Scala analysis: xen09-wilson-marwa-14a-08
Marwa permutation 8 from Figure 14a, Didymus 16/15 25/24 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: 32/25 427.372572 classic diminished fourth 3: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 128/75 925.417571 diminished seventh 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 6/5 315.6413 minor third 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 6/5 315.6413 minor third 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 9/8 203.9100 major whole tone
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: 2 10/9 182.404 cents minor whole tone 2: 1 75/64 274.582 cents classic augmented second 2: 1 5/4 386.314 cents major third 2: 2 32/25 427.373 cents classic diminished fourth 2: 1 27/20 519.551 cents acute 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 40/27 680.449 cents grave fifth 5: 2 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 128/75 925.418 cents diminished seventh 5: 2 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 : 315.6 427.4 498.0 813.7 925.4 996.1 1200.0 315.6 : 111.7 182.4 498.0 609.8 680.4 884.4 1200.0 427.4 : 70.7 386.3 498.0 568.7 772.6 1088.3 1200.0 498.0 : 315.6 427.4 498.0 702.0 1017.6 1129.3 1200.0 813.7 : 111.7 182.4 386.3 702.0 813.7 884.4 1200.0 925.4 : 70.7 274.6 590.2 702.0 772.6 1088.3 1200.0 996.1 : 203.9 519.6 631.3 702.0 1017.6 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 .. 519.5513 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 680.4487 .. 1017.5963 cents 243/200, 337.1476 cents 25/27,-133.2376 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 : 178.02067 cents, oct.: 1246.14472 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DBADBAC Scale is not a Constant Structure Scale diversity : 1.568476 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 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 : 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 Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords 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 : 1 = 14.2857% Scale is differentially coherent in interval class 1 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: 75 Scale harmonicity : 0.035971 Average absolute harmonicity : 0.232548 Specific harmonicity : 0.190741 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 384, 8.5850 octaves, 100464.217 Hz. Exponens Consonantiae : 8.640000E+04, 16.39874 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 159.5, average 22.78571 Mersenne's string divisions : 41366325 Sum of van Prooijen's expressibility: 6.10231, average 0.87176 Sum of Tenney's harmonic distance : 13.50312, average 1.92902 Vogel's harmonic complexity : 13.71429 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 95.57256, average 3.41331 Lattice compactness (without 2's) : 46.71425, average 1.66837 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.28571 23 1 3: -2 .. 1 -0.42857 5 2 5: -2 .. 0 -0.85714 6 4 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 11 / 7 = 1.57143
FIT/MODE
7: 2 1 0 2 0 1 1 N T3 SD: 48.0525 c. M:-86.9131 c. 8: 2 1 0 2 1 0 2 N SD: 49.2809 c. M: 96.0900 c. 9: 2 1 1 2 1 0 2 N SD: 35.0131 c. M: 62.7567 c. 11: 3 1 1 2 1 1 2 N SD: 33.6977 c. M: 52.6903 c. 12: 3 1 1 3 1 1 2 N SD: 16.2410 c. M: 27.3726 c. Chromatic Hypodorian inverse 16: 4 2 1 4 1 1 3 N SD: 19.6471 c. M:-26.9550 c. 17: 4 2 1 4 2 1 3 N SD: 19.4400 c. M: 37.2157 c. 18: 5 1 1 5 2 1 3 N SD: 18.1743 c. M: 31.3783 c. 19: 5 2 1 5 2 1 3 N SD: 12.0338 c. M:-21.9508 c. 22: 6 2 1 6 2 1 4 N SD: 8.4040 c. M: 14.2718 c. 31: 8 3 2 8 3 2 5 N SD: 5.1534 c. M:-10.3616 c. 34: 9 3 2 9 3 2 6 N SD: 4.7807 c. M: 7.8547 c. 53: 14 5 3 14 5 3 9 N SD: 1.6925 c. M:-2.8843 c. 65: 17 6 4 17 6 4 11 N SD: 1.6506 c. M: 2.7572 c. 87: 23 8 5 23 8 5 15 N SD: 1.4834 c. M: 2.9865 c. 118: 31 11 7 31 11 7 20 N SD: 0.2850 c. M:-0.5202 c. 289: 76 27 17 76 27 17 49 N SD: 0.3076 c. M:-0.5340 c. 323: 85 30 19 85 30 19 55 N SD: 0.2340 c. M: 0.4244 c. 376: 99 35 22 99 35 22 64 N SD: 0.2284 c. M: 0.3453 c. 441: 116 41 26 116 41 26 75 N SD: 0.1367 c. M: 0.2475 c. 494: 130 46 29 130 46 29 84 N SD: 0.1101 c. M:-0.1578 c. 559: 147 52 33 147 52 33 95 N SD: 0.1105 c. M: 0.1940 c. 612: 161 57 36 161 57 36 104 N SD: 0.0465 c. M:-0.0784 c. 730: 192 68 43 192 68 43 124 N SD: 0.0416 c. M:-0.0744 c. 1171: 308 109 69 308 109 69 199 N SD: 0.0297 c. M: 0.0546 c. 1665: 438 155 98 438 155 98 283 N SD: 0.0274 c. M: 0.0540 c. 1783: 469 166 105 469 166 105 303 N SD: 0.0084 c. M: 0.0160 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: 13.6863 cents 4 x 5 x 6 x 7:8 S SD: 30.5297 cents 5:6 x 7:8 x 9:10 S SD: 17.4324 cents 6:7 x 8 x 10:11:12 S SD: 16.6161 cents 7:8:9 x 11:12 x 14 SD: 18.1403 cents 8 x 10:11:13 x 14:16 SD: 15.4760 cents 9:11 x 12:14:15:16:18 SD: 11.8714 cents 10:12:13 x 16:17:18:20 SD: 5.8426 cents 13:16 x 17:21:22:23:26 SD: 10.0129 cents 14:17:18:19:22:24:25:28 SD: 7.1574 cents 15:18:19:20:24:26:27:30 S SD: 5.5542 cents 18:22:23:24:29:31:32:36 SD: 5.3613 cents 21:25:27:28:34:36:37:42 SD: 4.4494 cents 24:29:31:32:38:41:43:48 SD: 4.2935 cents 25:30:32:33:40:43:44:50 SD: 4.0076 cents 30:36:38:40:48:51:53:60 SD: 3.1699 cents 35:42:45:47:56:60:62:70 SD: 2.5117 cents 40:48:51:53:64:68:71:80 SD: 2.1043 cents 45:54:58:60:72:77:80:90 SD: 1.8284 cents 50:60:64:67:80:85:89:100 SD: 1.5981 cents 54:65:69:72:86:92:96:108 SD: 1.5058 cents 60:72:77:80:96:102:107:120 SD: 1.3951 cents 72:86:92:96:115:123:128:144 SD: 1.3209 cents 75:90:96:100:120:128:133:150 SD: 0.6191 cents 135:162:173:180:216:230:240:270 SD: 0.5163 cents 150:180:192:200:240:256:267:300 SD: 0.3090 cents 225:270:288:300:360:384:400:450 S SD: 0.0000 cents