Scala analysis: xen09-wilson-marwa-09-07
Marwa permutation 7 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: 1215/1024 296.088718 wide augmented second 3: 45/32 590.223716 diatonic tritone 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: 9/8 203.9100 major whole tone 3: 32/27 294.1350 Pythagorean minor third 4: 16/15 111.7313 minor diatonic semitone 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: 2 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 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: 1 8/5 813.686 cents minor sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 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 : 92.2 296.1 590.2 702.0 794.1 1088.3 1200.0 92.2 : 203.9 498.0 609.8 702.0 996.1 1107.8 1200.0 296.1 : 294.1 405.9 498.0 792.2 903.9 996.1 1200.0 590.2 : 111.7 203.9 498.0 609.8 702.0 905.9 1200.0 702.0 : 92.2 386.3 498.0 590.2 794.1 1088.3 1200.0 794.1 : 294.1 405.9 498.0 702.0 996.1 1107.8 1200.0 1088.3: 111.7 203.9 407.8 702.0 813.7 905.9 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 .. 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 : 172.59377 cents, oct.: 1208.15641 cents Scale is not proper Step pattern alph. order: ABCDACD Step pattern size order : ACDBADB Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.361761 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 Hypophrygian octave species of abstract tetrachord Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 2 and 3 combined 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: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.219373 Specific harmonicity : 0.160669 Fundamental : 1/1024, -10.0000 octaves, 0.2555 Hz. Guide tone : 2430, 11.2467 octaves, 635750.124 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 1635.5, average 233.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.12879, average 1.58983 Sum of Tenney's harmonic distance : 21.66484, average 3.09498 Vogel's harmonic complexity : 15.71429 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 152.61448, average 5.45052 Lattice compactness (without 2's) : 66.00503, average 2.35732 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -4.71429 35 1 3: 0 .. 5 2.28571 16 1 5: 0 .. 1 0.71429 5 5 Average exponent except 2's : 21 / 7 = 3.00000 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is weakly epimorphic with val: <7 10 17| Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 80.5215 c. M: 124.6601 c. 8: 1 1 2 1 0 2 1 N D3 SD: 36.2033 c. M:-57.8213 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 32.8246 c. M: 56.8904 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 32.6277 c. M:-63.9113 c. 11: 1 2 2 1 1 3 1 N D3 S SD: 30.3491 c. M: 47.4095 c. 12: 1 2 3 1 1 3 1 N SD: 7.0499 c. M:-11.7313 c. Todi That, Mela Shubhapantuvarali, Raga Gamakasamantam, Hemavanti, Kaam Ranjani, Multani, Harsh Minor, Chromatic Lydian inverse, Maqam Athar Kurd 39: 3 7 9 4 3 9 4 N SD: 7.1929 c. M:-11.6036 c. 41: 3 7 10 4 3 10 4 N SD: 3.7460 c. M: 5.3419 c. 53: 4 9 13 5 4 13 5 N SD: 1.3656 c. M: 1.7491 c. 65: 5 11 16 6 5 16 6 N SD: 0.5334 c. M:-0.9621 c. 183: 14 31 45 17 14 45 17 N SD: 0.5072 c. M: 1.0068 c. 248: 19 42 61 23 19 61 23 N SD: 0.4756 c. M: 0.9274 c. 299: 23 51 73 28 23 73 28 N SD: 0.4962 c. M:-0.9012 c. 301: 23 51 74 28 23 74 28 N SD: 0.5507 c. M: 1.0721 c. 311: 24 53 76 29 24 76 29 N SD: 0.5167 c. M:-1.0174 c. 313: 24 53 77 29 24 77 29 N SD: 0.4696 c. M: 0.8811 c. 352: 27 60 86 33 27 86 33 N SD: 0.4139 c. M: 0.7687 c. 364: 28 62 89 34 28 89 34 N SD: 0.3233 c. M:-0.6146 c. 376: 29 64 92 35 29 92 35 N SD: 0.3834 c. M:-0.7198 c. 417: 32 71 102 39 32 102 39 N SD: 0.2665 c. M: 0.4989 c. 429: 33 73 105 40 33 105 40 N SD: 0.2097 c. M:-0.4148 c. 482: 37 82 118 45 37 118 45 N SD: 0.1591 c. M: 0.3019 c. 494: 38 84 121 46 38 121 46 N SD: 0.1394 c. M:-0.2676 c. 547: 42 93 134 51 42 134 51 N SD: 0.0778 c. M: 0.1517 c. 612: 47 104 150 57 47 150 57 N SD: 0.0198 c. M: 0.0334 c. 1901: 146 323 466 177 146 466 177 N SD: 0.0178 c. M: 0.0340 c. 2395: 184 407 587 223 184 587 223 N SD: 0.0146 c. M:-0.0282 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: 42.9954 cents 4 x 5 x 6 x x 8 S SD: 30.0750 cents 5 x 6:7 x 8:9:10 S SD: 15.2560 cents 6 x 7:8:9:10:11:12 S SD: 22.9763 cents 7 x 8:10 x 11:13:14 SD: 14.6523 cents 8 x 10:11:12:13:15:16 SD: 18.1097 cents 9:10:11:13 x 14:17:18 SD: 19.6805 cents 10:11:12:14:15:16:19:20 SD: 11.6527 cents 11:12:13:15 x 17:21:22 SD: 15.7372 cents 12:13:14:17:18:19:23:24 SD: 9.7092 cents 14:15:17:20:21:22:26:28 SD: 8.4514 cents 15:16:18:21:23:24:28:30 SD: 7.4419 cents 16:17:19:23:24:25:30:32 SD: 6.5085 cents 17:18:20:24:26:27:32:34 SD: 5.5893 cents 20:21:24:28:30:32:38:40 SD: 5.3630 cents 22:23:26:31:33:35:41:44 SD: 3.1811 cents 32:34:38:45:48:51:60:64 SD: 2.5893 cents 38:40:45:53:57:60:71:76 SD: 2.3639 cents 50:53:59:70:75:79:94:100 SD: 2.2697 cents 52:55:62:73:78:82:98:104 SD: 2.0883 cents 54:57:64:76:81:85:101:108 SD: 1.4456 cents 72:76:85:101:108:114:135:144 SD: 1.4184 cents 74:78:88:104:111:117:139:148 SD: 0.7566 cents 96:101:114:135:144:152:180:192 SD: 0.6757 cents 128:135:152:180:192:203:240:256 SD: 0.6430 cents 146:154:173:205:219:231:274:292 SD: 0.5517 cents 150:158:178:211:225:237:281:300 SD: 0.5065 cents 160:169:190:225:240:253:300:320 SD: 0.4363 cents 182:192:216:256:273:288:341:364 SD: 0.2178 cents 256:270:304:360:384:405:480:512 SD: 0.2035 cents 328:346:389:461:492:519:615:656 SD: 0.1871 cents 402:424:477:565:603:636:754:804 SD: 0.1602 cents 440:464:522:619:660:696:825:880 SD: 0.1154 cents 584:616:693:821:876:924:1095:1168 SD: 0.0869 cents