Scala analysis: xen09-wilson-marwa-14b-04
Marwa permutation 4 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: 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 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: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 1: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 75/64 274.582 cents classic augmented second 2: 2 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: 1 81/64 407.820 cents Pythagorean 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 128/75 925.418 cents diminished seventh 6: 1 225/128 976.537 cents augmented sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 590.2 813.7 884.4 1088.3 1200.0 182.4 : 203.9 407.8 631.3 702.0 905.9 1017.6 1200.0 386.3 : 203.9 427.4 498.0 702.0 813.7 996.1 1200.0 590.2 : 223.5 294.1 498.0 609.8 792.2 996.1 1200.0 813.7 : 70.7 274.6 386.3 568.7 772.6 976.5 1200.0 884.4 : 203.9 315.6 498.0 702.0 905.9 1129.3 1200.0 1088.3: 111.7 294.1 498.0 702.0 925.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 223.4626 cents 2048/1875, 152.7901 cents 25/24, 70.6724 cents 2: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 16875/16384, 51.1199 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: 976.5374 .. 1129.3276 cents 2048/1875, 152.7901 cents 16875/16384, 51.1199 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 : 256/225, 223.4626 cents Average / Smallest step : 2.425678 Largest / Average step : 1.303532 Largest / Smallest step : 3.161948 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 180.94181 cents, oct.: 1266.59266 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : CDDEADB Scale is not a Constant Structure Scale diversity : 1.592693 Lumma stability : 0.202987 Lumma impropriety factor : 0.120569 Rothenberg efficiency : 0.397279 redundancy: 0.602721 Efficiency x scale size : 2.780952 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 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 : 2 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 n-1 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 : 0.031780 Average absolute harmonicity : 0.222413 Specific harmonicity : 0.195638 Fundamental : 1/1440, -10.4919 octaves, 0.1817 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 5.184000E+05, 18.98371 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 76.0, average 10.85714 Mersenne's string divisions : 31495464 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 : 18.14286 Wille's k value : 1012 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 102.70673, average 3.66810 Lattice compactness (without 2's) : 50.73012, average 1.81179 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.71429 15 1 3: -2 .. 2 0.00000 6 5: -1 .. 1 0.57143 6 6 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 44.6709 c. M: 75.9380 c. 8: 1 1 2 1 1 1 1 P M ME S SD: 45.2938 c. M: 86.3137 c. 9: 1 2 1 2 0 2 1 N D3 SD: 44.0812 c. M: 84.3587 c. 10: 2 1 2 2 0 2 1 N T3 SD: 31.2451 c. M:-57.5963 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 34.7164 c. M: 50.0499 c. 12: 2 2 2 2 1 2 1 P D3 S SD: 12.8847 c. M:-17.5963 c. Lydian Augmented, Lydian sharp 5 19: 3 3 3 4 1 3 2 N SD: 10.9974 c. M: 21.8027 c. 22: 3 4 4 4 1 4 2 N SD: 9.4904 c. M: 18.7673 c. 28: 4 5 5 5 2 4 3 N SD: 10.3163 c. M: 16.8401 c. 31: 5 5 5 6 2 5 3 N SD: 6.2345 c. M:-11.1447 c. 34: 5 6 6 6 2 6 3 N SD: 5.0199 c. M:-9.7763 c. 41: 6 7 7 8 2 7 4 N SD: 5.4247 c. M: 6.7940 c. 53: 8 9 9 10 3 9 5 N SD: 1.3062 c. M: 1.5445 c. 118: 18 20 20 22 7 20 11 N SD: 0.3323 c. M:-0.6471 c. 289: 44 49 49 54 17 49 27 N SD: 0.3045 c. M: 0.6043 c. 323: 49 55 55 60 19 55 30 N SD: 0.2604 c. M:-0.4884 c. 376: 57 64 64 70 22 64 35 N SD: 0.2454 c. M: 0.4888 c. 441: 67 75 75 82 26 75 41 N SD: 0.1270 c. M:-0.2525 c. 494: 75 84 84 92 29 84 46 N SD: 0.1104 c. M: 0.2175 c. 559: 85 95 95 104 33 95 52 N SD: 0.0852 c. M:-0.1162 c. 612: 93 104 104 114 36 104 57 N SD: 0.0369 c. M: 0.0508 c. 1171: 178 199 199 218 69 199 109 N SD: 0.0237 c. M:-0.0410 c. 1783: 271 303 303 332 105 303 166 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 x 5 x 6 S SD: 30.7262 cents 4 x 5:6 x 7 x 8 S SD: 35.0166 cents 5 x 6:7:8 x 9:10 S SD: 20.0486 cents 6:7 x 8 x 10:11:12 S SD: 26.1880 cents 7:8:9:10:11:12:13:14 H SD: 13.6476 cents 8:9:10:11:13 x 15:16 SD: 8.6549 cents 11:12:14:15 x 18:21:22 S SD: 13.7461 cents 12:13:15:17:19:20:23:24 SD: 8.8766 cents 15:17:19:21:24:25:28:30 SD: 6.0946 cents 17:19:21:24:27:28:32:34 SD: 4.9440 cents 20:22:25:28:32:33:38:40 SD: 4.9296 cents 24:27:30:34:38:40:45:48 SD: 4.4133 cents 25:28:31:35:40:42:47:50 SD: 3.6552 cents 27:30:34:38:43:45:51:54 SD: 2.8322 cents 35:39:44:49:56:58:66:70 SD: 2.7735 cents 37:41:46:52:59:62:69:74 SD: 2.5577 cents 44:49:55:62:70:73:83:88 SD: 2.4603 cents 45:50:56:63:72:75:84:90 SD: 1.9081 cents 55:61:69:77:88:92:103:110 SD: 1.7658 cents 57:63:71:80:91:95:107:114 SD: 1.7522 cents 63:70:79:89:101:105:118:126 SD: 1.4845 cents 64:71:80:90:102:107:120:128 SD: 1.2969 cents 72:80:90:101:115:120:135:144 SD: 0.7473 cents 108:120:135:152:173:180:203:216 SD: 0.7037 cents 128:142:160:180:205:213:240:256 SD: 0.5978 cents 135:150:169:190:216:225:253:270 SD: 0.4363 cents 153:170:191:215:245:255:287:306 SD: 0.4351 cents 180:200:225:253:288:300:338:360 SD: 0.3860 cents 207:230:259:291:331:345:388:414 SD: 0.3034 cents 280:311:350:394:448:467:525:560 SD: 0.2523 cents 288:320:360:405:461:480:540:576 SD: 0.1073 cents