Scala analysis: xen12-wilson-39-4C2-hexany-00
1-3-5-7 4C2 Hexany, Figure 39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 5/4 386.313714 major third 3: 35/24 653.184619 septimal semi-diminished fifth 4: 5/3 884.358713 major sixth, BP sixth 5: 7/4 968.825906 harmonic seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 7/6 266.8709 septimal minor third 2: 15/14 119.4428 major diatonic semitone 3: 7/6 266.8709 septimal minor third 4: 8/7 231.1741 septimal whole tone 5: 21/20 84.4672 minor semitone 6: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 8/7 231.174 cents septimal whole tone 1: 2 7/6 266.871 cents septimal 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: 1 48/35 546.815 cents septimal semi-augmented fourth 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 2 10/7 617.488 cents Euler's tritone 3: 1 35/24 653.185 cents septimal semi-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: 2 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 5: 1 28/15 1080.557 cents grave 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 : 266.9 386.3 653.2 884.4 968.8 1200.0 266.9 : 119.4 386.3 617.5 702.0 933.1 1200.0 386.3 : 266.9 498.0 582.5 813.7 1080.6 1200.0 653.2 : 231.2 315.6 546.8 813.7 933.1 1200.0 884.4 : 84.5 315.6 582.5 702.0 968.8 1200.0 968.8 : 231.2 498.0 617.5 884.4 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 266.8709 cents 10/9, 182.4037 cents 21/20, 84.4672 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 36/35, 48.7704 cents 3: 546.8154 .. 653.1846 cents 1225/1152, 106.3692 cents 36/35, 48.7704 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 36/35, 48.7704 cents 5: 933.1291 .. 1115.5328 cents 10/9, 182.4037 cents 36/35, 48.7704 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 : 7/6, 266.8709 cents Average / Smallest step : 2.367783 Largest / Average step : 1.334355 Largest / Smallest step : 3.159462 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 204.18260 cents, oct.: 1225.09560 cents Scale is strictly proper Step pattern alph. order: ABACDC Step pattern size order : DBDCAC Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.532269 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.303347 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 : 50/49, 34.9756 cents Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) 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 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 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 35 Scale harmonicity : 0.042822 Average absolute harmonicity : 0.237857 Specific harmonicity : 0.182680 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 70, 6.1293 octaves, 18313.790 Hz. Exponens Consonantiae : 1.680000E+03, 10.71425 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 51.5, average 8.58333 Mersenne's string divisions : 607464 Sum of van Prooijen's expressibility: 4.63220, average 0.77203 Sum of Tenney's harmonic distance : 8.77284, average 1.46214 Vogel's harmonic complexity : 9.33333 Wille's k value : 17 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 47.25224, average 2.25011 Lattice compactness (without 2's) : 26.24191, average 1.24961 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.16667 9 1 3: -1 .. 0 -0.50000 3 5: 0 .. 1 0.50000 3 2 7: 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 17| Scale is weakly epimorphic with val: <6 9 14 16| Scale is weakly epimorphic with val: <6 10 14 15| Scale is JI-epimorphic with val: <6 10 14 17| = patent Scale is weakly epimorphic with val: <6 10 14 19| Scale is weakly epimorphic with val: <6 11 13 15| Scale is weakly epimorphic with val: <6 11 14 16| Scale is weakly epimorphic with val: <6 11 15 19|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 50.9507 c. M: 84.3587 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 2 0 2 1 1 1 P D3 SD: 46.6026 c. M:-75.9862 c. 8: 2 1 1 2 0 2 N T3 SD: 46.4825 c. M: 68.8259 c. 9: 2 1 2 2 0 2 P D3 SD: 25.9080 c. M:-48.9746 c. 12: 3 1 3 2 1 2 P T3 SD: 27.9673 c. M:-46.8154 c. 15: 3 2 3 3 1 3 SP D3 SD: 14.0243 c. M: 26.8709 c. 19: 4 2 4 4 1 4 SP D3 SD: 14.0492 c. M: 21.6057 c. 22: 5 2 5 4 2 4 SP T3 SD: 7.7508 c. M:-12.9923 c. 27: 6 3 6 5 2 5 SP SD: 8.8485 c. M:-13.6863 c. 31: 7 3 7 6 2 6 SP SD: 3.6045 c. M:-5.9639 c. 53: 12 5 12 10 4 10 SP SD: 3.1994 c. M:-4.8272 c. 68: 15 7 15 13 5 13 SP SD: 1.6108 c. M: 2.1650 c. 99: 22 10 22 19 7 19 SP SD: 0.9435 c. M:-1.5651 c. 140: 31 14 31 27 10 27 SP SD: 1.0878 c. M: 1.7560 c. 167: 37 17 37 32 12 32 SP SD: 1.0190 c. M:-1.7102 c. 171: 38 17 38 33 12 33 SP SD: 0.3304 c. M: 0.5530 c. 270: 60 27 60 52 19 52 SP SD: 0.1824 c. M:-0.3530 c. 441: 98 44 98 85 31 85 SP SD: 0.1137 c. M: 0.2042 c. 665: 148 66 148 128 47 128 SP SD: 0.1436 c. M:-0.1968 c. 711: 158 71 158 137 50 137 SP SD: 0.1150 c. M: 0.2042 c. 836: 186 83 186 161 59 161 SP SD: 0.1169 c. M: 0.1893 c. 913: 203 91 203 176 64 176 SP SD: 0.1143 c. M:-0.1977 c. 935: 208 93 208 180 66 180 SP SD: 0.0857 c. M:-0.1581 c. 1106: 246 110 246 213 78 213 SP SD: 0.0553 c. M: 0.0911 c. 1376: 306 137 306 265 97 265 SP SD: 0.0384 c. M:-0.0694 c. 1547: 344 154 344 298 109 298 SP SD: 0.0376 c. M: 0.0665 c. 1578: 351 157 351 304 111 304 SP SD: 0.0351 c. M:-0.0519 c. 1749: 389 174 389 337 123 337 SP SD: 0.0288 c. M: 0.0437 c. 2019: 449 201 449 389 142 389 SP SD: 0.0217 c. M:-0.0395 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 24.3852 cents 3 x 4 x 5 x 6 S SD: 37.2438 cents 4 x 5:6 x 7:8 S SD: 12.1926 cents 5:6 x 7:8:9:10 S SD: 24.2869 cents 7:8:9:10 x 12:14 S SD: 15.7497 cents 8:9:10:12:13:14:16 S SD: 15.1509 cents 9 x 11:13:15:16:18 SD: 10.0627 cents 11:13:14:16:18:19:22 SD: 9.1495 cents 12:14:15:18:20:21:24 S SD: 8.1284 cents 13:15:16:19:22:23:26 SD: 7.7414 cents 16:19:20:23:27:28:32 SD: 7.4944 cents 17:20:21:25:28:30:34 SD: 6.3883 cents 19:22:24:28:32:33:38 SD: 6.0721 cents 20:23:25:29:33:35:40 SD: 5.3273 cents 24:28:30:35:40:42:48 S SD: 0.0000 cents