Scala analysis: xen09-wilson-marwa-14a-03
Marwa permutation 3 from Figure 14a, Didymus 16/15 25/24 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 32/25 427.372572 classic diminished fourth 3: 36/25 631.282574 classic diminished fifth 4: 8/5 813.686286 minor sixth 5: 128/75 925.417571 diminished seventh 6: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 6/5 315.6413 minor third 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 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 6/5 315.641 cents minor third 2: 1 75/64 274.582 cents classic augmented second 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 32/25 427.373 cents classic diminished fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 36/25 631.283 cents classic diminished fifth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 25/16 772.627 cents classic augmented 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: 1 128/75 925.418 cents diminished seventh 6: 1 5/3 884.359 cents major sixth, BP 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 48/25 1129.328 cents classic diminished octave 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 : 315.6 427.4 631.3 813.7 925.4 1129.3 1200.0 315.6 : 111.7 315.6 498.0 609.8 813.7 884.4 1200.0 427.4 : 203.9 386.3 498.0 702.0 772.6 1088.3 1200.0 631.3 : 182.4 294.1 498.0 568.7 884.4 996.1 1200.0 813.7 : 111.7 315.6 386.3 702.0 813.7 1017.6 1200.0 925.4 : 203.9 274.6 590.2 702.0 905.9 1088.3 1200.0 1129.3: 70.7 386.3 498.0 702.0 884.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 772.6274 .. 925.4176 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 125/128,-41.0589 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 186.58595 cents, oct.: 1306.10163 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EBDCBDA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.549589 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.425850 redundancy: 0.574150 Efficiency x scale size : 2.980952 Number of different interval sizes : 24 = 4.00000 / 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: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 75 Scale harmonicity : 0.035971 Average absolute harmonicity : 0.201064 Specific harmonicity : 0.190741 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 1152, 10.1699 octaves, 301392.651 Hz. Exponens Consonantiae : 8.640000E+04, 16.39874 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 210.5, average 30.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.46682, average 1.06669 Sum of Tenney's harmonic distance : 16.29900, average 2.32843 Vogel's harmonic complexity : 10.42857 Wille's k value : 37 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 95.30665, average 3.40381 Lattice compactness (without 2's) : 46.55854, average 1.66281 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.28571 23 1 3: -1 .. 2 0.42857 5 5: -2 .. 0 -1.42857 10 6 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 101.9933 c. M: 144.2127 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 42.6449 c. M: 79.3276 c. 9: 2 1 2 1 1 1 1 N D3 S SD: 35.0024 c. M: 62.6609 c. 11: 3 1 2 1 1 2 1 N T3 S SD: 32.7644 c. M: 52.6903 c. 12: 3 1 2 2 1 2 1 P D3 SD: 22.8847 c. M: 31.2826 c. Aeolian flat 1 13: 3 2 2 2 1 2 1 N SD: 22.8440 c. M: 38.7182 c. 15: 4 1 3 2 2 2 1 N SD: 18.1836 c. M:-34.5824 c. 18: 5 1 3 3 2 3 1 N SD: 18.1537 c. M: 31.2826 c. 19: 5 2 3 3 2 3 1 N SD: 10.7553 c. M:-21.9508 c. 22: 6 2 4 3 2 4 1 N SD: 12.1950 c. M:-23.2629 c. 23: 6 2 4 4 2 4 1 N SD: 12.5849 c. M:-21.0963 c. 28: 7 3 5 4 3 4 2 N SD: 11.4068 c. M:-17.4396 c. 30: 8 3 5 4 3 5 2 N SD: 8.9292 c. M: 13.6863 c. 31: 8 3 5 5 3 5 2 N SD: 5.8492 c. M: 11.9277 c. 34: 9 3 6 5 3 6 2 N SD: 3.7601 c. M: 7.7705 c. 53: 14 5 9 8 5 9 3 N SD: 2.2284 c. M:-2.8843 c. 84: 22 8 14 13 8 14 5 N SD: 1.7527 c. M:-3.1539 c. 87: 23 8 15 13 8 15 5 N SD: 1.5770 c. M:-3.2002 c. 118: 31 11 20 18 11 20 7 N SD: 0.3953 c. M: 0.7741 c. 289: 76 27 49 44 27 49 17 N SD: 0.2497 c. M:-0.5340 c. 323: 85 30 55 49 30 55 19 N SD: 0.1901 c. M: 0.3402 c. 441: 116 41 75 67 41 75 26 N SD: 0.1194 c. M: 0.2475 c. 559: 147 52 95 85 52 95 33 N SD: 0.1400 c. M: 0.1940 c. 612: 161 57 104 93 57 104 36 N SD: 0.0656 c. M:-0.0900 c. 730: 192 68 124 111 68 124 43 N SD: 0.0335 c. M:-0.0619 c. 1053: 277 98 179 160 98 179 62 N SD: 0.0352 c. M: 0.0614 c. 1171: 308 109 199 178 109 199 69 N SD: 0.0334 c. M: 0.0546 c. 1783: 469 166 303 271 166 303 105 N SD: 0.0072 c. M:-0.0130 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 35.3362 cents 3 x 4 x x 5 x 6 S SD: 27.2446 cents 4 x 5:6 x 7 x 8 S SD: 23.1364 cents 5:6 x 7:8:9 x 10 S SD: 20.8571 cents 6:7:8:9 x 10 x 12 S SD: 23.7095 cents 7:8:9:10:11:12:13:14 H SD: 15.4773 cents 8 x 10:12:13:14:15:16 S SD: 17.4571 cents 9:11:12:13:14:15:17:18 SD: 14.9123 cents 10:12:13:14:16:17:19:20 SD: 8.4196 cents 11:13:14:16:18:19:21:22 SD: 8.0068 cents 14:17:18:20:22:24:27:28 SD: 5.9958 cents 20:24:26:29:32:34:38:40 SD: 5.0276 cents 21:25:27:30:34:36:40:42 SD: 4.7586 cents 25:30:32:36:40:43:48:50 SD: 1.9247 cents 50:60:64:72:80:85:96:100 SD: 0.9680 cents 75:90:96:108:120:128:144:150 S SD: 0.0000 cents