Scala analysis: xen12-wilson-39-4C2-hexany-14
5-7-9-11 4C2 Hexany, Figure 39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 9/7 435.084095 septimal major third, BP third 3: 99/70 600.088324 2nd quasi-equal tritone 4: 11/7 782.492036 undecimal augmented fifth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 90/77 270.0799 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 10/9 182.4037 minor whole tone 5: 63/55 235.1043 6: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 63/55 235.104 cents 1: 1 90/77 270.080 cents 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 2 9/7 435.084 cents septimal major third, BP third 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 140/99 599.912 cents quasi-equal tritone 3: 1 99/70 600.088 cents 2nd quasi-equal tritone 3: 2 10/7 617.488 cents Euler's tritone 4: 2 14/9 764.916 cents septimal minor sixth 4: 2 11/7 782.492 cents undecimal augmented fifth 4: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 77/45 929.920 cents 5: 1 110/63 964.896 cents 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 5: 2 20/11 1034.996 cents large minor 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 : 165.0 435.1 600.1 782.5 1017.6 1200.0 165.0 : 270.1 435.1 617.5 852.6 1035.0 1200.0 435.1 : 165.0 347.4 582.5 764.9 929.9 1200.0 600.1 : 182.4 417.5 599.9 764.9 1035.0 1200.0 782.5 : 235.1 417.5 582.5 852.6 1017.6 1200.0 1017.6: 182.4 347.4 617.5 782.5 964.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 270.0799 cents 900/847, 105.0756 cents 11/10, 165.0042 cents 2: 347.4079 .. 435.0841 cents 81/77, 87.6762 cents 847/810, 77.3281 cents 3: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/45, 147.4281 cents 4: 764.9159 .. 852.5921 cents 81/77, 87.6762 cents 49/45, 147.4281 cents 5: 929.9201 .. 1034.9958 cents 900/847, 105.0756 cents 847/810, 77.3281 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 90/77, 270.0799 cents Average / Smallest step : 1.212090 Largest / Average step : 1.350399 Largest / Smallest step : 1.636806 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 200.58667 cents, oct.: 1203.52002 cents Scale is strictly proper Step pattern alph. order: ABACDC Step pattern size order : ADABCB Scale is a Constant Structure, by a margin of 77.32807 cents Scale diversity : 1.344157 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.649601 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 : 9801/9800, 0.1766 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 16.6667% Limited transpositions with margin 105.0756 cents: 3 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.207956 Specific harmonicity : 0.098312 Fundamental : 1/70, -6.1293 octaves, 3.7375 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 120.5, average 20.08333 Mersenne's string divisions : 170352 Sum of van Prooijen's expressibility: 5.98691, average 0.99782 Sum of Tenney's harmonic distance : 11.52220, average 1.92037 Vogel's harmonic complexity : 15.33333 Wille's k value : 49 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 45.29963, average 2.15713 Lattice compactness (without 2's) : 39.78526, average 1.89454 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.16667 3 1 3: 0 .. 2 1.00000 6 5: -1 .. 0 -0.50000 3 1 7: -1 .. 0 -0.50000 3 1 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 3 / 6 = 0.50000 Average absolute exponent except 2's: 15 / 6 = 2.50000 Scale is weakly epimorphic with val: <6 9 13 15 23| Scale is JI-epimorphic with val: <6 9 13 16 20| Scale is weakly epimorphic with val: <6 9 13 17 21| Scale is weakly epimorphic with val: <6 9 14 15 22| Scale is weakly epimorphic with val: <6 9 14 16 19| Scale is weakly epimorphic with val: <6 9 14 16 21| Scale is weakly epimorphic with val: <6 9 14 16 23| Scale is weakly epimorphic with val: <6 9 14 17 22| Scale is weakly epimorphic with val: <6 9 14 19 22| Scale is weakly epimorphic with val: <6 9 15 16 20| Scale is weakly epimorphic with val: <6 9 15 17 19| Scale is weakly epimorphic with val: <6 9 15 19 23| Scale is weakly epimorphic with val: <6 10 13 15 23| Scale is weakly epimorphic with val: <6 10 13 17 21| Scale is weakly epimorphic with val: <6 10 13 18 22| Scale is weakly epimorphic with val: <6 10 15 17 19| Scale is JI-epimorphic with val: <6 10 15 18 22| Scale is weakly epimorphic with val: <6 10 15 19 23| Scale is weakly epimorphic with val: <6 11 13 15 23| Scale is weakly epimorphic with val: <6 11 13 17 21| Scale is weakly epimorphic with val: <6 11 13 18 20| Scale is weakly epimorphic with val: <6 11 14 18 19| Scale is weakly epimorphic with val: <6 11 14 18 21| Scale is weakly epimorphic with val: <6 11 14 18 23| Scale is weakly epimorphic with val: <6 11 15 17 19| Scale is weakly epimorphic with val: <6 11 15 18 20| Scale is weakly epimorphic with val: <6 11 15 19 23|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 22.6265 c. M: 35.0841 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 8: 1 2 1 1 2 1 P B ME I SD: 20.6291 c. M: 32.4920 c. 14: 2 3 2 2 3 2 SP B ME I SD: 7.3773 c. M: 11.0635 c. Quasi-equal Hexatonic 38: 5 9 5 6 7 6 SP SD: 5.7529 c. M: 7.1095 c. 44: 6 10 6 7 8 7 SP SD: 4.9448 c. M: 8.5054 c. 46: 6 11 6 7 9 7 SP SD: 4.8730 c. M: 8.4825 c. 52: 7 12 7 8 10 8 SP SD: 2.3390 c. M: 3.4658 c. 58: 8 13 8 9 11 9 SP SD: 2.1946 c. M: 3.8032 c. 66: 9 15 9 10 13 10 SP SD: 0.8478 c. M: 1.3679 c. 138: 19 31 19 21 27 21 SP SD: 0.1825 c. M: 0.3015 c. 204: 28 46 28 31 40 31 SP SD: 0.1647 c. M: 0.2983 c. 342: 47 77 47 52 67 52 SP SD: 0.0582 c. M: 0.0919 c. 822: 113 185 113 125 161 125 SP SD: 0.0547 c. M: 0.0883 c. 1164: 160 262 160 177 228 177 SP SD: 0.0536 c. M: 0.0883 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 40.2685 cents 3 x 4 x 5 x 6 S SD: 39.9178 cents 4 x 5 x 6:7:8 S SD: 26.5086 cents 5 x 6:7:8:9:10 S SD: 24.9388 cents 6:7:8 x 9:11:12 SD: 29.5542 cents 7:8:9:10:11:13:14 SD: 14.5379 cents 9:10:12:13:14:16:18 S SD: 13.3048 cents 10:11:13:14:16:18:20 SD: 6.7658 cents 19:21:24:27:30:34:38 SD: 5.8853 cents 20:22:26:28:31:36:40 SD: 5.8687 cents 21:23:27:30:33:38:42 SD: 3.5064 cents 31:34:40:44:49:56:62 SD: 2.6005 cents 39:43:50:55:61:70:78 SD: 2.0742 cents 49:54:63:69:77:88:98 SD: 1.5107 cents 60:66:77:85:94:108:120 SD: 1.1351 cents 70:77:90:99:110:126:140 SD: 0.0000 cents