Scala analysis: xen09-wilson-marwa-14b-01
Marwa permutation 1 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: 27/20 519.551289 acute fourth 3: 45/32 590.223716 diatonic tritone 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: 9/8 203.9100 major whole tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 256/225 223.4626 Neapolitan diminished 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: 1 16/15 111.731 cents minor diatonic semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 256/225 223.463 cents Neapolitan diminished third 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 2 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor 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 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 225/128 976.537 cents augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 519.6 590.2 813.7 1017.6 1088.3 1200.0 315.6 : 203.9 274.6 498.0 702.0 772.6 884.4 1200.0 519.6 : 70.7 294.1 498.0 568.7 680.4 996.1 1200.0 590.2 : 223.5 427.4 498.0 609.8 925.4 1129.3 1200.0 813.7 : 203.9 274.6 386.3 702.0 905.9 976.5 1200.0 1017.6: 70.7 182.4 498.0 702.0 772.6 996.1 1200.0 1088.3: 111.7 427.4 631.3 702.0 925.4 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 188.55538 cents, oct.: 1319.88769 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : ECADCAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.613265 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / 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 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 n-1 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 : 225 (O: 225 U: 225) Highest odd numerator or denominator: 45 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.213508 Specific harmonicity : 0.176373 Fundamental : 1/160, -7.3219 octaves, 1.6352 Hz. Guide tone : 1080, 10.0768 octaves, 282555.611 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 94.0, average 13.42857 Mersenne's string divisions : 6492486 Sum of van Prooijen's expressibility: 6.61285, average 0.94469 Sum of Tenney's harmonic distance : 13.00336, average 1.85762 Vogel's harmonic complexity : 11.71429 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 104.56696, average 3.73453 Lattice compactness (without 2's) : 52.52681, average 1.87596 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.71429 15 1 3: 0 .. 3 1.28571 9 5: -1 .. 1 -0.28571 6 6 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 2 1 0 2 1 0 1 N T3 SD: 41.5893 c. M: 75.9380 c. 8: 2 1 1 1 2 0 1 N D3 SD: 40.9670 c. M: 69.5513 c. 9: 2 2 0 2 1 1 1 N T3 SD: 44.0441 c. M: 84.2630 c. 10: 3 1 1 2 1 1 1 N T3 SD: 33.1785 c. M: 57.5963 c. 11: 3 2 0 2 2 1 1 N G SD: 30.7120 c. M: 50.0499 c. 12: 3 2 1 2 2 1 1 N SD: 13.9235 c. M: 19.5513 c. 19: 5 3 1 4 3 1 2 N SD: 11.9313 c. M: 21.8027 c. 22: 6 4 1 4 4 1 2 N SD: 13.5290 c. M:-25.9033 c. 25: 7 4 1 5 4 2 2 N SD: 12.1484 c. M:-20.3587 c. 26: 7 4 2 5 4 2 2 N SD: 11.7443 c. M:-19.4236 c. 28: 7 5 2 5 5 1 3 N SD: 10.5041 c. M: 16.8401 c. 30: 8 5 2 5 5 2 3 N SD: 9.8568 c. M: 17.5963 c. 31: 8 5 2 6 5 2 3 N SD: 8.7668 c. M: 16.3255 c. 32: 8 6 2 6 5 2 3 N SD: 8.6559 c. M: 15.6413 c. 33: 9 5 2 6 6 2 3 N SD: 8.5356 c. M: 13.6863 c. 34: 9 6 2 6 6 2 3 N SD: 6.2098 c. M:-9.8605 c. 41: 11 7 2 8 7 2 4 N SD: 5.6697 c. M:-7.2780 c. 46: 12 8 3 8 8 3 4 N SD: 5.1627 c. M:-9.7763 c. 53: 14 9 3 10 9 3 5 N SD: 1.2766 c. M: 1.5445 c. 118: 31 20 7 22 20 7 11 N SD: 0.4751 c. M: 0.9072 c. 171: 45 29 10 32 29 10 16 N SD: 0.3918 c. M: 0.7500 c. 289: 76 49 17 54 49 17 27 N SD: 0.3577 c. M: 0.6043 c. 323: 85 55 19 60 55 19 30 N SD: 0.3377 c. M:-0.5726 c. 388: 102 66 23 72 66 23 36 N SD: 0.2724 c. M:-0.4979 c. 441: 116 75 26 82 75 26 41 N SD: 0.1402 c. M:-0.2525 c. 494: 130 84 29 92 84 29 46 N SD: 0.1518 c. M:-0.2868 c. 559: 147 95 33 104 95 33 52 N SD: 0.0805 c. M:-0.1162 c. 612: 161 104 36 114 104 36 57 N SD: 0.0400 c. M:-0.0566 c. 1171: 308 199 69 218 199 69 109 N SD: 0.0222 c. M:-0.0410 c. 1783: 469 303 105 332 303 105 166 N SD: 0.0128 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: 55.8656 cents 3 x 4 x 5 x x 6 S SD: 24.6241 cents 4:5 x 6 x 7 x 8 S SD: 35.2287 cents 5:6 x 7:8:9 x 10 S SD: 1.5423 cents 6:7:8 x 10:11 x 12 S SD: 18.8093 cents 7:8:9:10:11 x 13:14 SD: 21.2526 cents 8:10:11 x 13:14:15:16 SD: 15.9014 cents 9:11:12:13:14:16:17:18 SD: 11.6307 cents 10:12 x 14:16:18:19:20 S SD: 4.0321 cents 11:13:15 x 18:20:21:22 SD: 10.2616 cents 13:16 x 18:21:23:24:26 SD: 11.2145 cents 14:17:19:20:22:25:26:28 SD: 7.4016 cents 15:18:20:21:24:27:28:30 S SD: 3.4448 cents 25:30:34:35:40:45:47:50 SD: 2.2314 cents 35:42:47:49:56:63:66:70 SD: 2.2183 cents 40:48:54:56:64:72:75:80 S SD: 1.1016 cents 80:96:108:113:128:144:150:160 SD: 1.0968 cents 86:103:116:121:138:155:161:172 SD: 1.0279 cents 89:107:120:125:142:160:167:178 SD: 1.0093 cents 94:113:127:132:150:169:176:188 SD: 0.9979 cents 95:114:128:134:152:171:178:190 SD: 0.9094 cents 105:126:142:148:168:189:197:210 SD: 0.7384 cents 115:138:155:162:184:207:216:230 SD: 0.7268 cents 120:144:162:169:192:216:225:240 SD: 0.3661 cents 145:174:196:204:232:261:272:290 SD: 0.3542 cents 160:192:216:225:256:288:300:320 SD: 0.0000 cents