Scala analysis: xen09-wilson-marwa-09-04
Marwa permutation 4 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: 3645/2048 998.043719 wide augmented sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4096/3645 201.9563 narrow diminished third 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: 9/8 203.9100 major whole tone 7: 4096/3645 201.9563 narrow diminished third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 4096/3645 201.956 cents narrow diminished third 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 1215/1024 296.089 cents wide augmented second 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: 2 2048/1215 903.911 cents narrow diminished seventh 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 3645/2048 998.044 cents wide augmented sixth 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 92.2 296.1 590.2 702.0 794.1 998.0 1200.0 92.2 : 203.9 498.0 609.8 702.0 905.9 1107.8 1200.0 296.1 : 294.1 405.9 498.0 702.0 903.9 996.1 1200.0 590.2 : 111.7 203.9 407.8 609.8 702.0 905.9 1200.0 702.0 : 92.2 296.1 498.0 590.2 794.1 1088.3 1200.0 794.1 : 203.9 405.9 498.0 702.0 996.1 1107.8 1200.0 998.0 : 202.0 294.1 498.0 792.2 903.9 996.1 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 .. 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 : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 168.72699 cents, oct.: 1181.08891 cents Scale is not proper Step pattern alph. order: ABCDABE Step pattern size order : ADEBADC Scale is not a Constant Structure Scale diversity : 1.330644 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 : 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 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.211811 Specific harmonicity : 0.139636 Fundamental : 1/2048, -11.0000 octaves, 0.1277 Hz. Guide tone : 7290, 12.8317 octaves, 1907250.371 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 4470.5, average 638.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.51440, average 1.93063 Sum of Tenney's harmonic distance : 26.45869, average 3.77981 Vogel's harmonic complexity : 17.71429 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 176.69700, average 6.31061 Lattice compactness (without 2's) : 79.44115, average 2.83718 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 1 -5.85714 43 1 3: 0 .. 6 3.00000 21 1 5: 0 .. 1 0.71429 5 5 Average exponent except 2's : 26 / 7 = 3.71429 Average absolute exponent except 2's: 26 / 7 = 3.71429
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 93.8656 c. M: 140.9009 c. 8: 1 1 2 1 0 2 1 N D3 SD: 38.5630 c. M:-57.8213 c. 10: 1 1 3 1 1 1 2 N T3 SD: 33.5776 c. M: 56.0887 c. 12: 1 2 3 1 1 2 2 N SD: 5.5305 c. M:-9.7763 c. Mela Bhavapriya, Raga Bhavani, Kalamurti, Neveseri ascending: Greece 41: 3 7 10 4 3 7 7 N SD: 3.3430 c. M: 4.8579 c. 53: 4 9 13 5 4 9 9 N SD: 1.4232 c. M: 1.8173 c. 65: 5 11 16 6 5 11 11 N SD: 0.5759 c. M: 1.1206 c. 207: 16 35 51 19 16 35 35 N SD: 0.6367 c. M:-1.0806 c. 272: 21 46 67 25 21 46 46 N SD: 0.6074 c. M: 0.9849 c. 311: 24 53 76 29 24 53 52 N SD: 0.7137 c. M:-1.3132 c. 313: 24 53 77 29 24 53 53 N SD: 0.6298 c. M: 1.2386 c. 337: 26 57 83 31 26 57 57 N SD: 0.5937 c. M: 1.0111 c. 340: 26 58 83 32 26 58 57 N SD: 0.4990 c. M: 0.8120 c. 352: 27 60 86 33 27 60 59 N SD: 0.4277 c. M:-0.8199 c. 364: 28 62 89 34 28 62 61 N SD: 0.4375 c. M:-0.8574 c. 376: 29 64 92 35 29 64 63 N SD: 0.5106 c. M:-0.8925 c. 393: 30 67 96 37 30 67 66 N SD: 0.4667 c. M: 0.9107 c. 405: 31 69 99 38 31 69 68 N SD: 0.3388 c. M: 0.5941 c. 417: 32 71 102 39 32 71 70 N SD: 0.2715 c. M:-0.5174 c. 429: 33 73 105 40 33 73 72 N SD: 0.2914 c. M:-0.5577 c. 470: 36 80 115 44 36 80 79 N SD: 0.2297 c. M: 0.4365 c. 482: 37 82 118 45 37 82 81 N SD: 0.1576 c. M:-0.2965 c. 494: 38 84 121 46 38 84 83 N SD: 0.1887 c. M:-0.3368 c. 535: 41 91 131 50 41 91 90 N SD: 0.1597 c. M: 0.3172 c. 547: 42 93 134 51 42 93 92 N SD: 0.0715 c. M:-0.1281 c. 612: 47 104 150 57 47 104 103 N SD: 0.0154 c. M: 0.0276 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 7:8 S SD: 23.7095 cents 5 x 6:7 x 8:9:10 S SD: 6.9466 cents 6 x 7:8:9:10:11:12 S SD: 23.6437 cents 7 x 8:10 x 11:12:14 S SD: 19.2942 cents 8 x 10:11:12:13:14:16 S SD: 18.7530 cents 9:10:11:13 x 14:16:18 SD: 19.5676 cents 10:11:12:14:15:16:18:20 S SD: 11.5263 cents 11:12:13:15 x 17:20:22 SD: 16.0798 cents 12:13:14:17:18:19:21:24 SD: 9.0633 cents 14:15:17:20:21:22:25:28 SD: 8.1549 cents 15:16:18:21:23:24:27:30 SD: 7.8721 cents 16:17:19:23:24:25:28:32 SD: 7.7319 cents 17:18:20:24:26:27:30:34 SD: 5.8933 cents 20:21:24:28:30:32:36:40 S SD: 5.0827 cents 22:23:26:31:33:35:39:44 SD: 2.9707 cents 32:34:38:45:48:51:57:64 SD: 2.5973 cents 36:38:43:51:54:57:64:72 SD: 2.4900 cents 50:53:59:70:75:79:89:100 SD: 2.1723 cents 52:55:62:73:78:82:93:104 SD: 2.0511 cents 54:57:64:76:81:85:96:108 SD: 1.3393 cents 74:78:88:104:111:117:132:148 SD: 0.8260 cents 96:101:114:135:144:152:171:192 SD: 0.7057 cents 108:114:128:152:162:171:192:216 SD: 0.5291 cents 146:154:173:205:219:231:260:292 SD: 0.5236 cents 150:158:178:211:225:237:267:300 SD: 0.4573 cents 182:192:216:256:273:288:324:364 SD: 0.1350 cents 440:464:522:619:660:696:783:880 SD: 0.1201 cents 514:542:610:723:771:813:915:1028 SD: 0.1200 cents 586:618:695:824:879:927:1043:1172 SD: 0.1130 cents