Scala analysis: xen12-wilson-39-4C2-hexany-10
3-5-7-9 4C2 Hexany, Figure 39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 7/6 266.870906 septimal minor third 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 3/2 701.955001 perfect 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: 21/20 84.4672 minor semitone 2: 10/9 182.4037 minor whole tone 3: 6/5 315.6413 minor third 4: 15/14 119.4428 major diatonic semitone 5: 6/5 315.6413 minor third 6: 10/9 182.4037 minor 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 10/9 182.404 cents minor whole tone 1: 2 6/5 315.641 cents minor third 2: 2 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 4/3 498.045 cents perfect fourth 3: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 54/35 750.725 cents septimal semi-augmented fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 14/9 764.916 cents septimal minor sixth 4: 2 12/7 933.129 cents septimal major sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 9/5 1017.596 cents just minor seventh, BP 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 : 84.5 266.9 582.5 702.0 1017.6 1200.0 84.5 : 182.4 498.0 617.5 933.1 1115.5 1200.0 266.9 : 315.6 435.1 750.7 933.1 1017.6 1200.0 582.5 : 119.4 435.1 617.5 702.0 884.4 1200.0 702.0 : 315.6 498.0 582.5 764.9 1080.6 1200.0 1017.6: 182.4 266.9 449.3 764.9 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 315.6413 cents 8/7, 231.1741 cents 21/20, 84.4672 cents 2: 266.8709 .. 498.0450 cents 8/7, 231.1741 cents 35/36,-48.7704 cents 3: 449.2746 .. 750.7254 cents 1458/1225, 301.4508 cents 35/36,-48.7704 cents 4: 701.9550 .. 933.1291 cents 8/7, 231.1741 cents 35/36,-48.7704 cents 5: 884.3587 .. 1115.5328 cents 8/7, 231.1741 cents 35/36,-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 : 6/5, 315.6413 cents Average / Smallest step : 2.367783 Largest / Average step : 1.578206 Largest / Smallest step : 3.736851 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 191.88513 cents, oct.: 1151.31079 cents Scale is not proper Step pattern alph. order: ABCDCB Step pattern size order : ACDBDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.19052 cents Scale diversity : 1.529973 Lumma stability : 0.140779 Lumma impropriety factor : 0.162568 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 : 245/243, 14.1905 cents Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 21 Scale harmonicity : 0.036120 Average absolute harmonicity : 0.256065 Specific harmonicity : 0.170004 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 7.560000E+03, 12.88417 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 44.0, average 7.33333 Mersenne's string divisions : 223860 Sum of van Prooijen's expressibility: 4.44378, average 0.74063 Sum of Tenney's harmonic distance : 8.52296, average 1.42049 Vogel's harmonic complexity : 12.00000 Wille's k value : 31 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 45.04093, average 2.14481 Lattice compactness (without 2's) : 34.00683, average 1.61937 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.50000 5 1 3: -1 .. 2 0.50000 5 1 5: -1 .. 0 -0.50000 3 1 7: 0 .. 1 0.50000 3 3 Average exponent except 2's : 3 / 6 = 0.50000 Average absolute exponent except 2's: 11 / 6 = 1.83333 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 13 18| Scale is JI-epimorphic with val: <6 10 15 18| Scale is weakly epimorphic with val: <6 11 13 15| Scale is weakly epimorphic with val: <6 11 14 18| Scale is weakly epimorphic with val: <6 11 15 19|
FIT/MODE
6: 0 1 2 0 2 1 N T3 SD: 61.3958 c. M: 101.9550 c. 7: 0 1 2 1 2 1 N SD: 59.5581 c. M: 95.4423 c. 8: 1 1 2 1 2 1 P D3 SD: 38.8506 c. M:-65.5328 c. 10: 1 1 3 1 2 2 N T3 SD: 31.4468 c. M: 57.5963 c. 11: 1 1 3 1 3 2 N SD: 36.2353 c. M: 48.6891 c. 12: 1 2 3 1 3 2 P T3 SD: 18.0651 c. M:-33.1291 c. 14: 1 2 4 1 4 2 N T3 SD: 11.4472 c. M:-17.4878 c. 19: 1 3 5 2 5 3 N SD: 12.6326 c. M: 21.3093 c. 26: 2 4 7 2 7 4 N T3 SD: 9.7152 c. M:-17.4878 c. 27: 2 4 7 3 7 4 N SD: 4.9538 c. M:-9.1561 c. 39: 3 6 10 4 10 6 N SD: 5.8417 c. M:-10.0522 c. 41: 3 6 11 4 11 6 N SD: 3.5968 c. M:-6.7940 c. 53: 4 8 14 5 14 8 N SD: 4.0856 c. M:-6.1671 c. 58: 4 9 15 6 15 9 N SD: 2.3893 c. M: 3.8032 c. 72: 5 11 19 7 19 11 N SD: 1.0558 c. M: 1.9550 c. 99: 7 15 26 10 26 15 N SD: 0.6011 c. M:-1.0753 c. 171: 12 26 45 17 45 26 N SD: 0.1601 c. M: 0.2567 c. 441: 31 67 116 44 116 67 N SD: 0.1353 c. M: 0.2042 c. 612: 43 93 161 61 161 93 N SD: 0.1247 c. M: 0.2042 c. 783: 55 119 206 78 206 119 N SD: 0.1250 c. M: 0.2042 c. 935: 66 142 246 93 246 142 N SD: 0.1417 c. M:-0.2387 c. 954: 67 145 251 95 251 145 N SD: 0.1277 c. M: 0.2042 c. 993: 70 151 261 99 261 151 N SD: 0.1206 c. M:-0.1986 c. 1007: 71 153 265 100 265 153 N SD: 0.1141 c. M:-0.2088 c. 1065: 75 162 280 106 280 162 N SD: 0.0904 c. M:-0.1713 c. 1106: 78 168 291 110 291 168 N SD: 0.1007 c. M:-0.1621 c. 1164: 82 177 306 116 306 177 N SD: 0.0837 c. M:-0.1394 c. 1236: 87 188 325 123 325 188 N SD: 0.0697 c. M: 0.1206 c. 1277: 90 194 336 127 336 194 N SD: 0.0733 c. M:-0.1060 c. 1335: 94 203 351 133 351 203 N SD: 0.0587 c. M:-0.0954 c. 1448: 102 220 381 144 381 220 N SD: 0.0562 c. M:-0.0845 c. 1506: 106 229 396 150 396 229 N SD: 0.0435 c. M: 0.0664 c. 1677: 118 255 441 167 441 255 N SD: 0.0374 c. M: 0.0650 c. 1790: 126 272 471 178 471 272 N SD: 0.0461 c. M:-0.0576 c. 1848: 130 281 486 184 486 281 N SD: 0.0386 c. M: 0.0638 c. 2019: 142 307 531 201 531 307 N SD: 0.0435 c. M: 0.0690 c. 2060: 145 313 542 205 542 313 N SD: 0.0435 c. M: 0.0748 c. 2118: 149 322 557 211 557 322 N SD: 0.0411 c. M: 0.0759 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 x 5:6 S SD: 52.5853 cents 4 x 5 x 6:7:8 S SD: 32.2540 cents 5 x 6:7:8:9:10 S SD: 24.3823 cents 6 x 7:8:9:11:12 SD: 18.0486 cents 7 x 8:10:11:13:14 SD: 21.8277 cents 8 x 9:11:12:14:16 SD: 17.1064 cents 9 x 11:13:14:16:18 SD: 23.5289 cents 10:11:12:14:15:18:20 S SD: 15.6921 cents 12:13:14:17:18:22:24 SD: 11.0004 cents 14:15:16:20:21:25:28 SD: 10.4232 cents 16:17:19:22:24:29:32 SD: 8.2921 cents 17:18:20:24:26:31:34 SD: 7.9325 cents 18:19:21:25:27:32:36 SD: 4.5224 cents 20:21:23:28:30:36:40 SD: 4.1517 cents 35:37:41:49:53:63:70 SD: 3.5621 cents 36:38:42:50:54:65:72 SD: 2.8974 cents 40:42:47:56:60:72:80 SD: 2.0537 cents 42:44:49:59:63:76:84 SD: 1.9255 cents 60:63:70:84:90:108:120 S SD: 0.0000 cents