Scala analysis: xen12-wilson-40-5C2-dekany-03
1-3-7-9-11 5C2 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 21/16 470.780907 narrow fourth 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 3/2 701.955001 perfect fifth 7: 77/48 818.188848 8: 7/4 968.825906 harmonic seventh 9: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 77/72 116.2338 undecimal secor 8: 12/11 150.6371 undecimal neutral second, 3/4-tone 9: 22/21 80.5370 undecimal minor semitone 10: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 77/72 116.234 cents undecimal secor 1: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 2: 2 9/8 203.910 cents major whole tone 2: 1 112/99 213.598 cents 2: 3 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 33/28 284.447 cents undecimal minor third 3: 1 7/6 266.871 cents septimal minor third 3: 1 33/28 284.447 cents undecimal minor third 3: 3 11/9 347.408 cents undecimal neutral third 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 96/77 381.811 cents 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 21/16 470.781 cents narrow fourth 4: 5 4/3 498.045 cents perfect fourth 4: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 4/3 498.045 cents perfect fourth 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 88/63 578.582 cents 5: 1 108/77 585.721 cents 5: 1 77/54 614.279 cents 5: 1 63/44 621.418 cents 5: 2 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 3/2 701.955 cents perfect fifth 6: 1 16/11 648.682 cents undecimal semi-diminished fifth 6: 5 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 2 14/9 764.916 cents septimal minor sixth 6: 1 11/7 782.492 cents undecimal augmented fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 1 77/48 818.189 cents 7: 1 44/27 845.453 cents neutral sixth 7: 3 18/11 852.592 cents undecimal neutral sixth 7: 1 56/33 915.553 cents 7: 1 12/7 933.129 cents septimal major sixth 8: 1 56/33 915.553 cents 8: 3 12/7 933.129 cents septimal major sixth 8: 3 7/4 968.826 cents harmonic seventh 8: 1 99/56 986.402 cents 8: 2 16/9 996.090 cents Pythagorean minor seventh 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 144/77 1083.766 cents 9: 2 21/11 1119.463 cents undecimal major seventh 9: 1 27/14 1137.039 cents septimal major seventh 9: 1 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 53.3 203.9 266.9 470.8 551.3 702.0 818.2 968.8 1049.4 1200.0 53.3 : 150.6 213.6 417.5 498.0 648.7 764.9 915.6 996.1 1146.7 1200.0 203.9 : 63.0 266.9 347.4 498.0 614.3 764.9 845.5 996.1 1049.4 1200.0 266.9 : 203.9 284.4 435.1 551.3 702.0 782.5 933.1 986.4 1137.0 1200.0 470.8 : 80.5 231.2 347.4 498.0 578.6 729.2 782.5 933.1 996.1 1200.0 551.3 : 150.6 266.9 417.5 498.0 648.7 702.0 852.6 915.6 1119.5 1200.0 702.0 : 116.2 266.9 347.4 498.0 551.3 702.0 764.9 968.8 1049.4 1200.0 818.2 : 150.6 231.2 381.8 435.1 585.7 648.7 852.6 933.1 1083.8 1200.0 968.8 : 80.5 231.2 284.4 435.1 498.0 702.0 782.5 933.1 1049.4 1200.0 1049.4: 150.6 203.9 354.5 417.5 621.4 702.0 852.6 968.8 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 203.9100 cents 12/11, 150.6371 cents 33/32, 53.2729 cents 2: 203.9100 .. 284.4470 cents 22/21, 80.5370 cents 1/1, 0.0000 cents 3: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 4: 417.5080 .. 551.3179 cents 121/112, 133.8100 cents 98/99,-17.5761 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 32/33,-53.2729 cents 6: 648.6821 .. 782.4920 cents 121/112, 133.8100 cents 32/33,-53.2729 cents 7: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 8: 915.5530 .. 996.0900 cents 22/21, 80.5370 cents 98/99,-17.5761 cents 9: 996.0900 .. 1146.7271 cents 12/11, 150.6371 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 2.252551 Largest / Average step : 1.699250 Largest / Smallest step : 3.827647 Median interval of one step : 133.43545 cents, amount: 0 Most common interval of one step : 12/11, 150.6371 cents, amount: 4 Least squares average step : 116.97492 cents, oct.: 1169.74921 cents Scale is not proper Step pattern alph. order: ABCDEBFBEB Step pattern size order : AEBFCEDECE Scale is not a Constant Structure Scale diversity : 1.497083 Lumma stability : 0.088788 Lumma impropriety factor : 0.147375 Rothenberg efficiency : 0.343571 redundancy: 0.656429 Efficiency x scale size : 3.435714 Number of different interval sizes : 40 = 4.44444 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 77 Scale harmonicity : 0.023547 Average absolute harmonicity : 0.176491 Specific harmonicity : 0.111579 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 1.330560E+05, 17.02167 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 156.0, average 15.60000 Mersenne's string divisions : 640872375 Sum of van Prooijen's expressibility: 9.93157, average 0.99316 Sum of Tenney's harmonic distance : 18.88868, average 1.88887 Vogel's harmonic complexity : 13.50000 Wille's k value : 49 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 161.03049, average 2.92783 Lattice compactness (without 2's) : 87.83999, average 1.59709 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.30000 25 1 3: -1 .. 2 0.20000 8 2 7: 0 .. 1 0.40000 4 3 11: 0 .. 1 0.40000 4 4 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 16 / 10 = 1.60000
FIT/MODE
10: 1 1 0 2 1 1 1 1 1 1 N T3 SD: 32.7870 c. M:-66.7271 c. 13: 1 1 1 2 1 2 1 1 1 2 P D3 SD: 26.1292 c. M: 45.7490 c. 15: 1 2 0 3 1 2 1 2 1 2 N SD: 19.2906 c. M:-36.0900 c. 16: 1 2 1 2 1 2 2 2 1 2 P D3 SD: 19.8755 c. M:-33.1291 c. 17: 1 2 1 3 1 2 2 2 1 2 N SD: 16.2486 c. M:-28.8700 c. 19: 1 2 1 3 2 2 2 2 2 2 N SD: 16.5407 c. M: 28.6756 c. 21: 1 3 1 3 2 2 2 3 1 3 P SD: 16.1317 c. M:-24.6614 c. 22: 1 3 1 4 1 3 2 3 1 3 N SD: 10.3336 c. M:-20.1282 c. 26: 1 3 2 4 2 3 3 3 2 3 N SD: 10.0775 c. M: 19.2946 c. 31: 1 4 2 5 2 4 3 4 2 4 N SD: 7.3289 c. M: 14.5633 c. 38: 2 4 2 7 2 5 4 5 2 5 N SD: 9.7071 c. M: 14.4758 c. 40: 2 5 2 7 2 5 4 5 3 5 N SD: 7.7039 c. M: 11.9550 c. 41: 2 5 2 7 3 5 4 5 3 5 N SD: 3.1448 c. M:-5.2636 c. 63: 3 8 3 11 4 8 6 8 4 8 N SD: 3.0880 c. M:-5.6138 c. 72: 3 9 4 12 5 9 7 9 5 9 N SD: 2.3646 c. M: 4.1142 c. 89: 4 11 5 15 6 11 9 11 6 11 N SD: 2.0680 c. M:-4.2831 c. 94: 4 12 5 16 6 12 9 12 6 12 N SD: 1.5627 c. M: 2.5544 c. 135: 6 17 7 23 9 17 13 17 9 17 N SD: 0.3085 c. M:-0.5344 c. 477: 21 60 25 81 32 60 46 60 32 60 N SD: 0.3194 c. M: 0.5788 c. 494: 22 62 26 84 33 62 48 62 33 62 N SD: 0.2745 c. M:-0.4742 c. 566: 25 71 30 96 38 71 55 71 38 71 N SD: 0.1979 c. M: 0.3764 c. 629: 28 79 33 107 42 79 61 79 42 79 N SD: 0.2257 c. M:-0.4433 c. 670: 30 84 35 114 45 84 65 84 45 84 N SD: 0.2508 c. M:-0.4584 c. 701: 31 88 37 119 47 88 68 88 47 88 N SD: 0.1210 c. M: 0.2059 c. 836: 37 105 44 142 56 105 81 105 56 105 N SD: 0.0872 c. M: 0.1629 c. 877: 39 110 46 149 59 110 85 110 59 110 N SD: 0.0737 c. M:-0.1239 c. 1012: 45 127 53 172 68 127 98 127 68 127 N SD: 0.0498 c. M:-0.0867 c. 1713: 76 215 90 291 115 215 166 215 115 215 N SD: 0.0283 c. M: 0.0571 c. 1848: 82 232 97 314 124 232 179 232 124 232 N SD: 0.0130 c. M: 0.0262 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 23.8555 cents 4 x x x 5 x 6 x 7 x 8 S SD: 21.1168 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 13.2379 cents 6 x x 7:8 x 9:10 x 11:12 S SD: 11.9278 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 13.8826 cents 8 x 9 x x 11:12:13:14:15:16 SD: 6.4090 cents 9 x 10:11:12 x x 14:16:17:18 S SD: 16.8695 cents 10 x 11:12:13:14:15:16 x 18:20 S SD: 9.8180 cents 11 x 12:13:14:15:17:18:19:20:22 SD: 11.6294 cents 12 x x 14:16:17:18:19:21:22:24 SD: 7.8328 cents 13:14 x 15:17:18:20:21:23:24:26 SD: 10.3940 cents 14:15:16 x 18:19:21:22:25:26:28 SD: 11.0581 cents 15:16:17:18:20:21:23:24:26:28:30 SD: 10.1937 cents 16:17:18:19:21:22:24:26:28:29:32 SD: 6.7086 cents 18:19:20:21:24:25:27:29:32:33:36 SD: 6.2725 cents 20:21 x 23:26:28:30:32:35:37:40 SD: 6.1933 cents 22:23:25:26:29:30:33:35:39:40:44 SD: 5.0367 cents 23:24:26:27:30:32:35:37:40:42:46 SD: 4.4063 cents 24:25:27:28:32:33:36:39:42:44:48 SD: 3.9308 cents 25:26:28:29:33:34:38:40:44:46:50 SD: 3.8893 cents 29:30:33:34:38:40:44:47:51:53:58 SD: 3.6589 cents 30:31:34:35:39:41:45:48:53:55:60 SD: 2.9159 cents 32:33:36:37:42:44:48:51:56:59:64 SD: 2.1552 cents 48:50:54:56:63:66:72:77:84:88:96 SD: 1.7399 cents 58:60:65:68:76:80:87:93:102:106:116 SD: 1.6908 cents 61:63:69:71:80:84:92:98:107:112:122 SD: 1.5470 cents 64:66:72:75:84:88:96:103:112:117:128 SD: 1.0734 cents 90:93:101:105:118:124:135:144:158:165:180 SD: 0.9822 cents 96:99:108:112:126:132:144:154:168:176:192 SD: 0.0000 cents