Scala analysis: xen12-wilson-09-4C2-hexany-04
1-3-9-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 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: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 5/4 386.3137 major third 6: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 5/4 386.314 cents 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 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 3: 2 3/2 701.955 cents perfect 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 8/5 813.686 cents minor sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 5: 2 15/8 1088.269 cents classic 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 : 203.9 386.3 590.2 702.0 1088.3 1200.0 203.9 : 182.4 386.3 498.0 884.4 996.1 1200.0 386.3 : 203.9 315.6 702.0 813.7 1017.6 1200.0 590.2 : 111.7 498.0 609.8 813.7 996.1 1200.0 702.0 : 386.3 498.0 702.0 884.4 1088.3 1200.0 1088.3: 111.7 315.6 498.0 702.0 813.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 386.3137 cents 75/64, 274.5824 cents 16/15, 111.7313 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 3: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 5: 813.6863 .. 1088.2687 cents 75/64, 274.5824 cents 24/25,-70.6724 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 1.790009 Largest / Average step : 1.931569 Largest / Smallest step : 3.457525 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 199.96013 cents, oct.: 1199.76080 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : CBCADA Scale is not a Constant Structure Scale diversity : 1.419495 Lumma stability : 0.186219 Lumma impropriety factor : 0.117787 Rothenberg efficiency : 0.583333 redundancy: 0.416667 Efficiency x scale size : 3.500000 Number of different interval sizes : 14 = 2.80000 / 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete genus musicum : 2^m 3^2 5^1 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.056391 Average absolute harmonicity : 0.275734 Specific harmonicity : 0.261379 Fundamental : 1/32, -5.0000 octaves, 8.1758 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 2.880000E+03, 11.49185 octaves Euler's gradus suavitatis : 15 Sum of Mann's harmonic distance : 67.0, average 11.16667 Mersenne's string divisions : 1354815 Sum of van Prooijen's expressibility: 4.95964, average 0.82661 Sum of Tenney's harmonic distance : 9.47509, average 1.57918 Vogel's harmonic complexity : 8.33333 Wille's k value : 22 Wilson's harmonic complexity : 11 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 61.36836, average 2.92230 Lattice compactness (without 2's) : 28.77927, average 1.37044 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.16667 15 1 3: 0 .. 2 1.00000 6 2 5: 0 .. 1 0.50000 3 3 Average exponent except 2's : 9 / 6 = 1.50000 Average absolute exponent except 2's: 9 / 6 = 1.50000 Scale is weakly epimorphic with val: <6 10 13| Scale is weakly epimorphic with val: <6 10 15| Scale is weakly epimorphic with val: <6 11 15|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 54.3175 c. M:-98.0450 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 1 1 2 1 P M ME SD: 45.7122 c. M: 75.9380 c. 8: 1 2 1 1 2 1 P B ME I SD: 42.4865 c. M:-63.6863 c. 9: 1 2 1 1 3 1 N D3 SD: 41.0626 c. M: 70.5767 c. 10: 2 1 2 1 3 1 P D3 SD: 20.3489 c. M:-36.0900 c. 12: 2 2 2 1 4 1 N T3 SD: 8.5598 c. M:-13.6863 c. Raga Caturangini, Ratnakanthi 22: 4 3 4 2 7 2 N SD: 7.9306 c. M:-14.2718 c. 31: 5 5 5 3 10 3 N SD: 6.4019 c. M: 10.3616 c. 34: 6 5 6 3 11 3 N SD: 5.9245 c. M:-9.7763 c. 41: 7 6 7 4 13 4 N SD: 3.8133 c. M: 5.8259 c. 53: 9 8 9 5 17 5 N SD: 1.0465 c. M: 1.5445 c. 65: 11 10 11 6 21 6 N SD: 0.8156 c. M:-1.3786 c. 118: 20 18 20 11 38 11 N SD: 0.2963 c. M: 0.5202 c. 323: 55 49 55 30 104 30 N SD: 0.3011 c. M:-0.4884 c. 376: 64 57 64 35 121 35 N SD: 0.1876 c. M:-0.3453 c. 429: 73 65 73 40 138 40 N SD: 0.1901 c. M: 0.2997 c. 441: 75 67 75 41 142 41 N SD: 0.1499 c. M:-0.2525 c. 494: 84 75 84 46 159 46 N SD: 0.0751 c. M:-0.1386 c. 559: 95 85 95 52 180 52 N SD: 0.0744 c. M:-0.1162 c. 612: 104 93 104 57 197 57 N SD: 0.0244 c. M: 0.0392 c. 1171: 199 178 199 109 377 109 N SD: 0.0246 c. M:-0.0410 c. 1289: 219 196 219 120 415 120 N SD: 0.0205 c. M:-0.0323 c. 1783: 303 271 303 166 574 166 N SD: 0.0109 c. M:-0.0175 c. 1901: 323 289 323 177 612 177 N SD: 0.0094 c. M: 0.0173 c. 2395: 407 364 407 223 771 223 N SD: 0.0081 c. M:-0.0148 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 4:5 x 6 S SD: 68.1241 cents 4 x 5 x 6 x 8 S SD: 0.0000 cents 5 x 6:7:8:9:10 S SD: 30.0217 cents 6:7 x 8:9:11:12 SD: 23.6429 cents 7:8:9:10:11:13:14 SD: 17.1803 cents 8:9:10:11:12:15:16 S SD: 6.4843 cents 16:18:20:23:24:30:32 SD: 6.3418 cents 22:25:28:31:33:41:44 SD: 6.2334 cents 23:26:29:32:35:43:46 SD: 5.9681 cents 24:27:30:34:36:45:48 SD: 2.1294 cents 32:36:40:45:48:60:64 S SD: 0.0000 cents