Scala analysis: xen09-wilson-marwa-12-05
Marwa permutation 5 from Figure 12, Helmholtz 16/15 16/15 75/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75/64 274.582429 classic augmented second 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 25/16 772.627428 classic augmented fifth 5: 225/128 976.537429 augmented sixth 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: 75/64 274.5824 classic augmented second 2: 16/15 111.7313 minor diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 75/64 274.5824 classic augmented second 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 75/64 274.582 cents classic augmented second 2: 2 256/225 223.463 cents Neapolitan diminished third 2: 1 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 2: 1 675/512 478.492 cents wide augmented third 3: 1 32/25 427.373 cents classic diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 5: 1 1024/675 721.508 cents narrow diminished sixth 5: 3 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 225/128 976.537 cents augmented sixth 6: 2 128/75 925.418 cents diminished seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 274.6 386.3 498.0 772.6 976.5 1088.3 1200.0 274.6 : 111.7 223.5 498.0 702.0 813.7 925.4 1200.0 386.3 : 111.7 386.3 590.2 702.0 813.7 1088.3 1200.0 498.0 : 274.6 478.5 590.2 702.0 976.5 1088.3 1200.0 772.6 : 203.9 315.6 427.4 702.0 813.7 925.4 1200.0 976.5 : 111.7 223.5 498.0 609.8 721.5 996.1 1200.0 1088.3: 111.7 386.3 498.0 609.8 884.4 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 16/15, 111.7313 cents 2: 223.4626 .. 478.4924 cents 151875/131072, 255.0299 cents 16384/16875,-51.1199 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 721.5076 .. 976.5374 cents 151875/131072, 255.0299 cents 16384/16875,-51.1199 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.534293 Largest / Average step : 1.601731 Largest / Smallest step : 2.457525 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 181.74396 cents, oct.: 1272.20770 cents Scale is not proper Step pattern alph. order: ABBACBB Step pattern size order : LSSLMSS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.436072 Lumma stability : 0.202513 Lumma impropriety factor : 0.170400 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common triad is 0.0 111.731 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 675 (O: 675 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.033557 Average absolute harmonicity : 0.223157 Specific harmonicity : 0.168273 Fundamental : 1/384, -8.5850 octaves, 0.6813 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 3.456000E+05, 18.39874 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 287.5, average 41.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.97737, average 1.13962 Sum of Tenney's harmonic distance : 15.50312, average 2.21473 Vogel's harmonic complexity : 14.28571 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 121.31848, average 4.33280 Lattice compactness (without 2's) : 46.75645, average 1.66987 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -2.71429 25 1 3: -1 .. 2 0.42857 5 1 5: 0 .. 2 1.14286 8 5 Average exponent except 2's : 11 / 7 = 1.57143 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 94.1012 c. M: 155.1879 c. 8: 1 1 1 2 1 1 1 P M ME I SD: 68.7788 c. M: 124.5824 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 25.5727 c. M: 43.2041 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 27.5823 c. M: 52.6274 c. Pseudo Rast 12: 3 1 1 3 2 1 1 N SD: 18.0260 c. M:-27.3726 c. Chromatic Phrygian 17: 4 1 2 4 3 1 2 N SD: 17.7610 c. M: 33.3725 c. 19: 4 2 2 4 3 2 2 P SD: 16.3392 c. M: 29.1690 c. 21: 5 2 2 5 3 2 2 N SD: 13.9226 c. M:-27.3726 c. 22: 5 2 2 5 4 2 2 N SD: 5.2136 c. M: 8.9911 c. 31: 7 3 3 7 5 3 3 N SD: 4.4669 c. M: 8.7955 c. 43: 10 4 4 10 7 4 4 N SD: 4.3852 c. M:-8.7679 c. 53: 12 5 5 12 9 5 5 N SD: 2.0401 c. M: 2.9525 c. 65: 15 6 6 15 11 6 6 N SD: 1.6811 c. M:-2.7572 c. 87: 20 8 8 20 15 8 8 N SD: 1.3906 c. M:-2.7729 c. 96: 22 9 9 22 16 9 9 N SD: 1.4136 c. M:-2.3726 c. 118: 27 11 11 27 20 11 11 N SD: 0.1840 c. M: 0.2662 c. 376: 86 35 35 86 64 35 35 N SD: 0.1464 c. M: 0.2870 c. 494: 113 46 46 113 84 46 46 N SD: 0.0795 c. M: 0.1578 c. 612: 140 57 57 140 104 57 57 N SD: 0.0515 c. M: 0.0784 c. 730: 167 68 68 167 124 68 68 N SD: 0.0511 c. M: 0.0991 c. 1171: 268 109 109 268 199 109 109 N SD: 0.0392 c. M:-0.0638 c. 1289: 295 120 120 295 219 120 120 N SD: 0.0364 c. M:-0.0646 c. 1547: 354 144 144 354 263 144 144 N SD: 0.0359 c. M:-0.0624 c. 1665: 381 155 155 381 283 155 155 N SD: 0.0209 c. M:-0.0391 c. 1783: 408 166 166 408 303 166 166 N SD: 0.0096 c. M:-0.0189 c. 1901: 435 177 177 435 323 177 177 N SD: 0.0093 c. M:-0.0185 c. 2395: 548 223 223 548 407 223 223 N SD: 0.0090 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 17.7730 cents 5:6 x 7:8:9 x 10 S SD: 22.0837 cents 6:7 x 8:9 x 11:12 SD: 16.2083 cents 7:8:9 x 11:12:13:14 SD: 13.4566 cents 9 x 11:12:14:16:17:18 SD: 7.6715 cents 10:12 x 13:16:18:19:20 SD: 14.4381 cents 11:13:14:15:17:19:21:22 SD: 10.0560 cents 12:14:15:16:19:21:23:24 SD: 6.5350 cents 16:19:20:21:25:28:30:32 SD: 5.2072 cents 23:27:29:31:36:40:43:46 SD: 4.4274 cents 24:28:30:32:38:42:45:48 SD: 3.6274 cents 33:39:41:44:52:58:62:66 SD: 3.3531 cents 36:42:45:48:56:63:68:72 SD: 2.6405 cents 39:46:49:52:61:69:73:78 SD: 2.6405 cents 41:48:51:55:64:72:77:82 SD: 2.0148 cents 48:56:60:64:75:84:90:96 SD: 1.5580 cents 57:67:71:76:89:100:107:114 SD: 1.2908 cents 75:88:94:100:117:132:141:150 SD: 1.1017 cents 87:102:109:116:136:153:163:174 SD: 0.6303 cents 128:150:160:171:200:225:240:256 SD: 0.4826 cents 144:169:180:192:225:253:270:288 SD: 0.3860 cents 192:225:240:256:300:338:360:384 SD: 0.3661 cents 231:271:289:308:361:406:433:462 SD: 0.3568 cents 240:281:300:320:375:422:450:480 SD: 0.2318 cents 297:348:371:396:464:522:557:594 SD: 0.1848 cents 384:450:480:512:600:675:720:768 SD: 0.0000 cents