Scala analysis: xen12-wilson-40-5C3-dekany-00
1-3-5-7-9 5C3 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 21/16 470.780907 narrow fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 63/40 786.422194 narrow minor sixth 8: 7/4 968.825906 harmonic seventh 9: 9/5 1017.596288 just minor seventh, BP seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 15/14 119.4428 major diatonic semitone 7: 21/20 84.4672 minor semitone 8: 10/9 182.4037 minor whole tone 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 1 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 3 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 3: 1 7/6 266.871 cents septimal minor third 3: 3 6/5 315.641 cents minor third 3: 1 56/45 378.602 cents septimal narrow major third 3: 3 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 3: 1 9/7 435.084 cents septimal major third, BP third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 1 21/16 470.781 cents narrow fourth 4: 5 4/3 498.045 cents perfect fourth 4: 1 27/20 519.551 cents acute 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: 1 40/27 680.449 cents grave fifth 6: 5 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 54/35 750.725 cents septimal semi-augmented fifth 6: 2 14/9 764.916 cents septimal minor sixth 7: 1 14/9 764.916 cents septimal minor sixth 7: 1 63/40 786.422 cents narrow minor sixth 7: 3 8/5 813.686 cents minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 7: 3 5/3 884.359 cents major sixth, BP sixth 7: 1 12/7 933.129 cents septimal major sixth 8: 1 5/3 884.359 cents major sixth, BP sixth 8: 3 12/7 933.129 cents septimal major sixth 8: 3 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 1 9/5 1017.596 cents just minor seventh, BP 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 28/15 1080.557 cents grave major seventh 9: 1 15/8 1088.269 cents classic major seventh 9: 2 40/21 1115.533 cents acute major seventh 9: 1 27/14 1137.039 cents septimal major seventh 9: 1 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.77778 = 52/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 84.5 203.9 266.9 470.8 582.5 702.0 786.4 968.8 1017.6 1200.0 84.5 : 119.4 182.4 386.3 498.0 617.5 702.0 884.4 933.1 1115.5 1200.0 203.9 : 63.0 266.9 378.6 498.0 582.5 764.9 813.7 996.1 1080.6 1200.0 266.9 : 203.9 315.6 435.1 519.6 702.0 750.7 933.1 1017.6 1137.0 1200.0 470.8 : 111.7 231.2 315.6 498.0 546.8 729.2 813.7 933.1 996.1 1200.0 582.5 : 119.4 203.9 386.3 435.1 617.5 702.0 821.4 884.4 1088.3 1200.0 702.0 : 84.5 266.9 315.6 498.0 582.5 702.0 764.9 968.8 1080.6 1200.0 786.4 : 182.4 231.2 413.6 498.0 617.5 680.4 884.4 996.1 1115.5 1200.0 968.8 : 48.8 231.2 315.6 435.1 498.0 702.0 813.7 933.1 1017.6 1200.0 1017.6: 182.4 266.9 386.3 449.3 653.2 764.9 884.4 968.8 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 203.9100 cents 35/32, 155.1396 cents 36/35, 48.7704 cents 2: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 80/81,-21.5063 cents 3: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 35/36,-48.7704 cents 4: 435.0841 .. 519.5513 cents 21/20, 84.4672 cents 1/1, 0.0000 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 80/81,-21.5063 cents 6: 680.4487 .. 764.9159 cents 21/20, 84.4672 cents 80/81,-21.5063 cents 7: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 1/1, 0.0000 cents 8: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 35/36,-48.7704 cents 9: 996.0900 .. 1151.2296 cents 35/32, 155.1396 cents 80/81,-21.5063 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 2.460510 Largest / Average step : 1.699250 Largest / Smallest step : 4.181021 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 116.14089 cents, oct.: 1161.40893 cents Scale is not proper Step pattern alph. order: ABCDEBAFGF Step pattern size order : CEBGDECFAF Scale is not a Constant Structure Scale diversity : 1.507155 Lumma stability : 0.081284 Lumma impropriety factor : 0.152972 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 : 7 Highest interval variety : 7 Mean interval variety : 5.77778 = 52/9 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 225/224, 7.7115 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 10.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.183674 Specific harmonicity : 0.159118 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 128.0, average 12.80000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.36468, average 0.93647 Sum of Tenney's harmonic distance : 17.75519, average 1.77552 Vogel's harmonic complexity : 15.10000 Wille's k value : 157 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 145.67922, average 2.64871 Lattice compactness (without 2's) : 90.11134, average 1.63839 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.50000 17 1 3: -1 .. 2 0.80000 10 2 5: -1 .. 0 -0.40000 4 1 7: 0 .. 1 0.60000 6 6 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 20 / 10 = 2.00000
FIT/MODE
10: 1 1 0 2 1 1 1 1 1 1 N T3 SD: 32.9336 c. M:-62.4037 c. 11: 1 1 0 2 1 1 1 2 0 2 N SD: 31.5503 c. M: 48.6891 c. 12: 1 1 1 2 1 1 1 2 0 2 P D3 SD: 19.9582 c. M:-33.1291 c. 15: 1 2 0 3 1 2 1 2 1 2 N SD: 19.3031 c. M:-36.0900 c. 17: 1 2 1 3 1 2 1 3 0 3 P SD: 16.4588 c. M: 29.3610 c. 19: 1 2 1 3 2 2 1 3 1 3 N SD: 18.0622 c. M: 28.6756 c. 20: 1 2 1 4 2 2 1 3 1 3 N SD: 16.5340 c. M: 26.8709 c. 21: 1 3 1 3 2 2 2 3 1 3 P SD: 16.1061 c. M: 27.3243 c. 23: 2 2 1 4 2 3 1 4 1 3 N SD: 15.9072 c. M:-28.4798 c. 26: 2 2 2 4 3 2 2 4 1 4 N SD: 10.1363 c. M: 19.2946 c. 27: 2 3 1 5 2 3 2 4 1 4 N SD: 10.3681 c. M:-18.3122 c. 28: 2 3 1 5 3 2 2 5 1 4 N SD: 11.8504 c. M:-17.4878 c. 31: 2 3 2 5 3 3 2 5 1 5 N SD: 7.1994 c. M: 12.2286 c. 41: 3 4 2 7 4 4 3 6 2 6 N SD: 3.2892 c. M:-6.7940 c. 53: 4 5 3 9 5 5 4 8 2 8 N SD: 4.2567 c. M:-6.1671 c. 58: 4 6 3 10 5 6 4 9 2 9 N SD: 2.8620 c. M:-5.0812 c. 72: 5 7 4 12 7 7 5 11 3 11 N SD: 2.3045 c. M: 4.1142 c. 99: 7 10 5 17 9 10 7 15 4 15 N SD: 1.1602 c. M:-2.1506 c. 130: 9 13 7 22 12 13 9 20 5 20 N SD: 1.1289 c. M: 2.2117 c. 171: 12 17 9 29 16 17 12 26 7 26 N SD: 0.3247 c. M: 0.6055 c. 270: 19 27 14 46 25 27 19 41 11 41 N SD: 0.2625 c. M:-0.5344 c. 441: 31 44 23 75 41 44 31 67 18 67 N SD: 0.1246 c. M: 0.2042 c. 612: 43 61 32 104 57 61 43 93 25 93 N SD: 0.1385 c. M: 0.2042 c. 836: 59 83 44 142 78 83 59 127 34 127 N SD: 0.1380 c. M:-0.2629 c. 966: 68 96 51 164 90 96 68 147 39 147 N SD: 0.1263 c. M:-0.2098 c. 1007: 71 100 53 171 94 100 71 153 41 153 N SD: 0.1038 c. M:-0.2088 c. 1106: 78 110 58 188 103 110 78 168 45 168 N SD: 0.1096 c. M:-0.1963 c. 1178: 83 117 62 200 110 117 83 179 48 179 N SD: 0.1029 c. M: 0.1749 c. 1236: 87 123 65 210 115 123 87 188 50 188 N SD: 0.0706 c. M: 0.1206 c. 1277: 90 127 67 217 119 127 90 194 52 194 N SD: 0.0665 c. M:-0.1087 c. 1407: 99 140 74 239 131 140 99 214 57 214 N SD: 0.0576 c. M: 0.1123 c. 1448: 102 144 76 246 135 144 102 220 59 220 N SD: 0.0530 c. M:-0.0845 c. 1677: 118 167 88 285 156 167 118 255 68 255 N SD: 0.0390 c. M: 0.0650 c. 1848: 130 184 97 314 172 184 130 281 75 281 N SD: 0.0355 c. M: 0.0638 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 x 5 x 6 S SD: 29.5861 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: 11.1748 cents 6 x x 7:8 x 9 x x 11:12 SD: 8.3725 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 12.3371 cents 8 x 9 x x 11:12:13:14 x 16 SD: 10.4090 cents 9 x 10:11:12:13 x 14 x 16:18 S SD: 15.3493 cents 10 x 11:12:13:14:15:16 x 18:20 S SD: 8.7589 cents 11 x 12:13:14:15 x 17:19:20:22 SD: 12.5876 cents 12:13 x 14:16:17:18:19:21:22:24 SD: 7.9993 cents 13:14 x 15:17:18 x 20:23 x 26 SD: 9.7966 cents 14:15:16 x 18:20:21:22 x 25:28 SD: 8.5421 cents 15:16:17:18:20:21:23:24:26:27:30 SD: 8.0586 cents 16:17:18:19:21:22:24:25:28:29:32 SD: 5.1630 cents 18:19:20:21:24:25:27:28 x 32:36 SD: 5.4486 cents 20:21 x 23:26:28:30:32:35:36:40 SD: 4.4973 cents 23:24:26:27:30:32:35:36:40:41:46 SD: 4.0857 cents 24:25:27:28:32:34:36:38:42:43:48 SD: 3.8748 cents 25:26:28:29:33:35:38:39:44:45:50 SD: 3.7779 cents 32:34:36:37:42:45:48:50:56:58:64 SD: 3.2468 cents 35:37:39:41:46:49:53:55:61:63:70 SD: 2.8326 cents 38:40:43:44:50:53:57:60:67:68:76 SD: 2.5353 cents 40:42:45:47:53:56:60:63:70:72:80 SD: 2.0521 cents 42:44:47:49:55:59:63:66:74:76:84 SD: 1.9659 cents 48:50:54:56:63:67:72:76:84:86:96 SD: 1.9103 cents 54:57:61:63:71:76:81:85:95:97:108 SD: 1.8000 cents 55:58:62:64:72:77:83:87:96:99:110 SD: 1.7155 cents 60:63:68:70:79:84:90:95:105:108:120 SD: 1.6638 cents 64:67:72:75:84:90:96:101:112:115:128 SD: 1.2899 cents 78:82:88:91:102:109:117:123:137:140:156 SD: 1.2169 cents 80:84:90:93:105:112:120:126:140:144:160 SD: 0.6194 cents 120:126:135:140:158:168:180:189:210:216:240 SD: 0.5487 cents 144:151:162:168:189:202:216:227:252:259:288 SD: 0.4598 cents 160:168:180:187:210:224:240:252:280:288:320 SD: 0.3089 cents 240:252:270:280:315:336:360:378:420:432:480 S SD: 0.0000 cents