Scala analysis: xen12-wilson-39-4C2-hexany-01
1-3-5-9 4C2 Hexany, Figure 39
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: 3/2 701.955001 perfect fifth 4: 5/3 884.358713 major sixth, BP sixth 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: 6/5 315.6413 minor third 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 6/5 315.641 cents minor 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 27/20 519.551 cents acute fourth 3: 1 40/27 680.449 cents grave fifth 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 5/3 884.359 cents major sixth, BP sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 5: 1 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 : 203.9 386.3 702.0 884.4 1088.3 1200.0 203.9 : 182.4 498.0 680.4 884.4 996.1 1200.0 386.3 : 315.6 498.0 702.0 813.7 1017.6 1200.0 702.0 : 182.4 386.3 498.0 702.0 884.4 1200.0 884.4 : 203.9 315.6 519.6 702.0 1017.6 1200.0 1088.3: 111.7 315.6 498.0 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 315.6413 cents 9/8, 203.9100 cents 16/15, 111.7313 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 1/1, 0.0000 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: 884.3587 .. 1088.2687 cents 9/8, 203.9100 cents 1/1, 0.0000 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 : 6/5, 315.6413 cents Average / Smallest step : 1.790009 Largest / Average step : 1.578206 Largest / Smallest step : 2.825004 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 211.66133 cents, oct.: 1269.96797 cents Scale is proper Step pattern alph. order: ABCBAD Step pattern size order : CBDBCA Scale is not a Constant Structure Scale diversity : 1.374800 Rothenberg stability : 0.533333 = 8/15 Lumma stability : 0.186219 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 : 81/80, 21.5063 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 3 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 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 5 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 15 Scale harmonicity : 0.054348 Average absolute harmonicity : 0.284157 Specific harmonicity : 0.271017 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 2.160000E+03, 11.07682 octaves Euler's gradus suavitatis : 15 Sum of Mann's harmonic distance : 32.5, average 5.41667 Mersenne's string divisions : 140760 Sum of van Prooijen's expressibility: 4.00540, average 0.66757 Sum of Tenney's harmonic distance : 7.49282, average 1.24880 Vogel's harmonic complexity : 8.66667 Wille's k value : 22 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 52.96396, average 2.52209 Lattice compactness (without 2's) : 30.11969, average 1.43427 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.33333 10 1 3: -1 .. 2 0.50000 5 2 5: 0 .. 1 0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 8 / 6 = 1.33333 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 14|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 65.1986 c. M: 101.9550 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 2 1 1 1 P M ME SD: 35.3830 c. M: 59.6973 c. 10: 2 1 3 1 2 1 P D3 SD: 26.9462 c. M: 44.3587 c. 12: 2 2 3 2 2 1 P G D3 SD: 9.9054 c. M:-15.6413 c. Lydian Hexatonic, Raga Kumud, Sankara (Shankara), Prabhati 19: 3 3 5 3 3 2 P G D3 SD: 9.3764 c. M: 14.5845 c. 22: 4 3 6 3 4 2 P SD: 8.3374 c. M:-14.2718 c. 31: 5 5 8 5 5 3 P G D3 SD: 5.6232 c. M: 10.3616 c. 34: 6 5 9 5 6 3 P SD: 4.4543 c. M:-7.8547 c. 41: 7 6 11 6 7 4 P SD: 4.1526 c. M: 6.3099 c. 46: 8 7 12 7 8 4 P SD: 4.3741 c. M:-7.3835 c. 53: 9 8 14 8 9 5 P SD: 0.9984 c. M: 1.4763 c. 118: 20 18 31 18 20 11 P SD: 0.2949 c. M: 0.5202 c. 171: 29 26 45 26 29 16 P SD: 0.3283 c. M: 0.5494 c. 289: 49 44 76 44 49 27 P SD: 0.2664 c. M: 0.4498 c. 323: 55 49 85 49 55 30 P SD: 0.2336 c. M:-0.4244 c. 376: 64 57 99 57 64 35 P SD: 0.2123 c. M:-0.3453 c. 388: 66 59 102 59 66 36 P SD: 0.2318 c. M:-0.3911 c. 441: 75 67 116 67 75 41 P SD: 0.1089 c. M:-0.1716 c. 494: 84 75 130 75 84 46 P SD: 0.0933 c. M: 0.1482 c. 559: 95 85 147 85 95 52 P SD: 0.0655 c. M:-0.1034 c. 612: 104 93 161 93 104 57 P SD: 0.0284 c. M: 0.0450 c. 1171: 199 178 308 178 199 109 P SD: 0.0189 c. M:-0.0319 c. 1783: 303 271 469 271 303 166 P SD: 0.0087 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 0.0000 cents 3 x 4 x 5 x 6 S SD: 37.2438 cents 4 x 5:6:7 x 8 S SD: 21.1168 cents 5 x 6 x 8:9:10 S SD: 30.6021 cents 6:7:8:9:10:11:12 H SD: 22.3368 cents 7:8:9:11:12:13:14 SD: 18.4550 cents 8:9:10:12:13:15:16 SD: 7.3052 cents 16:18:20:24:27:30:32 S SD: 3.5844 cents 24:27:30:36:40:45:48 S SD: 0.0000 cents