Scala analysis: xen09-wilson-marwa-09-15
Marwa permutation 15 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: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 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: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 135/128 92.1787 major chroma, major limma 6: 32/27 294.1350 Pythagorean minor third 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 : 92.2 386.3 498.0 702.0 794.1 1088.3 1200.0 92.2 : 294.1 405.9 609.8 702.0 996.1 1107.8 1200.0 386.3 : 111.7 315.6 407.8 702.0 813.7 905.9 1200.0 498.0 : 203.9 296.1 590.2 702.0 794.1 1088.3 1200.0 702.0 : 92.2 386.3 498.0 590.2 884.4 996.1 1200.0 794.1 : 294.1 405.9 498.0 792.2 903.9 1107.8 1200.0 1088.3: 111.7 203.9 498.0 609.8 813.7 905.9 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 : 171.90744 cents, oct.: 1203.35210 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ADBCADB 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 405 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.253650 Specific harmonicity : 0.174672 Fundamental : 1/768, -9.5850 octaves, 0.3407 Hz. Guide tone : 1620, 10.6618 octaves, 423833.416 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 485.5, average 69.35714 Mersenne's string divisions : 1259492535 Sum of van Prooijen's expressibility: 7.56709, average 1.08101 Sum of Tenney's harmonic distance : 14.79181, average 2.11312 Vogel's harmonic complexity : 14.71429 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 135.11698, average 4.82561 Lattice compactness (without 2's) : 60.08416, average 2.14586 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 2 -2.57143 24 1 3: -1 .. 4 1.14286 10 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's : 12 / 7 = 1.71429 Average absolute exponent except 2's: 14 / 7 = 2.00000
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 48.1522 c. M:-79.2499 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 26.3835 c. M:-41.1546 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 24.7553 c. M:-45.8663 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 7.8209 c. M:-13.6863 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 38: 3 9 4 6 3 9 4 N SD: 7.5539 c. M: 14.5845 c. 41: 3 10 4 7 3 10 4 N SD: 3.7265 c. M: 5.8259 c. 53: 4 13 5 9 4 13 5 N SD: 1.1709 c. M: 1.6809 c. 65: 5 16 6 11 5 16 6 N SD: 0.6837 c. M:-1.3786 c. 118: 9 29 11 20 9 29 11 N SD: 0.4520 c. M: 0.9134 c. 183: 14 45 17 31 14 45 17 N SD: 0.4158 c. M: 0.6911 c. 301: 23 74 28 51 23 74 28 N SD: 0.4108 c. M: 0.7782 c. 311: 24 76 29 53 24 76 29 N SD: 0.3996 c. M:-0.7216 c. 323: 25 79 30 55 25 79 30 N SD: 0.4620 c. M:-0.9127 c. 364: 28 89 34 62 28 89 34 N SD: 0.3293 c. M: 0.5994 c. 376: 29 92 35 64 29 92 35 N SD: 0.2727 c. M:-0.5471 c. 429: 33 105 40 73 33 105 40 N SD: 0.1874 c. M: 0.2997 c. 441: 34 108 41 75 34 108 41 N SD: 0.2215 c. M:-0.4241 c. 482: 37 118 45 82 37 118 45 N SD: 0.2086 c. M: 0.4216 c. 494: 38 121 46 84 38 121 46 N SD: 0.1013 c. M:-0.1983 c. 547: 42 134 51 93 42 134 51 N SD: 0.1030 c. M: 0.2077 c. 559: 43 137 52 95 43 137 52 N SD: 0.0894 c. M:-0.1418 c. 612: 47 150 57 104 47 150 57 N SD: 0.0222 c. M: 0.0392 c. 1289: 99 316 120 219 99 316 120 N SD: 0.0203 c. M:-0.0323 c. 1783: 137 437 166 303 137 437 166 N SD: 0.0168 c. M:-0.0334 c. 1901: 146 466 177 323 146 466 177 N SD: 0.0129 c. M: 0.0254 c. 2395: 184 587 223 407 184 587 223 N SD: 0.0107 c. M:-0.0208 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: 30.0750 cents 4 x 5 x 6 x x 8 S SD: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 26.4622 cents 6 x x 8:9:10:11:12 S SD: 19.6512 cents 7:8:9 x x 11:13:14 SD: 29.7377 cents 8:9:10:11:12:13:15:16 SD: 18.8843 cents 9:10:11:12 x 14:17:18 SD: 17.2169 cents 10:11 x 13:15:16:19:20 SD: 15.0304 cents 11:12:14:15 x 17:21:22 SD: 15.3814 cents 12:13:15:16:18:19:23:24 SD: 8.5741 cents 15:16:19:20:23:24:28:30 SD: 7.5562 cents 16:17:20:21:24:25:30:32 SD: 5.2859 cents 24:25:30:32:36:38:45:48 SD: 3.0791 cents 36:38:45:48:54:57:68:72 SD: 1.8478 cents 48:51:60:64:72:76:90:96 SD: 1.8365 cents 56:59:70:75:84:89:105:112 SD: 1.6008 cents 60:63:75:80:90:95:113:120 SD: 1.5678 cents 72:76:90:96:108:114:135:144 SD: 0.2878 cents 240:253:300:320:360:380:450:480 SD: 0.2373 cents 312:329:390:416:468:494:585:624 SD: 0.2088 cents 328:346:410:437:492:519:615:656 SD: 0.1989 cents 400:422:500:533:600:633:750:800 SD: 0.1861 cents 440:464:550:587:660:696:825:880 SD: 0.1482 cents 456:481:570:608:684:721:855:912 SD: 0.1430 cents 512:540:640:683:768:810:960:1024 SD: 0.1207 cents 528:557:660:704:792:835:990:1056 SD: 0.1079 cents 600:633:750:800:900:949:1125:1200 SD: 0.0928 cents