Scala analysis: xen09-wilson-marwa-16a-01
Marwa permutation 1 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: 135/104 451.651055 3: 45/32 590.223716 diatonic tritone 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 45/26 949.696054 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: 9/8 203.9100 major whole tone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 128/117 155.5623 5: 9/8 203.9100 major whole tone 6: 13/12 138.5727 tridecimal 2/3-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 52/45 250.304 cents 2: 1 32/27 294.135 cents Pythagorean 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: 1 135/104 451.651 cents 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: 1 208/135 748.349 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 45/26 949.696 cents 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 : 247.7 451.7 590.2 745.8 949.7 1088.3 1200.0 247.7 : 203.9 342.5 498.0 702.0 840.5 952.3 1200.0 451.7 : 138.6 294.1 498.0 636.6 748.3 996.1 1200.0 590.2 : 155.6 359.5 498.0 609.8 857.5 1061.4 1200.0 745.8 : 203.9 342.5 454.2 702.0 905.9 1044.4 1200.0 949.7 : 138.6 250.3 498.0 702.0 840.5 996.1 1200.0 1088.3: 111.7 359.5 563.4 702.0 857.5 1061.4 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: 250.3039 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 676/675, 2.5629 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 : 182.73536 cents, oct.: 1279.14755 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : EDBCDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.512925 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 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 : 676/675, 2.5629 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 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 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.180191 Specific harmonicity : 0.105102 Fundamental : 1/416, -8.7004 octaves, 0.6289 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 237.0, average 33.85714 Mersenne's string divisions : 360625188 Sum of van Prooijen's expressibility: 8.90288, average 1.27184 Sum of Tenney's harmonic distance : 17.45913, average 2.49416 Vogel's harmonic complexity : 17.42857 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 97.15520, average 3.46983 Lattice compactness (without 2's) : 48.25431, average 1.72337 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.28571 15 1 3: 0 .. 3 1.28571 9 5: 0 .. 1 0.85714 6 2 13: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 11 / 7 = 1.57143 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is JI-epimorphic with val: <7 11 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 74.7995 c. M: 108.7939 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 31.1247 c. M:-52.2589 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 16.0296 c. M:-28.3489 c. 14: 3 2 2 2 2 2 1 P T3 SD: 17.3116 c. M:-26.0170 c. 18: 4 3 2 2 3 2 2 P SD: 14.9699 c. M: 21.6020 c. 19: 4 3 2 3 3 2 2 P SD: 11.6811 c. M: 21.8027 c. 23: 5 4 2 3 4 3 2 P SD: 12.8792 c. M:-17.9142 c. 24: 5 4 3 3 4 3 2 P SD: 6.0813 c. M:-11.7313 c. 34: 7 6 4 4 6 4 3 P SD: 5.5224 c. M:-9.7763 c. 43: 9 7 5 6 7 5 4 P SD: 4.0646 c. M:-7.7023 c. 53: 11 9 6 7 9 6 5 P SD: 1.2624 c. M: 1.5445 c. 130: 27 22 15 17 22 15 12 P SD: 1.1122 c. M:-1.9063 c. 183: 38 31 21 24 31 21 17 P SD: 1.0096 c. M:-1.7549 c. 224: 46 38 26 29 38 26 21 SP SD: 1.1602 c. M: 1.6511 c. 236: 49 40 27 31 40 27 22 P SD: 1.0056 c. M:-1.6716 c. 248: 51 42 29 32 42 29 23 SP SD: 0.9234 c. M: 1.6511 c. 258: 53 44 30 33 44 30 24 SP SD: 0.8687 c. M: 1.6000 c. 277: 57 47 32 36 47 32 26 SP SD: 0.8595 c. M: 1.1095 c. 301: 62 51 35 39 51 35 28 SP SD: 0.5983 c. M: 1.1527 c. 311: 64 53 36 40 53 36 29 SP SD: 0.5556 c. M: 1.0915 c. 335: 69 57 39 43 57 39 31 SP SD: 0.5701 c. M:-0.8211 c. 354: 73 60 41 46 60 41 33 SP SD: 0.4131 c. M: 0.8036 c. 364: 75 62 42 47 62 42 34 SP SD: 0.3729 c. M: 0.7311 c. 388: 80 66 45 50 66 45 36 SP SD: 0.3249 c. M:-0.4979 c. 417: 86 71 48 54 71 48 39 SP SD: 0.3029 c. M: 0.4989 c. 441: 91 75 51 57 75 51 41 SP SD: 0.1480 c. M:-0.2525 c. 494: 102 84 57 64 84 57 46 SP SD: 0.0807 c. M:-0.1708 c. 935: 193 159 108 121 159 108 87 SP SD: 0.0909 c. M:-0.1506 c. 1289: 266 219 149 167 219 149 120 SP SD: 0.0881 c. M: 0.1383 c. 1342: 277 228 155 174 228 155 125 SP SD: 0.0551 c. M: 0.0862 c. 1783: 368 303 206 231 303 206 166 SP SD: 0.0499 c. M: 0.0766 c. 1836: 379 312 212 238 312 212 171 SP SD: 0.0259 c. M: 0.0344 c. 2330: 481 396 269 302 396 269 217 SP SD: 0.0203 c. M: 0.0350 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 4 x x 5 x 6 S SD: 26.7111 cents 4 x 5 x 6:7 x 8 S SD: 20.2424 cents 5:6 x 7:8:9 x 10 S SD: 23.5718 cents 6:7:8 x 9:10:11:12 S SD: 16.8508 cents 7:8:9:10:11:12:13:14 H SD: 8.0667 cents 13:15:17:18:20:23:24:26 SD: 7.8921 cents 15:17:19:21:23:26:28:30 SD: 7.7217 cents 17:20:22:24:26:29:32:34 SD: 6.3615 cents 19:22:25:27:29:33:36:38 SD: 5.4765 cents 20:23:26:28:31:35:38:40 SD: 4.8625 cents 24:28:31:34:37:42:45:48 SD: 4.4757 cents 26:30:34:37:40:45:49:52 SD: 3.6859 cents 30:35:39:42:46:52:56:60 SD: 3.2933 cents 33:38:43:46:51:57:62:66 SD: 2.7611 cents 34:39:44:48:52:59:64:68 SD: 2.6683 cents 37:43:48:52:57:64:69:74 SD: 2.2648 cents 47:54:61:66:72:81:88:94 SD: 1.8934 cents 54:62:70:76:83:93:101:108 SD: 1.8924 cents 57:66:74:80:88:99:107:114 SD: 1.6027 cents 64:74:83:90:98:111:120:128 SD: 1.3902 cents 67:77:87:94:103:116:126:134 SD: 1.3763 cents 71:82:92:100:109:123:133:142 SD: 0.8818 cents 104:120:135:146:160:180:195:208 SD: 0.4231 cents 175:202:227:246:269:303:328:350 SD: 0.3349 cents 182:210:236:256:280:315:341:364 SD: 0.3241 cents 234:270:304:329:360:405:439:468 SD: 0.2519 cents 241:278:313:339:371:417:452:482 SD: 0.2431 cents 286:330:371:402:440:495:536:572 SD: 0.2331 cents 305:352:396:429:469:528:572:610 SD: 0.1715 cents 312:360:405:439:480:540:585:624 SD: 0.1409 cents 409:472:531:575:629:708:767:818 SD: 0.1387 cents 416:480:540:585:640:720:780:832 SD: 0.0000 cents