Scala analysis: xen12-wilson-09-4C2-hexany-07
1-7-9-15 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: 9/8 203.910002 major whole tone 3: 135/112 323.352810 septimal wide minor third 4: 9/7 435.084095 septimal major third, BP third 5: 15/8 1088.268715 classic major seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 21/20 84.4672 minor semitone 3: 15/14 119.4428 major diatonic semitone 4: 16/15 111.7313 minor diatonic semitone 5: 35/24 653.1846 septimal semi-diminished fifth 6: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 2 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 14/9 764.916 cents septimal minor sixth 3: 2 6/5 315.641 cents minor third 3: 1 135/112 323.353 cents septimal wide minor third 3: 1 224/135 876.647 cents narrow septimal major sixth 3: 2 5/3 884.359 cents major sixth, BP sixth 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 7/4 968.826 cents harmonic seventh 4: 2 16/9 996.090 cents Pythagorean minor seventh 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 2 28/15 1080.557 cents grave major seventh 5: 2 15/8 1088.269 cents classic major seventh 5: 1 40/21 1115.533 cents acute 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 : 119.4 203.9 323.4 435.1 1088.3 1200.0 119.4 : 84.5 203.9 315.6 968.8 1080.6 1200.0 203.9 : 119.4 231.2 884.4 996.1 1115.5 1200.0 323.4 : 111.7 764.9 876.6 996.1 1080.6 1200.0 435.1 : 653.2 764.9 884.4 968.8 1088.3 1200.0 1088.3: 111.7 231.2 315.6 435.1 546.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 653.1846 cents 25/18, 568.7174 cents 21/20, 84.4672 cents 2: 203.9100 .. 764.9159 cents 112/81, 561.0059 cents 27/35,-449.2746 cents 3: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 27/35,-449.2746 cents 4: 435.0841 .. 996.0900 cents 112/81, 561.0059 cents 27/35,-449.2746 cents 5: 546.8154 .. 1115.5328 cents 25/18, 568.7174 cents 27/35,-449.2746 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 35/24, 653.1846 cents Average / Smallest step : 2.367783 Largest / Average step : 3.265923 Largest / Smallest step : 7.732998 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 174.49452 cents, oct.: 1046.96711 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : CACBDB Scale is a Constant Structure, by a margin of 84.46719 cents Scale diversity : 1.449444 Lumma stability : 0.140779 Lumma impropriety factor : 0.660150 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 : 0 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.225148 Specific harmonicity : 0.151752 Fundamental : 1/112, -6.8074 octaves, 2.3359 Hz. Guide tone : 270, 8.0768 octaves, 70638.903 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 167.5, average 27.91667 Mersenne's string divisions : 134435184 Sum of van Prooijen's expressibility: 6.39100, average 1.06517 Sum of Tenney's harmonic distance : 12.53866, average 2.08978 Vogel's harmonic complexity : 12.83333 Wille's k value : 67 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 64.11656, average 3.05317 Lattice compactness (without 2's) : 37.07278, average 1.76537 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.66667 12 1 3: 0 .. 3 1.50000 9 1 5: 0 .. 1 0.50000 3 1 7: -1 .. 0 -0.50000 3 3 Average exponent except 2's : 9 / 6 = 1.50000 Average absolute exponent except 2's: 15 / 6 = 2.50000 Scale is JI-epimorphic with val: <6 10 13 16| Scale is weakly epimorphic with val: <6 10 15 16| Scale is weakly epimorphic with val: <6 11 15 15| Scale is weakly epimorphic with val: <6 11 15 17| Scale is weakly epimorphic with val: <6 11 15 19|
FIT/MODE
6: 0 1 0 1 3 1 N SD: 80.1250 c. M: 123.3528 c. 7: 1 0 1 1 3 1 N D3 SD: 48.2608 c. M:-79.2016 c. 8: 1 0 1 1 4 1 N D3 SD: 31.8129 c. M: 53.9100 c. 10: 1 1 1 1 5 1 N M DE SD: 28.0821 c. M:-44.9159 c. 11: 1 1 1 1 6 1 N M DE SD: 7.4702 c. M:-14.2718 c. 30: 3 2 3 3 16 3 N D3 SD: 4.4605 c. M: 8.2687 c. 41: 4 3 4 4 22 4 N D3 SD: 2.9602 c. M: 5.3419 c. 52: 5 4 5 5 28 5 N D3 SD: 3.0443 c. M: 4.0582 c. 77: 8 5 8 7 42 7 N SD: 2.9742 c. M:-5.2325 c. 83: 8 6 8 8 45 8 N D3 SD: 3.2068 c. M: 5.2805 c. 88: 9 6 9 8 48 8 N SD: 2.4210 c. M:-3.9199 c. 89: 9 6 9 8 49 8 N SD: 2.3990 c. M:-3.8661 c. 99: 10 7 10 9 54 9 N SD: 2.2996 c. M:-3.9199 c. 100: 10 7 10 9 55 9 N SD: 2.0071 c. M:-3.7313 c. 111: 11 8 11 10 61 10 N SD: 1.9838 c. M:-3.6232 c. 118: 12 8 12 11 64 11 N SD: 1.6406 c. M:-2.5911 c. 119: 12 8 12 11 65 11 N SD: 1.3339 c. M: 2.2293 c. 129: 13 9 13 12 70 12 N SD: 1.4292 c. M:-2.2286 c. 130: 13 9 13 12 71 12 N SD: 0.7680 c. M: 1.2379 c. 141: 14 10 14 13 77 13 N SD: 0.6439 c. M:-1.0930 c. 171: 17 12 17 16 93 16 N SD: 0.3609 c. M: 0.5494 c. 312: 31 22 31 29 170 29 N SD: 0.2523 c. M: 0.4687 c. 353: 35 25 35 33 192 33 N SD: 0.3128 c. M: 0.4626 c. 430: 43 30 43 40 234 40 N SD: 0.3062 c. M:-0.5572 c. 441: 44 31 44 41 240 41 N SD: 0.2681 c. M:-0.4567 c. 483: 48 34 48 45 263 45 N SD: 0.2246 c. M: 0.3714 c. 571: 57 40 57 53 311 53 N SD: 0.2352 c. M:-0.3477 c. 601: 60 42 60 56 327 56 N SD: 0.2020 c. M:-0.3575 c. 612: 61 43 61 57 333 57 N SD: 0.1315 c. M:-0.2100 c. 753: 75 53 75 70 410 70 N SD: 0.1059 c. M:-0.1775 c. 783: 78 55 78 73 426 73 N SD: 0.1037 c. M:-0.1649 c. 913: 91 64 91 85 497 85 N SD: 0.1025 c. M: 0.1860 c. 924: 92 65 92 86 503 86 N SD: 0.0271 c. M:-0.0430 c. 2019: 201 142 201 188 1099 188 N SD: 0.0246 c. M: 0.0467 c. 2030: 202 143 202 189 1105 189 N SD: 0.0195 c. M: 0.0339 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 133.4355 cents 3 x x x 4 x 6 S SD: 31.4805 cents 4 x x x 5 x 8 SD: 24.3852 cents 5 x x 6 x 9:10 S SD: 23.6973 cents 6 x x 7:8:11:12 SD: 23.2754 cents 7 x 8 x 9:13:14 SD: 7.9757 cents 8 x 9 x 10:15:16 S SD: 12.1926 cents 9 x 10:11:12:17:18 SD: 14.3784 cents 10 x 11:12:13:19:20 SD: 9.9295 cents 11:12 x 13:14:21:22 S SD: 11.6976 cents 12:13 x 14:15:23:24 SD: 17.1844 cents 13:14:15:16:17:24:26 SD: 11.6496 cents 14:15:16:17:18:26:28 SD: 5.7277 cents 15:16:17:18:19:28:30 SD: 5.2950 cents 24:26:27:29:31:45:48 SD: 3.5282 cents 25:27:28:30:32:47:50 SD: 3.2912 cents 38:41:43:46:49:71:76 SD: 3.1882 cents 39:42:44:47:50:73:78 SD: 1.9433 cents 55:59:62:66:71:103:110 SD: 1.8945 cents 57:61:64:69:73:107:114 SD: 1.8275 cents 70:75:79:84:90:131:140 SD: 1.6706 cents 72:77:81:87:93:135:144 SD: 1.6027 cents 73:78:82:88:94:137:146 SD: 1.0405 cents 87:93:98:105:112:163:174 SD: 0.9470 cents 97:104:109:117:125:182:194 SD: 0.8144 cents 112:120:126:135:144:210:224 SD: 0.0000 cents