Scala analysis: xen12-wilson-02-hexany
3-5-7-11 Hexany, Figure 2
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: 6/5 315.641287 minor third 3: 11/7 782.492036 undecimal augmented fifth 4: 12/7 933.129094 septimal major sixth 5: 66/35 1098.133323 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 35/33 101.8667 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 55/42 466.8507 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 35/33 101.8667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/33 101.867 cents 1: 2 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 55/42 466.851 cents 2: 2 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 2 10/7 617.488 cents Euler's tritone 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 77/60 431.875 cents 3: 1 120/77 768.125 cents 3: 2 11/7 782.492 cents undecimal augmented fifth 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 5/3 884.359 cents major sixth, BP sixth 4: 2 12/7 933.129 cents septimal major sixth 5: 1 84/55 733.149 cents 5: 2 20/11 1034.996 cents large minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 66/35 1098.133 cents 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 : 165.0 315.6 782.5 933.1 1098.1 1200.0 165.0 : 150.6 617.5 768.1 933.1 1035.0 1200.0 315.6 : 466.9 617.5 782.5 884.4 1049.4 1200.0 782.5 : 150.6 315.6 417.5 582.5 733.1 1200.0 933.1 : 165.0 266.9 431.9 582.5 1049.4 1200.0 1098.1: 101.9 266.9 417.5 884.4 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8667 .. 466.8507 cents 121/98, 364.9841 cents 35/33, 101.8667 cents 2: 266.8709 .. 617.4878 cents 60/49, 350.6169 cents 49/55,-199.9798 cents 3: 417.5080 .. 782.4920 cents 121/98, 364.9841 cents 49/55,-199.9798 cents 4: 582.5122 .. 933.1291 cents 60/49, 350.6169 cents 49/55,-199.9798 cents 5: 733.1493 .. 1098.1333 cents 121/98, 364.9841 cents 49/55,-199.9798 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 35/33, 101.8667 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 55/42, 466.8507 cents Average / Smallest step : 1.963351 Largest / Average step : 2.334254 Largest / Smallest step : 4.582958 Median interval of one step : 157.82064 cents, amount: 0 Least squares average step : 215.02138 cents, oct.: 1290.12830 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : CBDBCA Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.471972 Lumma stability : 0.169778 Lumma impropriety factor : 0.555215 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 : 121/120, 14.3672 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 35 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.211064 Specific harmonicity : 0.103286 Fundamental : 1/70, -6.1293 octaves, 3.7375 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 86.5, average 14.41667 Mersenne's string divisions : 2659734 Sum of van Prooijen's expressibility: 5.17092, average 0.86182 Sum of Tenney's harmonic distance : 10.99393, average 1.83232 Vogel's harmonic complexity : 14.66667 Wille's k value : 38 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 41.42418, average 1.97258 Lattice compactness (without 2's) : 30.62742, average 1.45845 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 6 1 3: 0 .. 1 0.50000 3 5: -1 .. 0 -0.50000 3 1 7: -1 .. 0 -0.50000 3 1 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 0 / 6 = 0.00000 Average absolute exponent except 2's: 12 / 6 = 2.00000 Scale is weakly epimorphic with val: <6 9 13 16 23| Scale is JI-epimorphic with val: <6 9 13 17 20| Scale is weakly epimorphic with val: <6 9 13 17 22| Scale is weakly epimorphic with val: <6 9 13 18 23| Scale is weakly epimorphic with val: <6 9 14 17 19| Scale is weakly epimorphic with val: <6 9 14 18 22| Scale is weakly epimorphic with val: <6 9 14 19 23| Scale is weakly epimorphic with val: <6 10 13 15 23| Scale is weakly epimorphic with val: <6 10 13 17 21| Scale is weakly epimorphic with val: <6 10 13 18 20| Scale is weakly epimorphic with val: <6 10 14 18 19| Scale is JI-epimorphic with val: <6 10 14 18 21| Scale is weakly epimorphic with val: <6 10 14 18 23| Scale is weakly epimorphic with val: <6 10 15 17 19| Scale is weakly epimorphic with val: <6 10 15 18 20| Scale is weakly epimorphic with val: <6 10 15 19 23| Scale is weakly epimorphic with val: <6 11 13 15 20| Scale is weakly epimorphic with val: <6 11 13 15 22| Scale is weakly epimorphic with val: <6 11 13 16 21| Scale is weakly epimorphic with val: <6 11 13 18 21| Scale is weakly epimorphic with val: <6 11 14 15 19| Scale is weakly epimorphic with val: <6 11 14 18 22| Scale is weakly epimorphic with val: <6 11 14 19 21| Scale is weakly epimorphic with val: <6 11 15 16 19| Scale is weakly epimorphic with val: <6 11 15 18 19| Scale is weakly epimorphic with val: <6 11 15 19 20| Scale is JI-epimorphic with val: <6 11 15 19 22|
FIT/MODE
6: 0 1 2 1 1 1 N T3 SD: 129.9078 c. M: 182.4920 c. 7: 1 1 3 0 1 1 N SD: 53.1781 c. M: 75.9862 c. 8: 1 1 3 1 1 1 N M DE SD: 28.6934 c. M: 48.1333 c. 9: 1 1 4 1 1 1 N M DE SD: 27.9830 c. M: 48.9746 c. 12: 2 1 5 1 2 1 N SD: 21.8971 c. M:-34.9958 c. 14: 2 2 5 2 2 1 N D3 SD: 14.4909 c. M:-27.2159 c. 15: 2 2 6 2 2 1 N D3 SD: 16.0767 c. M:-26.8709 c. 19: 3 2 7 3 2 2 N SD: 18.2771 c. M: 24.5973 c. 20: 3 2 8 3 2 2 N SD: 15.9509 c. M:-26.8709 c. 22: 3 3 8 3 3 2 N D3 SD: 9.8250 c. M: 18.8557 c. 23: 3 3 9 3 3 2 N D3 SD: 4.4886 c. M: 8.4825 c. 35: 5 4 14 4 5 3 N SD: 5.5404 c. M: 7.4148 c. 37: 5 5 14 5 5 3 N D3 SD: 5.4192 c. M:-8.6830 c. 45: 6 6 17 6 6 4 N D3 SD: 5.0167 c. M: 9.1587 c. 49: 7 6 19 6 7 4 N SD: 3.4569 c. M:-6.4243 c. 58: 8 7 23 7 8 5 N SD: 2.8579 c. M: 5.2965 c. 72: 10 9 28 9 10 6 N SD: 1.1582 c. M:-1.8667 c. 95: 13 12 37 12 13 8 N SD: 0.8508 c. M:-1.6077 c. 152: 21 19 59 19 21 13 N SD: 0.8622 c. M: 1.5501 c. 167: 23 21 65 21 23 14 N SD: 0.7649 c. M:-1.2679 c. 175: 24 22 68 22 24 15 N SD: 0.5957 c. M: 0.9905 c. 247: 34 31 96 31 34 21 N SD: 0.2178 c. M: 0.3356 c. 342: 47 43 133 43 47 29 N SD: 0.1197 c. M:-0.2042 c. 589: 81 74 229 74 81 50 N SD: 0.0867 c. M: 0.1491 c. 931: 128 117 362 117 128 79 N SD: 0.0809 c. M:-0.1482 c. 1201: 165 151 467 151 165 102 N SD: 0.1008 c. M: 0.1440 c. 1236: 170 155 481 155 170 105 N SD: 0.0757 c. M: 0.1194 c. 1331: 183 167 518 167 183 113 N SD: 0.0489 c. M: 0.0891 c. 1578: 217 198 614 198 217 134 N SD: 0.0337 c. M: 0.0519 c. 1920: 264 241 747 241 264 163 N SD: 0.0085 c. M: 0.0163 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 40.2685 cents 3 x 4 x 5 x 6 S SD: 62.9371 cents 4 x 5:6:7 x 8 S SD: 28.2346 cents 5 x 6:8 x 9:10 S SD: 21.5918 cents 6 x 7:9:10:11:12 SD: 23.3425 cents 7:8 x 11:12:13:14 SD: 14.2507 cents 9:10:11:14:15:17:18 SD: 10.5512 cents 10:11:12:16:17:19:20 SD: 6.1321 cents 19:21:23:30:33:36:38 SD: 5.1252 cents 20:22:24:31:34:38:40 SD: 5.1252 cents 21:23:25:33:36:40:42 SD: 3.9067 cents 30:33:36:47:51:57:60 SD: 3.3674 cents 39:43:47:61:67:74:78 SD: 2.7128 cents 40:44:48:63:69:75:80 SD: 2.5227 cents 49:54:59:77:84:92:98 SD: 1.6772 cents 59:65:71:93:101:111:118 SD: 1.5034 cents 60:66:72:94:103:113:120 SD: 1.0296 cents 70:77:84:110:120:132:140 SD: 0.0000 cents