Scala analysis: xen12-wilson-09-4C2-hexany-05
1-3-11-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 55/32 937.631656 4: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 5: 15/8 1088.268715 classic major seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 5/4 386.3137 major third 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 5/4 386.3137 major third 4: 16/15 111.7313 minor diatonic semitone 5: 45/44 38.9058 1/5-tone 6: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 5/4 386.314 cents major third 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 4/3 498.045 cents perfect fourth 2: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 64/55 262.368 cents 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 2 22/15 663.049 cents undecimal diminished fifth 3: 1 55/32 937.632 cents 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 2 8/5 813.686 cents minor sixth 5: 1 20/11 1034.996 cents large minor seventh 5: 2 15/8 1088.269 cents classic major seventh 5: 1 88/45 1161.094 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 : 386.3 551.3 937.6 1049.4 1088.3 1200.0 386.3 : 165.0 551.3 663.0 702.0 813.7 1200.0 551.3 : 386.3 498.0 537.0 648.7 1035.0 1200.0 937.6 : 111.7 150.6 262.4 648.7 813.7 1200.0 1049.4: 38.9 150.6 537.0 702.0 1088.3 1200.0 1088.3: 111.7 498.0 663.0 1049.4 1161.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 386.3137 cents 11/9, 347.4079 cents 45/44, 38.9058 cents 2: 150.6371 .. 551.3179 cents 121/96, 400.6809 cents 48/55,-235.6767 cents 3: 262.3683 .. 937.6317 cents 3025/2048, 675.2633 cents 512/605,-288.9496 cents 4: 648.6821 .. 1049.3629 cents 121/96, 400.6809 cents 512/605,-288.9496 cents 5: 813.6863 .. 1161.0942 cents 11/9, 347.4079 cents 48/55,-235.6767 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 5.140625 Largest / Average step : 1.931569 Largest / Smallest step : 9.929470 Median interval of one step : 138.36776 cents, amount: 0 Least squares average step : 232.31472 cents, oct.: 1393.88835 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : DCDBAB Scale is a Constant Structure, by a margin of 14.36717 cents Scale diversity : 1.463259 Lumma stability : 0.064843 Lumma impropriety factor : 0.667801 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 : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Scale is 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 : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.027843 Average absolute harmonicity : 0.221450 Specific harmonicity : 0.129293 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 3.168000E+04, 14.95128 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 79.0, average 13.16667 Mersenne's string divisions : 1938969 Sum of van Prooijen's expressibility: 5.69821, average 0.94970 Sum of Tenney's harmonic distance : 10.69078, average 1.78180 Vogel's harmonic complexity : 13.83333 Wille's k value : 82 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 61.15224, average 2.91201 Lattice compactness (without 2's) : 26.64151, average 1.26864 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.16667 15 1 3: -1 .. 1 0.00000 2 5: 0 .. 1 0.50000 3 2 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 8 / 6 = 1.33333 Scale is weakly epimorphic with val: <6 9 13 20| Scale is weakly epimorphic with val: <6 9 14 19| Scale is JI-epimorphic with val: <6 10 13 20| Scale is weakly epimorphic with val: <6 10 15 20| Scale is weakly epimorphic with val: <6 11 14 21| Scale is weakly epimorphic with val: <6 11 15 22|
FIT/MODE
6: 2 1 2 0 0 1 N SD: 52.7180 c. M: 88.2687 c. 7: 2 1 2 1 0 1 N SD: 47.8441 c. M: 80.4888 c. 8: 3 1 2 1 0 1 N SD: 39.3847 c. M:-63.6863 c. 9: 3 1 3 1 0 1 N SD: 14.6930 c. M: 21.6020 c. 15: 5 2 5 1 1 1 N SD: 17.5953 c. M:-31.7313 c. 18: 6 2 6 2 0 2 N SD: 14.6930 c. M: 21.6020 c. 19: 6 3 6 2 0 2 N SD: 14.4096 c. M:-24.3213 c. 22: 7 3 7 2 1 2 N SD: 7.5039 c. M: 12.9993 c. 31: 10 4 10 3 1 3 N SD: 5.7675 c. M: 9.3825 c. 41: 13 6 13 4 1 4 N SD: 4.1807 c. M: 5.8259 c. 55: 18 7 18 5 2 5 N SD: 3.8113 c. M:-6.4136 c. 56: 18 8 18 5 2 5 N SD: 3.7205 c. M:-5.8249 c. 63: 20 9 20 6 2 6 N SD: 3.1069 c. M: 5.3613 c. 65: 21 9 21 6 2 6 N SD: 2.3506 c. M:-3.9068 c. 87: 28 12 28 8 3 8 N SD: 0.7494 c. M:-1.3865 c. 96: 31 13 31 9 3 9 N SD: 0.8325 c. M: 1.3179 c. 183: 59 25 59 17 6 17 N SD: 0.3364 c. M:-0.5715 c. 311: 100 43 100 29 10 29 N SD: 0.2792 c. M: 0.4616 c. 398: 128 55 128 37 13 37 N SD: 0.2546 c. M:-0.4409 c. 407: 131 56 131 38 13 38 N SD: 0.1708 c. M: 0.3080 c. 494: 159 68 159 46 16 46 N SD: 0.0539 c. M:-0.0991 c. 677: 218 93 218 63 22 63 N SD: 0.0564 c. M:-0.0969 c. 1084: 349 149 349 101 35 101 N SD: 0.0495 c. M:-0.0836 c. 1171: 377 161 377 109 38 109 N SD: 0.0200 c. M:-0.0319 c. 1665: 536 229 536 155 54 155 N SD: 0.0195 c. M:-0.0334 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x 3 x x x 4 S SD: 75.3185 cents 3 x 4:5 x x 6 S SD: 25.1131 cents 4:5:6:7 x x 8 S SD: 38.4583 cents 5:6:7 x 9 x 10 SD: 20.8818 cents 6 x 8:10:11 x 12 S SD: 18.8348 cents 7:9:10:12 x 13:14 SD: 16.7949 cents 8:10:11:14 x 15:16 SD: 6.2389 cents 9:11:12:15 x 17:18 SD: 17.1498 cents 10:13:14:17:18:19:20 SD: 14.4136 cents 11:14:15:19:20:21:22 SD: 8.2198 cents 13:16:18:22:24 x 26 SD: 8.3235 cents 14:18:19:24 x 26:28 SD: 11.2879 cents 15:19:21:26 x 28:30 SD: 8.4198 cents 16:20:22:28:29:30:32 SD: 6.1567 cents 19:24:26:33:35:36:38 SD: 5.5855 cents 21:26:29:36 x 39:42 SD: 5.0005 cents 24:30:33:41:44:45:48 SD: 1.7540 cents 32:40:44:55:59:60:64 SD: 1.6348 cents 56:70:77:96:103:105:112 SD: 1.1991 cents 64:80:88:110:117:120:128 SD: 0.8209 cents 72:90:99:124:132:135:144 SD: 0.5823 cents 96:120:132:165:176:180:192 S SD: 0.0000 cents