Scala analysis: xen09-wilson-marwa-14b-10
Marwa permutation 10 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 5/3 884.358713 major sixth, BP sixth 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: 10/9 182.4037 minor whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 6/5 315.6413 minor third 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
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 : 182.4 294.1 498.0 813.7 884.4 996.1 1200.0 182.4 : 111.7 315.6 631.3 702.0 813.7 1017.6 1200.0 294.1 : 203.9 519.6 590.2 702.0 905.9 1088.3 1200.0 498.0 : 315.6 386.3 498.0 702.0 884.4 996.1 1200.0 813.7 : 70.7 182.4 386.3 568.7 680.4 884.4 1200.0 884.4 : 111.7 315.6 498.0 609.8 813.7 1129.3 1200.0 996.1 : 203.9 386.3 498.0 702.0 1017.6 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 : 173.69920 cents, oct.: 1215.89437 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : CBDEABD 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 : 2 at degree 6 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 n-1 differentially coherent in interval classes 2 and 3 combined 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 : 0.038760 Average absolute harmonicity : 0.241937 Specific harmonicity : 0.226735 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 160, 7.3219 octaves, 41860.090 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 67.0, average 9.57143 Mersenne's string divisions : 61206600 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 11.20748, average 1.60107 Vogel's harmonic complexity : 13.14286 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 81.68100, average 2.91718 Lattice compactness (without 2's) : 46.65633, average 1.66630 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 5 2.28571 16 1 3: -3 .. 0 -1.28571 9 3 5: -1 .. 1 0.14286 3 3 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 30.3369 c. M:-48.7221 c. 12: 2 1 2 3 1 1 2 N SD: 10.6577 c. M:-17.5963 c. 19: 3 2 3 5 1 2 3 N SD: 10.9133 c. M:-21.6545 c. 28: 4 3 5 7 2 2 5 N SD: 10.4968 c. M:-16.2407 c. 31: 5 3 5 8 2 3 5 N SD: 8.7518 c. M:-15.5424 c. 34: 5 3 6 9 2 3 6 N SD: 6.0811 c. M: 11.7821 c. 41: 6 4 7 11 2 4 7 N SD: 4.1951 c. M: 6.7940 c. 46: 7 4 8 12 3 4 8 N SD: 3.9974 c. M: 7.1785 c. 53: 8 5 9 14 3 5 9 N SD: 0.8832 c. M:-1.4081 c. 118: 18 11 20 31 7 11 20 N SD: 0.4678 c. M:-0.7803 c. 171: 26 16 29 45 10 16 29 N SD: 0.3184 c. M:-0.6018 c. 224: 34 21 38 59 13 21 38 N SD: 0.3805 c. M:-0.5994 c. 289: 44 27 49 76 17 27 49 N SD: 0.3431 c. M:-0.6747 c. 323: 49 30 55 85 19 30 55 N SD: 0.3351 c. M: 0.6365 c. 335: 51 31 57 88 20 31 57 N SD: 0.3407 c. M: 0.5520 c. 376: 57 35 64 99 22 35 64 N SD: 0.3331 c. M: 0.5180 c. 388: 59 36 66 102 23 36 66 N SD: 0.1989 c. M: 0.3206 c. 441: 67 41 75 116 26 41 75 N SD: 0.1298 c. M: 0.2574 c. 494: 75 46 84 130 29 46 84 N SD: 0.1428 c. M: 0.2175 c. 559: 85 52 95 147 33 52 95 N SD: 0.0545 c. M: 0.0906 c. 612: 93 57 104 161 36 57 104 N SD: 0.0307 c. M: 0.0508 c. 1171: 178 109 199 308 69 109 199 N SD: 0.0164 c. M: 0.0274 c. 1783: 271 166 303 469 105 166 303 N SD: 0.0128 c. M: 0.0239 c. 2395: 364 223 407 630 141 223 407 N SD: 0.0155 c. M: 0.0238 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 36.8478 cents 5 x 6:7:8 x 9:10 S SD: 17.9552 cents 6 x 7:8 x 10:11:12 S SD: 11.9689 cents 7:8 x 9:11:12 x 14 SD: 19.6919 cents 8:9 x 11:13 x 14:16 SD: 13.8048 cents 9:10:11:12:14:15:16:18 S SD: 10.3180 cents 10:11:12:13:16:17:18:20 SD: 9.3942 cents 11:12:13:15 x 18:20:22 SD: 11.8671 cents 12:13:14:16:19:20:21:24 SD: 8.7324 cents 15:17:18:20:24:25:27:30 SD: 6.5471 cents 17:19:20:23:27:28:30:34 SD: 5.8053 cents 18:20:21:24:29:30:32:36 SD: 4.2543 cents 27:30:32:36:43:45:48:54 SD: 1.1477 cents 72:80:85:96:115:120:128:144 SD: 1.0591 cents 81:90:96:108:130:135:144:162 SD: 0.7622 cents 108:120:128:144:173:180:192:216 SD: 0.2861 cents 135:150:160:180:216:225:240:270 S SD: 0.0000 cents