Scala analysis: xen12-wilson-09-4C2-hexany-01
1-3-7-11 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 77/48 818.188848 4: 7/4 968.825906 harmonic seventh 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: 7/6 266.8709 septimal minor third 2: 33/28 284.4470 undecimal minor third 3: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 22/21 80.5370 undecimal minor semitone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 7/6 266.871 cents septimal minor third 1: 1 33/28 284.447 cents undecimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 96/77 381.811 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 3: 1 77/48 818.189 cents 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 11/7 782.492 cents undecimal augmented fifth 4: 2 7/4 968.826 cents harmonic seventh 5: 1 56/33 915.553 cents 5: 2 12/7 933.129 cents septimal major sixth 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 21/11 1119.463 cents undecimal major seventh 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 : 266.9 551.3 818.2 968.8 1049.4 1200.0 266.9 : 284.4 551.3 702.0 782.5 933.1 1200.0 551.3 : 266.9 417.5 498.0 648.7 915.6 1200.0 818.2 : 150.6 231.2 381.8 648.7 933.1 1200.0 968.8 : 80.5 231.2 498.0 782.5 1049.4 1200.0 1049.4: 150.6 417.5 702.0 968.8 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 284.4470 cents 9/8, 203.9100 cents 22/21, 80.5370 cents 2: 231.1741 .. 551.3179 cents 77/64, 320.1438 cents 32/33,-53.2729 cents 3: 381.8112 .. 818.1888 cents 5929/4608, 436.3777 cents 768/847,-169.5068 cents 4: 648.6821 .. 968.8259 cents 77/64, 320.1438 cents 768/847,-169.5068 cents 5: 915.5530 .. 1119.4630 cents 9/8, 203.9100 cents 32/33,-53.2729 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 2.483330 Largest / Average step : 1.422235 Largest / Smallest step : 3.531879 Median interval of one step : 208.75398 cents, amount: 0 Least squares average step : 221.38672 cents, oct.: 1328.32033 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : CDCBAB Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.556315 Lumma stability : 0.134228 Lumma impropriety factor : 0.371300 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 : 99/98, 17.5761 cents Number of recognisable fifths : 2, 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 n-1 differentially coherent in interval classes 2 and 3 combined 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 : 0.027675 Average absolute harmonicity : 0.212418 Specific harmonicity : 0.117334 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 154, 7.2668 octaves, 40290.337 Hz. Exponens Consonantiae : 7.392000E+03, 12.85175 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 94.0, average 15.66667 Mersenne's string divisions : 17320875 Sum of van Prooijen's expressibility: 5.65947, average 0.94325 Sum of Tenney's harmonic distance : 10.70320, average 1.78387 Vogel's harmonic complexity : 12.83333 Wille's k value : 38 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 53.64560, average 2.55455 Lattice compactness (without 2's) : 26.24191, average 1.24961 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.66667 12 1 3: -1 .. 0 -0.50000 3 7: 0 .. 1 0.50000 3 2 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 3 / 6 = 0.50000 Average absolute exponent except 2's: 9 / 6 = 1.50000 Scale is JI-epimorphic with val: <6 9 16 20| Scale is weakly epimorphic with val: <6 9 17 19| Scale is weakly epimorphic with val: <6 9 19 23| Scale is weakly epimorphic with val: <6 10 15 20| Scale is weakly epimorphic with val: <6 10 17 20| Scale is weakly epimorphic with val: <6 10 19 20| Scale is weakly epimorphic with val: <6 11 15 19| Scale is weakly epimorphic with val: <6 11 16 20| Scale is weakly epimorphic with val: <6 11 19 21|
FIT/MODE
6: 1 2 1 1 0 1 N D3 SD: 41.9941 c. M: 66.8709 c. 9: 2 2 2 1 1 1 N SD: 19.2070 c. M: 35.4926 c. 15: 3 4 3 2 1 2 N SD: 14.6846 c. M: 26.8709 c. 17: 4 4 4 2 1 2 N SD: 16.9245 c. M:-28.8700 c. 19: 4 5 4 2 2 2 N SD: 16.1008 c. M:-24.3213 c. 21: 5 5 4 3 1 3 N SD: 15.9656 c. M: 20.7915 c. 22: 5 5 5 3 1 3 N SD: 8.2306 c. M: 12.9993 c. 26: 6 6 6 3 2 3 N SD: 8.3077 c. M:-12.5804 c. 31: 7 7 7 4 2 4 N SD: 5.0263 c. M: 9.3825 c. 41: 9 10 9 5 3 5 N SD: 3.2616 c. M:-4.7796 c. 63: 14 15 14 8 4 8 N SD: 1.3979 c. M:-2.6027 c. 72: 16 17 16 9 5 9 N SD: 1.2358 c. M: 2.1592 c. 135: 30 32 30 17 9 17 N SD: 0.2835 c. M: 0.4741 c. 431: 96 102 96 54 29 54 N SD: 0.2591 c. M:-0.4145 c. 503: 112 119 112 63 34 63 N SD: 0.2374 c. M:-0.3388 c. 566: 126 134 126 71 38 71 N SD: 0.1472 c. M:-0.2669 c. 638: 142 151 142 80 43 80 N SD: 0.1594 c. M: 0.2208 c. 701: 156 166 156 88 47 88 N SD: 0.0939 c. M:-0.1762 c. 836: 186 198 186 105 56 105 N SD: 0.0816 c. M: 0.1218 c. 877: 195 208 195 110 59 110 N SD: 0.0789 c. M:-0.1239 c. 1012: 225 240 225 127 68 127 N SD: 0.0486 c. M: 0.0725 c. 1147: 255 272 255 144 77 144 N SD: 0.0475 c. M: 0.0880 c. 1578: 351 374 351 198 106 198 N SD: 0.0427 c. M:-0.0667 c. 1713: 381 406 381 215 115 215 N SD: 0.0186 c. M:-0.0293 c. 1848: 411 438 411 232 124 232 N SD: 0.0112 c. M: 0.0192 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 58.1169 cents 3 x 4:5 x x 6 S SD: 28.3166 cents 4:5 x 6:7 x 8 S SD: 41.6660 cents 5:6:7:8 x 9:10 S SD: 13.2379 cents 6:7:8:10 x 11:12 S SD: 16.9899 cents 7:8:10:11:12:13:14 S SD: 15.5459 cents 8:9:11:13:14:15:16 SD: 12.8849 cents 10:12:14:16 x 18:20 S SD: 13.2379 cents 11:13:15:18:19:20:22 SD: 8.5108 cents 13:15:18:21:23:24:26 SD: 5.6779 cents 18:21:25:29:32:33:36 SD: 5.5327 cents 23:27:32:37:40:42:46 SD: 4.4677 cents 24:28:33:39:42:44:48 SD: 3.7231 cents 30:35:41:48:53:55:60 SD: 3.3347 cents 35:41:48:56:61:64:70 SD: 2.1127 cents 43:50:59:69:75:79:86 SD: 1.6111 cents 48:56:66:77:84:88:96 SD: 0.0000 cents