Scala analysis: xen12-wilson-09-4C2-hexany-03
1-3-9-11 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 9/8 203.910002 major whole tone 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 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: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 11/9 347.4079 undecimal neutral third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 11/9 347.4079 undecimal neutral third 6: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/9 347.408 cents undecimal neutral third 2: 2 9/8 203.910 cents major whole tone 2: 4 4/3 498.045 cents perfect fourth 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 2 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 44/27 845.453 cents neutral sixth 4: 4 3/2 701.955 cents perfect fifth 4: 2 16/9 996.090 cents Pythagorean minor seventh 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.80000 = 14/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 53.3 203.9 551.3 702.0 1049.4 1200.0 53.3 : 150.6 498.0 648.7 996.1 1146.7 1200.0 203.9 : 347.4 498.0 845.5 996.1 1049.4 1200.0 551.3 : 150.6 498.0 648.7 702.0 852.6 1200.0 702.0 : 347.4 498.0 551.3 702.0 1049.4 1200.0 1049.4: 150.6 203.9 354.5 702.0 852.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 347.4079 cents 32/27, 294.1350 cents 33/32, 53.2729 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 81/88,-143.4979 cents 3: 354.5471 .. 845.4529 cents 968/729, 490.9059 cents 81/88,-143.4979 cents 4: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 81/88,-143.4979 cents 5: 852.5921 .. 1146.7271 cents 32/27, 294.1350 cents 81/88,-143.4979 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 3.754251 Largest / Average step : 1.737040 Largest / Smallest step : 6.521283 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 190.87562 cents, oct.: 1145.25372 cents Scale is not proper Step pattern alph. order: ABCBCB Step pattern size order : SMLMLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.13912 cents Scale diversity : 1.351113 Lumma stability : 0.088788 Lumma impropriety factor : 0.478326 Rothenberg efficiency : 0.583333 redundancy: 0.416667 Efficiency x scale size : 3.500000 Number of different interval sizes : 14 = 2.80000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.80000 = 14/5 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents 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 n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 33 (O: 33 U: 33) Highest odd numerator or denominator: 33 Scale harmonicity : 0.031073 Average absolute harmonicity : 0.254065 Specific harmonicity : 0.146626 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.900800E+04, 14.21432 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 63.0, average 10.50000 Mersenne's string divisions : 62985 Sum of van Prooijen's expressibility: 5.03266, average 0.83878 Sum of Tenney's harmonic distance : 9.72420, average 1.62070 Vogel's harmonic complexity : 13.00000 Wille's k value : 49 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 63.97168, average 3.04627 Lattice compactness (without 2's) : 30.11969, average 1.43427 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.00000 14 1 3: -1 .. 2 0.50000 5 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 10 19| Scale is JI-epimorphic with val: <6 10 21| = patent Scale is weakly epimorphic with val: <6 10 23| Scale is weakly epimorphic with val: <6 11 20|
FIT/MODE
6: 0 1 2 1 1 1 N T3 SD: 53.6544 c. M:-98.0450 c. 7: 0 1 2 1 2 1 N SD: 31.5185 c. M: 53.2729 c. 15: 1 2 4 2 4 2 N SD: 20.4348 c. M:-36.0900 c. 16: 1 2 4 2 5 2 N SD: 19.7335 c. M: 26.9550 c. 17: 1 2 5 2 5 2 N SD: 10.3737 c. M:-17.3153 c. 22: 1 3 6 3 6 3 N SD: 8.7520 c. M:-14.2718 c. 24: 1 3 7 3 7 3 N SD: 2.3081 c. M: 3.9100 c. 65: 3 8 19 8 19 8 N SD: 1.8435 c. M:-2.9448 c. 87: 4 11 25 11 25 11 N SD: 1.6383 c. M:-2.9865 c. 89: 4 11 26 11 26 11 N SD: 1.3849 c. M:-2.3225 c. 111: 5 14 32 14 32 14 N SD: 0.8080 c. M:-1.4954 c. 135: 6 17 39 17 39 17 N SD: 0.3236 c. M:-0.5344 c. 159: 7 20 46 20 46 20 N SD: 0.2749 c. M: 0.4428 c. 294: 13 37 85 37 85 37 N SD: 0.2299 c. M: 0.3833 c. 335: 15 42 97 42 97 42 N SD: 0.2712 c. M:-0.4584 c. 359: 16 45 104 45 104 45 N SD: 0.1515 c. M:-0.2192 c. 494: 22 62 143 62 143 62 N SD: 0.1025 c. M:-0.1684 c. 518: 23 65 150 65 150 65 N SD: 0.0355 c. M:-0.0579 c. 1171: 52 147 339 147 339 147 N SD: 0.0107 c. M:-0.0183 c. 1689: 75 212 489 212 489 212 N SD: 0.0101 c. M:-0.0154 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 0.0000 cents 3 x x 4 x x 6 S SD: 26.6365 cents 4 x x x 6:7:8 S SD: 26.8457 cents 5 x 6:7:8:9:10 S SD: 32.8329 cents 6 x 7:8:9:11:12 SD: 16.4949 cents 7 x 8:10:11:13:14 SD: 22.0064 cents 8 x 9:11:12:15:16 SD: 7.7812 cents 9 x 10:12:14:17:18 SD: 19.9356 cents 10 x 11:14:15:18:20 SD: 11.8252 cents 11 x 12:15:17:20:22 SD: 15.3908 cents 12 x 14:17:18:22:24 SD: 16.2913 cents 14:15:16:19:21:26:28 SD: 13.0522 cents 16:17:18:22:24:29:32 SD: 9.2234 cents 18:19:20:25:27:33:36 SD: 8.1510 cents 22:23:25:30:33:40:44 SD: 5.9546 cents 24:25:27:33:36:44:48 SD: 2.8999 cents 30:31:34:41:45:55:60 SD: 2.8196 cents 32:33:36:44:48:59:64 SD: 1.6348 cents 56:58:63:77:84:103:112 SD: 1.5583 cents 64:66:72:88:96:117:128 SD: 0.8209 cents 96:99:108:132:144:176:192 SD: 0.0000 cents