Scala analysis: xen09-wilson-marwa-12-01
Marwa permutation 1 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: 675/512 478.492430 wide augmented third 3: 45/32 590.223716 diatonic tritone 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: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 10/9 182.4037 minor whole tone 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: 3 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 225/128 976.537 cents augmented sixth 6: 1 128/75 925.418 cents diminished seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 274.6 478.5 590.2 772.6 976.5 1088.3 1200.0 274.6 : 203.9 315.6 498.0 702.0 813.7 925.4 1200.0 478.5 : 111.7 294.1 498.0 609.8 721.5 996.1 1200.0 590.2 : 182.4 386.3 498.0 609.8 884.4 1088.3 1200.0 772.6 : 203.9 315.6 427.4 702.0 905.9 1017.6 1200.0 976.5 : 111.7 223.5 498.0 702.0 813.7 996.1 1200.0 1088.3: 111.7 386.3 590.2 702.0 884.4 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 : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 185.03605 cents, oct.: 1295.25238 cents Scale is not proper Step pattern alph. order: ABCDBCC Step pattern size order : DCABCAA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.483493 Lumma stability : 0.202513 Lumma impropriety factor : 0.170400 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 : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 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 subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 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: 675 Scale harmonicity : 0.032468 Average absolute harmonicity : 0.188869 Specific harmonicity : 0.162905 Fundamental : 1/512, -9.0000 octaves, 0.5110 Hz. Guide tone : 1350, 10.3987 octaves, 353194.513 Hz. Exponens Consonantiae : 6.912000E+05, 19.39874 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 911.5, average 130.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.28379, average 1.61197 Sum of Tenney's harmonic distance : 21.81984, average 3.11712 Vogel's harmonic complexity : 15.28571 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 127.77395, average 4.56336 Lattice compactness (without 2's) : 51.76965, average 1.84892 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -9 .. 1 -4.71429 35 1 3: 0 .. 3 1.28571 9 5: 0 .. 2 1.42857 10 6 Average exponent except 2's : 19 / 7 = 2.71429 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 92.7184 c. M: 135.6353 c. Lebeng 8: 2 1 1 1 2 0 1 N D3 SD: 35.7105 c. M:-73.4626 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 42.3299 c. M: 78.4924 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 25.0864 c. M: 52.6274 c. 12: 3 2 1 2 2 1 1 N SD: 19.4260 c. M:-27.3726 c. 17: 4 3 1 3 3 1 2 N SD: 16.7942 c. M: 29.4452 c. 20: 5 3 2 3 3 2 2 N SD: 12.7622 c. M:-25.4176 c. 22: 5 4 2 3 4 2 2 N SD: 7.2594 c. M:-12.4167 c. 31: 7 5 3 5 5 3 3 N SD: 7.5527 c. M: 13.9763 c. 41: 9 7 4 6 7 4 4 N SD: 8.7079 c. M: 11.6518 c. 42: 10 7 4 6 7 4 4 N SD: 6.6086 c. M:-11.1319 c. 43: 10 7 4 7 7 4 4 N SD: 4.3278 c. M:-8.7679 c. 53: 12 9 5 8 9 5 5 N SD: 2.3500 c. M: 3.0207 c. 65: 15 11 6 10 11 6 6 N SD: 1.7020 c. M:-2.7572 c. 118: 27 20 11 18 20 11 11 N SD: 0.2890 c. M: 0.5263 c. 376: 86 64 35 57 64 35 35 N SD: 0.1664 c. M: 0.2870 c. 494: 113 84 46 75 84 46 46 N SD: 0.0749 c. M: 0.1578 c. 612: 140 104 57 93 104 57 57 N SD: 0.0554 c. M: 0.0784 c. 1171: 268 199 109 178 199 109 109 N SD: 0.0495 c. M:-0.0729 c. 1289: 295 219 120 196 219 120 120 N SD: 0.0345 c. M:-0.0646 c. 1783: 408 303 166 271 303 166 166 N SD: 0.0151 c. M:-0.0269 c. 1901: 435 323 177 289 323 177 177 N SD: 0.0090 c. M:-0.0185 c. 2395: 548 407 223 364 407 223 223 N SD: 0.0084 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 4 x x 5 x 6 S SD: 31.4099 cents 4 x 5 x 6:7 x 8 S SD: 29.1022 cents 5:6 x 7:8:9 x 10 S SD: 14.3066 cents 6:7:8 x 9 x 11:12 SD: 16.6734 cents 7:8:9:10:11:12:13:14 H SD: 11.7525 cents 8:9 x 11:13:14:15:16 SD: 17.6211 cents 9:11:12:13:14:16:17:18 SD: 13.1268 cents 10:12:13:14:16:18:19:20 S SD: 11.2778 cents 11:13 x 15:17:19:21:22 SD: 12.1408 cents 12:14:16:17:19:21:23:24 SD: 7.3376 cents 16:19:21:23:25:28:30:32 SD: 6.5350 cents 17:20:22:24:27:30:32:34 SD: 6.4140 cents 18:21:24:25:28:32:34:36 SD: 5.5500 cents 22:26:29:31:34:39:41:44 SD: 4.3131 cents 25:29:33:35:39:44:47:50 SD: 2.8877 cents 34:40:45:48:53:60:64:68 SD: 2.2415 cents 41:48:54:58:64:72:77:82 SD: 1.5987 cents 57:67:75:80:89:100:107:114 SD: 1.1731 cents 69:81:91:97:108:121:129:138 SD: 1.1169 cents 82:96:108:115:128:144:154:164 SD: 0.9192 cents 94:110:124:132:147:165:176:188 SD: 0.7478 cents 116:136:153:163:181:204:218:232 SD: 0.7168 cents 123:144:162:173:192:216:231:246 SD: 0.6297 cents 128:150:169:180:200:225:240:256 SD: 0.3661 cents 185:217:244:260:289:325:347:370 SD: 0.3459 cents 226:265:298:318:353:397:424:452 SD: 0.3172 cents 251:294:331:353:392:441:471:502 SD: 0.2932 cents 261:306:344:367:408:459:489:522 SD: 0.2820 cents 286:335:377:402:447:503:536:572 SD: 0.2507 cents 320:375:422:450:500:563:600:640 SD: 0.2316 cents 327:383:431:460:511:575:613:654 SD: 0.1957 cents 377:442:497:530:589:663:707:754 SD: 0.1841 cents 384:450:506:540:600:675:720:768 SD: 0.1222 cents 512:600:675:720:800:900:960:1024 SD: 0.0000 cents