Scala analysis: xen09-wilson-marwa-14b-03
Marwa permutation 3 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: 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: 9/8 203.9100 major whole tone 4: 256/225 223.4626 Neapolitan diminished 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: 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: 2 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 386.3 590.2 813.7 884.4 1088.3 1200.0 315.6 : 70.7 274.6 498.0 568.7 772.6 884.4 1200.0 386.3 : 203.9 427.4 498.0 702.0 813.7 1129.3 1200.0 590.2 : 223.5 294.1 498.0 609.8 925.4 996.1 1200.0 813.7 : 70.7 274.6 386.3 702.0 772.6 976.5 1200.0 884.4 : 203.9 315.6 631.3 702.0 905.9 1129.3 1200.0 1088.3: 111.7 427.4 498.0 702.0 925.4 996.1 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 181.89351 cents, oct.: 1273.25454 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EACDACB Scale is not a Constant Structure Scale diversity : 1.534657 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.435374 redundancy: 0.564626 Efficiency x scale size : 3.047619 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 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 n-1 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 : 225 (O: 225 U: 225) Highest odd numerator or denominator: 45 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.225385 Specific harmonicity : 0.187390 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 72.0, average 10.28571 Mersenne's string divisions : 1657656 Sum of van Prooijen's expressibility: 5.62518, average 0.80360 Sum of Tenney's harmonic distance : 11.09488, average 1.58498 Vogel's harmonic complexity : 15.00000 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 100.32545, average 3.58305 Lattice compactness (without 2's) : 46.55854, average 1.66281 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.71429 15 1 3: -1 .. 2 0.42857 5 5: -1 .. 1 0.28571 6 6 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 45.6519 c. M: 75.9380 c. 8: 2 1 1 1 1 1 1 P M ME S SD: 38.1000 c. M: 63.6863 c. 9: 2 1 1 2 0 2 1 N D3 SD: 44.0660 c. M: 84.3587 c. 10: 3 0 2 2 0 2 1 N SD: 27.9902 c. M:-44.3587 c. 12: 3 1 2 2 1 2 1 P D3 SD: 12.5193 c. M: 15.6413 c. Aeolian flat 1 19: 5 1 3 4 1 3 2 N SD: 10.6679 c. M: 21.8027 c. 22: 6 1 4 4 1 4 2 N SD: 7.6862 c. M:-11.6314 c. 31: 8 2 5 6 2 5 3 N SD: 5.1193 c. M: 9.5786 c. 34: 9 2 6 6 2 6 3 N SD: 4.5547 c. M:-9.7763 c. 35: 9 2 6 7 2 6 3 N SD: 7.5705 c. M: 9.1709 c. 41: 11 2 7 8 2 7 4 N SD: 5.3405 c. M:-6.3099 c. 49: 13 3 8 9 3 8 5 N SD: 5.3027 c. M: 10.7177 c. 53: 14 3 9 10 3 9 5 N SD: 1.3159 c. M: 1.5445 c. 65: 17 4 11 12 4 11 6 N SD: 1.2800 c. M:-1.7951 c. 118: 31 7 20 22 7 20 11 N SD: 0.2684 c. M: 0.3932 c. 289: 76 17 49 54 17 49 27 N SD: 0.2846 c. M: 0.6043 c. 323: 85 19 55 60 19 55 30 N SD: 0.2289 c. M:-0.4884 c. 376: 99 22 64 70 22 64 35 N SD: 0.2010 c. M: 0.3162 c. 441: 116 26 75 82 26 75 41 N SD: 0.1223 c. M:-0.2525 c. 494: 130 29 84 92 29 84 46 N SD: 0.0926 c. M: 0.1482 c. 559: 147 33 95 104 33 95 52 N SD: 0.0868 c. M:-0.1162 c. 612: 161 36 104 114 36 104 57 N SD: 0.0359 c. M:-0.0450 c. 1171: 308 69 199 218 69 199 109 N SD: 0.0242 c. M:-0.0410 c. 1783: 469 105 303 332 105 303 166 N SD: 0.0083 c. M:-0.0175 c. 2395: 630 141 407 446 141 407 223 N SD: 0.0102 c. M:-0.0163 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 x 5 x 6 S SD: 30.7262 cents 4 x 5:6 x 7 x 8 S SD: 35.0166 cents 5:6 x 7:8 x 9:10 S SD: 14.2184 cents 6:7 x 8 x 10:11:12 S SD: 22.2613 cents 7:8:9:10:11:12:13:14 H SD: 16.8321 cents 8 x 10:11:13 x 15:16 SD: 9.4533 cents 9:11 x 13:14:15:17:18 SD: 12.5867 cents 10:12:13:14:16:17:19:20 SD: 11.4027 cents 11:13:14:15 x 18:21:22 SD: 13.4287 cents 12:14:15:17:19:20:23:24 SD: 9.3877 cents 13 x 16:18:21:22:24:26 SD: 9.3311 cents 15:18:19:21:24:25:28:30 SD: 3.6274 cents 24:29:30:34:38:40:45:48 SD: 3.6011 cents 25:30:31:35:40:42:47:50 SD: 3.0785 cents 35:42:44:49:56:58:66:70 SD: 2.6822 cents 39:47:49:55:62:65:73:78 SD: 2.4324 cents 40:48:50:56:64:67:75:80 SD: 1.6538 cents 60:72:75:84:96:100:113:120 SD: 1.5545 cents 64:77:80:90:102:107:120:128 SD: 1.3951 cents 72:86:90:101:115:120:135:144 SD: 1.3695 cents 79:95:99:111:126:132:148:158 SD: 1.3249 cents 80:96:100:113:128:133:150:160 SD: 1.2594 cents 81:97:101:114:130:135:152:162 SD: 1.1389 cents 95:114:119:134:152:158:178:190 SD: 1.0660 cents 96:115:120:135:154:160:180:192 SD: 0.7736 cents 105:126:131:148:168:175:197:210 SD: 0.7601 cents 120:144:150:169:192:200:225:240 SD: 0.3661 cents 160:192:200:225:256:267:300:320 SD: 0.3090 cents 280:336:350:394:448:467:525:560 SD: 0.2363 cents 300:360:375:422:480:500:563:600 SD: 0.2316 cents 315:378:394:443:504:525:591:630 SD: 0.2227 cents 320:384:400:450:512:533:600:640 SD: 0.1546 cents 360:432:450:506:576:600:675:720 SD: 0.1222 cents 465:558:581:654:744:775:872:930 SD: 0.1176 cents 480:576:600:675:768:800:900:960 SD: 0.0000 cents