Scala analysis: xen12-wilson-39-4C2-hexany-12
3-5-9-11 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: 3/2 701.955001 perfect fifth 3: 33/20 866.959229 4: 9/5 1017.596288 just minor seventh, BP seventh 5: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 15/11 536.9508 undecimal augmented fourth 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 55/54 31.7667 telepathma 6: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 15/11 536.951 cents undecimal augmented fourth 2: 2 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 2 3/2 701.955 cents perfect fifth 3: 1 40/33 333.041 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 2 18/11 852.592 cents undecimal neutral sixth 3: 1 33/20 866.959 cents 4: 2 4/3 498.045 cents perfect fourth 4: 2 5/3 884.359 cents major sixth, BP sixth 4: 2 9/5 1017.596 cents just minor seventh, BP seventh 5: 1 22/15 663.049 cents undecimal diminished fifth 5: 2 20/11 1034.996 cents large minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 108/55 1168.233 cents 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 : 165.0 702.0 867.0 1017.6 1049.4 1200.0 165.0 : 537.0 702.0 852.6 884.4 1035.0 1200.0 702.0 : 165.0 315.6 347.4 498.0 663.0 1200.0 867.0 : 150.6 182.4 333.0 498.0 1035.0 1200.0 1017.6: 31.8 182.4 347.4 884.4 1049.4 1200.0 1049.4: 150.6 315.6 852.6 1017.6 1168.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 536.9508 cents 162/121, 505.1841 cents 55/54, 31.7667 cents 2: 182.4037 .. 701.9550 cents 27/20, 519.5513 cents 22/27,-354.5471 cents 3: 333.0408 .. 866.9592 cents 1089/800, 533.9185 cents 80/99,-368.9142 cents 4: 498.0450 .. 1017.5963 cents 27/20, 519.5513 cents 80/99,-368.9142 cents 5: 663.0492 .. 1168.2333 cents 162/121, 505.1841 cents 22/27,-354.5471 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 15/11, 536.9508 cents Average / Smallest step : 6.295910 Largest / Average step : 2.684754 Largest / Smallest step : 16.902969 Median interval of one step : 157.82064 cents, amount: 0 Least squares average step : 227.32958 cents, oct.: 1363.97748 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : CDCBAB Scale is a Constant Structure, by a margin of 17.39948 cents Scale diversity : 1.333106 Lumma stability : 0.052944 Lumma impropriety factor : 0.695994 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 : 121/120, 14.3672 cents Number of recognisable fifths : 2, average 701.9550 cents 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 n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 33 Scale harmonicity : 0.028104 Average absolute harmonicity : 0.246167 Specific harmonicity : 0.127943 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.188000E+04, 13.53625 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 56.5, average 9.41667 Mersenne's string divisions : 189210 Sum of van Prooijen's expressibility: 5.03266, average 0.83878 Sum of Tenney's harmonic distance : 9.41287, average 1.56881 Vogel's harmonic complexity : 13.83333 Wille's k value : 49 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 44.88199, average 2.13724 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 -0.66667 6 1 3: -1 .. 2 0.50000 5 1 5: -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: 11 / 6 = 1.83333 Scale is weakly epimorphic with val: <6 9 13 23| Scale is weakly epimorphic with val: <6 9 14 22| Scale is weakly epimorphic with val: <6 11 13 21| Scale is weakly epimorphic with val: <6 11 15 19|
FIT/MODE
6: 1 2 1 1 0 1 N D3 SD: 56.0497 c. M: 101.9550 c. 7: 1 3 1 1 0 1 N D3 SD: 12.6104 c. M: 20.7915 c. 22: 3 10 3 3 0 3 N D3 SD: 10.0603 c. M:-18.7673 c. 24: 3 11 3 3 1 3 N D3 SD: 11.7374 c. M: 17.5963 c. 26: 4 11 4 3 1 3 N SD: 11.0309 c. M:-19.6112 c. 27: 4 12 4 3 1 3 N SD: 13.2207 c. M:-21.9297 c. 28: 4 12 4 4 0 4 N D3 SD: 12.6104 c. M: 20.7915 c. 29: 4 13 4 4 0 4 N D3 SD: 9.2474 c. M:-16.8865 c. 31: 4 14 4 4 1 4 N D3 SD: 9.1973 c. M: 15.3463 c. 32: 4 15 4 4 1 4 N D3 SD: 7.9853 c. M: 15.0042 c. 34: 5 15 5 4 1 4 N SD: 9.2066 c. M:-15.3937 c. 38: 5 17 5 5 1 5 N D3 SD: 8.2723 c. M: 14.3277 c. 39: 5 18 5 5 1 5 N D3 SD: 5.8022 c. M: 11.1581 c. 41: 6 18 6 5 1 5 N SD: 7.0746 c. M:-11.0896 c. 46: 6 21 6 6 1 6 N D3 SD: 4.9906 c. M: 8.4825 c. 53: 7 24 7 7 1 7 N D3 SD: 4.9841 c. M: 7.8535 c. 57: 8 25 8 7 2 7 N SD: 4.8114 c. M: 7.2182 c. 58: 8 26 8 7 2 7 N SD: 3.0203 c. M:-5.8095 c. 65: 9 29 9 8 2 8 N SD: 1.6122 c. M:-2.9448 c. 72: 10 32 10 9 2 9 N SD: 1.1505 c. M: 1.9550 c. 137: 19 61 19 17 4 17 N SD: 1.2191 c. M:-1.7319 c. 145: 20 65 20 18 4 18 N SD: 1.2533 c. M:-2.0063 c. 152: 21 68 21 19 4 19 N SD: 0.8463 c. M:-1.4618 c. 159: 22 71 22 20 4 20 N SD: 0.7869 c. M:-1.2716 c. 224: 31 100 31 28 6 28 N SD: 0.6387 c. M:-1.0672 c. 263: 36 118 36 33 7 33 N SD: 0.4228 c. M: 0.7457 c. 270: 37 121 37 34 7 34 N SD: 0.3483 c. M: 0.5598 c. 335: 46 150 46 42 9 42 N SD: 0.1802 c. M: 0.2829 c. 342: 47 153 47 43 9 43 N SD: 0.1801 c. M: 0.2926 c. 494: 68 221 68 62 13 62 N SD: 0.1559 c. M:-0.2472 c. 677: 93 303 93 85 18 85 N SD: 0.1243 c. M: 0.1941 c. 829: 114 371 114 104 22 104 N SD: 0.0712 c. M:-0.1095 c. 836: 115 374 115 105 22 105 N SD: 0.0644 c. M:-0.1071 c. 1171: 161 524 161 147 31 147 N SD: 0.0088 c. M: 0.0170 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x 3 x x x 4 S SD: 0.0000 cents 3 x x 5 x x 6 SD: 8.6997 cents 4:5:6 x 7 x 8 S SD: 56.6549 cents 5:6 x 8:9 x 10 S SD: 39.9449 cents 6:7:9:10 x 11:12 SD: 20.6684 cents 7:8:11:12 x 13:14 SD: 25.0935 cents 8:9:12:13:14:15:16 S SD: 13.0219 cents 10:11:15:17:18 x 20 SD: 10.3365 cents 11:12:17:18 x 20:22 SD: 11.4723 cents 12:13:18:20 x 22:24 SD: 6.3289 cents 16:18:24:26:29 x 32 SD: 9.7074 cents 17:19:26:28 x 31:34 SD: 8.9107 cents 18:20:27:30:32:33:36 SD: 5.4467 cents 20:22:30:33:36:37:40 SD: 2.6112 cents 22:24:33:36 x 40:44 SD: 4.9769 cents 26:29:39:43:47:48:52 SD: 4.6977 cents 28:31:42:46:50:51:56 SD: 3.7248 cents 30:33:45:50:54:55:60 SD: 2.8999 cents 40:44:60:66:72:73:80 SD: 1.3145 cents 60:66:90:99:108:110:120 SD: 0.0000 cents