Scala analysis: xen12-wilson-39-4C2-hexany-06
1-5-7-9 4C2 Hexany, Figure 39
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: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 3: 63/40 786.422194 narrow minor sixth 4: 7/4 968.825906 harmonic seventh 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 56/45 378.6022 septimal narrow major third 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 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: 2 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 56/45 378.602 cents septimal narrow major third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 5/4 386.314 cents major third 2: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 80/63 413.578 cents wide major third 3: 2 9/7 435.084 cents septimal major third, BP third 3: 2 14/9 764.916 cents septimal minor sixth 3: 1 63/40 786.422 cents narrow minor sixth 4: 2 10/7 617.488 cents Euler's tritone 4: 2 8/5 813.686 cents minor sixth 4: 2 7/4 968.826 cents harmonic seventh 5: 1 45/28 821.398 cents septimale wide minor sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 5: 1 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 203.9 582.5 786.4 968.8 1017.6 1200.0 203.9 : 378.6 582.5 764.9 813.7 996.1 1200.0 582.5 : 203.9 386.3 435.1 617.5 821.4 1200.0 786.4 : 182.4 231.2 413.6 617.5 996.1 1200.0 968.8 : 48.8 231.2 435.1 813.7 1017.6 1200.0 1017.6: 182.4 386.3 764.9 968.8 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 378.6022 cents 98/81, 329.8318 cents 36/35, 48.7704 cents 2: 231.1741 .. 582.5122 cents 49/40, 351.3381 cents 45/49,-147.4281 cents 3: 413.5778 .. 786.4222 cents 3969/3200, 372.8444 cents 400/441,-168.9344 cents 4: 617.4878 .. 968.8259 cents 49/40, 351.3381 cents 400/441,-168.9344 cents 5: 821.3978 .. 1151.2296 cents 98/81, 329.8318 cents 45/49,-147.4281 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 4.100850 Largest / Average step : 1.893011 Largest / Smallest step : 7.762953 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 218.58776 cents, oct.: 1311.52655 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : CDCBAB Scale is a Constant Structure, by a margin of 7.71152 cents Scale diversity : 1.327024 Lumma stability : 0.081284 Lumma impropriety factor : 0.527271 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 2.800000 Number of different interval sizes : 18 = 3.60000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 225/224, 7.7115 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.231087 Specific harmonicity : 0.161063 Fundamental : 1/40, -5.3219 octaves, 6.5406 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 80.0, average 13.33333 Mersenne's string divisions : 1617924 Sum of van Prooijen's expressibility: 5.39802, average 0.89967 Sum of Tenney's harmonic distance : 10.20420, average 1.70070 Vogel's harmonic complexity : 10.83333 Wille's k value : 31 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 58.62195, average 2.79152 Lattice compactness (without 2's) : 36.22094, average 1.72481 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.16667 9 1 3: 0 .. 2 1.00000 6 1 5: -1 .. 0 -0.50000 3 1 7: 0 .. 1 0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 12 / 6 = 2.00000 Scale is weakly epimorphic with val: <6 10 13 16| Scale is weakly epimorphic with val: <6 10 15 16| Scale is weakly epimorphic with val: <6 11 14 15| Scale is weakly epimorphic with val: <6 11 14 17| Scale is weakly epimorphic with val: <6 11 14 19|
FIT/MODE
6: 1 2 1 1 0 1 N D3 SD: 17.2575 c. M:-31.1741 c. 17: 3 5 3 3 0 3 N D3 SD: 16.9144 c. M: 29.3610 c. 19: 3 6 3 3 1 3 N D3 SD: 16.9862 c. M: 28.5275 c. 20: 3 7 3 3 1 3 N D3 SD: 12.9256 c. M: 23.9100 c. 25: 4 8 4 4 1 4 N D3 SD: 10.7519 c. M: 18.4222 c. 26: 4 9 4 4 1 4 N D3 SD: 10.6960 c. M: 19.2946 c. 27: 5 8 5 4 1 4 N SD: 10.3573 c. M:-18.3122 c. 29: 5 9 5 4 2 4 N SD: 9.9736 c. M: 17.1018 c. 31: 5 10 5 5 1 5 N D3 SD: 8.0184 c. M: 12.2286 c. 35: 6 11 6 5 2 5 N SD: 5.8644 c. M:-10.9751 c. 41: 7 13 7 6 2 6 N SD: 3.6212 c. M:-6.7940 c. 47: 8 15 8 7 2 7 N SD: 3.2547 c. M:-5.0672 c. 52: 9 16 9 8 2 8 N SD: 2.9962 c. M: 5.5891 c. 58: 10 18 10 9 2 9 N SD: 2.7855 c. M: 3.8032 c. 72: 12 23 12 11 3 11 N SD: 2.2741 c. M: 3.9100 c. 78: 13 25 13 12 3 12 N SD: 2.1615 c. M: 3.9100 c. 87: 15 27 15 13 4 13 N SD: 2.5734 c. M: 3.3087 c. 93: 16 29 16 14 4 14 N SD: 1.5636 c. M:-2.5416 c. 99: 17 31 17 15 4 15 N SD: 1.1783 c. M:-2.1506 c. 165: 28 52 28 25 7 25 N SD: 0.8414 c. M: 1.5532 c. 171: 29 54 29 26 7 26 N SD: 0.3000 c. M: 0.4573 c. 270: 46 85 46 41 11 41 N SD: 0.2788 c. M:-0.5344 c. 348: 59 110 59 53 14 53 N SD: 0.2786 c. M: 0.4617 c. 441: 75 139 75 67 18 67 N SD: 0.1240 c. M: 0.1993 c. 612: 104 193 104 93 25 93 N SD: 0.1220 c. M: 0.1985 c. 618: 105 195 105 94 25 94 N SD: 0.0669 c. M: 0.1206 c. 789: 134 249 134 120 32 120 N SD: 0.0764 c. M: 0.1104 c. 1059: 180 334 180 161 43 161 N SD: 0.0419 c. M: 0.0759 c. 1677: 285 529 285 255 68 255 N SD: 0.0394 c. M: 0.0650 c. 1848: 314 583 314 281 75 281 N SD: 0.0402 c. M: 0.0638 c. 2066: 351 652 351 314 84 314 N SD: 0.0329 c. M:-0.0628 c. 2336: 397 737 397 355 95 355 N SD: 0.0305 c. M:-0.0504 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 42.2336 cents 3 x 4 x 5 x 6 S SD: 39.8182 cents 4:5 x 6:7 x 8 S SD: 50.2530 cents 5:6:7:8 x 9:10 S SD: 23.0019 cents 6:7:8:9 x 11:12 SD: 27.7435 cents 7:8:10:11:12:13:14 S SD: 13.1061 cents 8:9:11:13:14 x 16 SD: 12.4908 cents 9:10:13:14 x 16:18 SD: 13.1377 cents 10:11:14:16 x 18:20 SD: 9.5016 cents 13:15:18:20:23 x 26 SD: 13.1094 cents 14:16:20:22 x 25:28 SD: 9.3217 cents 15:17:21:24:26:27:30 SD: 5.7277 cents 18:20:25:28 x 32:36 SD: 7.9444 cents 19:21:27:30:33:34:38 SD: 7.2634 cents 21:24:29:33:37:38:42 SD: 6.5457 cents 22:25:31:35:39:40:44 SD: 6.5252 cents 23:26:32:36:40:41:46 SD: 4.4133 cents 24:27:34:38:42:43:48 SD: 3.9713 cents 25:28:35:39:44:45:50 SD: 3.4611 cents 32:36:45:50:56:58:64 SD: 3.3053 cents 33:37:46:52:58:59:66 SD: 2.8085 cents 40:45:56:63:70:72:80 SD: 0.0000 cents