Scala analysis: xen09-wilson-marwa-16a-08
Marwa permutation 8 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: 4/3 498.044999 perfect fourth 4: 20/13 745.786052 tridecimal semi-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: 15/13 247.7411 tridecimal 5/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 16/15 111.7313 minor diatonic semitone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 13/12 138.5727 tridecimal 2/3-tone 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: 2 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 2 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 5/4 386.314 cents major 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 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 45/26 949.696 cents 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 247.7 386.3 498.0 745.8 884.4 996.1 1200.0 247.7 : 138.6 250.3 498.0 636.6 748.3 952.3 1200.0 386.3 : 111.7 359.5 498.0 609.8 813.7 1061.4 1200.0 498.0 : 247.7 386.3 498.0 702.0 949.7 1088.3 1200.0 745.8 : 138.6 250.3 454.2 702.0 840.5 952.3 1200.0 884.4 : 111.7 315.6 563.4 702.0 813.7 1061.4 1200.0 996.1 : 203.9 451.7 590.2 702.0 949.7 1088.3 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 173.54272 cents, oct.: 1214.79906 cents Scale is strictly proper Step pattern alph. order: ABCABCD Step pattern size order : DBADBAC Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.515941 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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 0.0 701.955 1088.269 cents, amount: 2 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 : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 15 Scale harmonicity : 0.023500 Average absolute harmonicity : 0.230789 Specific harmonicity : 0.126838 Fundamental : 1/468, -8.8704 octaves, 0.5590 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.123200E+05, 16.77726 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 56.5, average 8.07143 Mersenne's string divisions : 138600 Sum of van Prooijen's expressibility: 5.11934, average 0.73133 Sum of Tenney's harmonic distance : 10.72070, average 1.53153 Vogel's harmonic complexity : 19.85714 Wille's k value : 292 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 77.52976, average 2.76892 Lattice compactness (without 2's) : 42.19760, average 1.50706 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 11 1 3: -2 .. 1 -0.42857 5 2 5: 0 .. 1 0.57143 4 2 13: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 11 15 24| 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: 43.7202 c. M: 76.3125 c. Lebeng 8: 2 1 0 2 1 1 1 N D3 SD: 41.8568 c. M:-63.6863 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 26.7610 c. M: 44.3587 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 26.2587 c. M: 47.7411 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 13: 3 1 1 3 2 1 2 N S SD: 25.0747 c. M:-38.7182 c. 15: 3 2 1 3 2 1 3 N SD: 19.1209 c. M: 36.0900 c. 16: 3 2 2 3 2 1 3 P SD: 17.2334 c. M:-26.9550 c. 18: 4 2 1 4 2 2 3 N SD: 16.9599 c. M: 31.3783 c. 19: 4 2 2 4 2 2 3 P SD: 8.3266 c. M:-14.4363 c. 24: 5 3 2 5 3 2 4 P SD: 8.2283 c. M:-15.6413 c. 29: 6 3 3 6 3 3 5 P SD: 7.9509 c. M: 15.3932 c. 34: 7 4 3 7 4 3 6 P SD: 3.9015 c. M: 7.8547 c. 53: 11 6 5 11 6 5 9 P SD: 1.0314 c. M: 1.4081 c. 140: 29 16 13 29 16 13 24 P SD: 1.0266 c. M: 1.8043 c. 164: 34 19 15 34 19 15 28 P SD: 0.9101 c. M:-1.4912 c. 183: 38 21 17 38 21 17 31 P SD: 0.9829 c. M:-1.7549 c. 193: 40 22 18 40 22 18 33 P SD: 0.9145 c. M: 1.4572 c. 217: 45 25 20 45 25 20 37 P SD: 0.6772 c. M:-1.1069 c. 270: 56 31 25 56 31 25 46 P SD: 0.6073 c. M:-1.1478 c. 277: 57 32 26 57 32 26 47 SP SD: 0.5525 c. M: 0.8096 c. 301: 62 35 28 62 35 28 51 SP SD: 0.4567 c. M:-0.6911 c. 335: 69 39 31 69 39 31 57 SP SD: 0.4485 c. M: 0.7114 c. 354: 73 41 33 73 41 33 60 SP SD: 0.2891 c. M:-0.5202 c. 388: 80 45 36 80 45 36 66 SP SD: 0.2540 c. M: 0.4252 c. 407: 84 47 38 84 47 38 69 SP SD: 0.2201 c. M:-0.4702 c. 441: 91 51 41 91 51 41 75 SP SD: 0.1204 c. M: 0.2078 c. 494: 102 57 46 102 57 46 84 SP SD: 0.0883 c. M: 0.1482 c. 848: 175 98 79 175 98 79 144 SP SD: 0.0755 c. M:-0.1364 c. 901: 186 104 84 186 104 84 153 SP SD: 0.0677 c. M:-0.1364 c. 1289: 266 149 120 266 149 120 219 SP SD: 0.0591 c. M: 0.1072 c. 1342: 277 155 125 277 155 125 228 SP SD: 0.0291 c. M: 0.0510 c. 1836: 379 212 171 379 212 171 312 SP SD: 0.0286 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 12.9047 cents 5:6 x 7:8 x 9:10 S SD: 25.9369 cents 6:7 x 8:9:10:11:12 S SD: 11.9317 cents 7:8:9 x 11:12 x 14 SD: 15.9736 cents 8:9:10:11:12:13:14:16 S SD: 13.8098 cents 9:10:11:12:14:15:16:18 S SD: 11.2018 cents 10:12 x 13:15:17:18:20 SD: 16.7420 cents 11:13:14:15:17:18:20:22 SD: 11.7723 cents 12:14:15:16:18:20:21:24 S SD: 7.8642 cents 13:15:16:17:20:22:23:26 SD: 7.3106 cents 15:17:19:20:23:25:27:30 SD: 6.3666 cents 19:22:24:25:29:32:34:38 SD: 5.6007 cents 20:23:25:27:31:33:36:40 SD: 5.3994 cents 21:24:26:28:32:35:37:42 SD: 4.6609 cents 24:28:30:32:37:40:43:48 SD: 3.3820 cents 32:37:40:43:49:53:57:64 SD: 2.8208 cents 33:38:41:44:51:55:59:66 SD: 2.3942 cents 39:45:49:52:60:65:69:78 SD: 1.7381 cents 45:52:56:60:69:75:80:90 SD: 1.4246 cents 60:69:75:80:92:100:107:120 SD: 1.3997 cents 63:73:79:84:97:105:112:126 SD: 1.3207 cents 72:83:90:96:111:120:128:144 SD: 0.5634 cents 117:135:146:156:180:195:208:234 SD: 0.4231 cents 156:180:195:208:240:260:277:312 SD: 0.2974 cents 228:263:285:304:351:380:405:456 SD: 0.2703 cents 240:277:300:320:369:400:427:480 SD: 0.2568 cents 273:315:341:364:420:455:485:546 SD: 0.2484 cents 279:322:349:372:429:465:496:558 SD: 0.2293 cents 312:360:390:416:480:520:555:624 SD: 0.1486 cents 351:405:439:468:540:585:624:702 SD: 0.1409 cents 396:457:495:528:609:660:704:792 SD: 0.1025 cents 468:540:585:624:720:780:832:936 SD: 0.0000 cents