Scala analysis: xen12-wilson-40-5C2-dekany-00
1-3-5-7-9 5C2 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 7/6 266.870906 septimal minor third 3: 5/4 386.313714 major third 4: 21/16 470.780907 narrow fourth 5: 35/24 653.184619 septimal semi-diminished fifth 6: 3/2 701.955001 perfect fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 7/4 968.825906 harmonic seventh 9: 15/8 1088.268715 classic major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 15/14 119.4428 major diatonic semitone 4: 21/20 84.4672 minor semitone 5: 10/9 182.4037 minor whole tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 10/9 182.4037 minor whole tone 8: 21/20 84.4672 minor semitone 9: 15/14 119.4428 major diatonic semitone 10: 16/15 111.7313 minor diatonic semitone
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 : 203.9 266.9 386.3 470.8 653.2 702.0 884.4 968.8 1088.3 1200.0 203.9 : 63.0 182.4 266.9 449.3 498.0 680.4 764.9 884.4 996.1 1200.0 266.9 : 119.4 203.9 386.3 435.1 617.5 702.0 821.4 933.1 1137.0 1200.0 386.3 : 84.5 266.9 315.6 498.0 582.5 702.0 813.7 1017.6 1080.6 1200.0 470.8 : 182.4 231.2 413.6 498.0 617.5 729.2 933.1 996.1 1115.5 1200.0 653.2 : 48.8 231.2 315.6 435.1 546.8 750.7 813.7 933.1 1017.6 1200.0 702.0 : 182.4 266.9 386.3 498.0 702.0 764.9 884.4 968.8 1151.2 1200.0 884.4 : 84.5 203.9 315.6 519.6 582.5 702.0 786.4 968.8 1017.6 1200.0 968.8 : 119.4 231.2 435.1 498.0 617.5 702.0 884.4 933.1 1115.5 1200.0 1088.3: 111.7 315.6 378.6 498.0 582.5 764.9 813.7 996.1 1080.6 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 : 122.05950 cents, oct.: 1220.59497 cents Scale is not proper Step pattern alph. order: ABCDEFEDCG Step pattern size order : GBECFAFCED 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 : 2 at degree 8 Length of longest subharmonic part : 1 at degree 0 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 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Scale is differentially coherent in interval classes 6 and 7 combined Scale is differentially coherent in interval classes 7 and 8 combined Scale is n-1 differentially coherent in interval classes 8 and 9 combined -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 35 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.196173 Specific harmonicity : 0.164730 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 92.5, average 9.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.56188, average 0.85619 Sum of Tenney's harmonic distance : 16.01384, average 1.60138 Vogel's harmonic complexity : 10.60000 Wille's k value : 31 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 144.16448, average 2.62117 Lattice compactness (without 2's) : 87.83999, average 1.59709 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.80000 20 1 3: -1 .. 2 0.20000 8 2 5: 0 .. 1 0.40000 4 3 7: 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: 2 0 1 1 1 1 1 1 1 1 N T3 SD: 28.4080 c. M: 53.1846 c. 11: 2 0 1 1 2 0 2 1 1 1 N SD: 31.3134 c. M: 59.0410 c. 12: 2 1 1 1 2 0 2 1 1 1 P D3 SD: 23.8820 c. M:-46.8154 c. 13: 2 1 1 1 2 1 2 1 1 1 P D3 SD: 25.0536 c. M:-46.5587 c. 15: 3 0 2 1 2 1 2 1 2 1 N SD: 19.7486 c. M:-36.0900 c. 18: 3 1 2 1 3 1 2 2 1 2 N T3 SD: 17.7128 c. M:-31.3783 c. 19: 3 1 2 1 3 1 3 1 2 2 N SD: 15.7473 c. M: 28.6756 c. 20: 3 1 2 2 3 1 3 1 2 2 P T3 SD: 16.8349 c. M: 26.8709 c. 22: 4 1 2 2 3 1 3 2 2 2 N SD: 10.1349 c. M:-20.1282 c. 29: 5 1 3 2 5 1 4 2 3 3 N SD: 12.4741 c. M: 18.5950 c. 30: 5 2 3 2 4 2 4 2 3 3 N SD: 10.6051 c. M:-18.0450 c. 31: 5 2 3 2 5 1 5 2 3 3 N SD: 5.2033 c. M: 10.3616 c. 41: 7 2 4 3 6 2 6 3 4 4 N SD: 4.6540 c. M: 9.2822 c. 46: 8 2 5 3 7 2 7 3 5 4 N SD: 4.0784 c. M:-7.3835 c. 53: 9 3 5 4 8 2 8 4 5 5 N SD: 2.9262 c. M:-4.8272 c. 72: 12 4 7 5 11 3 11 5 7 7 N SD: 2.9185 c. M: 4.9354 c. 77: 13 4 8 5 12 3 12 5 8 7 N SD: 2.4185 c. M:-3.9530 c. 94: 16 5 9 7 14 4 14 7 9 9 N SD: 2.0953 c. M: 3.5076 c. 99: 17 5 10 7 15 4 15 7 10 9 N SD: 1.4793 c. M:-2.6404 c. 130: 22 7 13 9 20 5 20 9 13 12 N SD: 1.1223 c. M:-2.2000 c. 140: 24 7 14 10 21 6 21 10 14 13 N SD: 1.0808 c. M:-1.8043 c. 171: 29 9 17 12 26 7 26 12 17 16 N SD: 0.3905 c. M: 0.6055 c. 270: 46 14 27 19 41 11 41 19 27 25 N SD: 0.3241 c. M:-0.6202 c. 441: 75 23 44 31 67 18 67 31 44 41 N SD: 0.1197 c. M: 0.2042 c. 612: 104 32 61 43 93 25 93 43 61 57 N SD: 0.1350 c. M: 0.2434 c. 665: 113 35 66 47 101 27 101 47 66 62 N SD: 0.1358 c. M:-0.1968 c. 836: 142 44 83 59 127 34 127 59 83 78 N SD: 0.1202 c. M: 0.2304 c. 935: 159 49 93 66 142 38 142 66 93 87 N SD: 0.1160 c. M:-0.2351 c. 1053: 179 55 105 74 160 43 160 74 105 98 N SD: 0.1154 c. M: 0.2042 c. 1106: 188 58 110 78 168 45 168 78 110 103 N SD: 0.0598 c. M:-0.1052 c. 1277: 217 67 127 90 194 52 194 90 127 119 N SD: 0.0602 c. M: 0.0987 c. 1547: 263 81 154 109 235 63 235 109 154 144 N SD: 0.0508 c. M:-0.0978 c. 1718: 292 90 171 121 261 70 261 121 171 160 N SD: 0.0497 c. M: 0.0996 c. 1848: 314 97 184 130 281 75 281 130 184 172 N SD: 0.0344 c. M:-0.0621 c. 2019: 343 106 201 142 307 82 307 142 201 188 N SD: 0.0290 c. M: 0.0528 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: 9.0880 cents 4 x x 5 x x 6 x 7 x 8 S SD: 0.0000 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 24.2869 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 7.9180 cents 7:8 x x 9:10:11 x 12:13:14 S SD: 15.2039 cents 8:9 x 10:11 x 12:13:14:15:16 S SD: 11.4615 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 9.8536 cents 10:11:12 x 13 x 15:17:18:19:20 SD: 11.3512 cents 11:12:13:14 x 16:17:18:19:21:22 SD: 10.8274 cents 12 x 14:15:16 x 18:20:21:23:24 SD: 5.8513 cents 13 x 15:16:17:19:20:22:23:24:26 SD: 7.7296 cents 14:16 x x 18:20:21:23:25:26:28 SD: 9.1942 cents 15:17:18:19:20:22:23:25:26:28:30 SD: 7.5432 cents 16:18:19:20:21:23:24:27:28:30:32 SD: 4.4966 cents 20 x 23:25:26:29:30:33:35:38:40 SD: 4.7427 cents 23:26:27:29:30:34:35:38:40:43:46 SD: 4.5479 cents 24:27:28:30:32:35:36:40:42:45:48 SD: 2.7264 cents 32:36:37:40:42:47:48:53:56:60:64 SD: 2.2599 cents 48:54:56:60:63:70:72:80:84:90:96 S SD: 0.0000 cents