Scala analysis: xen09-wilson-marwa-12-08
Marwa permutation 8 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: 5/3 884.358713 major sixth, BP sixth 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: 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: 16/15 111.7313 minor diatonic semitone 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
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 : 274.6 386.3 498.0 772.6 884.4 996.1 1200.0 274.6 : 111.7 223.5 498.0 609.8 721.5 925.4 1200.0 386.3 : 111.7 386.3 498.0 609.8 813.7 1088.3 1200.0 498.0 : 274.6 386.3 498.0 702.0 976.5 1088.3 1200.0 772.6 : 111.7 223.5 427.4 702.0 813.7 925.4 1200.0 884.4 : 111.7 315.6 590.2 702.0 813.7 1088.3 1200.0 996.1 : 203.9 478.5 590.2 702.0 976.5 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 : 174.50134 cents, oct.: 1221.50941 cents Scale is not proper Step pattern alph. order: ABBABBC Step pattern size order : LSSLSSM 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 0.0 701.955 1088.269 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 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: 75 Scale harmonicity : 0.032468 Average absolute harmonicity : 0.236696 Specific harmonicity : 0.175086 Fundamental : 1/576, -9.1699 octaves, 0.4542 Hz. Guide tone : 1200, 10.2288 octaves, 313950.678 Hz. Exponens Consonantiae : 6.912000E+05, 19.39874 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 116.0, average 16.57143 Mersenne's string divisions : 71807400 Sum of van Prooijen's expressibility: 6.10231, average 0.87176 Sum of Tenney's harmonic distance : 12.29900, average 1.75700 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 : 119.84246, average 4.28009 Lattice compactness (without 2's) : 45.92803, average 1.64029 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -0.71429 19 1 3: -2 .. 1 -0.42857 5 2 5: 0 .. 2 0.85714 6 4 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 47.4376 c. M:-84.5154 c. 8: 2 1 0 2 1 1 1 N D3 SD: 39.0481 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 37.0792 c. M:-70.5767 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 34.3382 c. M: 52.6274 c. 12: 3 1 1 3 1 1 2 N SD: 16.2410 c. M:-27.3726 c. Chromatic Hypodorian inverse 16: 4 1 2 3 2 1 3 N SD: 19.6471 c. M:-26.9550 c. 17: 4 1 2 4 1 2 3 N SD: 19.4836 c. M: 37.2999 c. 19: 4 2 2 4 2 2 3 P SD: 12.0338 c. M: 21.9508 c. 22: 5 2 2 5 2 2 4 N SD: 8.4040 c. M: 14.2718 c. 31: 7 3 3 7 3 3 5 N SD: 5.1534 c. M:-10.3616 c. 34: 8 3 3 8 3 3 6 N SD: 4.7807 c. M: 7.8547 c. 53: 12 5 5 12 5 5 9 N SD: 1.6925 c. M: 2.8843 c. 65: 15 6 6 15 6 6 11 N SD: 1.6506 c. M:-2.7572 c. 87: 20 8 8 20 8 8 15 N SD: 1.4834 c. M: 2.9865 c. 118: 27 11 11 27 11 11 20 N SD: 0.2850 c. M:-0.5202 c. 323: 74 30 30 74 30 30 55 N SD: 0.2340 c. M: 0.4244 c. 376: 86 35 35 86 35 35 64 N SD: 0.2284 c. M: 0.3453 c. 441: 101 41 41 101 41 41 75 N SD: 0.1367 c. M:-0.2475 c. 494: 113 46 46 113 46 46 84 N SD: 0.1101 c. M: 0.1578 c. 612: 140 57 57 140 57 57 104 N SD: 0.0465 c. M: 0.0784 c. 730: 167 68 68 167 68 68 124 N SD: 0.0416 c. M:-0.0744 c. 1171: 268 109 109 268 109 109 199 N SD: 0.0297 c. M:-0.0546 c. 1665: 381 155 155 381 155 155 283 N SD: 0.0274 c. M: 0.0540 c. 1783: 408 166 166 408 166 166 303 N SD: 0.0084 c. M: 0.0160 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 18.9373 cents 5:6 x 7:8 x 9:10 S SD: 20.9465 cents 6:7 x 8:9:10:11:12 S SD: 14.8062 cents 7:8:9 x 11:12 x 14 SD: 16.4179 cents 8:9:10:11 x 13:14:16 SD: 17.0759 cents 9 x 11:12:14:15:16:18 SD: 6.6104 cents 10:12 x 13:16:17:18:20 SD: 13.8751 cents 11:13:14:15:17:18:20:22 SD: 10.6753 cents 12:14:15:16:19:20:21:24 SD: 5.2072 cents 23:27:29:31:36:38:41:46 SD: 4.1496 cents 24:28:30:32:38:40:43:48 SD: 3.9559 cents 27:32:34:36:42:45:48:54 SD: 3.5139 cents 35:41:44:47:55:58:62:70 SD: 3.1418 cents 36:42:45:48:56:60:64:72 S SD: 1.5580 cents 48:56:60:64:75:80:85:96 SD: 1.4665 cents 57:67:71:76:89:95:101:114 SD: 1.4191 cents 64:75:80:85:100:107:114:128 SD: 1.3287 cents 69:81:86:92:108:115:123:138 SD: 1.1555 cents 75:88:94:100:117:125:133:150 SD: 1.0337 cents 87:102:109:116:136:145:155:174 SD: 0.7949 cents 99:116:124:132:155:165:176:198 SD: 0.7067 cents 105:123:131:140:164:175:187:210 SD: 0.6594 cents 117:137:146:156:183:195:208:234 SD: 0.5313 cents 135:158:169:180:211:225:240:270 SD: 0.4903 cents 144:169:180:192:225:240:256:288 SD: 0.3661 cents 180:211:225:240:281:300:320:360 SD: 0.2318 cents 279:327:349:372:436:465:496:558 SD: 0.1842 cents 297:348:371:396:464:495:528:594 SD: 0.1731 cents 372:436:465:496:581:620:661:744 SD: 0.1677 cents 384:450:480:512:600:640:683:768 SD: 0.1207 cents 396:464:495:528:619:660:704:792 SD: 0.1053 cents 540:633:675:720:844:900:960:1080 SD: 0.1036 cents 576:675:720:768:900:960:1024:1152 SD: 0.0000 cents