Scala analysis: xen12-wilson-39-4C2-hexany-11
3-5-7-11 4C2 Hexany, Figure 39
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: 7/6 266.870906 septimal minor third 3: 77/60 431.875134 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 35/33 101.8667 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 55/42 466.8507 6: 12/11 150.6371 undecimal neutral second, 3/4-tone
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 : 165.0 266.9 431.9 582.5 1049.4 1200.0 165.0 : 101.9 266.9 417.5 884.4 1035.0 1200.0 266.9 : 165.0 315.6 782.5 933.1 1098.1 1200.0 431.9 : 150.6 617.5 768.1 933.1 1035.0 1200.0 582.5 : 466.9 617.5 782.5 884.4 1049.4 1200.0 1049.4: 150.6 315.6 417.5 582.5 733.1 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 : 184.29928 cents, oct.: 1105.79571 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : CACBDB 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 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 classes 1 and 2 combined 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 : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 77 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.206959 Specific harmonicity : 0.103286 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 154, 7.2668 octaves, 40290.337 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 101.5, average 16.91667 Mersenne's string divisions : 2543268 Sum of van Prooijen's expressibility: 5.65947, average 0.94325 Sum of Tenney's harmonic distance : 10.99393, average 1.83232 Vogel's harmonic complexity : 14.33333 Wille's k value : 38 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 41.29910, average 1.96662 Lattice compactness (without 2's) : 30.62742, average 1.45845 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.66667 6 1 3: -1 .. 0 -0.50000 3 5: -1 .. 0 -0.50000 3 7: 0 .. 1 0.50000 3 2 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: 1 0 1 1 2 1 N D3 SD: 39.6967 c. M: 66.8709 c. 8: 1 1 1 1 3 1 N M DE SD: 18.0619 c. M:-33.1291 c. 14: 2 1 2 2 5 2 N D3 SD: 12.1445 c. M: 20.7915 c. 22: 3 2 3 3 8 3 N D3 SD: 9.4085 c. M:-17.4878 c. 23: 3 2 3 3 9 3 N D3 SD: 8.4294 c. M: 14.4838 c. 31: 4 3 4 4 12 4 N D3 SD: 5.4481 c. M: 10.1655 c. 45: 6 4 6 6 17 6 N D3 SD: 5.1176 c. M: 9.3629 c. 49: 7 4 7 6 19 6 N SD: 5.3028 c. M:-8.9412 c. 50: 7 4 7 6 20 6 N SD: 4.1572 c. M:-6.6371 c. 58: 8 5 8 7 23 7 N SD: 3.0401 c. M:-5.8095 c. 64: 9 5 9 8 25 8 N SD: 2.4333 c. M: 4.3709 c. 72: 10 6 10 9 28 9 N SD: 1.0010 c. M:-1.6624 c. 161: 22 14 22 20 63 20 N SD: 1.0893 c. M:-1.5687 c. 167: 23 14 23 21 65 21 N SD: 0.5649 c. M: 1.0026 c. 175: 24 15 24 22 68 22 N SD: 0.3370 c. M:-0.5577 c. 247: 34 21 34 31 96 31 N SD: 0.3273 c. M:-0.5135 c. 342: 47 29 47 43 133 43 N SD: 0.1820 c. M: 0.2962 c. 414: 57 35 57 52 161 52 N SD: 0.1318 c. M:-0.2132 c. 589: 81 50 81 74 229 74 N SD: 0.0894 c. M:-0.1703 c. 931: 128 79 128 117 362 117 N SD: 0.0883 c. M: 0.1685 c. 1003: 138 85 138 126 390 126 N SD: 0.0893 c. M:-0.1399 c. 1164: 160 99 160 146 453 146 N SD: 0.0873 c. M:-0.1394 c. 1331: 183 113 183 167 518 167 N SD: 0.0495 c. M: 0.0930 c. 1506: 207 128 207 189 586 189 N SD: 0.0432 c. M: 0.0640 c. 1578: 217 134 217 198 614 198 N SD: 0.0432 c. M:-0.0667 c. 1745: 240 148 240 219 679 219 N SD: 0.0362 c. M: 0.0514 c. 1920: 264 163 264 241 747 241 N SD: 0.0074 c. M: 0.0122 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 59.7214 cents 3 x x 4 x x 6 S SD: 33.0849 cents 4 x x 5:6:7:8 S SD: 37.7729 cents 5 x 6 x 7:9:10 SD: 14.5509 cents 6 x 7:8 x 11:12 SD: 16.5425 cents 7 x 8:9:10:13:14 SD: 10.9670 cents 8:9 x 10:11:15:16 SD: 15.5901 cents 10:11:12:13:14:18:20 SD: 10.3906 cents 11:12:13:14:15:20:22 S SD: 9.4194 cents 15 x 18:19:21:28:30 SD: 12.4319 cents 16:18:19:21:22:29:32 SD: 12.1687 cents 17:19:20:22:24:31:34 SD: 6.4010 cents 18:20:21:23:25:33:36 SD: 3.9067 cents 29:32:34:37:41:53:58 SD: 3.8062 cents 30:33:35:39:42:55:60 SD: 3.7231 cents 31:34:36:40:43:57:62 SD: 3.5780 cents 38:42:44:49:53:70:76 SD: 3.4079 cents 40:44:47:51:56:73:80 SD: 3.0788 cents 42:46:49:54:59:77:84 SD: 1.6772 cents 60:66:70:77:84:110:120 SD: 0.0000 cents