Scala analysis: xen09-wilson-marwa-14b-07
Marwa permutation 7 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: 10/9 182.403712 minor whole tone 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 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: 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 : 182.4 386.3 498.0 813.7 884.4 1088.3 1200.0 182.4 : 203.9 315.6 631.3 702.0 905.9 1017.6 1200.0 386.3 : 111.7 427.4 498.0 702.0 813.7 996.1 1200.0 498.0 : 315.6 386.3 590.2 702.0 884.4 1088.3 1200.0 813.7 : 70.7 274.6 386.3 568.7 772.6 884.4 1200.0 884.4 : 203.9 315.6 498.0 702.0 813.7 1129.3 1200.0 1088.3: 111.7 294.1 498.0 609.8 925.4 996.1 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: 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 : 178.96655 cents, oct.: 1252.76586 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : CDBEADB 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 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 : 2 at degree 0 Formal octave complements present : 3 = 42.8571% 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 : 0.037313 Average absolute harmonicity : 0.244488 Specific harmonicity : 0.220284 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 41.0, average 5.85714 Mersenne's string divisions : 2863224 Sum of van Prooijen's expressibility: 4.70437, average 0.67205 Sum of Tenney's harmonic distance : 9.49282, average 1.35612 Vogel's harmonic complexity : 15.14286 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 82.52774, average 2.94742 Lattice compactness (without 2's) : 42.90826, average 1.53244 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 12 1 3: -2 .. 1 -0.42857 5 1 5: -1 .. 1 0.42857 5 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 34.7761 c. M: 59.6973 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 31.3801 c. M: 49.0704 c. 10: 1 2 1 3 0 2 1 N SD: 33.0384 c. M: 62.4037 c. 12: 2 2 1 3 1 2 1 P D3 SD: 12.3656 c. M:-17.5963 c. Ionian Augmented, Ionian sharp 5 19: 3 3 2 5 1 3 2 N SD: 7.7767 c. M: 14.5845 c. 22: 3 4 2 6 1 4 2 N SD: 9.1481 c. M: 18.7673 c. 31: 5 5 3 8 2 5 3 N SD: 5.4403 c. M:-11.1447 c. 34: 5 6 3 9 2 6 3 N SD: 3.7080 c. M: 5.9331 c. 53: 8 9 5 14 3 9 5 N SD: 1.1687 c. M: 1.4763 c. 118: 18 20 11 31 7 20 11 N SD: 0.3131 c. M:-0.6471 c. 171: 26 29 16 45 10 29 16 N SD: 0.2952 c. M: 0.5494 c. 289: 44 49 27 76 17 49 27 N SD: 0.2186 c. M: 0.3794 c. 323: 49 55 30 85 19 55 30 N SD: 0.2005 c. M: 0.3604 c. 441: 67 75 41 116 26 75 41 N SD: 0.0898 c. M:-0.1667 c. 559: 85 95 52 147 33 95 52 N SD: 0.0732 c. M:-0.1034 c. 612: 93 104 57 161 36 104 57 N SD: 0.0355 c. M: 0.0508 c. 730: 111 124 68 192 43 124 68 N SD: 0.0351 c. M:-0.0620 c. 1171: 178 199 109 308 69 199 109 N SD: 0.0183 c. M:-0.0319 c. 1783: 271 303 166 469 105 303 166 N SD: 0.0077 c. M: 0.0145 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 x 6:7:8 x 9:10 S SD: 26.1717 cents 6:7 x 8 x 10:11:12 S SD: 18.5993 cents 7:8:9 x 11:12:13:14 SD: 15.2600 cents 8:9:10:11:13 x 15:16 SD: 10.5685 cents 9:10:11:12:14:15:17:18 SD: 9.0975 cents 10:11 x 13:16:17:19:20 SD: 10.4417 cents 11:12:14:15 x 18:21:22 S SD: 12.3357 cents 12:13:15:16:19:20:23:24 SD: 8.6869 cents 15:17:19:20:24:25:28:30 SD: 5.9942 cents 18:20:23:24:29:30:34:36 SD: 5.9841 cents 20:22:25:27:32:33:38:40 SD: 5.7032 cents 21:23:26:28:34:35:39:42 SD: 5.6950 cents 24:27:30:32:38:40:45:48 SD: 4.0182 cents 27:30:34:36:43:45:51:54 SD: 2.8249 cents 36:40:45:48:58:60:68:72 SD: 2.5022 cents 45:50:56:60:72:75:84:90 SD: 1.5580 cents 63:70:79:84:101:105:118:126 SD: 0.9609 cents 72:80:90:96:115:120:135:144 SD: 0.4297 cents 135:150:169:180:216:225:253:270 SD: 0.3860 cents 180:200:225:240:288:300:338:360 SD: 0.3661 cents 207:230:259:276:331:345:388:414 SD: 0.2928 cents 216:240:270:288:346:360:405:432 SD: 0.2861 cents 225:250:281:300:360:375:422:450 SD: 0.2318 cents 288:320:360:384:461:480:540:576 SD: 0.1073 cents 360:400:450:480:576:600:675:720 S SD: 0.0000 cents