Scala analysis: xen09-wilson-marwa-14a-07
Marwa permutation 7 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: 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: 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: 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: 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: 2 75/64 274.582 cents classic augmented second 2: 1 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: 2 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: 2 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished 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 : 223.5 427.4 498.0 813.7 925.4 1129.3 1200.0 223.5 : 203.9 274.6 590.2 702.0 905.9 976.5 1200.0 427.4 : 70.7 386.3 498.0 702.0 772.6 996.1 1200.0 498.0 : 315.6 427.4 631.3 702.0 925.4 1129.3 1200.0 813.7 : 111.7 315.6 386.3 609.8 813.7 884.4 1200.0 925.4 : 203.9 274.6 498.0 702.0 772.6 1088.3 1200.0 1129.3: 70.7 294.1 498.0 568.7 884.4 996.1 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: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 125/128,-41.0589 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: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 125/128,-41.0589 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 : 183.07244 cents, oct.: 1281.50706 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DCAEBCA Scale is not a Constant Structure Scale diversity : 1.534657 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.435374 redundancy: 0.564626 Efficiency x scale size : 3.047619 Number of different interval sizes : 24 = 4.00000 / 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 Best fifths form a closed circle 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 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 225 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.215856 Specific harmonicity : 0.172166 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 418.5, average 59.78571 Mersenne's string divisions : 406292523 Sum of van Prooijen's expressibility: 8.19922, average 1.17132 Sum of Tenney's harmonic distance : 17.70724, average 2.52961 Vogel's harmonic complexity : 12.57143 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 109.70655, average 3.91809 Lattice compactness (without 2's) : 49.38040, average 1.76359 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.28571 30 1 3: -2 .. 1 -0.42857 5 1 5: -2 .. 0 -1.28571 9 5 Average exponent except 2's :-12 / 7 =-1.71429 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 61.8938 c. M: 100.7561 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 52.3886 c. M: 79.3276 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 33.8853 c. M: 62.6609 c. 10: 2 2 0 3 1 1 1 N SD: 33.1454 c. M:-52.6274 c. 11: 2 2 0 3 1 2 1 N SD: 39.0431 c. M: 61.6814 c. 12: 2 2 1 3 1 2 1 P D3 SD: 20.6918 c. M: 29.3276 c. Ionian Augmented, Ionian sharp 5 16: 3 3 1 4 1 3 1 N SD: 17.0450 c. M:-26.9550 c. 17: 3 3 1 4 2 3 1 N SD: 15.1772 c. M: 37.2157 c. 19: 4 3 1 5 2 3 1 N SD: 15.6413 c. M:-29.1690 c. 21: 4 3 2 5 2 4 1 N SD: 14.8006 c. M: 27.3726 c. 22: 4 4 1 6 2 4 1 N SD: 7.9586 c. M:-16.1270 c. 31: 6 5 2 8 3 5 2 N SD: 4.8676 c. M:-8.7955 c. 34: 6 6 2 9 3 6 2 N SD: 5.7460 c. M: 11.6979 c. 48: 9 8 3 13 4 8 3 N SD: 4.7617 c. M:-11.3137 c. 53: 10 9 3 14 5 9 3 N SD: 2.2202 c. M:-2.9525 c. 65: 12 11 4 17 6 11 4 N SD: 2.0329 c. M: 3.1737 c. 87: 16 15 5 23 8 15 5 N SD: 1.4406 c. M: 2.7729 c. 118: 22 20 7 31 11 20 7 N SD: 0.2628 c. M: 0.5140 c. 323: 60 55 19 85 30 55 19 N SD: 0.2655 c. M: 0.5524 c. 376: 70 64 22 99 35 64 22 N SD: 0.2269 c. M:-0.4597 c. 441: 82 75 26 116 41 75 26 N SD: 0.1765 c. M: 0.3333 c. 494: 92 84 29 130 46 84 29 N SD: 0.1169 c. M:-0.2271 c. 559: 104 95 33 147 52 95 33 N SD: 0.1463 c. M: 0.2068 c. 612: 114 104 36 161 57 104 36 N SD: 0.0592 c. M:-0.0842 c. 730: 136 124 43 192 68 124 43 N SD: 0.0477 c. M:-0.0991 c. 1171: 218 199 69 308 109 199 69 N SD: 0.0397 c. M: 0.0638 c. 1665: 310 283 98 438 155 283 98 N SD: 0.0252 c. M:-0.0418 c. 1783: 332 303 105 469 166 303 105 N SD: 0.0091 c. M: 0.0189 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 6:7 x 8 S SD: 31.6761 cents 5:6 x 7:8:9 x 10 S SD: 31.0667 cents 6:7 x 8 x 10 x 12 S SD: 14.9376 cents 7:8:9 x 11:12:13:14 SD: 11.1458 cents 9:10 x 12:14:15:17:18 SD: 13.4888 cents 10:11:13 x 16:17:19:20 SD: 11.1957 cents 12:14:15:16:19:20:23:24 SD: 10.6844 cents 13:15 x 17:21:22:25:26 SD: 7.8452 cents 14:16:18:19:22:24:27:28 SD: 6.6238 cents 15:17:19:20:24:26:29:30 SD: 5.0276 cents 21:24:27:28:34:36:40:42 SD: 4.0114 cents 28:32:36:37:45:48:54:56 SD: 3.3148 cents 35:40:45:47:56:60:67:70 SD: 2.6987 cents 36:41:46:48:58:61:69:72 SD: 2.5528 cents 42:48:54:56:67:72:81:84 SD: 2.3233 cents 50:57:64:67:80:85:96:100 SD: 1.6406 cents 51:58:65:68:82:87:98:102 SD: 1.6308 cents 57:65:73:76:91:97:109:114 SD: 1.4582 cents 65:74:83:87:104:111:125:130 SD: 1.2069 cents 72:82:92:96:115:123:138:144 SD: 0.8189 cents 115:131:147:153:184:196:221:230 SD: 0.8077 cents 117:133:150:156:187:200:225:234 SD: 0.7682 cents 123:140:157:164:197:210:236:246 SD: 0.7668 cents 125:142:160:167:200:213:240:250 SD: 0.7371 cents 129:147:165:172:206:220:248:258 SD: 0.7365 cents 132:150:169:176:211:225:253:264 SD: 0.6574 cents 147:167:188:196:235:251:282:294 SD: 0.5360 cents 150:171:192:200:240:256:288:300 SD: 0.4826 cents 153:174:196:204:245:261:294:306 SD: 0.3850 cents 210:239:269:280:336:358:403:420 SD: 0.3605 cents 225:256:288:300:360:384:432:450 SD: 0.0000 cents