Scala analysis: xen09-wilson-marwa-16a-03
Marwa permutation 3 from Figure 16a, Schlesinger 16/15 15/13 13/12
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/13 247.741053 tridecimal 5/4-tone 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 5/3 884.358713 major sixth, BP 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: 15/13 247.7411 tridecimal 5/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 9/8 203.9100 major whole tone 4: 128/117 155.5623 5: 13/12 138.5727 tridecimal 2/3-tone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 247.7 386.3 590.2 745.8 884.4 1088.3 1200.0 247.7 : 138.6 342.5 498.0 636.6 840.5 952.3 1200.0 386.3 : 203.9 359.5 498.0 702.0 813.7 1061.4 1200.0 590.2 : 155.6 294.1 498.0 609.8 857.5 996.1 1200.0 745.8 : 138.6 342.5 454.2 702.0 840.5 1044.4 1200.0 884.4 : 203.9 315.6 563.4 702.0 905.9 1061.4 1200.0 1088.3: 111.7 359.5 498.0 702.0 857.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 416/405, 46.3939 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 416/405, 46.3939 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 : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 128/117, 155.5623 cents, amount: 1 Least squares average step : 179.46850 cents, oct.: 1256.27948 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : EBDCBDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.571781 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393003 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / 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 : 512/507, 16.9897 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 Best major thirds form a closed circle 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 n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 45 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.205247 Specific harmonicity : 0.129298 Fundamental : 1/1248, -10.2854 octaves, 0.2096 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 90.5, average 12.92857 Mersenne's string divisions : 127512 Sum of van Prooijen's expressibility: 6.51728, average 0.93104 Sum of Tenney's harmonic distance : 12.72070, average 1.81724 Vogel's harmonic complexity : 21.85714 Wille's k value : 877 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 90.22349, average 3.22227 Lattice compactness (without 2's) : 41.55051, average 1.48395 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.00000 13 1 3: -1 .. 2 0.42857 5 5: 0 .. 1 0.85714 6 4 13: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 55.2808 c. M: 76.3125 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 35.0702 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 37.0064 c. M: 56.8904 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 22.5163 c. M: 44.3587 c. 13: 3 1 2 2 2 2 1 P D3 S SD: 25.0621 c. M:-38.7182 c. 14: 3 2 2 2 1 3 1 P T3 SD: 24.0381 c. M:-42.2577 c. 16: 3 2 3 2 2 3 1 P D3 SD: 18.3316 c. M:-36.7313 c. 18: 4 2 3 2 2 3 2 P T3 S SD: 15.0038 c. M: 21.6020 c. 19: 4 2 3 3 2 3 2 SP D3 SD: 11.4198 c. M: 21.8027 c. 23: 5 2 4 3 3 4 2 SP S SD: 12.9856 c. M: 21.0963 c. 24: 5 3 4 3 3 4 2 P SD: 9.9141 c. M:-15.6413 c. 29: 6 3 5 4 3 5 3 SP SD: 10.0313 c. M: 15.3932 c. 30: 6 4 5 4 3 5 3 P SD: 9.5035 c. M:-14.2139 c. 31: 6 4 5 4 4 5 3 SP SD: 8.3933 c. M: 15.4830 c. 34: 7 4 6 4 4 6 3 P SD: 4.7692 c. M:-9.7763 c. 35: 7 4 6 5 4 6 3 SP SD: 7.5524 c. M: 9.1709 c. 42: 9 5 7 5 5 7 4 P SD: 7.4472 c. M:-13.6863 c. 43: 9 5 7 6 5 7 4 SP SD: 5.1100 c. M:-8.6645 c. 53: 11 6 9 7 6 9 5 SP SD: 1.3087 c. M: 1.5445 c. 130: 27 15 22 17 15 22 12 SP SD: 1.3201 c. M:-1.9063 c. 140: 29 16 24 18 16 24 13 SP SD: 0.8326 c. M: 1.5016 c. 193: 40 22 33 25 22 33 18 SP SD: 0.7626 c. M: 1.4572 c. 224: 46 26 38 29 26 38 21 SP SD: 0.8489 c. M: 1.3125 c. 246: 51 28 42 32 28 42 23 SP SD: 0.8065 c. M: 1.4319 c. 248: 51 29 42 32 29 42 23 SP SD: 0.6978 c. M:-1.1252 c. 270: 56 31 46 35 31 46 25 SP SD: 0.6966 c. M:-1.1478 c. 277: 57 32 47 36 32 47 26 SP SD: 0.7515 c. M: 1.0540 c. 301: 62 35 51 39 35 51 28 SP SD: 0.3919 c. M:-0.6911 c. 354: 73 41 60 46 41 60 33 SP SD: 0.2447 c. M: 0.3932 c. 407: 84 47 69 53 47 69 38 SP SD: 0.2543 c. M: 0.5431 c. 441: 91 51 75 57 51 75 41 SP SD: 0.1494 c. M:-0.2525 c. 494: 102 57 84 64 57 84 46 SP SD: 0.0699 c. M: 0.1482 c. 848: 175 98 144 110 98 144 79 SP SD: 0.0728 c. M: 0.1294 c. 1289: 266 149 219 167 149 219 120 SP SD: 0.0580 c. M: 0.1072 c. 1342: 277 155 228 174 155 228 125 SP SD: 0.0373 c. M: 0.0598 c. 1836: 379 212 312 238 212 312 171 SP SD: 0.0326 c. M: 0.0450 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 23.7906 cents 5:6 x 7:8 x 9:10 S SD: 23.8956 cents 6:7 x 8:9:10:11:12 S SD: 18.4825 cents 7:8:9:10:11:12:13:14 H SD: 12.2863 cents 8:9:10:11:12:13:15:16 SD: 12.1866 cents 12:14:15:17:18:20:23:24 SD: 8.9194 cents 13:15:16:18:20:22:24:26 SD: 7.6399 cents 15:17:19:21:23:25:28:30 SD: 5.7897 cents 19:22:24:27:29:32:36:38 SD: 5.6054 cents 20:23:25:28:31:33:38:40 SD: 4.7138 cents 24:28:30:34:37:40:45:48 SD: 3.3264 cents 32:37:40:45:49:53:60:64 SD: 2.0049 cents 39:45:49:55:60:65:73:78 SD: 1.5081 cents 64:74:80:90:98:107:120:128 SD: 1.4868 cents 71:82:89:100:109:118:133:142 SD: 1.2255 cents 72:83:90:101:111:120:135:144 SD: 0.8314 cents 96:111:120:135:148:160:180:192 SD: 0.7279 cents 104:120:130:146:160:173:195:208 SD: 0.6369 cents 111:128:139:156:171:185:208:222 SD: 0.6132 cents 136:157:170:191:209:227:255:272 SD: 0.5709 cents 143:165:179:201:220:238:268:286 SD: 0.5157 cents 175:202:219:246:269:292:328:350 SD: 0.4808 cents 189:218:236:266:291:315:354:378 SD: 0.4740 cents 195:225:244:274:300:325:366:390 SD: 0.4093 cents 216:249:270:304:332:360:405:432 SD: 0.3826 cents 241:278:301:339:371:402:452:482 SD: 0.3492 cents 273:315:341:384:420:455:512:546 SD: 0.2004 cents 312:360:390:439:480:520:585:624 SD: 0.1409 cents 384:443:480:540:591:640:720:768 SD: 0.1057 cents