Scala analysis: xen12-wilson-40-5C2-dekany-04
1-5-7-9-11 5C2 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 9/8 203.910002 major whole tone 3: 99/80 368.914230 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 63/40 786.422194 narrow minor sixth 7: 7/4 968.825906 harmonic seventh 8: 9/5 1017.596288 just minor seventh, BP seventh 9: 77/40 1133.830135 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80/77 66.1699 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 45/44 38.9058 1/5-tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 10/9 182.4037 minor whole tone 5: 56/55 31.1943 undecimal diesis, konbini comma 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 77/72 116.2338 undecimal secor 10: 80/77 66.1699
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 45/44 38.906 cents 1/5-tone 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 80/77 66.170 cents 1: 1 77/72 116.234 cents undecimal secor 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 1 112/99 213.598 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 1 63/55 235.104 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major third 3: 1 8/7 231.174 cents septimal whole tone 3: 1 90/77 270.080 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 1 99/80 368.914 cents 3: 1 56/45 378.602 cents septimal narrow major third 3: 1 5/4 386.314 cents major third 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 5/4 386.314 cents major third 4: 1 44/35 396.178 cents 4: 1 80/63 413.578 cents wide major third 4: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 72/55 466.278 cents undecimal semi-diminished fourth 4: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 140/99 599.912 cents quasi-equal tritone 5: 1 9/7 435.084 cents septimal major third, BP third 5: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 88/63 578.582 cents 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 5: 1 63/44 621.418 cents 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 14/9 764.916 cents septimal minor sixth 6: 1 99/70 600.088 cents 2nd quasi-equal tritone 6: 1 10/7 617.488 cents Euler's tritone 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 55/36 733.722 cents undecimal semi-augmented fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 11/7 782.492 cents undecimal augmented fifth 6: 1 63/40 786.422 cents narrow minor sixth 6: 1 35/22 803.822 cents 6: 1 8/5 813.686 cents minor sixth 7: 1 14/9 764.916 cents septimal minor sixth 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 1 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 1 160/99 831.086 cents 7: 2 18/11 852.592 cents undecimal neutral sixth 7: 1 77/45 929.920 cents 7: 1 7/4 968.826 cents harmonic seventh 8: 1 8/5 813.686 cents minor sixth 8: 1 18/11 852.592 cents undecimal neutral sixth 8: 1 110/63 964.896 cents 8: 2 7/4 968.826 cents harmonic seventh 8: 1 99/56 986.402 cents 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 20/11 1034.996 cents large minor seventh 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 20/11 1034.996 cents large minor seventh 9: 1 144/77 1083.766 cents 9: 1 77/40 1133.830 cents 9: 1 35/18 1151.230 cents septimal semi-diminished octave 9: 1 88/45 1161.094 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: 8.22222 = 74/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 165.0 203.9 368.9 551.3 582.5 786.4 968.8 1017.6 1133.8 1200.0 165.0 : 38.9 203.9 386.3 417.5 621.4 803.8 852.6 968.8 1035.0 1200.0 203.9 : 165.0 347.4 378.6 582.5 764.9 813.7 929.9 996.1 1161.1 1200.0 368.9 : 182.4 213.6 417.5 599.9 648.7 764.9 831.1 996.1 1035.0 1200.0 551.3 : 31.2 235.1 417.5 466.3 582.5 648.7 813.7 852.6 1017.6 1200.0 582.5 : 203.9 386.3 435.1 551.3 617.5 782.5 821.4 986.4 1168.8 1200.0 786.4 : 182.4 231.2 347.4 413.6 578.6 617.5 782.5 964.9 996.1 1200.0 968.8 : 48.8 165.0 231.2 396.2 435.1 600.1 782.5 813.7 1017.6 1200.0 1017.6: 116.2 182.4 347.4 386.3 551.3 733.7 764.9 968.8 1151.2 1200.0 1133.8: 66.2 231.2 270.1 435.1 617.5 648.7 852.6 1035.0 1083.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 203.9100 cents 495/448, 172.7158 cents 56/55, 31.1943 cents 2: 165.0042 .. 386.3137 cents 25/22, 221.3095 cents 44/45,-38.9058 cents 3: 231.1741 .. 435.0841 cents 9/8, 203.9100 cents 32/35,-155.1396 cents 4: 386.3137 .. 599.9117 cents 112/99, 213.5980 cents 35/36,-48.7704 cents 5: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 891/980,-164.8276 cents 6: 600.0883 .. 813.6863 cents 112/99, 213.5980 cents 891/980,-164.8276 cents 7: 764.9159 .. 968.8259 cents 9/8, 203.9100 cents 35/36,-48.7704 cents 8: 813.6863 .. 1034.9958 cents 25/22, 221.3095 cents 32/35,-155.1396 cents 9: 996.0900 .. 1168.8057 cents 495/448, 172.7158 cents 44/45,-38.9058 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 : 9/8, 203.9100 cents Average / Smallest step : 3.846863 Largest / Average step : 1.699250 Largest / Smallest step : 6.536782 Median interval of one step : 140.61904 cents, amount: 0 Least squares average step : 126.34534 cents, oct.: 1263.45339 cents Scale is not proper Step pattern alph. order: ABACDECFGH Step pattern size order : FBFGAHGCED Scale is not a Constant Structure Scale diversity : 1.454030 Lumma stability : 0.051990 Lumma impropriety factor : 0.679406 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 : 8 Highest interval variety : 9 Mean interval variety : 8.22222 = 74/9 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 9801/9800, 0.1766 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.022123 Average absolute harmonicity : 0.152871 Specific harmonicity : 0.097077 Fundamental : 1/80, -6.3219 octaves, 3.2703 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 1.108800E+05, 16.75864 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 248.0, average 24.80000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.36293, average 1.13629 Sum of Tenney's harmonic distance : 21.57735, average 2.15774 Vogel's harmonic complexity : 13.80000 Wille's k value : 49 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 158.26137, average 2.87748 Lattice compactness (without 2's) : 98.72687, average 1.79503 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.80000 20 1 3: 0 .. 2 0.80000 8 1 5: -1 .. 0 -0.60000 6 1 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: 22 / 10 = 2.20000
FIT/MODE
10: 1 0 2 1 1 1 2 0 1 1 N T3 SD: 50.2420 c. M: 83.9100 c. 11: 1 1 1 2 0 2 2 0 1 1 N SD: 32.0654 c. M: 55.9133 c. 12: 2 0 2 2 0 2 2 0 1 1 N SD: 27.3722 c. M:-48.6821 c. 13: 2 0 2 2 0 2 2 1 1 1 N SD: 25.8193 c. M: 47.9607 c. 14: 2 0 2 2 1 2 2 1 1 1 N SD: 22.0321 c. M: 37.0322 c. 15: 2 1 2 2 0 3 2 1 1 1 N SD: 19.5742 c. M:-36.0900 c. 17: 2 1 2 3 0 3 3 0 2 1 N SD: 16.5477 c. M: 29.3610 c. 19: 3 0 3 3 0 3 3 1 2 1 N SD: 16.5294 c. M: 28.5275 c. 20: 3 0 3 3 1 3 3 1 2 1 N SD: 12.1364 c. M: 23.9100 c. 26: 4 0 4 4 1 4 4 1 3 1 N SD: 12.1579 c. M:-20.0160 c. 29: 4 1 4 4 1 5 4 1 3 2 N SD: 11.7409 c. M: 24.4928 c. 31: 4 1 4 5 1 5 5 1 3 2 N SD: 10.6068 c. M: 20.5271 c. 32: 4 1 5 5 1 5 5 1 3 2 N SD: 10.5145 c. M:-17.4878 c. 33: 5 1 4 5 1 6 5 1 3 2 N SD: 9.7242 c. M:-16.8140 c. 35: 5 1 5 5 1 6 5 2 3 2 N SD: 5.7327 c. M:-10.9751 c. 41: 6 1 6 6 1 7 6 2 4 2 N SD: 6.3735 c. M:-11.5736 c. 46: 6 2 6 7 1 8 7 2 4 3 N SD: 6.0701 c. M: 12.0910 c. 52: 7 2 7 8 1 9 8 2 5 3 N SD: 2.8590 c. M: 5.5891 c. 72: 10 2 10 11 2 12 11 3 7 4 N SD: 2.0206 c. M: 3.9100 c. 87: 12 3 12 13 2 15 13 4 8 5 N SD: 2.4541 c. M:-3.4996 c. 107: 15 3 15 16 3 18 16 5 10 6 N SD: 2.2433 c. M: 4.3399 c. 111: 15 4 15 17 3 19 17 4 11 6 N SD: 2.0544 c. M:-4.1471 c. 124: 17 4 17 19 3 21 19 5 12 7 N SD: 1.3402 c. M: 2.5512 c. 130: 18 4 18 20 3 22 20 5 13 7 N SD: 1.4210 c. M:-2.5282 c. 146: 20 5 20 22 4 25 22 6 14 8 N SD: 1.2594 c. M:-2.6189 c. 165: 23 5 23 25 4 28 25 7 16 9 N SD: 1.2598 c. M:-2.2685 c. 183: 25 6 25 28 5 31 28 7 18 10 N SD: 1.0332 c. M: 1.7011 c. 218: 30 7 30 33 6 37 33 9 21 12 N SD: 0.5378 c. M:-0.9740 c. 270: 37 9 37 41 7 46 41 11 26 15 N SD: 0.3271 c. M: 0.5598 c. 342: 47 11 47 52 9 58 52 14 33 19 N SD: 0.3511 c. M: 0.4968 c. 488: 67 16 67 74 13 83 74 20 47 27 N SD: 0.2969 c. M: 0.4983 c. 546: 75 18 75 83 14 93 83 22 53 30 N SD: 0.2925 c. M:-0.4856 c. 566: 78 18 78 86 15 96 86 23 55 31 N SD: 0.2815 c. M:-0.5267 c. 612: 84 20 84 93 16 104 93 25 59 34 N SD: 0.2493 c. M: 0.4968 c. 618: 85 20 85 94 16 105 94 25 60 34 N SD: 0.0842 c. M:-0.1504 c. 888: 122 29 122 135 23 151 135 36 86 49 N SD: 0.0796 c. M:-0.1441 c. 1230: 169 40 169 187 32 209 187 50 119 68 N SD: 0.0939 c. M: 0.1716 c. 1454: 200 47 200 221 38 247 221 59 141 80 N SD: 0.0835 c. M:-0.1563 c. 1506: 207 49 207 229 39 256 229 61 146 83 N SD: 0.0580 c. M:-0.0984 c. 1724: 237 56 237 262 45 293 262 70 167 95 N SD: 0.0607 c. M:-0.1207 c. 1848: 254 60 254 281 48 314 281 75 179 102 N SD: 0.0508 c. M: 0.0831 c. 2342: 322 76 322 356 61 398 356 95 227 129 N SD: 0.0506 c. M:-0.0896 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: 42.2336 cents 3 x x x 4 x x 5 x x 6 S SD: 33.2878 cents 4 x x 5 x x 6:7 x x 8 S SD: 21.5602 cents 5 x x 6 x 7:8 x 9 x 10 S SD: 11.9689 cents 6 x 7 x 8 x 9 x 11 x 12 SD: 24.4507 cents 7 x 8:9 x 10:11:12:13 x 14 S SD: 14.6818 cents 8 x 9:10:11 x 13:14 x 15:16 SD: 10.4060 cents 9:10 x 11:12:13:14 x 16:17:18 S SD: 11.5451 cents 10:11 x 12 x 14:16 x 18:19:20 S SD: 9.1401 cents 11:12 x 14:15 x 17:19:20:21:22 SD: 8.7235 cents 12:13:14:15 x 17:19:21:22:23:24 SD: 8.9816 cents 13:14:15:16:18 x 20:23 x 25:26 SD: 9.2833 cents 14:15:16:17:19:20:22 x 25:27:28 SD: 8.4951 cents 15 x 17:19 x 21:24:26:27:29:30 SD: 6.6889 cents 16 x 18:20:22 x 25:28:29:31:32 SD: 3.4509 cents 17 x 19:21:23:24:27:30:31:33:34 SD: 5.2908 cents 18:20 x 22 x 25:28 x 32:35:36 SD: 6.6752 cents 19:21 x 24:26:27:30:33:34:37:38 SD: 5.8371 cents 20:22:23:25 x 28:32:35:36:39:40 SD: 6.0786 cents 21:23:24:26:29 x 33:37:38:40:42 SD: 4.1985 cents 23:25:26:28 x 32:36:40:41:44:46 SD: 5.0289 cents 24:26:27:30:33:34:38:42:43:46:48 SD: 4.0318 cents 25 x 28:31:34:35:39:44:45:48:50 SD: 3.1901 cents 26 x 29:32:36 x 41:46:47:50:52 SD: 3.6986 cents 27:30 x 33:37:38:43:47:49:52:54 SD: 4.3590 cents 28:31:32:35 x 39:44:49:50:54:56 SD: 4.2544 cents 29:32:33:36:40:41:46:51:52:56:58 SD: 3.2622 cents 30:33:34:37:41:42:47:53:54:58:60 SD: 2.6789 cents 31:34:35:38:43 x 49:54:56:60:62 SD: 3.1298 cents 32:35:36:40:44:45:50:56:58:62:64 SD: 3.0314 cents 33:36:37:41:45:46:52:58:59:64:66 SD: 3.0173 cents 35 x 39:43:48:49:55:61:63:67:70 SD: 2.7461 cents 36:40:41:45 x 50:57:63:65:69:72 SD: 4.1801 cents 37:41:42:46:51:52:58:65:67:71:74 SD: 2.7903 cents 38:42:43:47:52:53:60:67:68:73:76 SD: 2.4191 cents 40:44:45:50:55:56:63:70:72:77:80 SD: 1.7399 cents 50:55:56:62:69:70:79:88:90:96:100 SD: 1.6089 cents 59:65:66:73:81:83:93:103:106:114:118 SD: 1.5890 cents 63:69:71:78:87:88:99:110:113:121:126 SD: 1.4884 cents 64:70:72:79:88:90:101:112:115:123:128 SD: 1.4306 cents 70:77:79:87:96:98:110:123:126:135:140 SD: 1.3483 cents 71:78:80:88:98:99:112:124:128:137:142 SD: 1.2493 cents 72:79:81:89:99:101:113:126:130:139:144 SD: 1.1202 cents 80:88:90:99:110:112:126:140:144:154:160 SD: 0.0000 cents