Scala analysis: xen09-wilson-marwa-09-10
Marwa permutation 10 from Figure 9, Hawkins 16/15 135/128 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect 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: 135/128 92.1787 major chroma, major limma 2: 32/27 294.1350 Pythagorean minor third 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 10/9 182.4037 minor whole 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: 1 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 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 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 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 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 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 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 256/135 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 : 92.2 386.3 590.2 702.0 884.4 1088.3 1200.0 92.2 : 294.1 498.0 609.8 792.2 996.1 1107.8 1200.0 386.3 : 203.9 315.6 498.0 702.0 813.7 905.9 1200.0 590.2 : 111.7 294.1 498.0 609.8 702.0 996.1 1200.0 702.0 : 182.4 386.3 498.0 590.2 884.4 1088.3 1200.0 884.4 : 203.9 315.6 407.8 702.0 905.9 1017.6 1200.0 1088.3: 111.7 203.9 498.0 702.0 813.7 996.1 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 .. 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 177.10502 cents, oct.: 1239.73516 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : AEDBCDB Scale is not a Constant Structure Scale diversity : 1.422264 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 : 2048/2025, 19.5526 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 Length of longest subharmonic part : 2 at degree 4 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 n-1 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 : 135 (O: 135 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.039894 Average absolute harmonicity : 0.241633 Specific harmonicity : 0.214046 Fundamental : 1/384, -8.5850 octaves, 0.6813 Hz. Guide tone : 270, 8.0768 octaves, 70638.903 Hz. Exponens Consonantiae : 1.036800E+05, 16.66178 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 194.0, average 27.71429 Mersenne's string divisions : 167678280 Sum of van Prooijen's expressibility: 6.83470, average 0.97639 Sum of Tenney's harmonic distance : 13.03139, average 1.86163 Vogel's harmonic complexity : 13.71429 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 105.51117, average 3.76826 Lattice compactness (without 2's) : 48.75411, average 1.74122 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -2.42857 19 1 3: -1 .. 3 0.85714 8 1 5: 0 .. 1 0.71429 5 5 Average exponent except 2's : 11 / 7 = 1.57143 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 54.4061 c. M: 92.1787 c. 8: 1 2 1 1 1 1 1 P M ME S SD: 40.5538 c. M:-63.6863 c. 9: 1 2 1 1 2 1 1 P M ME S SD: 36.3081 c. M: 56.8904 c. Pelog Saptanada: Sunda 10: 1 2 2 1 1 2 1 P D3 S SD: 23.6755 c. M: 44.3587 c. 12: 1 3 2 1 2 2 1 N SD: 10.2131 c. M:-15.6413 c. Marva That, Mela Gamanasrama, Raga Bairari, Malavi, Partiravam, Puriya, Puriya Kalyan, Purvikalyani, Sohani, Harsh-intense Major, Peiraiotikos: Greece 22: 2 5 4 2 3 4 2 N SD: 9.2195 c. M:-16.9122 c. 29: 2 7 5 3 4 5 3 N SD: 10.6513 c. M: 15.3932 c. 31: 2 8 5 3 5 5 3 N SD: 7.4828 c. M: 14.7594 c. 34: 3 8 6 3 5 6 3 N SD: 6.9766 c. M:-13.7036 c. 39: 3 10 6 4 6 6 4 N SD: 7.9607 c. M:-13.6863 c. 41: 3 10 7 4 6 7 4 N SD: 4.5553 c. M: 6.3099 c. 53: 4 13 9 5 8 9 5 N SD: 1.2506 c. M: 1.6127 c. 65: 5 16 11 6 10 11 6 N SD: 0.9663 c. M:-1.7951 c. 118: 9 29 20 11 18 20 11 N SD: 0.3449 c. M: 0.6533 c. 323: 25 79 55 30 49 55 30 N SD: 0.3539 c. M:-0.7005 c. 376: 29 92 64 35 57 64 35 N SD: 0.2178 c. M:-0.3745 c. 441: 34 108 75 41 67 75 41 N SD: 0.1772 c. M:-0.3383 c. 494: 38 121 84 46 75 84 46 N SD: 0.0872 c. M: 0.1482 c. 559: 43 137 95 52 85 95 52 N SD: 0.0888 c. M:-0.1290 c. 612: 47 150 104 57 93 104 57 N SD: 0.0292 c. M: 0.0450 c. 1171: 90 287 199 109 178 199 109 N SD: 0.0293 c. M:-0.0501 c. 1289: 99 316 219 120 196 219 120 N SD: 0.0241 c. M:-0.0478 c. 1783: 137 437 303 166 271 303 166 N SD: 0.0128 c. M:-0.0254 c. 1901: 146 466 323 177 289 323 177 N SD: 0.0109 c. M:-0.0179 c. 2395: 184 587 407 223 364 407 223 N SD: 0.0094 c. M: 0.0163 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 24.5302 cents 6 x x 8:9:10:11:12 S SD: 20.0106 cents 8:9:10:11:12:13:15:16 SD: 18.0242 cents 10:11:13:14:15:17:19:20 SD: 15.4356 cents 12:13:15:17:18:20:23:24 SD: 8.7639 cents 15:16:19:21:23:25:28:30 SD: 7.1069 cents 16:17:20:23:24:27:30:32 SD: 6.5053 cents 20:21:25:28:30:33:38:40 SD: 4.3973 cents 24:25:30:34:36:40:45:48 SD: 3.5736 cents 32:34:40:45:48:53:60:64 SD: 2.3950 cents 40:42:50:56:60:67:75:80 SD: 1.9872 cents 52:55:65:73:78:87:98:104 SD: 1.7821 cents 56:59:70:79:84:93:105:112 SD: 1.2108 cents 72:76:90:101:108:120:135:144 SD: 0.6444 cents 96:101:120:135:144:160:180:192 SD: 0.6114 cents 128:135:160:180:192:213:240:256 SD: 0.3867 cents 168:177:210:236:252:280:315:336 SD: 0.3703 cents 184:194:230:259:276:307:345:368 SD: 0.3682 cents 200:211:250:281:300:333:375:400 SD: 0.3391 cents 216:228:270:304:324:360:405:432 SD: 0.2878 cents 256:270:320:360:384:427:480:512 SD: 0.1931 cents 312:329:390:439:468:520:585:624 SD: 0.1485 cents 384:405:480:540:576:640:720:768 SD: 0.0000 cents