Scala analysis: xen09-wilson-marwa-11a-01
Marwa permutation 1 from Figure 11a, 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: 32/27 294.134997 Pythagorean minor third 2: 4/3 498.044999 perfect fourth 3: 64/45 609.776284 2nd tritone 4: 128/81 792.179997 Pythagorean minor sixth 5: 16/9 996.089998 Pythagorean minor seventh 6: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 32/27 294.1350 Pythagorean minor third 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma
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 : 294.1 498.0 609.8 792.2 996.1 1107.8 1200.0 294.1 : 203.9 315.6 498.0 702.0 813.7 905.9 1200.0 498.0 : 111.7 294.1 498.0 609.8 702.0 996.1 1200.0 609.8 : 182.4 386.3 498.0 590.2 884.4 1088.3 1200.0 792.2 : 203.9 315.6 407.8 702.0 905.9 1017.6 1200.0 996.1 : 111.7 203.9 498.0 702.0 813.7 996.1 1200.0 1107.8: 92.2 386.3 590.2 702.0 884.4 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 187.96894 cents, oct.: 1315.78258 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EDBCDBA 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 3 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 : 0.222284 Specific harmonicity : 0.208831 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 1.036800E+05, 16.66178 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 401.5, average 57.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.55476, average 1.22211 Sum of Tenney's harmonic distance : 18.48875, average 2.64125 Vogel's harmonic complexity : 13.85714 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 114.36092, average 4.08432 Lattice compactness (without 2's) : 53.92568, average 1.92592 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.71429 33 1 3: -4 .. 0 -2.14286 15 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-17 / 7 =-2.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 110.3115 c. M: 155.1879 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 48.9811 c. M: 96.0900 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 38.9840 c. M: 72.1800 c. 12: 3 2 1 2 2 1 1 N SD: 6.2268 c. M: 9.7763 c. 29: 7 5 3 4 5 3 2 N SD: 6.2648 c. M:-10.9134 c. 41: 10 7 4 6 7 4 3 N SD: 2.6661 c. M:-4.8579 c. 53: 13 9 5 8 9 5 4 N SD: 0.8557 c. M:-1.6127 c. 118: 29 20 11 18 20 11 9 N SD: 0.6107 c. M:-1.0403 c. 171: 42 29 16 26 29 16 13 N SD: 0.6180 c. M:-0.9506 c. 289: 71 49 27 44 49 27 22 N SD: 0.6059 c. M:-0.8996 c. 323: 79 55 30 49 55 30 25 N SD: 0.5451 c. M: 0.8487 c. 364: 89 62 34 55 62 34 28 N SD: 0.5068 c. M: 0.9712 c. 376: 92 64 35 57 64 35 29 N SD: 0.3919 c. M: 0.6906 c. 388: 95 66 36 59 66 36 30 N SD: 0.3696 c. M: 0.6048 c. 429: 105 73 40 65 73 40 33 N SD: 0.2999 c. M: 0.5716 c. 441: 108 75 41 67 75 41 34 N SD: 0.2388 c. M: 0.3433 c. 494: 121 84 46 75 84 46 38 N SD: 0.1532 c. M: 0.2772 c. 547: 134 93 51 83 93 51 42 N SD: 0.1223 c. M: 0.2239 c. 559: 137 95 52 85 95 52 43 N SD: 0.0708 c. M: 0.1290 c. 612: 150 104 57 93 104 57 47 N SD: 0.0179 c. M:-0.0276 c. 1783: 437 303 166 271 303 166 137 N SD: 0.0202 c. M: 0.0319 c. 1901: 466 323 177 289 323 177 146 N SD: 0.0192 c. M:-0.0346 c. 2395: 587 407 223 364 407 223 184 N SD: 0.0163 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 4 x 5 x x 6 S SD: 30.7262 cents 4:5 x x 6:7 x 8 S SD: 32.9591 cents 5:6 x 7:8:9 x 10 S SD: 9.2323 cents 6:7:8 x 9:11 x 12 SD: 21.6535 cents 7:8:9:10:11:12:13:14 H SD: 16.5061 cents 8:9:11 x 13:14:15:16 SD: 20.0289 cents 9:11:12:13:14:16:17:18 SD: 9.4196 cents 10:12:13:14:16:18:19:20 S SD: 9.1065 cents 12:14:16:17:19:21:23:24 SD: 6.2043 cents 17:20:23:24:27:30:32:34 SD: 5.2837 cents 21:25:28:30:33:37:40:42 SD: 3.2367 cents 31:37:41:44:49:55:59:62 SD: 2.8898 cents 33:39:44:47:52:59:63:66 SD: 2.4172 cents 36:43:48:51:57:64:68:72 SD: 2.4106 cents 38:45:51:54:60:68:72:76 SD: 2.3294 cents 45:53:60:64:71:80:85:90 SD: 1.8684 cents 48:57:64:68:76:85:91:96 SD: 1.5308 cents 54:64:72:77:85:96:102:108 SD: 1.5125 cents 59:70:79:84:93:105:112:118 SD: 1.3251 cents 66:78:88:94:104:117:125:132 SD: 1.3050 cents 69:82:92:98:109:123:131:138 SD: 1.0523 cents 76:90:101:108:120:135:144:152 SD: 0.9333 cents 81:96:108:115:128:144:154:162 SD: 0.7736 cents 114:135:152:162:180:203:216:228 SD: 0.5751 cents 135:160:180:192:213:240:256:270 SD: 0.3867 cents 216:256:288:307:341:384:410:432 SD: 0.3776 cents 222:263:296:316:351:395:421:444 SD: 0.3396 cents 243:288:324:346:384:432:461:486 SD: 0.3056 cents 270:320:360:384:427:480:512:540 SD: 0.1931 cents 384:455:512:546:607:683:728:768 SD: 0.1767 cents 405:480:540:576:640:720:768:810 SD: 0.0000 cents