Scala analysis: xen09-wilson-marwa-14b-02
Marwa permutation 2 from Figure 14b, Didymus 25/24 16/15 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: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 8/5 813.686286 minor sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 6/5 315.6413 minor third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 9/8 203.9100 major whole tone 4: 256/225 223.4626 Neapolitan diminished third 5: 9/8 203.9100 major whole tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 256/225 223.463 cents Neapolitan diminished third 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 2 75/64 274.582 cents classic augmented second 2: 1 5/4 386.314 cents major third 2: 3 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: 3 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 225/128 976.537 cents augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 386.3 590.2 813.7 1017.6 1088.3 1200.0 315.6 : 70.7 274.6 498.0 702.0 772.6 884.4 1200.0 386.3 : 203.9 427.4 631.3 702.0 813.7 1129.3 1200.0 590.2 : 223.5 427.4 498.0 609.8 925.4 996.1 1200.0 813.7 : 203.9 274.6 386.3 702.0 772.6 976.5 1200.0 1017.6: 70.7 182.4 498.0 568.7 772.6 996.1 1200.0 1088.3: 111.7 427.4 498.0 702.0 925.4 1129.3 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: 182.4037 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 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 .. 1017.5963 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 25/27,-133.2376 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 186.65199 cents, oct.: 1306.56394 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : EACDCAB Scale is not a Constant Structure Scale diversity : 1.566731 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / 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 : 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 Scale contains a complete diamond : 1 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 45 Scale harmonicity : 0.038265 Average absolute harmonicity : 0.221804 Specific harmonicity : 0.181990 Fundamental : 1/160, -7.3219 octaves, 1.6352 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 5.760000E+04, 15.81378 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 75.0, average 10.71429 Mersenne's string divisions : 414414 Sum of van Prooijen's expressibility: 5.88046, average 0.84007 Sum of Tenney's harmonic distance : 11.57200, average 1.65314 Vogel's harmonic complexity : 11.85714 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 101.06121, average 3.60933 Lattice compactness (without 2's) : 47.20225, average 1.68579 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.71429 15 1 3: 0 .. 2 0.85714 6 5: -1 .. 1 0.00000 6 6 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 44.6709 c. M: 75.9380 c. 8: 2 1 1 1 2 0 1 N D3 SD: 39.5810 c. M: 63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 44.0398 c. M: 84.2630 c. 10: 3 0 2 2 1 1 1 N SD: 31.2451 c. M: 57.5963 c. 11: 3 0 2 2 2 1 1 N G SD: 36.6790 c. M: 59.0410 c. 12: 3 1 2 2 2 1 1 N T3 SD: 12.8847 c. M: 17.5963 c. 19: 5 1 3 4 3 1 2 N SD: 10.9974 c. M: 21.8027 c. 22: 6 1 4 4 4 1 2 N SD: 9.4904 c. M:-18.7673 c. 28: 7 2 5 5 5 1 3 N SD: 10.3163 c. M: 16.8401 c. 31: 8 2 5 6 5 2 3 N SD: 6.2345 c. M: 11.1447 c. 34: 9 2 6 6 6 2 3 N SD: 5.0199 c. M:-9.7763 c. 41: 11 2 7 8 7 2 4 N SD: 5.4247 c. M:-6.7940 c. 53: 14 3 9 10 9 3 5 N SD: 1.3062 c. M: 1.5445 c. 118: 31 7 20 22 20 7 11 N SD: 0.3323 c. M: 0.6471 c. 289: 76 17 49 54 49 17 27 N SD: 0.3045 c. M: 0.6043 c. 323: 85 19 55 60 55 19 30 N SD: 0.2604 c. M:-0.4884 c. 376: 99 22 64 70 64 22 35 N SD: 0.2454 c. M:-0.4888 c. 441: 116 26 75 82 75 26 41 N SD: 0.1270 c. M:-0.2525 c. 494: 130 29 84 92 84 29 46 N SD: 0.1104 c. M:-0.2175 c. 559: 147 33 95 104 95 33 52 N SD: 0.0852 c. M:-0.1162 c. 612: 161 36 104 114 104 36 57 N SD: 0.0369 c. M:-0.0508 c. 1171: 308 69 199 218 199 69 109 N SD: 0.0237 c. M:-0.0410 c. 1783: 469 105 303 332 303 105 166 N SD: 0.0096 c. M:-0.0175 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: 55.8656 cents 3 x x 4:5 x x 6 S SD: 38.7176 cents 4 x 5:6 x 7 x 8 S SD: 30.4779 cents 5:6 x 7:8:9 x 10 S SD: 1.5423 cents 6:7 x 8:10:11 x 12 S SD: 25.9840 cents 7:8:9:10:11 x 13:14 SD: 17.8762 cents 8 x 10:11:13:14:15:16 SD: 11.3194 cents 9:11 x 13:14:16:17:18 SD: 13.0871 cents 10:12:13:14:16:18:19:20 S SD: 10.2973 cents 13 x 16:18:21:23:24:26 SD: 9.6131 cents 15:18:19:21:24:27:28:30 SD: 3.6274 cents 20:24:25:28:32:36:38:40 SD: 3.4561 cents 25:30:31:35:40:45:47:50 SD: 2.3651 cents 35:42:44:49:56:63:66:70 SD: 2.2772 cents 40:48:50:56:64:72:75:80 SD: 1.1016 cents 80:96:100:113:128:144:150:160 SD: 1.0968 cents 95:114:119:134:152:171:178:190 SD: 0.9298 cents 96:115:120:135:154:173:180:192 SD: 0.8248 cents 105:126:131:148:168:189:197:210 SD: 0.7601 cents 115:138:144:162:184:207:216:230 SD: 0.7443 cents 120:144:150:169:192:216:225:240 SD: 0.3661 cents 160:192:200:225:256:288:300:320 SD: 0.0000 cents