Scala analysis: xen09-wilson-marwa-17a-01
Marwa permutation 1 from Figure 17a, Archytas 28/27 36/35 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 45/32 590.223716 diatonic tritone 3: 35/24 653.184619 septimal semi-diminished fifth 4: 5/3 884.358713 major sixth, BP sixth 5: 15/8 1088.268715 classic major seventh 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 5/4 386.3137 major third 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 8/7 231.1741 septimal whole tone 5: 9/8 203.9100 major whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 45/32 590.224 cents diatonic tritone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 64/45 609.776 cents 2nd tritone 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 35/18 1151.230 cents septimal semi-diminished octave 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 : 386.3 590.2 653.2 884.4 1088.3 1151.2 1200.0 386.3 : 203.9 266.9 498.0 702.0 764.9 813.7 1200.0 590.2 : 63.0 294.1 498.0 561.0 609.8 996.1 1200.0 653.2 : 231.2 435.1 498.0 546.8 933.1 1137.0 1200.0 884.4 : 203.9 266.9 315.6 702.0 905.9 968.8 1200.0 1088.3: 63.0 111.7 498.0 702.0 764.9 996.1 1200.0 1151.2: 48.8 435.1 639.0 702.0 933.1 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 198.66051 cents, oct.: 1390.62356 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : ECBDCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.605831 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 245/243, 14.1905 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 45 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.208593 Specific harmonicity : 0.169958 Fundamental : 1/288, -8.1699 octaves, 0.9084 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 116.0, average 16.57143 Mersenne's string divisions : 398730024 Sum of van Prooijen's expressibility: 7.31538, average 1.04505 Sum of Tenney's harmonic distance : 13.73931, average 1.96276 Vogel's harmonic complexity : 15.00000 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 88.31954, average 3.15427 Lattice compactness (without 2's) : 50.24030, average 1.79430 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.85714 15 1 3: -2 .. 2 -0.14286 7 5: 0 .. 1 0.85714 6 4 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 1 1 1 1 1 0 N T3 SD: 46.8984 c. M: 75.9380 c. 8: 3 1 0 2 1 1 0 N SD: 39.7633 c. M:-63.6863 c. 9: 3 1 1 2 1 1 0 N SD: 35.5554 c. M: 56.8904 c. 10: 3 2 0 2 2 0 1 N SD: 39.1450 c. M: 71.2296 c. 11: 4 1 1 2 2 1 0 N G SD: 31.6948 c. M:-50.0499 c. 12: 4 2 1 2 2 1 0 N SD: 27.3480 c. M:-48.7704 c. 15: 5 2 1 3 2 1 1 N SD: 25.6314 c. M: 48.2687 c. 16: 5 3 1 3 3 0 1 N SD: 20.6374 c. M:-36.7313 c. 18: 6 3 1 3 3 1 1 N SD: 14.9503 c. M: 21.6020 c. 19: 6 3 1 4 3 1 1 N SD: 14.2235 c. M: 21.8027 c. 20: 6 4 1 4 3 1 1 N SD: 13.4884 c. M: 26.3137 c. 22: 7 4 1 4 4 1 1 N SD: 6.4725 c. M: 11.6314 c. 31: 10 5 2 6 5 2 1 N SD: 6.2370 c. M:-10.0607 c. 41: 13 7 2 8 7 2 2 N SD: 6.6271 c. M: 9.7662 c. 43: 14 7 2 9 7 2 2 N SD: 6.4321 c. M: 11.3242 c. 46: 15 8 2 9 8 2 2 N SD: 5.2692 c. M:-9.7763 c. 53: 17 9 3 10 9 3 2 N SD: 2.1446 c. M:-3.4874 c. 77: 25 13 4 15 13 4 3 N SD: 2.4878 c. M:-3.9530 c. 94: 30 16 5 18 16 5 4 N SD: 2.7287 c. M: 3.5076 c. 96: 31 16 5 19 16 5 4 N SD: 2.1023 c. M: 3.1846 c. 99: 32 17 5 19 17 5 4 N SD: 1.9049 c. M:-3.7157 c. 118: 38 20 6 23 20 6 5 N SD: 1.2021 c. M: 2.3372 c. 149: 48 25 8 29 25 8 6 N SD: 1.1780 c. M: 2.3043 c. 152: 49 26 8 29 26 8 6 N SD: 1.2861 c. M:-2.0785 c. 171: 55 29 9 33 29 9 7 N SD: 0.4533 c. M: 0.7500 c. 270: 87 46 14 52 46 14 11 N SD: 0.4376 c. M:-0.8874 c. 323: 104 55 17 62 55 17 13 N SD: 0.3844 c. M:-0.6853 c. 419: 135 71 22 81 71 22 17 N SD: 0.2878 c. M:-0.6055 c. 441: 142 75 23 85 75 23 18 N SD: 0.1498 c. M:-0.2525 c. 494: 159 84 26 95 84 26 20 N SD: 0.1378 c. M:-0.2567 c. 612: 197 104 32 118 104 32 25 N SD: 0.1346 c. M: 0.2492 c. 665: 214 113 35 128 113 35 27 N SD: 0.1151 c. M: 0.1485 c. 913: 294 155 48 176 155 48 37 N SD: 0.1058 c. M:-0.1977 c. 935: 301 159 49 180 159 49 38 N SD: 0.0762 c. M:-0.1506 c. 1106: 356 188 58 213 188 58 45 N SD: 0.0471 c. M: 0.0911 c. 1848: 595 314 97 356 314 97 75 N SD: 0.0500 c. M:-0.0691 c. 2019: 650 343 106 389 343 106 82 N SD: 0.0240 c. M:-0.0395 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 24.3852 cents 3 x 4 x 5 x x 6 S SD: 30.7262 cents 4:5 x 6:7 x x 8 S SD: 24.3840 cents 5:6:7 x 8:9 x 10 S SD: 24.5302 cents 6 x 8:9:10:11 x 12 S SD: 22.2613 cents 7:9:10 x 12:13 x 14 SD: 15.1985 cents 8:10:11:12:13:15 x 16 SD: 12.7076 cents 9:11 x 13:15:17 x 18 SD: 8.8349 cents 10:13:14:15:17:19 x 20 SD: 15.5899 cents 11:14:15:16:18:21 x 22 SD: 12.7078 cents 12:15:17:18:20 x 23:24 SD: 9.3724 cents 13:16:18:19:22:24:25:26 SD: 8.1321 cents 14:18:20 x 23:26:27:28 SD: 10.8247 cents 15:19:21:22:25:28:29:30 SD: 4.1416 cents 16:20 x 23:27:30:31:32 SD: 5.5812 cents 17:21:24:25:28:32:33:34 SD: 4.8439 cents 20:25:28:29:33:38:39:40 SD: 4.5420 cents 24:30:34:35:40:45:47:48 SD: 2.5358 cents 32:40:45:47:53:60:62:64 SD: 2.5072 cents 37:46:52:54:62:69:72:74 SD: 2.3380 cents 39:49:55:57:65:73:76:78 SD: 1.6924 cents 56:70:79:82:93:105:109:112 SD: 1.5735 cents 57:71:80:83:95:107:111:114 SD: 1.1614 cents 72:90:101:105:120:135:140:144 SD: 0.6114 cents 96:120:135:140:160:180:187:192 SD: 0.4412 cents 168:210:236:245:280:315:327:336 SD: 0.3636 cents 177:221:249:258:295:332:344:354 SD: 0.3525 cents 192:240:270:280:320:360:373:384 SD: 0.2209 cents 216:270:304:315:360:405:420:432 SD: 0.2035 cents 288:360:405:420:480:540:560:576 S SD: 0.0000 cents