Scala analysis: xen09-wilson-marwa-11a-09
Marwa permutation 9 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: 512/405 405.866283 narrow diminished fourth 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: 9/8 203.9100 major whole tone 3: 135/128 92.1787 major chroma, major limma 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: 2 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 3 512/405 405.866 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: 3 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 2048/1215 903.911 cents narrow diminished seventh 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 202.0 405.9 498.0 792.2 903.9 996.1 1200.0 202.0 : 203.9 296.1 590.2 702.0 794.1 998.0 1200.0 405.9 : 92.2 386.3 498.0 590.2 794.1 996.1 1200.0 498.0 : 294.1 405.9 498.0 702.0 903.9 1107.8 1200.0 792.2 : 111.7 203.9 407.8 609.8 813.7 905.9 1200.0 903.9 : 92.2 296.1 498.0 702.0 794.1 1088.3 1200.0 996.1 : 203.9 405.9 609.8 702.0 996.1 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 .. 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 : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 175.51886 cents, oct.: 1228.63201 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : CDAEBAD Scale is not a Constant Structure Scale diversity : 1.365334 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 5 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 Formal octave complements present : 1 = 14.2857% 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 : 0.211143 Specific harmonicity : 0.138528 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 : 6082.5, average 868.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.59358, average 1.79908 Sum of Tenney's harmonic distance : 26.44096, average 3.77728 Vogel's harmonic complexity : 18.00000 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 178.12190, average 6.36150 Lattice compactness (without 2's) : 81.16591, average 2.89878 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 12 6.57143 46 1 3: -6 .. 0 -3.14286 22 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-25 / 7 =-3.57143 Average absolute exponent except 2's: 25 / 7 = 3.57143
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 42.4741 c. M:-64.9629 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 40.3113 c. M:-70.5767 c. 11: 2 2 1 2 1 1 2 N D3 SD: 27.8565 c. M:-47.4095 c. 12: 2 2 1 3 1 1 2 N T3 SD: 4.3720 c. M:-7.8200 c. 41: 7 7 3 10 4 3 7 N SD: 2.3960 c. M:-3.8898 c. 53: 9 9 4 13 5 4 9 N SD: 1.1517 c. M:-1.8173 c. 65: 11 11 5 16 6 5 11 N SD: 0.8846 c. M:-1.6662 c. 118: 20 20 9 29 11 9 20 N SD: 0.9013 c. M:-1.4335 c. 183: 31 31 14 45 17 14 31 N SD: 0.8728 c. M:-1.3224 c. 248: 42 42 19 61 23 19 42 N SD: 0.8678 c. M:-1.3684 c. 304: 51 52 23 75 28 23 52 N SD: 0.8236 c. M: 1.3532 c. 308: 52 52 24 75 29 24 52 N SD: 0.8134 c. M:-1.3126 c. 311: 52 53 24 76 29 24 53 N SD: 0.8550 c. M: 1.3132 c. 316: 53 54 24 78 29 24 54 N SD: 0.8097 c. M:-1.4909 c. 320: 54 54 25 78 30 25 54 N SD: 0.7948 c. M:-1.4100 c. 340: 57 58 26 83 32 26 58 N SD: 0.7634 c. M: 1.5918 c. 345: 58 59 26 85 32 26 59 N SD: 0.7845 c. M: 1.3074 c. 349: 59 59 27 85 33 27 59 N SD: 0.7726 c. M: 1.3491 c. 352: 59 60 27 86 33 27 60 N SD: 0.6632 c. M: 1.2709 c. 357: 60 61 27 88 33 27 61 N SD: 0.7270 c. M: 1.1320 c. 361: 61 61 28 88 34 28 61 N SD: 0.7114 c. M:-1.1399 c. 364: 61 62 28 89 34 28 62 N SD: 0.5963 c. M: 0.9712 c. 376: 63 64 29 92 35 29 64 N SD: 0.5657 c. M: 0.8925 c. 405: 68 69 31 99 38 31 69 N SD: 0.5031 c. M: 1.0689 c. 417: 70 71 32 102 39 32 71 N SD: 0.4220 c. M: 0.8131 c. 429: 72 73 33 105 40 33 73 N SD: 0.3753 c. M: 0.5716 c. 441: 74 75 34 108 41 34 75 N SD: 0.3683 c. M: 0.5957 c. 470: 79 80 36 115 44 36 80 N SD: 0.3175 c. M: 0.6906 c. 482: 81 82 37 118 45 37 82 N SD: 0.2459 c. M: 0.4788 c. 494: 83 84 38 121 46 38 84 N SD: 0.2155 c. M: 0.3368 c. 535: 90 91 41 131 50 41 91 N SD: 0.1834 c. M: 0.4043 c. 547: 92 93 42 134 51 42 93 N SD: 0.1119 c. M: 0.2239 c. 559: 94 95 43 137 52 43 95 N SD: 0.1038 c. M: 0.1674 c. 600: 101 102 46 147 56 46 102 N SD: 0.1001 c. M: 0.1800 c. 612: 103 104 47 150 57 47 104 N SD: 0.0125 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: 24.0653 cents 5 x 6:7:8 x 9:10 S SD: 25.4561 cents 6:7 x 8:9:10:11:12 S SD: 20.7998 cents 7:8:9 x 11:12 x 14 SD: 10.3051 cents 8:9:10:11:13 x 14:16 SD: 13.2340 cents 9:10:11:12:14:15:16:18 S SD: 10.0258 cents 10:11 x 13:16:17:18:20 SD: 11.0913 cents 12:13:15:16:19:20:21:24 SD: 10.6300 cents 14:16:18:19:22:24:25:28 SD: 8.6347 cents 15:17:19:20:24:25:27:30 SD: 5.5984 cents 19:21:24:25:30:32:34:38 SD: 5.5029 cents 22:25:28:29:35:37:39:44 SD: 4.6870 cents 23:26:29:31:36:39:41:46 SD: 4.2353 cents 26:29:33:35:41:44:46:52 SD: 3.5531 cents 31:35:39:41:49:52:55:62 SD: 2.9174 cents 33:37:42:44:52:56:59:66 SD: 2.8807 cents 39:44:49:52:62:66:69:78 SD: 2.8077 cents 41:46:52:55:65:69:73:82 SD: 1.9973 cents 48:54:61:64:76:81:85:96 SD: 1.7327 cents 57:64:72:76:90:96:101:114 SD: 0.9109 cents 90:101:114:120:142:152:160:180 SD: 0.8519 cents 105:118:133:140:166:177:187:210 SD: 0.6636 cents 114:128:144:152:180:192:203:228 SD: 0.5751 cents 162:182:205:216:256:273:288:324 SD: 0.2561 cents 315:354:398:420:498:531:560:630 SD: 0.1784 cents 405:455:512:540:640:683:720:810 SD: 0.1350 cents 477:536:603:636:754:804:848:954 SD: 0.0746 cents