Scala analysis: xen12-wilson-09-4C2-hexany-11
3-7-9-15 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: 9/7 435.084095 septimal major third, BP third 4: 3/2 701.955001 perfect fifth 5: 45/28 821.397809 septimale wide minor sixth 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/45 378.6022 septimal narrow major third 1: 15/14 119.4428 major diatonic semitone 2: 7/6 266.8709 septimal minor third 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 7/6 266.8709 septimal minor third 5: 15/14 119.4428 major diatonic semitone 6: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 7/6 266.871 cents septimal minor third 1: 1 56/45 378.602 cents septimal narrow major third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 4/3 498.045 cents perfect fourth 3: 2 9/7 435.084 cents septimal major third, BP third 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 3: 2 14/9 764.916 cents septimal minor sixth 4: 2 3/2 701.955 cents perfect fifth 4: 2 8/5 813.686 cents minor sixth 4: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 45/28 821.398 cents septimale wide minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 2 28/15 1080.557 cents grave major seventh 5: 1 35/18 1151.230 cents septimal semi-diminished octave 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 : 119.4 386.3 435.1 702.0 821.4 1200.0 119.4 : 266.9 315.6 582.5 702.0 1080.6 1200.0 386.3 : 48.8 315.6 435.1 813.7 933.1 1200.0 435.1 : 266.9 386.3 764.9 884.4 1151.2 1200.0 702.0 : 119.4 498.0 617.5 884.4 933.1 1200.0 821.4 : 378.6 498.0 764.9 813.7 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 378.6022 cents 98/81, 329.8318 cents 36/35, 48.7704 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 27/28,-62.9609 cents 3: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 27/28,-62.9609 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 27/28,-62.9609 cents 5: 821.3978 .. 1151.2296 cents 98/81, 329.8318 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 4.100850 Largest / Average step : 1.893011 Largest / Smallest step : 7.762953 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 179.25419 cents, oct.: 1075.52516 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : BCACBD Scale is a Constant Structure, by a margin of 7.71152 cents Scale diversity : 1.493100 Lumma stability : 0.081284 Lumma impropriety factor : 0.209870 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 : 225/224, 7.7115 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 differentially coherent in interval class 2 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.039970 Average absolute harmonicity : 0.257761 Specific harmonicity : 0.170794 Fundamental : 1/28, -4.8074 octaves, 9.3438 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 2.520000E+03, 11.29921 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 67.5, average 11.25000 Mersenne's string divisions : 1524240 Sum of van Prooijen's expressibility: 4.95964, average 0.82661 Sum of Tenney's harmonic distance : 9.60214, average 1.60036 Vogel's harmonic complexity : 10.16667 Wille's k value : 22 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 45.80624, average 2.18125 Lattice compactness (without 2's) : 32.32389, average 1.53923 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.83333 7 1 3: 0 .. 2 1.00000 6 1 5: 0 .. 1 0.50000 3 1 7: -1 .. 0 -0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 12 / 6 = 2.00000 Scale is weakly epimorphic with val: <6 9 14 19| Scale is weakly epimorphic with val: <6 10 13 18| Scale is weakly epimorphic with val: <6 10 14 15| Scale is JI-epimorphic with val: <6 10 14 17| = patent Scale is weakly epimorphic with val: <6 10 14 19| Scale is weakly epimorphic with val: <6 10 15 18| Scale is weakly epimorphic with val: <6 11 14 15| Scale is weakly epimorphic with val: <6 11 15 18|
FIT/MODE
6: 1 1 0 2 0 2 N T3 SD: 54.7393 c. M:-98.0450 c. 7: 1 1 1 1 1 2 P M ME SD: 45.4704 c. M:-79.2016 c. 9: 1 2 0 2 1 3 N G SD: 23.5028 c. M: 35.2883 c. 12: 1 3 0 3 1 4 N SD: 19.3990 c. M: 35.0841 c. 16: 2 3 1 3 2 5 N SD: 18.3656 c. M:-30.5572 c. 19: 2 4 1 4 2 6 N SD: 5.8169 c. M: 7.3663 c. 22: 2 5 1 5 2 7 N SD: 5.6314 c. M: 10.3519 c. 31: 3 7 1 7 3 10 N SD: 5.7252 c. M: 9.2776 c. 41: 4 9 2 9 4 13 N SD: 3.1324 c. M: 5.8259 c. 50: 5 11 2 11 5 16 N SD: 3.6463 c. M: 5.9550 c. 60: 6 13 3 13 6 19 N SD: 3.4185 c. M: 6.3137 c. 63: 6 14 3 14 6 20 N SD: 3.6011 c. M: 5.3613 c. 69: 7 15 3 15 7 22 N SD: 3.5324 c. M: 6.3028 c. 72: 7 16 3 16 7 23 N SD: 2.7647 c. M: 4.7311 c. 80: 8 18 3 18 8 25 N SD: 2.4547 c. M:-3.6863 c. 99: 10 22 4 22 10 31 N SD: 1.6566 c. M:-2.8446 c. 108: 11 24 4 24 11 34 N SD: 1.9115 c. M:-2.7794 c. 111: 11 25 4 25 11 35 N SD: 1.6423 c. M:-2.8755 c. 118: 12 26 5 26 12 37 N SD: 1.6876 c. M:-2.5911 c. 121: 12 27 5 27 12 38 N SD: 1.2792 c. M:-2.1772 c. 130: 13 29 5 29 13 41 N SD: 0.8100 c. M:-1.3786 c. 149: 15 33 6 33 15 47 N SD: 0.7762 c. M:-1.3626 c. 152: 15 34 6 34 15 48 N SD: 0.6662 c. M: 1.0218 c. 171: 17 38 7 38 17 54 N SD: 0.2243 c. M: 0.3488 c. 441: 44 98 18 98 44 139 N SD: 0.2298 c. M:-0.3709 c. 472: 47 105 19 105 47 149 N SD: 0.2022 c. M: 0.3383 c. 593: 59 132 24 132 59 187 N SD: 0.1484 c. M:-0.2372 c. 612: 61 136 25 136 61 193 N SD: 0.1304 c. M:-0.2100 c. 764: 76 170 31 170 76 241 N SD: 0.0759 c. M:-0.1392 c. 935: 93 208 38 208 93 295 N SD: 0.0468 c. M: 0.0845 c. 1106: 110 246 45 246 110 349 N SD: 0.0529 c. M: 0.0938 c. 1547: 154 344 63 344 154 488 N SD: 0.0473 c. M:-0.0807 c. 1718: 171 382 70 382 171 542 N SD: 0.0387 c. M:-0.0731 c. 1848: 184 411 75 411 184 583 N SD: 0.0297 c. M:-0.0499 c. 2019: 201 449 82 449 201 637 N SD: 0.0163 c. M: 0.0234 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 5:6 S SD: 29.6801 cents 4 x 5 x 6 x 8 S SD: 0.0000 cents 5 x 6 x x 8:10 S SD: 23.6973 cents 6 x x 8:9:10:12 S SD: 22.2600 cents 7:8 x 9 x 11:14 SD: 29.5778 cents 8:9:10 x 12:13:16 SD: 17.3213 cents 9:10:11:12 x 14:18 SD: 22.4784 cents 10:11 x 13:15:16:20 SD: 10.0025 cents 11:12 x 14:17:18:22 SD: 14.0373 cents 12:13:15 x 18:19:24 SD: 6.4301 cents 14:15 x 18:21:23:28 SD: 7.6101 cents 15:16:19 x 23:24:30 SD: 9.1490 cents 16:17:20:21:24:26:32 SD: 7.1688 cents 18:19 x 23:27:29:36 SD: 5.6598 cents 19:20:24 x 29:31:38 SD: 10.6895 cents 20:21:25:26:30:32:40 SD: 6.7674 cents 22:24 x 28:33:35:44 SD: 7.9773 cents 23:25:29:30:35:37:46 SD: 7.6177 cents 24:26:30:31:36:39:48 SD: 4.7018 cents 26:28 x 33:39:42:52 SD: 5.1220 cents 28:30:35:36:42:45:56 SD: 0.0000 cents