Scala analysis: xen12-wilson-09-4C2-hexany-10
3-7-9-11 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/28 284.447037 undecimal minor third 2: 9/7 435.084095 septimal major third, BP third 3: 3/2 701.955001 perfect fifth 4: 11/7 782.492036 undecimal augmented 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: 33/28 284.4470 undecimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 7/6 266.8709 septimal minor third 4: 22/21 80.5370 undecimal minor semitone 5: 7/6 266.8709 septimal minor third 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 11/9 347.408 cents undecimal neutral third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 2 9/7 435.084 cents septimal major third, BP third 3: 2 4/3 498.045 cents perfect fourth 3: 1 108/77 585.721 cents 3: 1 77/54 614.279 cents 3: 2 3/2 701.955 cents perfect fifth 4: 2 14/9 764.916 cents septimal minor sixth 4: 2 11/7 782.492 cents undecimal augmented fifth 4: 2 18/11 852.592 cents undecimal neutral sixth 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 : 284.4 435.1 702.0 782.5 1049.4 1200.0 284.4 : 150.6 417.5 498.0 764.9 915.6 1200.0 435.1 : 266.9 347.4 614.3 764.9 1049.4 1200.0 702.0 : 80.5 347.4 498.0 782.5 933.1 1200.0 782.5 : 266.9 417.5 702.0 852.6 1119.5 1200.0 1049.4: 150.6 435.1 585.7 852.6 933.1 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: 347.4079 .. 435.0841 cents 81/77, 87.6762 cents 28/27, 62.9609 cents 3: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 4: 764.9159 .. 852.5921 cents 81/77, 87.6762 cents 28/27, 62.9609 cents 5: 915.5530 .. 1119.4630 cents 9/8, 203.9100 cents 28/27, 62.9609 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 : 207.00289 cents, oct.: 1242.01735 cents Scale is strictly proper Step pattern alph. order: ABCDCB Step pattern size order : DBCACB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 1.529526 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.344098 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 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 33 Scale harmonicity : 0.025337 Average absolute harmonicity : 0.241304 Specific harmonicity : 0.114056 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.663200E+04, 14.02167 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 60.0, average 10.00000 Mersenne's string divisions : 746640 Sum of van Prooijen's expressibility: 5.03266, average 0.83878 Sum of Tenney's harmonic distance : 9.55023, average 1.59170 Vogel's harmonic complexity : 15.00000 Wille's k value : 49 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 45.04093, average 2.14481 Lattice compactness (without 2's) : 34.00683, average 1.61937 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.50000 5 1 3: -1 .. 2 0.50000 5 1 7: -1 .. 0 -0.50000 3 1 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 3 / 6 = 0.50000 Average absolute exponent except 2's: 11 / 6 = 1.83333 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 18 19| Scale is weakly epimorphic with val: <6 10 18 21| Scale is weakly epimorphic with val: <6 10 18 23| Scale is weakly epimorphic with val: <6 11 15 19| Scale is weakly epimorphic with val: <6 11 18 20| Scale is weakly epimorphic with val: <6 11 19 21|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 59.8613 c. M: 101.9550 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 8: 2 1 2 0 2 1 P D3 SD: 25.2614 c. M:-48.0450 c. 9: 2 1 2 1 2 1 SP B ME SD: 23.7986 c. M: 35.2883 c. August-6 14: 3 2 3 1 3 2 SP D3 SD: 16.3625 c. M: 27.3042 c. 17: 4 2 4 1 4 2 SP SD: 6.8201 c. M: 11.5547 c. 31: 7 4 7 2 7 4 SP SD: 7.9700 c. M: 13.4793 c. 38: 9 5 8 3 8 5 SP SD: 5.8148 c. M: 7.2577 c. 41: 10 5 9 3 9 5 SP SD: 5.1983 c. M:-8.2359 c. 46: 11 6 10 3 10 6 SP SD: 4.4183 c. M:-8.3942 c. 55: 13 7 12 4 12 7 SP SD: 2.2240 c. M: 3.7732 c. 63: 15 8 14 4 14 8 SP SD: 1.9985 c. M:-3.0111 c. 72: 17 9 16 5 16 9 SP SD: 1.2410 c. M: 1.9550 c. 118: 28 15 26 8 26 15 SP SD: 1.2218 c. M:-2.2040 c. 135: 32 17 30 9 30 17 SP SD: 0.3139 c. M: 0.4741 c. 207: 49 26 46 14 46 26 SP SD: 0.2942 c. M: 0.5057 c. 342: 81 43 76 23 76 43 SP SD: 0.1608 c. M: 0.2401 c. 629: 149 79 140 42 140 79 SP SD: 0.1601 c. M: 0.2981 c. 670: 159 84 149 45 149 84 SP SD: 0.1913 c. M:-0.3291 c. 701: 166 88 156 47 156 88 SP SD: 0.1820 c. M: 0.2816 c. 742: 176 93 165 50 165 93 SP SD: 0.1647 c. M:-0.2573 c. 764: 181 96 170 51 170 96 SP SD: 0.1586 c. M: 0.2931 c. 805: 191 101 179 54 179 101 SP SD: 0.1619 c. M:-0.2735 c. 819: 194 103 182 55 182 103 SP SD: 0.1550 c. M: 0.2787 c. 836: 198 105 186 56 186 105 SP SD: 0.1453 c. M: 0.2365 c. 877: 208 110 195 59 195 110 SP SD: 0.1106 c. M:-0.1762 c. 1012: 240 127 225 68 225 127 SP SD: 0.0855 c. M:-0.1379 c. 1147: 272 144 255 77 255 144 SP SD: 0.0834 c. M:-0.1382 c. 1164: 276 146 259 78 259 146 SP SD: 0.0769 c. M:-0.1216 c. 1219: 289 153 271 82 271 153 SP SD: 0.0603 c. M:-0.1167 c. 1354: 321 170 301 91 301 170 SP SD: 0.0500 c. M:-0.0781 c. 1371: 325 172 305 92 305 172 SP SD: 0.0482 c. M:-0.0900 c. 1506: 357 189 335 101 335 189 SP SD: 0.0265 c. M:-0.0394 c. 1848: 438 232 411 124 411 232 SP SD: 0.0190 c. M: 0.0315 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 0.0000 cents 3 x 4 x 5 x 6 S SD: 39.9178 cents 4 x 5:6 x 7:8 S SD: 23.5382 cents 5:6 x x 8:9:10 S SD: 13.5906 cents 6:7:8:9 x 11:12 SD: 13.0736 cents 7:8:9 x 11:13:14 SD: 11.5534 cents 9:11:12 x 14:17:18 SD: 20.8884 cents 10:12:13:15:16:18:20 SD: 9.6050 cents 11:13:14 x 17:20:22 SD: 7.4043 cents 13:15:17 x 20:24:26 SD: 12.1676 cents 14:17:18:21:22:26:28 SD: 9.3839 cents 16:19:21:24:25:29:32 SD: 7.3291 cents 17:20:22:26:27:31:34 SD: 6.8561 cents 18:21:23:27:28:33:36 SD: 4.5116 cents 24:28:31:36:38:44:48 SD: 3.8858 cents 28:33:36:42:44:51:56 SD: 1.8797 cents 56:66:72:84:88:103:112 SD: 0.9353 cents 84:99:108:126:132:154:168 SD: 0.0000 cents