Scala analysis: xen09-wilson-marwa-09-17
Marwa permutation 17 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: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 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: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 135/128 92.1787 major chroma, major limma 6: 4096/3645 201.9563 narrow diminished third 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 512/405 405.866 cents narrow diminished fourth 2: 1 81/64 407.820 cents Pythagorean major third 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 498.0 702.0 794.1 996.1 1200.0 203.9 : 182.4 294.1 498.0 590.2 792.2 996.1 1200.0 386.3 : 111.7 315.6 407.8 609.8 813.7 1017.6 1200.0 498.0 : 203.9 296.1 498.0 702.0 905.9 1088.3 1200.0 702.0 : 92.2 294.1 498.0 702.0 884.4 996.1 1200.0 794.1 : 202.0 405.9 609.8 792.2 903.9 1107.8 1200.0 996.1 : 203.9 407.8 590.2 702.0 905.9 998.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 203.9100 cents 16/15, 111.7313 cents 135/128, 92.1787 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 1/1, 0.0000 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 1/1, 0.0000 cents 6: 996.0900 .. 1107.8213 cents 16/15, 111.7313 cents 256/243, 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 : 9/8, 203.9100 cents Average / Smallest step : 1.859741 Largest / Average step : 1.189475 Largest / Smallest step : 2.212116 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 168.75501 cents, oct.: 1181.28505 cents Scale is not proper Step pattern alph. order: ABCADEA Step pattern size order : ECBEADE Scale is not a Constant Structure Scale diversity : 1.424875 Lumma stability : 0.304006 Lumma impropriety factor : 0.016294 Rothenberg efficiency : 0.410884 redundancy: 0.589116 Efficiency x scale size : 2.876190 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 405 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.267585 Specific harmonicity : 0.179876 Fundamental : 1/2304, -11.1699 octaves, 0.1136 Hz. Guide tone : 6480, 12.6618 octaves, 1695333.663 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 363.5, average 51.92857 Mersenne's string divisions : 17698275 Sum of van Prooijen's expressibility: 6.16915, average 0.88131 Sum of Tenney's harmonic distance : 12.49078, average 1.78440 Vogel's harmonic complexity : 16.14286 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 136.43100, average 4.87254 Lattice compactness (without 2's) : 64.12690, average 2.29025 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 4 -1.00000 21 1 3: -2 .. 4 0.57143 10 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.8389 c. M:-63.0091 c. Lebeng 9: 2 1 1 1 1 1 2 N D3 I SD: 38.8937 c. M:-62.7567 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 29.4044 c. M:-45.8663 c. 12: 2 2 1 2 1 2 2 P D3 I SD: 6.0939 c. M:-13.6863 c. Major-Minor, Melodic Major, Mischung 6, Mixolydian flat 6, Mela Carukesi, Raga Charukeshi, Tarangini, Heptatonia secunda 41: 7 6 4 7 3 7 7 N SD: 2.7102 c. M: 5.8259 c. 53: 9 8 5 9 4 9 9 N SD: 0.8328 c. M: 1.6809 c. 65: 11 10 6 11 5 11 11 N SD: 0.7288 c. M:-1.3786 c. 118: 20 18 11 20 9 20 20 N SD: 0.4670 c. M: 0.9134 c. 183: 31 28 17 31 14 31 31 N SD: 0.5072 c. M: 0.6911 c. 289: 49 44 27 49 22 49 49 N SD: 0.4842 c. M: 1.0541 c. 301: 51 46 28 51 23 51 51 N SD: 0.4821 c. M: 0.7782 c. 311: 53 47 29 53 24 52 53 N SD: 0.4794 c. M:-0.7216 c. 323: 55 49 30 55 25 54 55 N SD: 0.4288 c. M:-0.9127 c. 364: 62 55 34 62 28 61 62 N SD: 0.3941 c. M: 0.5994 c. 376: 64 57 35 64 29 63 64 N SD: 0.2971 c. M:-0.5471 c. 388: 66 59 36 66 30 65 66 N SD: 0.3165 c. M:-0.7116 c. 429: 73 65 40 73 33 72 73 N SD: 0.2293 c. M: 0.2997 c. 441: 75 67 41 75 34 74 75 N SD: 0.1927 c. M:-0.4241 c. 494: 84 75 46 84 38 83 84 N SD: 0.1156 c. M:-0.1983 c. 547: 93 83 51 93 42 92 93 N SD: 0.1033 c. M: 0.2077 c. 559: 95 85 52 95 43 94 95 N SD: 0.0654 c. M:-0.1418 c. 612: 104 93 57 104 47 103 104 N SD: 0.0174 c. M: 0.0392 c. 1289: 219 196 120 219 99 217 219 N SD: 0.0249 c. M:-0.0323 c. 1783: 303 271 166 303 137 300 303 N SD: 0.0158 c. M:-0.0334 c. 1901: 323 289 177 323 146 320 323 N SD: 0.0145 c. M: 0.0254 c. 2395: 407 364 223 407 184 403 407 N SD: 0.0123 c. M:-0.0208 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: 30.0750 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 22.7808 cents 6:7 x 8:9:10:11:12 S SD: 20.3733 cents 7:8:9 x x 11:12:14 SD: 16.9959 cents 8:9:10:11:12:13:14:16 S SD: 10.8173 cents 9:10:11:12 x 14:16:18 S SD: 8.8661 cents 10:11 x 13:15:16:18:20 SD: 10.9032 cents 11:12:14:15 x 17:20:22 SD: 15.3463 cents 12:14:15:16:18:19:21:24 SD: 9.8036 cents 14:16:18:19:21:22:25:28 SD: 9.3195 cents 15:17:19:20:23:24:27:30 SD: 7.8007 cents 16:18:20:21:24:25:28:32 SD: 6.3071 cents 22:25:28:29:33:35:39:44 SD: 6.0363 cents 23:26:29:31:35:36:41:46 SD: 5.7665 cents 24:27:30:32:36:38:43:48 SD: 1.9354 cents 48:54:60:64:72:76:85:96 SD: 0.9891 cents 72:81:90:96:108:114:128:144 SD: 0.2035 cents 328:369:410:437:492:519:583:656 SD: 0.1994 cents 392:441:490:523:588:620:697:784 SD: 0.1741 cents 432:486:540:576:648:683:768:864 SD: 0.1584 cents 464:522:580:619:696:734:825:928 SD: 0.1389 cents 504:567:630:672:756:797:896:1008 SD: 0.1066 cents 576:648:720:768:864:911:1024:1152 SD: 0.0679 cents