Scala analysis: xen09-wilson-marwa-11a-10
Marwa permutation 10 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: 4096/3645 201.956281 narrow diminished third 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean minor sixth 5: 2048/1215 903.911282 narrow diminished seventh 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 4096/3645 201.9563 narrow diminished third 2: 135/128 92.1787 major chroma, major limma 3: 9/8 203.9100 major whole tone 4: 32/27 294.1350 Pythagorean minor third 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 9/8 203.9100 major whole tone
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 : 202.0 294.1 498.0 792.2 903.9 996.1 1200.0 202.0 : 92.2 296.1 590.2 702.0 794.1 998.0 1200.0 294.1 : 203.9 498.0 609.8 702.0 905.9 1107.8 1200.0 498.0 : 294.1 405.9 498.0 702.0 903.9 996.1 1200.0 792.2 : 111.7 203.9 407.8 609.8 702.0 905.9 1200.0 903.9 : 92.2 296.1 498.0 590.2 794.1 1088.3 1200.0 996.1 : 203.9 405.9 498.0 702.0 996.1 1107.8 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 : 173.92270 cents, oct.: 1217.45888 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : CADEBAD 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 : 0.216651 Specific harmonicity : 0.148102 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 4096, 12.0000 octaves, 1071618.315 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 5653.5, average 807.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.41749, average 1.63107 Sum of Tenney's harmonic distance : 24.06075, average 3.43725 Vogel's harmonic complexity : 18.57143 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 170.15740, average 6.07705 Lattice compactness (without 2's) : 78.91970, average 2.81856 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 12 6.00000 42 1 3: -6 .. 0 -3.00000 21 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-23 / 7 =-3.28571 Average absolute exponent except 2's: 23 / 7 = 3.28571
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 39.6990 c. M:-64.9629 c. 9: 2 0 2 2 1 1 1 N T3 SD: 41.5676 c. M:-70.5767 c. 11: 2 1 2 2 1 1 2 P D3 S SD: 28.2840 c. M:-47.4095 c. 12: 2 1 2 3 1 1 2 N SD: 4.3718 c. M:-7.8200 c. 29: 5 2 5 7 3 2 5 N SD: 4.3539 c. M:-6.4335 c. 41: 7 3 7 10 4 3 7 N SD: 1.9699 c. M:-3.4058 c. 53: 9 4 9 13 5 4 9 N SD: 0.9637 c. M:-1.8173 c. 65: 11 5 11 16 6 5 11 N SD: 0.9969 c. M:-1.6662 c. 118: 20 9 20 29 11 9 20 N SD: 0.8833 c. M:-1.4335 c. 171: 29 13 29 42 16 13 29 N SD: 0.8820 c. M:-1.5525 c. 183: 31 14 31 45 17 14 31 N SD: 0.9064 c. M:-1.3224 c. 224: 38 17 38 55 21 17 38 N SD: 0.8911 c. M:-1.6151 c. 289: 49 22 49 71 27 22 49 N SD: 0.8795 c. M:-1.5039 c. 311: 52 24 53 76 29 24 53 N SD: 0.8771 c. M: 1.3132 c. 323: 54 25 55 79 30 25 55 N SD: 0.7932 c. M: 1.3371 c. 335: 56 26 57 82 31 26 57 N SD: 0.7455 c. M: 1.3593 c. 347: 58 27 59 85 32 27 59 N SD: 0.7326 c. M: 1.3799 c. 352: 59 27 60 86 33 27 60 N SD: 0.7515 c. M: 1.2709 c. 359: 60 28 61 88 33 28 61 N SD: 0.7493 c. M: 1.4043 c. 364: 61 28 62 89 34 28 62 N SD: 0.6416 c. M: 0.9712 c. 376: 63 29 64 92 35 29 64 N SD: 0.5617 c. M: 0.8925 c. 388: 65 30 66 95 36 30 66 N SD: 0.5167 c. M: 0.9254 c. 400: 67 31 68 98 37 31 68 N SD: 0.5079 c. M: 0.9563 c. 417: 70 32 71 102 39 32 71 N SD: 0.4790 c. M: 0.8131 c. 429: 72 33 73 105 40 33 73 N SD: 0.3956 c. M: 0.5716 c. 441: 74 34 75 108 41 34 75 N SD: 0.3456 c. M: 0.5957 c. 453: 76 35 77 111 42 35 77 N SD: 0.3358 c. M: 0.6318 c. 482: 81 37 82 118 45 37 82 N SD: 0.2800 c. M: 0.4788 c. 494: 83 38 84 121 46 38 84 N SD: 0.2168 c. M: 0.3368 c. 506: 85 39 86 124 47 39 86 N SD: 0.1999 c. M: 0.3753 c. 547: 92 42 93 134 51 42 93 N SD: 0.1285 c. M: 0.2239 c. 559: 94 43 95 137 52 43 95 N SD: 0.0901 c. M: 0.1674 c. 612: 103 47 104 150 57 47 104 N SD: 0.0127 c. M: 0.0231 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 x 4 x 5 x 6 S SD: 6.5175 cents 4 x 5 x 6 x 7:8 S SD: 32.9591 cents 5 x 6:7:8 x 9:10 S SD: 18.4632 cents 6 x 7:8:9:10:11:12 S SD: 18.3365 cents 7:8 x 9:11:12 x 14 SD: 15.1859 cents 8:9 x 11:13 x 14:16 SD: 15.3918 cents 9:10:11:12:14:15:16:18 S SD: 9.4177 cents 13:15 x 17:21:22:23:26 SD: 11.5384 cents 14:16:17:19:22:24:25:28 SD: 9.6502 cents 15:17:18:20:24:25:27:30 SD: 6.3677 cents 16:18:19:21:25:27:28:32 SD: 6.2073 cents 17:19:20:23:27:29:30:34 SD: 5.6401 cents 22:25:26:29:35:37:39:44 SD: 4.4382 cents 26:29:31:35:41:44:46:52 SD: 3.7221 cents 31:35:37:41:49:52:55:62 SD: 3.1763 cents 32:36:38:43:51:54:57:64 SD: 2.9587 cents 33:37:39:44:52:56:59:66 SD: 2.4551 cents 42:47:50:56:66:71:75:84 SD: 2.4333 cents 48:54:57:64:76:81:85:96 SD: 1.2484 cents 81:91:96:108:128:137:144:162 SD: 0.8460 cents 112:126:133:149:177:189:199:224 SD: 0.8447 cents 114:128:135:152:180:192:203:228 SD: 0.5751 cents 153:172:181:204:242:258:272:306 SD: 0.5277 cents 162:182:192:216:256:273:288:324 SD: 0.0854 cents