Scala analysis: xen12-wilson-39-4C2-hexany-02
1-3-5-11 4C2 Hexany, Figure 39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/48 235.676655 undecimal semi-augmented whole tone 2: 5/4 386.313714 major third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 5/3 884.358713 major sixth, BP sixth 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: 55/48 235.6767 undecimal semi-augmented whole tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 40/33 333.0408 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 55/48 235.677 cents undecimal semi-augmented whole tone 1: 1 40/33 333.041 cents 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: 1 15/11 536.951 cents undecimal augmented fourth 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 2 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 22/15 663.049 cents undecimal diminished fifth 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 33/20 866.959 cents 5: 1 96/55 964.323 cents 5: 2 20/11 1034.996 cents large minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 235.7 386.3 551.3 884.4 1049.4 1200.0 235.7 : 150.6 315.6 648.7 813.7 964.3 1200.0 386.3 : 165.0 498.0 663.0 813.7 1049.4 1200.0 551.3 : 333.0 498.0 648.7 884.4 1035.0 1200.0 884.4 : 165.0 315.6 551.3 702.0 867.0 1200.0 1049.4: 150.6 386.3 537.0 702.0 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 333.0408 cents 10/9, 182.4037 cents 12/11, 150.6371 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 99/100,-17.3995 cents 3: 536.9508 .. 663.0492 cents 242/225, 126.0985 cents 45/44, 38.9058 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 45/44, 38.9058 cents 5: 866.9592 .. 1049.3629 cents 10/9, 182.4037 cents 99/100,-17.3995 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 1.327695 Largest / Average step : 1.665204 Largest / Smallest step : 2.210882 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 204.90668 cents, oct.: 1229.44005 cents Scale is not proper Step pattern alph. order: ABCDCB Step pattern size order : CABDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.39948 cents Scale diversity : 1.421669 Lumma stability : 0.315905 Lumma impropriety factor : 0.028999 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 : 121/120, 14.3672 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.031009 Average absolute harmonicity : 0.225720 Specific harmonicity : 0.131373 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 110, 6.7814 octaves, 28778.812 Hz. Exponens Consonantiae : 5.280000E+03, 12.36632 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 79.5, average 13.25000 Mersenne's string divisions : 2395368 Sum of van Prooijen's expressibility: 5.22109, average 0.87018 Sum of Tenney's harmonic distance : 9.96378, average 1.66063 Vogel's harmonic complexity : 12.00000 Wille's k value : 27 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 55.52920, average 2.64425 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 -1.50000 11 1 3: -1 .. 0 -0.50000 3 5: 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 weakly epimorphic with val: <6 9 13 23| Scale is weakly epimorphic with val: <6 9 14 22| Scale is weakly epimorphic with val: <6 10 13 20| Scale is weakly epimorphic with val: <6 10 14 19| Scale is JI-epimorphic with val: <6 10 14 21| = patent Scale is weakly epimorphic with val: <6 10 14 23| Scale is weakly epimorphic with val: <6 10 15 20| Scale is weakly epimorphic with val: <6 11 13 21| Scale is weakly epimorphic with val: <6 11 14 22| Scale is weakly epimorphic with val: <6 11 15 19|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 47.2285 c. M: 84.3587 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 1 2 1 1 P M ME SD: 37.7727 c. M: 64.2481 c. 9: 2 1 1 3 1 1 N D3 SD: 26.3599 c. M:-48.9746 c. 10: 2 1 2 2 2 1 P D3 SD: 31.5895 c. M:-48.6821 c. 14: 3 1 2 4 2 2 N SD: 28.5588 c. M: 43.4566 c. 15: 3 2 2 4 2 2 P D3 SD: 8.0420 c. M:-13.6863 c. 31: 6 4 4 9 4 4 N D3 SD: 5.0589 c. M: 9.3825 c. 41: 8 5 6 11 6 5 P SD: 4.4233 c. M: 6.3099 c. 46: 9 6 6 13 6 6 N D3 SD: 3.6349 c. M: 5.8847 c. 50: 10 6 7 14 7 6 N SD: 3.6928 c. M:-6.6371 c. 56: 11 7 8 15 8 7 P SD: 3.3712 c. M:-5.8249 c. 65: 13 8 9 18 9 8 N SD: 2.5455 c. M:-4.3233 c. 72: 14 9 10 20 10 9 N SD: 1.7111 c. M: 2.9804 c. 87: 17 11 12 24 12 11 N SD: 0.9437 c. M: 1.6001 c. 137: 27 17 19 38 19 17 N SD: 0.8999 c. M:-1.7319 c. 152: 30 19 21 42 21 19 N SD: 0.7949 c. M:-1.3136 c. 183: 36 23 25 51 25 23 N SD: 0.5077 c. M:-0.8872 c. 224: 44 28 31 62 31 28 N SD: 0.4417 c. M:-0.6371 c. 255: 50 32 35 71 35 32 N SD: 0.4057 c. M: 0.7297 c. 270: 53 34 37 75 37 34 N SD: 0.2627 c. M: 0.4741 c. 407: 80 51 56 113 56 51 N SD: 0.1544 c. M:-0.2685 c. 494: 97 62 68 137 68 62 N SD: 0.0830 c. M: 0.1482 c. 677: 133 85 93 188 93 85 N SD: 0.0777 c. M:-0.1317 c. 901: 177 113 124 250 124 113 N SD: 0.0746 c. M:-0.1376 c. 1084: 213 136 149 301 149 136 N SD: 0.0845 c. M:-0.1431 c. 1171: 230 147 161 325 161 147 N SD: 0.0137 c. M:-0.0228 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 75.3185 cents 3 x x 4:5 x 6 S SD: 17.7576 cents 4 x 5:6 x 7:8 S SD: 42.7037 cents 5 x 6:7:8:9:10 S SD: 21.8828 cents 6:7 x 8:10:11:12 S SD: 12.3468 cents 8:9:10:11:13:15:16 SD: 11.1105 cents 12:14:15:17:20:22:24 SD: 10.0611 cents 13:15:16:18:22:24:26 SD: 7.1797 cents 19:22:24:26:32:35:38 SD: 5.5855 cents 21:24:26:29:35:39:42 SD: 4.8582 cents 27:31:34:37:45:50:54 SD: 3.7723 cents 29:33:36:40:48:53:58 SD: 3.6876 cents 32:37:40:44:53:59:64 SD: 3.5726 cents 35:40:44:48:58:64:70 SD: 2.6696 cents 40:46:50:55:67:73:80 SD: 2.2127 cents 48:55:60:66:80:88:96 SD: 0.0000 cents