Scala analysis: xen09-wilson-marwa-14a-01
Marwa permutation 1 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: 27/20 519.551289 acute fourth 3: 36/25 631.282574 classic diminished fifth 4: 8/5 813.686286 minor sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 6/5 315.6413 minor third 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma
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 10/9 182.404 cents minor whole tone 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 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 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 9/5 1017.596 cents just minor seventh, BP 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 : 315.6 519.6 631.3 813.7 1017.6 1129.3 1200.0 315.6 : 203.9 315.6 498.0 702.0 813.7 884.4 1200.0 519.6 : 111.7 294.1 498.0 609.8 680.4 996.1 1200.0 631.3 : 182.4 386.3 498.0 568.7 884.4 1088.3 1200.0 813.7 : 203.9 315.6 386.3 702.0 905.9 1017.6 1200.0 1017.6: 111.7 182.4 498.0 702.0 813.7 996.1 1200.0 1129.3: 70.7 386.3 590.2 702.0 884.4 1088.3 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 191.19488 cents, oct.: 1338.36418 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EDBCDBA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.463320 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 27 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.207566 Specific harmonicity : 0.203002 Fundamental : 1/100, -6.6439 octaves, 2.6163 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 111.0, average 15.85714 Mersenne's string divisions : 1257001746 Sum of van Prooijen's expressibility: 6.57943, average 0.93992 Sum of Tenney's harmonic distance : 13.79924, average 1.97132 Vogel's harmonic complexity : 11.42857 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 84.48387, average 3.01728 Lattice compactness (without 2's) : 48.88310, average 1.74582 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.28571 13 1 3: 0 .. 3 1.28571 9 5: -2 .. 0 -1.14286 8 6 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 17 / 7 = 2.42857
FIT/MODE
7: 2 1 1 1 1 1 0 N T3 SD: 39.1604 c. M:-70.6724 c. 9: 2 2 1 1 2 0 1 N SD: 38.4747 c. M: 62.6609 c. 10: 3 1 1 2 1 1 1 N T3 SD: 39.5575 c. M: 57.5963 c. 11: 3 2 1 1 2 1 1 N SD: 30.7257 c. M: 50.0499 c. 12: 3 2 1 2 2 1 1 N SD: 20.5724 c. M: 31.2826 c. 15: 4 2 2 2 3 1 1 N SD: 18.6530 c. M: 39.5513 c. 18: 5 3 1 3 3 2 1 N SD: 16.8800 c. M: 31.2826 c. 19: 5 3 2 3 3 2 1 N SD: 7.2208 c. M: 14.2881 c. 33: 9 5 3 5 6 3 2 N SD: 9.3214 c. M: 13.6863 c. 34: 9 6 3 5 6 3 2 N SD: 4.7245 c. M:-9.8605 c. 46: 12 8 4 7 8 4 3 N SD: 4.1587 c. M: 7.5884 c. 53: 14 9 5 8 9 5 3 N SD: 1.7556 c. M:-2.7479 c. 99: 26 17 9 15 17 9 6 N SD: 1.2520 c. M: 2.0548 c. 118: 31 20 11 18 20 11 7 N SD: 0.5696 c. M: 0.9072 c. 171: 45 29 16 26 29 16 10 N SD: 0.2791 c. M:-0.4970 c. 270: 71 46 25 41 46 25 16 N SD: 0.2898 c. M:-0.4487 c. 289: 76 49 27 44 49 27 17 N SD: 0.2430 c. M: 0.5201 c. 323: 85 55 30 49 55 30 19 N SD: 0.2875 c. M:-0.5726 c. 388: 102 66 36 59 66 36 23 N SD: 0.2556 c. M: 0.4616 c. 441: 116 75 41 67 75 41 26 N SD: 0.0861 c. M:-0.1766 c. 559: 147 95 52 85 95 52 33 N SD: 0.1026 c. M: 0.1684 c. 612: 161 104 57 93 104 57 36 N SD: 0.0592 c. M:-0.0900 c. 730: 192 124 68 111 124 68 43 N SD: 0.0494 c. M: 0.0992 c. 1171: 308 199 109 178 199 109 69 N SD: 0.0200 c. M: 0.0364 c. 1342: 353 228 125 204 228 125 79 N SD: 0.0198 c. M:-0.0316 c. 1783: 469 303 166 271 303 166 105 N SD: 0.0117 c. M:-0.0225 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: 35.3362 cents 3 x 4 x 5 x x 6 S SD: 24.6241 cents 4:5 x 6 x 7 x 8 S SD: 27.8026 cents 5:6 x 7:8:9 x 10 S SD: 9.7541 cents 6:7:8:9:10:11 x 12 S SD: 19.6068 cents 7:8:9:10:11:13 x 14 SD: 22.5833 cents 8:10:11:12:13:14:15:16 S SD: 17.9473 cents 9:11:12:13:14:16:17:18 SD: 10.2430 cents 10:12 x 14:16:18:19:20 S SD: 8.6718 cents 11:13:15:16:18:20:21:22 SD: 8.1037 cents 14:17:19:20:22:25:27:28 SD: 6.2538 cents 15:18:20:22:24:27:29:30 SD: 5.7413 cents 20:24:27:29:32:36:38:40 SD: 3.1042 cents 25:30:34:36:40:45:48:50 SD: 1.8252 cents 45:54:61:65:72:81:86:90 SD: 1.7116 cents 55:66:74:79:88:99:106:110 SD: 1.4004 cents 60:72:81:86:96:108:115:120 SD: 1.2255 cents 75:90:101:108:120:135:144:150 SD: 0.6114 cents 100:120:135:144:160:180:192:200 S SD: 0.0000 cents