Scala analysis: xen09-wilson-marwa-14a-09
Marwa permutation 9 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: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 128/75 925.417571 diminished seventh 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: 256/225 223.4626 Neapolitan diminished third 2: 9/8 203.9100 major whole tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 6/5 315.6413 minor third 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 9/8 203.9100 major whole tone
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 5/4 386.314 cents major third 2: 3 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: 3 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 223.5 427.4 498.0 813.7 925.4 996.1 1200.0 223.5 : 203.9 274.6 590.2 702.0 772.6 976.5 1200.0 427.4 : 70.7 386.3 498.0 568.7 772.6 996.1 1200.0 498.0 : 315.6 427.4 498.0 702.0 925.4 1129.3 1200.0 813.7 : 111.7 182.4 386.3 609.8 813.7 884.4 1200.0 925.4 : 70.7 274.6 498.0 702.0 772.6 1088.3 1200.0 996.1 : 203.9 427.4 631.3 702.0 1017.6 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 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 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 .. 1017.5963 cents 144/125, 244.9689 cents 125/128,-41.0589 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 : 177.36226 cents, oct.: 1241.53579 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : DCAEBAC Scale is not a Constant Structure Scale diversity : 1.566731 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 5 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 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: 225 Scale harmonicity : 0.038265 Average absolute harmonicity : 0.223823 Specific harmonicity : 0.173410 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 5.760000E+04, 15.81378 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 394.5, average 56.35714 Mersenne's string divisions : 139141275 Sum of van Prooijen's expressibility: 7.75552, average 1.10793 Sum of Tenney's harmonic distance : 16.78642, average 2.39806 Vogel's harmonic complexity : 12.71429 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 110.14344, average 3.93369 Lattice compactness (without 2's) : 48.96618, average 1.74879 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.28571 30 1 3: -2 .. 0 -0.85714 6 2 5: -2 .. 0 -1.00000 7 4 Average exponent except 2's :-13 / 7 =-1.85714 Average absolute exponent except 2's: 13 / 7 = 1.85714
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 50.3120 c. M: 84.5154 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 47.5475 c. M: 73.4626 c. 9: 2 1 1 2 1 0 2 N SD: 33.9106 c. M: 62.7567 c. 10: 2 2 0 3 1 0 2 N SD: 30.6119 c. M:-52.6274 c. 11: 2 2 0 3 1 1 2 N G SD: 36.6416 c. M: 61.6814 c. 12: 2 2 1 3 1 1 2 N T3 SD: 17.5346 c. M: 27.3726 c. 16: 3 3 1 4 1 1 3 N SD: 18.7456 c. M:-26.9550 c. 17: 3 3 1 4 2 1 3 N SD: 15.4648 c. M: 37.2157 c. 19: 4 3 1 5 2 1 3 N SD: 16.3204 c. M:-29.1690 c. 22: 4 4 1 6 2 1 4 N SD: 7.4353 c. M: 14.2718 c. 31: 6 5 2 8 3 2 5 N SD: 5.7033 c. M:-10.3616 c. 34: 6 6 2 9 3 2 6 N SD: 6.4675 c. M: 11.6979 c. 43: 8 7 3 11 4 3 7 N SD: 5.4497 c. M: 8.7679 c. 48: 9 8 3 13 4 3 8 N SD: 4.7098 c. M:-11.3137 c. 53: 10 9 3 14 5 3 9 N SD: 1.9630 c. M:-2.9525 c. 65: 12 11 4 17 6 4 11 N SD: 1.6712 c. M: 2.7572 c. 87: 16 15 5 23 8 5 15 N SD: 1.7127 c. M: 2.9865 c. 118: 22 20 7 31 11 7 20 N SD: 0.2645 c. M:-0.5202 c. 323: 60 55 19 85 30 19 55 N SD: 0.3085 c. M: 0.5524 c. 376: 70 64 22 99 35 22 64 N SD: 0.1958 c. M: 0.3453 c. 441: 82 75 26 116 41 26 75 N SD: 0.1859 c. M: 0.3333 c. 494: 92 84 29 130 46 29 84 N SD: 0.0951 c. M:-0.1578 c. 612: 114 104 36 161 57 36 104 N SD: 0.0501 c. M:-0.0784 c. 730: 136 124 43 192 68 43 124 N SD: 0.0552 c. M:-0.0991 c. 1171: 218 199 69 308 109 69 199 N SD: 0.0379 c. M: 0.0638 c. 1289: 240 219 76 339 120 76 219 N SD: 0.0377 c. M: 0.0646 c. 1665: 310 283 98 438 155 98 283 N SD: 0.0283 c. M: 0.0540 c. 1783: 332 303 105 469 166 105 303 N SD: 0.0107 c. M: 0.0189 c. 1901: 354 323 112 500 177 112 323 N SD: 0.0114 c. M: 0.0185 c. 2395: 446 407 141 630 223 141 407 N SD: 0.0106 c. M:-0.0178 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: 13.6863 cents 4 x 5 x 6 x 7:8 S SD: 30.5297 cents 5:6 x 7:8 x 9:10 S SD: 25.3725 cents 6:7 x 8 x 10:11:12 S SD: 16.0101 cents 7:8:9 x 11:12 x 14 SD: 6.7867 cents 8:9:10:11:13 x 14:16 SD: 13.3020 cents 9:10 x 12:14:15:16:18 S SD: 12.6384 cents 10:11:13 x 16:17:18:20 SD: 11.3606 cents 13:15 x 17:21:22:23:26 SD: 7.9540 cents 14:16:18:19:22:24:25:28 SD: 6.6238 cents 15:17:19:20:24:26:27:30 SD: 5.6379 cents 21:24:27:28:34:36:37:42 SD: 4.1386 cents 27:31:35:36:43:46:48:54 SD: 4.0407 cents 28:32:36:37:45:48:50:56 SD: 3.3148 cents 30:34:38:40:48:51:53:60 SD: 3.3144 cents 35:40:45:47:56:60:62:70 SD: 2.7427 cents 36:41:46:48:58:61:64:72 SD: 2.5164 cents 42:48:54:56:67:72:75:84 SD: 2.3233 cents 45:51:58:60:72:77:80:90 SD: 2.0689 cents 50:57:64:67:80:85:89:100 SD: 1.6694 cents 57:65:73:76:91:97:101:114 SD: 1.3407 cents 72:82:92:96:115:123:128:144 SD: 0.6971 cents 117:133:150:156:187:200:208:234 SD: 0.6583 cents 132:150:169:176:211:225:235:264 SD: 0.6089 cents 147:167:188:196:235:251:261:294 SD: 0.5854 cents 150:171:192:200:240:256:267:300 SD: 0.5730 cents 153:174:196:204:245:261:272:306 SD: 0.3278 cents 225:256:288:300:360:384:400:450 SD: 0.0000 cents