Scala analysis: xen09-wilson-marwa-09-20
Marwa permutation 20 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 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: 135/128 92.1787 major chroma, major limma 2: 4096/3645 201.9563 narrow diminished third 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 16/15 111.7313 minor diatonic semitone 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 : 92.2 294.1 498.0 702.0 884.4 996.1 1200.0 92.2 : 202.0 405.9 609.8 792.2 903.9 1107.8 1200.0 294.1 : 203.9 407.8 590.2 702.0 905.9 998.0 1200.0 498.0 : 203.9 386.3 498.0 702.0 794.1 996.1 1200.0 702.0 : 182.4 294.1 498.0 590.2 792.2 996.1 1200.0 884.4 : 111.7 315.6 407.8 609.8 813.7 1017.6 1200.0 996.1 : 203.9 296.1 498.0 702.0 905.9 1088.3 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 : 169.86241 cents, oct.: 1189.03686 cents Scale is not proper Step pattern alph. order: ABCCDEC Step pattern size order : ADEECBE 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 Length of longest harmonic part : 2 at degree 3 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 113.6850 cents: 6 -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 135 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.261157 Specific harmonicity : 0.180045 Fundamental : 1/3456, -11.7549 octaves, 0.0757 Hz. Guide tone : 4320, 12.0768 octaves, 1130222.442 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 185.0, average 26.42857 Mersenne's string divisions : 65171400 Sum of van Prooijen's expressibility: 6.16915, average 0.88131 Sum of Tenney's harmonic distance : 12.66687, average 1.80955 Vogel's harmonic complexity : 16.71429 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 134.89066, average 4.81752 Lattice compactness (without 2's) : 64.58029, average 2.30644 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 5 0.57143 20 1 3: -3 .. 3 -0.42857 11 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.6010 c. M:-79.2499 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 39.9022 c. M:-57.8213 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 33.0066 c. M: 54.1350 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 29.8052 c. M:-47.4095 c. Orgone-7 12: 1 2 2 2 2 1 2 P D3 S SD: 7.2027 c. M:-15.6413 c. Mela Natakapriya, Jazz Minor inverse, Phrygian-Mixolydian, Dorian flat 2, Raga Natabharanam, Motaki, Ahiri Todi 29: 2 5 5 5 4 3 5 N SD: 7.1628 c. M: 15.3932 c. 34: 3 5 6 6 5 3 6 P S SD: 7.7752 c. M:-13.7036 c. 37: 3 6 6 7 5 4 6 N SD: 8.1117 c. M:-11.5585 c. 38: 3 6 7 6 6 4 6 P SD: 7.7245 c. M:-14.4363 c. 41: 3 7 7 7 6 4 7 N SD: 2.9871 c. M: 6.3099 c. 53: 4 9 9 9 8 5 9 N SD: 0.7987 c. M: 1.6127 c. 118: 9 20 20 20 18 11 20 N SD: 0.4768 c. M:-0.7803 c. 171: 13 29 29 29 26 16 29 N SD: 0.4674 c. M: 0.9506 c. 289: 22 49 49 49 44 27 49 N SD: 0.4553 c. M: 0.8292 c. 323: 25 54 55 55 49 30 55 N SD: 0.4120 c. M:-0.7005 c. 364: 28 61 62 62 55 34 62 N SD: 0.4796 c. M: 0.8422 c. 376: 29 63 64 64 57 35 64 N SD: 0.3134 c. M: 0.5180 c. 388: 30 65 66 66 59 36 66 N SD: 0.2850 c. M:-0.6048 c. 429: 33 72 73 73 65 40 73 N SD: 0.2723 c. M: 0.4426 c. 441: 34 74 75 75 67 41 75 N SD: 0.1793 c. M:-0.3383 c. 494: 38 83 84 84 75 46 84 N SD: 0.1257 c. M: 0.2079 c. 547: 42 92 93 93 83 51 93 N SD: 0.1299 c. M: 0.2636 c. 559: 43 94 95 95 85 52 95 N SD: 0.0599 c. M:-0.1290 c. 612: 47 103 104 104 93 57 104 N SD: 0.0207 c. M: 0.0450 c. 1783: 137 300 303 303 271 166 303 N SD: 0.0153 c. M:-0.0254 c. 1901: 146 320 323 323 289 177 323 N SD: 0.0157 c. M:-0.0260 c. 2395: 184 403 407 407 364 223 407 N SD: 0.0135 c. M: 0.0223 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 22.8511 cents 6 x 7:8:9:10:11:12 S SD: 9.9740 cents 7 x 8:9:11:12 x 14 SD: 25.9175 cents 8 x 9:11:12:13:14:16 SD: 19.4672 cents 9:10:11:12:14:15:16:18 S SD: 17.4629 cents 10:11:12:13:15:17:18:20 SD: 13.7952 cents 12:13:14:16:18:20:21:24 S SD: 8.6178 cents 15:16:18:20:23:25:27:30 SD: 7.4986 cents 16:17:19:21:24:27:28:32 SD: 6.5836 cents 18:19:21:24:27:30:32:36 SD: 3.9002 cents 32:34:38:43:48:53:57:64 SD: 3.1474 cents 36:38:43:48:54:60:64:72 SD: 1.9354 cents 54:57:64:72:81:90:96:108 SD: 0.2035 cents 330:348:391:440:495:550:587:660 SD: 0.1606 cents 384:405:455:512:576:640:683:768 SD: 0.1350 cents 438:462:519:584:657:730:779:876 SD: 0.1210 cents 492:519:583:656:738:820:875:984 SD: 0.1144 cents 546:576:647:728:819:910:971:1092 SD: 0.1125 cents 588:620:697:784:882:980:1045:1176 SD: 0.1080 cents