Scala analysis: xen12-wilson-40-5C2-dekany-01
1-3-5-7-11 5C2 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/48 235.676655 undecimal semi-augmented whole tone 2: 7/6 266.870906 septimal minor third 3: 5/4 386.313714 major third 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 35/24 653.184619 septimal semi-diminished fifth 6: 77/48 818.188848 7: 5/3 884.358713 major sixth, BP sixth 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: 55/48 235.6767 undecimal semi-augmented whole tone 2: 56/55 31.1943 undecimal diesis, konbini comma 3: 15/14 119.4428 major diatonic semitone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 35/33 101.8667 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 80/77 66.1699 8: 21/20 84.4672 minor semitone 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 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 80/77 66.170 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/20 84.467 cents minor semitone 1: 1 35/33 101.867 cents 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 55/48 235.677 cents undecimal semi-augmented whole tone 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 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 2: 1 5/4 386.314 cents major third 3: 1 8/7 231.174 cents septimal whole tone 3: 3 6/5 315.641 cents minor third 3: 1 40/33 333.041 cents 3: 2 5/4 386.314 cents major third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 77/60 431.875 cents 3: 1 55/42 466.851 cents 4: 1 96/77 381.811 cents 4: 1 44/35 396.178 cents 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 2 4/3 498.045 cents perfect fourth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 3 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 4/3 498.045 cents perfect fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 3 10/7 617.488 cents Euler's tritone 5: 1 35/24 653.185 cents septimal semi-diminished fifth 5: 1 3/2 701.955 cents perfect fifth 6: 3 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 22/15 663.049 cents undecimal diminished fifth 6: 2 3/2 701.955 cents perfect fifth 6: 2 11/7 782.492 cents undecimal augmented fifth 6: 1 35/22 803.822 cents 6: 1 77/48 818.189 cents 7: 1 84/55 733.149 cents 7: 1 120/77 768.125 cents 7: 1 11/7 782.492 cents undecimal augmented fifth 7: 2 8/5 813.686 cents minor sixth 7: 1 33/20 866.959 cents 7: 3 5/3 884.359 cents major sixth, BP sixth 7: 1 7/4 968.826 cents harmonic seventh 8: 1 8/5 813.686 cents minor sixth 8: 1 56/33 915.553 cents 8: 3 12/7 933.129 cents septimal major sixth 8: 2 7/4 968.826 cents harmonic seventh 8: 1 20/11 1034.996 cents large minor seventh 8: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 96/55 964.323 cents 9: 2 20/11 1034.996 cents large minor seventh 9: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 28/15 1080.557 cents grave major seventh 9: 1 66/35 1098.133 cents 9: 1 40/21 1115.533 cents acute major seventh 9: 1 21/11 1119.463 cents undecimal major seventh 9: 1 77/40 1133.830 cents 9: 1 55/28 1168.806 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 6.88889 = 62/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 235.7 266.9 386.3 551.3 653.2 818.2 884.4 968.8 1049.4 1200.0 235.7 : 31.2 150.6 315.6 417.5 582.5 648.7 733.1 813.7 964.3 1200.0 266.9 : 119.4 284.4 386.3 551.3 617.5 702.0 782.5 933.1 1168.8 1200.0 386.3 : 165.0 266.9 431.9 498.0 582.5 663.0 813.7 1049.4 1080.6 1200.0 551.3 : 101.9 266.9 333.0 417.5 498.0 648.7 884.4 915.6 1035.0 1200.0 653.2 : 165.0 231.2 315.6 396.2 546.8 782.5 813.7 933.1 1098.1 1200.0 818.2 : 66.2 150.6 231.2 381.8 617.5 648.7 768.1 933.1 1035.0 1200.0 884.4 : 84.5 165.0 315.6 551.3 582.5 702.0 867.0 968.8 1133.8 1200.0 968.8 : 80.5 231.2 466.9 498.0 617.5 782.5 884.4 1049.4 1115.5 1200.0 1049.4: 150.6 386.3 417.5 537.0 702.0 803.8 968.8 1035.0 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 235.6767 cents 3025/2688, 204.4824 cents 56/55, 31.1943 cents 2: 150.6371 .. 386.3137 cents 55/48, 235.6767 cents 576/605,-85.0396 cents 3: 231.1741 .. 466.8507 cents 55/48, 235.6767 cents 32/35,-155.1396 cents 4: 381.8112 .. 551.3179 cents 847/768, 169.5068 cents 576/605,-85.0396 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 32/33,-53.2729 cents 6: 648.6821 .. 818.1888 cents 847/768, 169.5068 cents 32/33,-53.2729 cents 7: 733.1493 .. 968.8259 cents 55/48, 235.6767 cents 576/605,-85.0396 cents 8: 813.6863 .. 1049.3629 cents 55/48, 235.6767 cents 32/35,-155.1396 cents 9: 964.3233 .. 1168.8057 cents 3025/2688, 204.4824 cents 576/605,-85.0396 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 55/48, 235.6767 cents Average / Smallest step : 3.846863 Largest / Average step : 1.963972 Largest / Smallest step : 7.555131 Median interval of one step : 110.65474 cents, amount: 0 Most common interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 123.88071 cents, oct.: 1238.80707 cents Scale is not proper Step pattern alph. order: ABCDEDFGHI Step pattern size order : IAFHEHBDCG Scale is not a Constant Structure Scale diversity : 1.562078 Lumma stability : 0.051990 Lumma impropriety factor : 0.615811 Rothenberg efficiency : 0.283333 redundancy: 0.716667 Efficiency x scale size : 2.833333 Number of different interval sizes : 50 = 5.55556 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 6.88889 = 62/9 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 441/440, 3.9302 cents Most common triad is 0.0 165.004 315.641 cents, amount: 2 Number of recognisable fifths : 3, average 701.9550 cents Length of longest harmonic part : 2 at degree 7 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 77 Scale harmonicity : 0.023510 Average absolute harmonicity : 0.158059 Specific harmonicity : 0.103747 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 770, 9.5887 octaves, 201451.685 Hz. Exponens Consonantiae : 3.696000E+04, 15.17368 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 183.5, average 18.35000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.34184, average 1.03418 Sum of Tenney's harmonic distance : 19.52620, average 1.95262 Vogel's harmonic complexity : 12.50000 Wille's k value : 38 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 141.95320, average 2.58097 Lattice compactness (without 2's) : 76.67925, average 1.39417 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.90000 21 1 3: -1 .. 0 -0.60000 6 5: 0 .. 1 0.40000 4 2 7: 0 .. 1 0.40000 4 3 11: 0 .. 1 0.40000 4 4 Average exponent except 2's : 6 / 10 = 0.60000 Average absolute exponent except 2's: 18 / 10 = 1.80000
FIT/MODE
10: 2 0 1 2 0 2 0 1 1 1 N T3 SD: 31.7673 c. M: 53.1846 c. 11: 2 1 1 1 1 2 0 1 1 1 N D3 SD: 33.9121 c. M:-60.4018 c. 13: 3 0 1 2 1 2 1 0 1 2 N SD: 26.5609 c. M: 45.7490 c. 15: 3 0 2 2 1 2 1 1 1 2 N SD: 13.0102 c. M: 26.8709 c. 19: 4 0 2 3 1 3 1 1 2 2 N SD: 15.3753 c. M:-24.3213 c. 22: 4 1 2 3 2 3 1 2 1 3 N SD: 9.3267 c. M: 17.4948 c. 26: 5 1 2 4 2 4 1 2 2 3 N SD: 9.1364 c. M: 17.0829 c. 31: 6 1 3 4 3 4 2 2 2 4 N SD: 4.7251 c. M: 9.3825 c. 41: 8 1 4 6 3 6 2 3 3 5 N SD: 4.7548 c. M: 9.2822 c. 46: 9 1 5 6 4 6 3 3 3 6 N SD: 4.6846 c. M: 9.4932 c. 50: 10 1 5 7 4 7 3 3 4 6 N SD: 4.4680 c. M: 8.8259 c. 57: 11 2 5 8 5 8 3 4 4 7 N SD: 3.9045 c. M: 7.3663 c. 63: 12 2 6 9 5 9 3 5 4 8 N SD: 4.3434 c. M: 8.1682 c. 66: 13 2 6 9 6 9 4 4 5 8 N SD: 4.3348 c. M:-6.5504 c. 68: 13 2 7 9 6 9 4 5 4 9 N SD: 4.2573 c. M: 8.1865 c. 72: 14 2 7 10 6 10 4 5 5 9 N SD: 1.8636 c. M: 3.1846 c. 152: 30 4 15 21 13 21 8 11 10 19 N SD: 1.5386 c. M:-2.8638 c. 161: 32 4 16 22 14 22 9 11 11 20 N SD: 1.7672 c. M:-2.8327 c. 167: 33 4 17 23 14 23 9 12 11 21 N SD: 1.1510 c. M:-1.9755 c. 198: 39 5 20 27 17 27 11 14 13 25 N SD: 0.8139 c. M:-1.5651 c. 224: 44 6 22 31 19 31 12 16 15 28 N SD: 0.7123 c. M:-1.4540 c. 239: 47 6 24 33 20 33 13 17 16 30 N SD: 0.4998 c. M:-0.9833 c. 270: 53 7 27 37 23 37 15 19 18 34 N SD: 0.2551 c. M: 0.4741 c. 494: 97 13 49 68 42 68 27 35 33 62 N SD: 0.2393 c. M:-0.4346 c. 566: 111 15 56 78 48 78 31 40 38 71 N SD: 0.2339 c. M: 0.4480 c. 733: 144 19 73 101 62 101 40 52 49 92 N SD: 0.2260 c. M:-0.3874 c. 742: 146 19 74 102 63 102 41 52 50 93 N SD: 0.2145 c. M:-0.4419 c. 764: 150 20 76 105 65 105 42 54 51 96 N SD: 0.1432 c. M:-0.2840 c. 814: 160 21 81 112 69 112 45 57 55 102 N SD: 0.1528 c. M: 0.2755 c. 836: 164 22 83 115 71 115 46 59 56 105 N SD: 0.1327 c. M: 0.2700 c. 1003: 197 26 100 138 85 138 55 71 67 126 N SD: 0.1512 c. M:-0.2668 c. 1034: 203 27 103 142 88 142 57 73 69 130 N SD: 0.1349 c. M: 0.2333 c. 1075: 211 28 107 148 91 148 59 76 72 135 N SD: 0.1271 c. M: 0.2657 c. 1084: 213 28 108 149 92 149 60 76 73 136 N SD: 0.1000 c. M: 0.1912 c. 1106: 217 29 110 152 94 152 61 78 74 139 N SD: 0.1165 c. M: 0.2336 c. 1308: 257 34 130 180 111 180 72 92 88 164 N SD: 0.0951 c. M:-0.1783 c. 1354: 266 35 135 186 115 186 75 95 91 170 N SD: 0.0977 c. M: 0.1682 c. 1578: 310 41 157 217 134 217 87 111 106 198 N SD: 0.0448 c. M:-0.0667 c. 1848: 363 48 184 254 157 254 102 130 124 232 N SD: 0.0343 c. M:-0.0621 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 24.3852 cents 3 x x x 4 x x 5 x x 6 S SD: 17.7576 cents 4 x x 5 x 6 x x 7 x 8 S SD: 12.1926 cents 5 x 6 x 7 x 8 x x 9:10 S SD: 13.2379 cents 6 x 7 x 8:9 x 10 x 11:12 S SD: 12.0376 cents 7:8 x 9 x 10:11 x 12:13:14 S SD: 11.7114 cents 8:9 x 10:11:12:13 x 14:15:16 S SD: 9.1859 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 13.0131 cents 10:11:12:13:14:15:16:17 x 18:20 S SD: 14.7154 cents 11 x 13:14:15:16 x 18:19:20:22 SD: 7.3170 cents 12 x 14:15 x 18:19:20:21:22:24 S SD: 6.7207 cents 13:15 x 16:18:19:21:22:23:24:26 SD: 5.4134 cents 14:16 x 18:19:20:22:23:25:26:28 SD: 9.8145 cents 15:17:18:19:21:22:24:25:26:28:30 SD: 7.4854 cents 16:18:19:20:22:23:26:27:28:29:32 SD: 6.2623 cents 18 x 21:23:25:26:29:30:32:33:36 SD: 5.9049 cents 19 x 22:24:26:28:30:32:33:35:38 SD: 5.2319 cents 20:23 x 25:28:29:32:33:35:37:40 SD: 4.5535 cents 24 x 28:30:33:35:39:40:42:44:48 SD: 2.4821 cents 25 x 29:31:34:36:40:42:44:46:50 SD: 4.2738 cents 26:30 x 33:36:38:42:43:46:48:52 SD: 4.7557 cents 27:31:32:34:37:39:43:45:47:50:54 SD: 4.2090 cents 28:32:33:35:39:41:45:47:49:51:56 SD: 3.4165 cents 29:33:34:36:40:42:47:48:51:53:58 SD: 3.3054 cents 31 x 36:39:43:45:50:52:54:57:62 SD: 3.1107 cents 32 x 37:40:44:47:51:53:56:59:64 SD: 3.0106 cents 35:40:41:44:48:51:56:58:61:64:70 SD: 1.9460 cents 38 x 44:48:52:55:61:63:67:70:76 SD: 3.6181 cents 39:45:46:49:54:57:63:65:68:72:78 SD: 3.2763 cents 40:46:47:50:55:58:64:67:70:73:80 SD: 2.1137 cents 41:47:48:51:56:60:66:68:72:75:82 SD: 2.0910 cents 43:49:50:54:59:63:69:72:75:79:86 SD: 1.9445 cents 48:55:56:60:66:70:77:80:84:88:96 SD: 0.0000 cents