Scala analysis: xen09-wilson-marwa-14b-05
Marwa permutation 5 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: 9/5 1017.596288 just minor seventh, BP seventh 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: 9/8 203.9100 major whole tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 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 : 315.6 386.3 498.0 813.7 1017.6 1088.3 1200.0 315.6 : 70.7 182.4 498.0 702.0 772.6 884.4 1200.0 386.3 : 111.7 427.4 631.3 702.0 813.7 1129.3 1200.0 498.0 : 315.6 519.6 590.2 702.0 1017.6 1088.3 1200.0 813.7 : 203.9 274.6 386.3 702.0 772.6 884.4 1200.0 1017.6: 70.7 182.4 498.0 568.7 680.4 996.1 1200.0 1088.3: 111.7 427.4 498.0 609.8 925.4 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 : 184.67673 cents, oct.: 1292.73713 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DABDCAB 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian 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 : 3 = 42.8571% 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: 15 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.243879 Specific harmonicity : 0.202446 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 40.0, average 5.71429 Mersenne's string divisions : 414414 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 : 11.85714 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 84.35901, average 3.01282 Lattice compactness (without 2's) : 45.12846, average 1.61173 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 12 1 3: -1 .. 2 0.42857 5 1 5: -1 .. 1 -0.14286 5 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 34.7761 c. M: 59.6973 c. 9: 2 1 1 2 2 0 1 N SD: 31.3801 c. M:-49.0704 c. 10: 3 0 1 3 1 1 1 N SD: 31.7667 c. M: 57.5963 c. 12: 3 1 1 3 2 1 1 N SD: 12.3656 c. M: 17.5963 c. Chromatic Phrygian 19: 5 1 2 5 3 1 2 N SD: 7.7767 c. M: 14.5845 c. Ratio 1:2 Chromatic Phrygian 31: 8 2 3 8 5 2 3 N SD: 5.4403 c. M: 11.1447 c. Ratio 2:3 Chromatic Phrygian 34: 9 2 3 9 6 2 3 N SD: 3.7080 c. M:-5.9331 c. 53: 14 3 5 14 9 3 5 N SD: 1.1687 c. M: 1.4763 c. 118: 31 7 11 31 20 7 11 N SD: 0.3131 c. M: 0.6471 c. 171: 45 10 16 45 29 10 16 N SD: 0.2952 c. M: 0.5494 c. 289: 76 17 27 76 49 17 27 N SD: 0.2186 c. M: 0.3794 c. 323: 85 19 30 85 55 19 30 N SD: 0.2005 c. M:-0.3604 c. 441: 116 26 41 116 75 26 41 N SD: 0.0898 c. M:-0.1667 c. 559: 147 33 52 147 95 33 52 N SD: 0.0732 c. M:-0.1034 c. 612: 161 36 57 161 104 36 57 N SD: 0.0355 c. M:-0.0508 c. 730: 192 43 68 192 124 43 68 N SD: 0.0351 c. M: 0.0620 c. 1171: 308 69 109 308 199 69 109 N SD: 0.0183 c. M:-0.0319 c. 1783: 469 105 166 469 303 105 166 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 4:5 x x 6 S SD: 23.5575 cents 4 x 5 x 6:7 x 8 S SD: 30.4779 cents 5:6 x 7:8:9 x 10 S SD: 16.8934 cents 6:7 x 8:10:11 x 12 S SD: 18.3109 cents 7:8:9 x 11 x 13:14 SD: 20.7469 cents 8 x 10:11:13:14:15:16 SD: 12.8420 cents 9:11 x 12:14:16:17:18 SD: 10.5586 cents 10:12 x 13:16:18:19:20 SD: 8.2445 cents 13 x 16:17:21:23:24:26 SD: 10.1878 cents 15:18:19:20:24:27:28:30 S SD: 3.4561 cents 24:29:30:32:38:43:45:48 SD: 3.3096 cents 25:30:31:33:40:45:47:50 SD: 3.2494 cents 35:42:44:47:56:63:66:70 SD: 2.6590 cents 39:47:49:52:62:70:73:78 SD: 2.4330 cents 40:48:50:53:64:72:75:80 SD: 1.5506 cents 55:66:69:73:88:99:103:110 SD: 1.4715 cents 60:72:75:80:96:108:113:120 SD: 1.0968 cents 75:90:94:100:120:135:141:150 SD: 0.9315 cents 80:96:100:107:128:144:150:160 SD: 0.7717 cents 105:126:131:140:168:189:197:210 SD: 0.4970 cents 120:144:150:160:192:216:225:240 S SD: 0.0000 cents