Scala analysis: xen09-wilson-marwa-14a-04
Marwa permutation 4 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: 256/225 223.462571 Neapolitan diminished third 2: 32/25 427.372572 classic diminished fourth 3: 36/25 631.282574 classic diminished fifth 4: 8/5 813.686286 minor sixth 5: 128/75 925.417571 diminished 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: 256/225 223.4626 Neapolitan diminished third 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 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: 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 : 223.5 427.4 631.3 813.7 925.4 1129.3 1200.0 223.5 : 203.9 407.8 590.2 702.0 905.9 976.5 1200.0 427.4 : 203.9 386.3 498.0 702.0 772.6 996.1 1200.0 631.3 : 182.4 294.1 498.0 568.7 792.2 996.1 1200.0 813.7 : 111.7 315.6 386.3 609.8 813.7 1017.6 1200.0 925.4 : 203.9 274.6 498.0 702.0 905.9 1088.3 1200.0 1129.3: 70.7 294.1 498.0 702.0 884.4 996.1 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 : 185.92753 cents, oct.: 1301.49269 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : EDDCBDA Scale is sum-free (all different intervals) 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 Length of longest harmonic part : 2 at degree 2 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 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: 225 Scale harmonicity : 0.031780 Average absolute harmonicity : 0.192339 Specific harmonicity : 0.172910 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 2304, 11.1699 octaves, 602785.302 Hz. Exponens Consonantiae : 5.184000E+05, 18.98371 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 445.5, average 63.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.12003, average 1.30286 Sum of Tenney's harmonic distance : 19.58230, average 2.79747 Vogel's harmonic complexity : 12.42857 Wille's k value : 112 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 113.12744, average 4.04027 Lattice compactness (without 2's) : 54.55854, average 1.94852 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.28571 30 1 3: -2 .. 2 0.00000 6 5: -2 .. 0 -1.57143 11 6 Average exponent except 2's :-11 / 7 =-1.57143 Average absolute exponent except 2's: 17 / 7 = 2.42857
FIT/MODE
7: 1 2 1 1 1 1 0 N T3 SD: 66.2765 c. M:-103.1539 c. 8: 1 2 1 1 1 1 1 P M ME S SD: 50.5431 c. M: 79.3276 c. 9: 2 1 2 1 1 1 1 N D3 S SD: 33.8995 c. M: 62.6609 c. 10: 2 2 1 2 1 1 1 N D3 SD: 34.5239 c. M:-52.6274 c. 11: 2 2 2 1 1 2 1 N D3 SD: 32.5294 c. M: 52.6903 c. 12: 2 2 2 2 1 2 1 P D3 S SD: 23.8202 c. M: 31.2826 c. Lydian Augmented, Lydian sharp 5 13: 2 3 2 2 1 2 1 N SD: 22.8753 c. M: 38.8472 c. 15: 3 2 3 2 2 2 1 N SD: 19.1572 c. M:-34.5824 c. 16: 3 3 2 3 1 3 1 N SD: 18.0703 c. M: 31.2826 c. 17: 3 3 3 3 1 3 1 N D3 S SD: 13.8451 c. M:-33.3725 c. 19: 4 3 3 3 2 3 1 N SD: 15.4020 c. M:-29.1690 c. 21: 4 3 4 3 2 4 1 N SD: 13.5066 c. M: 27.3726 c. 22: 4 4 4 3 2 4 1 N SD: 11.5488 c. M:-23.2629 c. 23: 4 4 4 4 2 4 1 N SD: 13.7320 c. M:-21.0963 c. 25: 5 4 4 4 2 5 1 N SD: 12.2320 c. M:-22.6724 c. 28: 5 5 5 4 3 4 2 N SD: 10.3536 c. M:-17.4396 c. 30: 6 5 5 4 3 5 2 N SD: 10.7743 c. M:-16.5374 c. 31: 6 5 5 5 3 5 2 N SD: 6.3390 c. M: 11.9277 c. 34: 6 6 6 5 3 6 2 N SD: 5.7543 c. M: 11.6979 c. 44: 8 8 7 7 4 7 3 N SD: 6.2414 c. M: 11.1458 c. 47: 9 8 8 7 4 8 3 N SD: 5.5960 c. M:-7.0153 c. 53: 10 9 9 8 5 9 3 N SD: 2.4402 c. M:-2.9525 c. 65: 12 11 11 10 6 11 4 N SD: 2.4391 c. M: 3.5903 c. 87: 16 15 15 13 8 15 5 N SD: 1.7944 c. M:-3.2002 c. 118: 22 20 20 18 11 20 7 N SD: 0.3808 c. M: 0.7741 c. 289: 54 49 49 44 27 49 17 N SD: 0.3794 c. M:-0.7589 c. 323: 60 55 55 49 30 55 19 N SD: 0.2768 c. M: 0.5524 c. 376: 70 64 64 57 35 64 22 N SD: 0.3231 c. M:-0.6323 c. 407: 76 69 69 62 38 69 24 N SD: 0.3081 c. M:-0.6161 c. 441: 82 75 75 67 41 75 26 N SD: 0.1736 c. M: 0.3333 c. 494: 92 84 84 75 46 84 29 N SD: 0.1598 c. M:-0.2964 c. 559: 104 95 95 85 52 95 33 N SD: 0.1576 c. M: 0.2068 c. 612: 114 104 104 93 57 104 36 N SD: 0.0683 c. M:-0.0900 c. 730: 136 124 124 111 68 124 43 N SD: 0.0493 c. M:-0.0991 c. 1171: 218 199 199 178 109 199 69 N SD: 0.0409 c. M: 0.0638 c. 1665: 310 283 283 253 155 283 98 N SD: 0.0347 c. M:-0.0688 c. 1783: 332 303 303 271 166 303 105 N SD: 0.0099 c. M: 0.0189 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 x 5 x 6 S SD: 27.2446 cents 4 x 5:6 x 7 x 8 S SD: 23.1364 cents 5:6 x 7:8:9 x 10 S SD: 27.8369 cents 6:7:8:9 x 10 x 12 S SD: 23.2889 cents 7:8:9:10:11:12:13:14 H SD: 9.7547 cents 13:15:17:19:21:22:25:26 SD: 7.9786 cents 14:16:18:20:22:24:27:28 S SD: 5.3476 cents 21:24:27:30:34:36:40:42 SD: 4.4693 cents 25:28:32:36:40:43:48:50 SD: 4.3445 cents 27:31:35:39:43:46:52:54 SD: 4.1820 cents 28:32:36:40:45:48:54:56 S SD: 3.1546 cents 35:40:45:50:56:60:67:70 SD: 2.8404 cents 36:41:46:52:58:61:69:72 SD: 2.6641 cents 37:42:47:53:59:63:71:74 SD: 2.5770 cents 43:49:55:62:69:73:83:86 SD: 2.0568 cents 50:57:64:72:80:85:96:100 SD: 1.0816 cents 75:85:96:108:120:128:144:150 SD: 0.9680 cents 93:106:119:134:149:159:179:186 SD: 0.9432 cents 100:114:128:144:160:171:192:200 SD: 0.6825 cents 125:142:160:180:200:213:240:250 SD: 0.5469 cents 150:171:192:216:240:256:288:300 SD: 0.4826 cents 175:199:224:252:280:299:336:350 SD: 0.3085 cents 225:256:288:324:360:384:432:450 SD: 0.0000 cents