Scala analysis: xen09-wilson-marwa-14b-06
Marwa permutation 6 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: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 5/3 884.358713 major sixth, BP sixth 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: 16/15 111.7313 minor diatonic semitone 4: 6/5 315.6413 minor third 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 9/8 203.9100 major whole tone 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: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 75/64 274.582 cents classic augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 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: 2 25/16 772.627 cents classic augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 315.6 386.3 498.0 813.7 884.4 1088.3 1200.0 315.6 : 70.7 182.4 498.0 568.7 772.6 884.4 1200.0 386.3 : 111.7 427.4 498.0 702.0 813.7 1129.3 1200.0 498.0 : 315.6 386.3 590.2 702.0 1017.6 1088.3 1200.0 813.7 : 70.7 274.6 386.3 702.0 772.6 884.4 1200.0 884.4 : 203.9 315.6 631.3 702.0 813.7 1129.3 1200.0 1088.3: 111.7 427.4 498.0 609.8 925.4 996.1 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: 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 179.91825 cents, oct.: 1259.42774 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DABDACB Scale is not a Constant Structure Scale diversity : 1.537490 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 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 : 4 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 0.0 701.955 1129.328 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Scale contains a complete diamond : 1 5 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is differentially coherent in interval class 1 Scale is 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 : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.041436 Average absolute harmonicity : 0.247460 Specific harmonicity : 0.211360 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.440000E+04, 13.81378 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 37.0, average 5.28571 Mersenne's string divisions : 1657656 Sum of van Prooijen's expressibility: 4.44909, average 0.63558 Sum of Tenney's harmonic distance : 9.01569, average 1.28796 Vogel's harmonic complexity : 12.00000 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 81.67188, average 2.91685 Lattice compactness (without 2's) : 41.32248, average 1.47580 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 12 1 3: -1 .. 1 0.00000 4 1 5: -1 .. 1 0.14286 5 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 36.0275 c. M: 59.6973 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 31.3587 c. M: 48.9746 c. 10: 3 0 1 3 0 2 1 N SD: 28.5712 c. M:-44.3587 c. 12: 3 1 1 3 1 2 1 N T3 S SD: 11.9844 c. M: 15.6413 c. 19: 5 1 2 5 1 3 2 N SD: 7.3034 c. M: 14.5845 c. 22: 6 1 2 6 1 4 2 N SD: 7.2594 c. M:-11.6314 c. 31: 8 2 3 8 2 5 3 N SD: 4.1152 c. M: 5.9639 c. 34: 9 2 3 9 2 6 3 N SD: 3.0488 c. M:-5.8489 c. 53: 14 3 5 14 3 9 5 N SD: 1.1796 c. M: 1.4763 c. 87: 23 5 8 23 5 15 8 N SD: 1.1524 c. M:-1.6001 c. 118: 31 7 11 31 7 20 11 N SD: 0.2441 c. M:-0.3870 c. 289: 76 17 27 76 17 49 27 N SD: 0.1898 c. M: 0.3794 c. 323: 85 19 30 85 19 55 30 N SD: 0.1574 c. M:-0.2762 c. 441: 116 26 41 116 26 75 41 N SD: 0.0830 c. M:-0.1667 c. 494: 130 29 46 130 29 84 46 N SD: 0.0935 c. M: 0.1482 c. 559: 147 33 52 147 33 95 52 N SD: 0.0750 c. M:-0.1034 c. 612: 161 36 57 161 36 104 57 N SD: 0.0344 c. M:-0.0450 c. 730: 192 43 68 192 43 124 68 N SD: 0.0277 c. M: 0.0495 c. 1171: 308 69 109 308 69 199 109 N SD: 0.0189 c. M:-0.0319 c. 1783: 469 105 166 469 105 303 166 N SD: 0.0059 c. M:-0.0095 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: 55.8656 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 35.0166 cents 5:6 x 7:8 x 9:10 S SD: 22.0266 cents 6:7 x 8 x 10:11:12 S SD: 12.4775 cents 7:8:9 x 11:12:13:14 SD: 19.1045 cents 8 x 10:11:13 x 15:16 SD: 11.9306 cents 9:11 x 12:14:15:17:18 SD: 9.9316 cents 10:12 x 13:16:17:19:20 SD: 10.0309 cents 11:13:14:15 x 18:21:22 SD: 11.9810 cents 12:14:15:16:19:20:23:24 SD: 9.2085 cents 13 x 16:17:21:22:24:26 SD: 9.9221 cents 15:18:19:20:24:25:28:30 SD: 3.4561 cents 24:29:30:32:38:40:45:48 SD: 3.1042 cents 33:40:41:44:53:55:62:66 SD: 3.0923 cents 35:42:44:47:56:58:66:70 SD: 3.0132 cents 36:43:45:48:58:60:68:72 SD: 2.7528 cents 39:47:49:52:62:65:73:78 SD: 2.3284 cents 40:48:50:53:64:67:75:80 SD: 1.9814 cents 45:54:56:60:72:75:84:90 SD: 1.5580 cents 60:72:75:80:96:100:113:120 SD: 1.0968 cents 75:90:94:100:120:125:141:150 SD: 0.9315 cents 96:115:120:128:154:160:180:192 SD: 0.7736 cents 105:126:131:140:168:175:197:210 SD: 0.4970 cents 120:144:150:160:192:200:225:240 S SD: 0.0000 cents