents 27:32:34:36:43:45:48:54 SD: 2.6525 cents 33:39:41:44:52:55:59:66 SD: 2.2834 cents 36:43:45:48:57:60:64:72 SD: 1.9842 cents 45:53:56:60:71:75:80:90 SD: 1.9410 cents 48:57:60:64:76:80:85:96 SD: 1.1844 cents 60:71:75:80:95:100:107:120 SD: 0.9889 cents 81:96:101:108:128:135:144:162 SD: 0.6114 cents 108:128:135:144:171:180:192:216 SD: 0.4826 cents 183:217:229:244:289:305:325:366 SD: 0.4224 cents 189:224:236:252:299:315:336:378 SD: 0.3804 cents 216:256:270:288:341:360:384:432 SD: 0.2416 cents 243:288:304:324:384:405:432:486 SD: 0.2035 cents 324:384:405:432:512:540:576:648 SD: 0.0000 cents