Scala analysis: xen12-wilson-09-4C2-hexany-13
3-9-11-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/9 347.407941 undecimal neutral third 2: 5/4 386.313714 major third 3: 55/36 733.721654 undecimal semi-augmented fifth 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: 11/9 347.4079 undecimal neutral third 2: 45/44 38.9058 1/5-tone 3: 11/9 347.4079 undecimal neutral third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 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: 1 45/44 38.906 cents 1/5-tone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 11/9 347.408 cents undecimal neutral 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: 1 72/55 466.278 cents undecimal semi-diminished fourth 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 2 22/15 663.049 cents undecimal diminished fifth 3: 1 55/36 733.722 cents undecimal semi-augmented 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: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 20/11 1034.996 cents large minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 88/45 1161.094 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 : 347.4 386.3 733.7 884.4 1049.4 1200.0 347.4 : 38.9 386.3 537.0 702.0 852.6 1200.0 386.3 : 347.4 498.0 663.0 813.7 1161.1 1200.0 733.7 : 150.6 315.6 466.3 813.7 852.6 1200.0 884.4 : 165.0 315.6 663.0 702.0 1049.4 1200.0 1049.4: 150.6 498.0 537.0 884.4 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 347.4079 cents 484/405, 308.5022 cents 45/44, 38.9058 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 54/55,-31.7667 cents 3: 466.2783 .. 733.7217 cents 3025/2592, 267.4433 cents 54/55,-31.7667 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 54/55,-31.7667 cents 5: 852.5921 .. 1161.0942 cents 484/405, 308.5022 cents 54/55,-31.7667 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 5.140625 Largest / Average step : 1.737040 Largest / Smallest step : 8.929470 Median interval of one step : 157.82064 cents, amount: 0 Least squares average step : 212.14780 cents, oct.: 1272.88681 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : DADBCB Scale is a Constant Structure, by a margin of 31.76665 cents Scale diversity : 1.422517 Lumma stability : 0.064843 Lumma impropriety factor : 0.105889 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 3 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 : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.030381 Average absolute harmonicity : 0.224828 Specific harmonicity : 0.128390 Fundamental : 1/36, -5.1699 octaves, 7.2674 Hz. Guide tone : 110, 6.7814 octaves, 28778.812 Hz. Exponens Consonantiae : 3.960000E+03, 11.95128 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 74.0, average 12.33333 Mersenne's string divisions : 556920 Sum of van Prooijen's expressibility: 5.22109, average 0.87018 Sum of Tenney's harmonic distance : 9.89000, average 1.64833 Vogel's harmonic complexity : 12.33333 Wille's k value : 27 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 46.37731, average 2.20844 Lattice compactness (without 2's) : 32.42027, average 1.54382 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.66667 6 1 3: -2 .. 0 -1.00000 6 5: 0 .. 1 0.50000 3 2 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 0 / 6 = 0.00000 Average absolute exponent except 2's: 12 / 6 = 2.00000 Scale is weakly epimorphic with val: <6 9 13 20| Scale is weakly epimorphic with val: <6 9 14 19| 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 11 13 20| Scale is weakly epimorphic with val: <6 11 14 21|
FIT/MODE
6: 2 0 2 0 1 1 N T3 SD: 53.0709 c. M: 84.3587 c. 7: 2 0 2 1 1 1 P D3 SD: 29.9635 c. M: 48.0074 c. 10: 3 0 3 1 2 1 P SD: 25.6436 c. M: 44.3587 c. 13: 4 0 4 2 1 2 N SD: 23.9588 c. M:-38.7182 c. 15: 4 1 4 2 2 2 P SD: 14.3379 c. M: 27.4079 c. 18: 5 1 5 2 3 2 P SD: 12.8969 c. M: 17.6920 c. 22: 6 1 6 3 3 3 P SD: 14.9253 c. M: 24.6307 c. 23: 7 0 7 3 3 3 N SD: 11.6506 c. M: 21.0963 c. 24: 7 1 7 3 3 3 N SD: 10.8326 c. M:-16.2783 c. 30: 9 1 8 4 4 4 N SD: 10.3346 c. M: 13.7217 c. 31: 9 1 9 4 4 4 N SD: 3.1064 c. M:-5.9639 c. 49: 14 2 14 6 7 6 N SD: 3.4945 c. M:-5.5230 c. 56: 16 2 16 7 8 7 N SD: 3.6854 c. M: 5.7873 c. 65: 19 2 19 8 9 8 N SD: 2.8154 c. M:-4.7399 c. 72: 21 2 21 9 10 9 N SD: 1.6936 c. M: 2.9804 c. 87: 25 3 25 11 12 11 N SD: 1.7143 c. M: 2.6872 c. 103: 30 3 30 13 14 13 N SD: 1.2749 c. M:-2.1066 c. 118: 34 4 34 15 16 15 N SD: 1.2116 c. M: 1.9053 c. 121: 35 4 35 15 17 15 N SD: 1.0639 c. M:-1.8767 c. 152: 44 5 44 19 21 19 N SD: 0.3974 c. M:-0.6371 c. 335: 97 11 97 42 46 42 N SD: 0.3842 c. M:-0.6067 c. 342: 99 11 99 43 47 43 N SD: 0.2428 c. M: 0.3883 c. 494: 143 16 143 62 68 62 N SD: 0.0863 c. M: 0.1482 c. 677: 196 22 196 85 93 85 N SD: 0.0800 c. M:-0.1317 c. 1019: 295 33 295 128 140 128 N SD: 0.0545 c. M: 0.0990 c. 1171: 339 38 339 147 161 147 N SD: 0.0128 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: 15.8833 cents 3 x 4 x 5 x 6 S SD: 37.2438 cents 4 x 5:6 x 7:8 S SD: 21.6439 cents 5:6 x x 8:9:10 S SD: 20.9357 cents 7 x 9:11:12:13:14 SD: 17.4753 cents 8 x 10:12:13:15:16 SD: 13.3326 cents 9:11 x 14:15:17:18 SD: 12.0734 cents 12 x 15:18:20:22:24 S SD: 6.3533 cents 13:16 x 20:22:24:26 SD: 6.7388 cents 16 x 20:24:27:29:32 SD: 8.6328 cents 17:21 x 26:28:31:34 SD: 5.8260 cents 19:23:24:29:32:35:38 SD: 5.2847 cents 21 x 26:32:35:39:42 SD: 5.6347 cents 23:28:29:35:38:42:46 SD: 4.0631 cents 25 x 31:38:42:46:50 SD: 4.4776 cents 27:33:34:41:45:50:54 SD: 4.0026 cents 28:34:35:43:47:51:56 SD: 3.6769 cents 31:38:39:47:52:57:62 SD: 3.6320 cents 32:39:40:49:53:59:64 SD: 2.6548 cents 36:44:45:55:60:66:72 SD: 0.0000 cents