Scala analysis: xen12-wilson-09-4C2-hexany-12
3-7-11-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 5/4 386.313714 major third 3: 11/7 782.492036 undecimal augmented fifth 4: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 5: 55/28 1168.805750 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/55 31.1943 undecimal diesis, konbini comma 1: 15/14 119.4428 major diatonic semitone 2: 7/6 266.8709 septimal minor third 3: 44/35 396.1783 4: 7/6 266.8709 septimal minor third 5: 15/14 119.4428 major diatonic semitone 6: 56/55 31.1943 undecimal diesis, konbini comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 7/6 266.871 cents septimal minor third 1: 1 44/35 396.178 cents 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 5/4 386.314 cents major third 2: 2 22/15 663.049 cents undecimal diminished fifth 3: 1 90/77 270.080 cents 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 2 11/7 782.492 cents undecimal augmented fifth 3: 1 77/45 929.920 cents 4: 2 15/11 536.951 cents undecimal augmented fourth 4: 2 8/5 813.686 cents minor sixth 4: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 35/22 803.822 cents 5: 2 12/7 933.129 cents septimal major sixth 5: 2 28/15 1080.557 cents grave major seventh 5: 1 55/28 1168.806 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 : 119.4 386.3 782.5 1049.4 1168.8 1200.0 119.4 : 266.9 663.0 929.9 1049.4 1080.6 1200.0 386.3 : 396.2 663.0 782.5 813.7 933.1 1200.0 782.5 : 266.9 386.3 417.5 537.0 803.8 1200.0 1049.4: 119.4 150.6 270.1 537.0 933.1 1200.0 1168.8: 31.2 150.6 417.5 813.7 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 396.1783 cents 121/98, 364.9841 cents 56/55, 31.1943 cents 2: 150.6371 .. 663.0492 cents 121/90, 512.4122 cents 105/121,-245.5413 cents 3: 270.0799 .. 929.9201 cents 5929/4050, 659.8403 cents 675/847,-392.9694 cents 4: 536.9508 .. 1049.3629 cents 121/90, 512.4122 cents 675/847,-392.9694 cents 5: 803.8217 .. 1168.8057 cents 121/98, 364.9841 cents 105/121,-245.5413 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 44/35, 396.1783 cents Average / Smallest step : 6.411438 Largest / Average step : 1.980892 Largest / Smallest step : 12.700364 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 225.06623 cents, oct.: 1350.39738 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : BCDCBA Scale is a Constant Structure, by a margin of 3.20896 cents Scale diversity : 1.391203 Lumma stability : 0.051990 Lumma impropriety factor : 0.748938 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 : 540/539, 3.2090 cents Number of recognisable fifths : 0 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 class 2 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 55 Scale harmonicity : 0.023148 Average absolute harmonicity : 0.212700 Specific harmonicity : 0.102422 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 2.772000E+04, 14.75864 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 79.5, average 13.25000 Mersenne's string divisions : 736542 Sum of van Prooijen's expressibility: 5.69821, average 0.94970 Sum of Tenney's harmonic distance : 10.81783, average 1.80297 Vogel's harmonic complexity : 15.66667 Wille's k value : 82 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 44.61969, average 2.12475 Lattice compactness (without 2's) : 30.81587, average 1.46742 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.83333 7 1 3: -1 .. 1 0.00000 2 5: 0 .. 1 0.50000 3 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 weakly epimorphic with val: <6 9 13 17 19| Scale is weakly epimorphic with val: <6 9 13 18 20| Scale is weakly epimorphic with val: <6 9 13 19 23| Scale is JI-epimorphic with val: <6 9 14 16 19| Scale is weakly epimorphic with val: <6 9 14 18 19| Scale is weakly epimorphic with val: <6 9 14 19 20| Scale is weakly epimorphic with val: <6 9 14 19 22| Scale is weakly epimorphic with val: <6 9 15 16 20| Scale is weakly epimorphic with val: <6 9 15 17 19| Scale is weakly epimorphic with val: <6 9 15 19 23| Scale is weakly epimorphic with val: <6 10 13 15 19| Scale is weakly epimorphic with val: <6 10 13 18 20| Scale is weakly epimorphic with val: <6 10 13 19 21| Scale is weakly epimorphic with val: <6 10 14 15 20| Scale is JI-epimorphic with val: <6 10 14 17 20| Scale is weakly epimorphic with val: <6 10 14 19 20| Scale is weakly epimorphic with val: <6 10 15 15 23| Scale is weakly epimorphic with val: <6 10 15 17 21| Scale is weakly epimorphic with val: <6 10 15 18 20| Scale is weakly epimorphic with val: <6 11 13 15 19| Scale is weakly epimorphic with val: <6 11 13 16 20| Scale is weakly epimorphic with val: <6 11 13 19 21| Scale is weakly epimorphic with val: <6 11 14 15 20| Scale is weakly epimorphic with val: <6 11 14 15 22| Scale is weakly epimorphic with val: <6 11 14 16 21| Scale is JI-epimorphic with val: <6 11 14 18 21| Scale is weakly epimorphic with val: <6 11 15 15 19| Scale is weakly epimorphic with val: <6 11 15 18 22| Scale is weakly epimorphic with val: <6 11 15 19 21|
FIT/MODE
6: 1 1 2 1 1 0 N D3 SD: 41.6195 c. M:-80.5572 c. 7: 1 1 3 1 1 0 N D3 SD: 43.9111 c. M:-74.6508 c. 8: 1 2 2 2 1 0 N SD: 34.2026 c. M:-63.6863 c. 9: 1 2 3 2 1 0 N G SD: 18.0706 c. M:-31.1943 c. 20: 2 4 7 4 2 1 N SD: 19.9620 c. M: 29.3629 c. 21: 2 5 7 4 2 1 N SD: 16.4624 c. M: 25.9486 c. 22: 2 5 7 5 2 1 N SD: 14.1254 c. M: 23.3512 c. 23: 2 5 8 5 2 1 N SD: 13.8305 c. M: 21.0963 c. 24: 2 6 8 5 2 1 N SD: 14.2941 c. M: 19.4428 c. 25: 2 6 8 6 2 1 N SD: 13.4872 c. M: 23.4428 c. 26: 3 5 9 6 2 1 N SD: 13.1027 c. M:-19.0187 c. 28: 3 6 9 6 3 1 N SD: 11.3608 c. M: 20.7915 c. 29: 3 6 10 6 3 1 N SD: 9.6108 c. M: 14.8802 c. 31: 3 7 10 7 3 1 N SD: 5.0760 c. M: 8.2985 c. 38: 4 8 13 8 4 1 N SD: 5.8176 c. M: 7.3663 c. 40: 4 9 13 9 4 1 N SD: 1.9123 c. M:-3.6863 c. 72: 7 16 24 16 7 2 N SD: 1.9270 c. M: 2.9804 c. 81: 8 18 27 18 8 2 N SD: 1.7332 c. M:-2.6931 c. 112: 11 25 37 25 11 3 N SD: 0.8467 c. M: 1.5857 c. 152: 15 34 50 34 15 4 N SD: 0.6722 c. M: 1.0218 c. 230: 23 51 76 51 23 6 N SD: 0.3726 c. M: 0.6673 c. 270: 27 60 89 60 27 7 N SD: 0.3511 c. M:-0.5572 c. 342: 34 76 113 76 34 9 N SD: 0.2414 c. M: 0.3847 c. 382: 38 85 126 85 38 10 N SD: 0.1666 c. M: 0.2931 c. 652: 65 145 215 145 65 17 N SD: 0.2004 c. M: 0.2834 c. 693: 69 154 229 154 69 18 N SD: 0.1055 c. M:-0.1919 c. 733: 73 163 242 163 73 19 N SD: 0.0530 c. M:-0.0892 c. 1075: 107 239 355 239 107 28 N SD: 0.0490 c. M: 0.0812 c. 1115: 111 248 368 248 111 29 N SD: 0.0404 c. M: 0.0705 c. 1578: 157 351 521 351 157 41 N SD: 0.0356 c. M:-0.0667 c. 1808: 180 402 597 402 180 47 N SD: 0.0232 c. M: 0.0305 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 40.2685 cents 3 x 4:5 x x 6 S SD: 50.3992 cents 4 x 5:6:7 x 8 S SD: 28.4741 cents 5 x 6:8:9 x 10 S SD: 20.8818 cents 6 x 8:9:11 x 12 SD: 34.4330 cents 7:8:9:11:13 x 14 SD: 24.7883 cents 8:9:10:13:15 x 16 SD: 21.9240 cents 9:10:11:14:17 x 18 SD: 18.3932 cents 10:11:13:16:18 x 20 SD: 18.6209 cents 11:12:14:17:20 x 22 SD: 10.9273 cents 12:13:15:19:22 x 24 SD: 4.6332 cents 13:14:16:20:24 x 26 S SD: 9.5745 cents 14:15:18:22:26 x 28 SD: 10.7286 cents 15:16:19:24:28:29:30 SD: 9.5562 cents 16:17:20:25:29:31:32 SD: 5.9247 cents 23:25:29:36:42:45:46 SD: 5.2340 cents 24:26:30:38:44:47:48 SD: 3.9591 cents 28:30:35:44:51:55:56 SD: 1.8797 cents 55:59:69:86:101:108:110 SD: 1.8742 cents 56:60:70:88:103:110:112 SD: 0.9353 cents 84:90:105:132:154:165:168 SD: 0.0000 cents