Scala analysis: xen09-wilson-marwa-16b-01
Marwa permutation 1 from Figure 16b, Schlesinger 13/12 15/13 16/15
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: 18/13 563.382340 tridecimal augmented fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 45/26 949.696054 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 15/13 247.7411 tridecimal 5/4-tone 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: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 10/9 182.404 cents minor whole tone 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 6/5 315.641 cents minor 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: 2 5/3 884.359 cents major sixth, BP sixth 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 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 247.7 451.7 563.4 745.8 949.7 1061.4 1200.0 247.7 : 203.9 315.6 498.0 702.0 813.7 952.3 1200.0 451.7 : 111.7 294.1 498.0 609.8 748.3 996.1 1200.0 563.4 : 182.4 386.3 498.0 636.6 884.4 1088.3 1200.0 745.8 : 203.9 315.6 454.2 702.0 905.9 1017.6 1200.0 949.7 : 111.7 250.3 498.0 702.0 813.7 996.1 1200.0 1061.4: 138.6 386.3 590.2 702.0 884.4 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 181.00985 cents, oct.: 1267.06893 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : EDACDAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.535644 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 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 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.023500 Average absolute harmonicity : 0.169964 Specific harmonicity : 0.121232 Fundamental : 1/104, -6.7004 octaves, 2.5156 Hz. Guide tone : 1080, 10.0768 octaves, 282555.611 Hz. Exponens Consonantiae : 1.123200E+05, 16.77726 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 221.0, average 31.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.30147, average 1.18592 Sum of Tenney's harmonic distance : 17.08496, average 2.44071 Vogel's harmonic complexity : 12.00000 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 82.20640, average 2.93594 Lattice compactness (without 2's) : 48.25431, average 1.72337 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42857 11 1 3: 0 .. 3 1.28571 9 5: 0 .. 1 0.57143 4 13: -1 .. 0 -0.85714 6 6 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 16 28| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 68.9973 c. M: 108.7939 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 30.9207 c. M:-52.2589 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 21.7797 c. M:-36.6177 c. 11: 2 2 1 2 2 1 1 P D3 S SD: 22.8301 c. M:-32.1221 c. 15: 3 3 1 2 3 1 2 N SD: 17.3421 c. M:-28.3489 c. 18: 4 3 1 3 3 2 2 P SD: 16.6341 c. M: 30.0490 c. 19: 4 3 2 3 3 2 2 P SD: 7.9525 c. M:-12.2569 c. 24: 5 4 2 4 4 2 3 P SD: 6.9215 c. M: 13.3823 c. 34: 7 6 3 5 6 3 4 P SD: 3.6296 c. M:-7.1725 c. 53: 11 9 5 8 9 5 6 P SD: 1.7346 c. M:-2.7236 c. 77: 16 13 7 12 13 7 9 P SD: 1.5611 c. M: 2.3434 c. 111: 23 19 10 17 19 10 13 P SD: 1.4504 c. M:-2.4030 c. 130: 27 22 12 20 22 12 15 P SD: 1.0380 c. M:-1.9063 c. 183: 38 31 17 28 31 17 21 P SD: 1.0773 c. M:-1.7549 c. 217: 45 37 20 33 37 20 25 P SD: 1.0512 c. M:-1.8052 c. 224: 46 38 21 34 38 21 26 SP SD: 1.1488 c. M: 1.6511 c. 234: 48 40 22 35 40 22 27 SP SD: 1.1318 c. M: 2.1963 c. 236: 49 40 22 36 40 22 27 P SD: 1.1715 c. M:-1.6716 c. 241: 50 41 22 37 41 22 28 P SD: 1.0613 c. M:-1.4610 c. 253: 52 43 24 38 43 24 29 SP SD: 0.9924 c. M: 1.1220 c. 258: 53 44 24 39 44 24 30 SP SD: 0.9504 c. M: 1.6000 c. 277: 57 47 26 42 47 26 32 SP SD: 0.6853 c. M: 1.1095 c. 311: 64 53 29 47 53 29 36 SP SD: 0.5643 c. M: 1.0915 c. 330: 68 56 31 50 56 31 38 SP SD: 0.4572 c. M: 0.7420 c. 354: 73 60 33 54 60 33 41 SP SD: 0.4840 c. M: 0.8036 c. 364: 75 62 34 55 62 34 42 SP SD: 0.3724 c. M: 0.7311 c. 383: 79 65 36 58 65 36 44 SP SD: 0.4242 c. M:-0.7137 c. 388: 80 66 36 59 66 36 45 SP SD: 0.3678 c. M: 0.6026 c. 407: 84 69 38 62 69 38 47 SP SD: 0.2622 c. M: 0.5454 c. 441: 91 75 41 67 75 41 51 SP SD: 0.1291 c. M: 0.2078 c. 494: 102 84 46 75 84 46 57 SP SD: 0.1113 c. M:-0.1804 c. 901: 186 153 84 137 153 84 104 SP SD: 0.0728 c. M: 0.1527 c. 935: 193 159 87 142 159 87 108 SP SD: 0.0683 c. M: 0.1176 c. 1342: 277 228 125 204 228 125 155 SP SD: 0.0514 c. M: 0.0862 c. 1395: 288 237 130 212 237 130 161 SP SD: 0.0409 c. M:-0.0780 c. 1783: 368 303 166 271 303 166 206 SP SD: 0.0607 c. M: 0.0766 c. 1836: 379 312 171 279 312 171 212 SP SD: 0.0214 c. M: 0.0344 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 x 9:10 S SD: 21.4551 cents 6:7:8 x 9:10:11:12 S SD: 15.6826 cents 7:8:9:10:11:12:13:14 H SD: 10.3052 cents 9:10:12 x 14:16:17:18 S SD: 17.0858 cents 10:12:13:14:15:17:18:20 SD: 14.1347 cents 11:13:14:15:17:19:20:22 SD: 9.4292 cents 13:15:17:18:20:23:24:26 SD: 5.7341 cents 19:22:25:26:29:33:35:38 SD: 5.0339 cents 20:23:26:28:31:35:37:40 SD: 4.4083 cents 26:30:34:36:40:45:48:52 SD: 1.8252 cents 57:66:74:79:88:99:105:114 SD: 1.6140 cents 60:69:78:83:92:104:111:120 SD: 1.3962 cents 67:77:87:93:103:116:124:134 SD: 1.3325 cents 70:81:91:97:108:121:129:140 SD: 1.2093 cents 71:82:92:98:109:123:131:142 SD: 1.0937 cents 78:90:101:108:120:135:144:156 SD: 0.6114 cents 104:120:135:144:160:180:192:208 SD: 0.0000 cents