Scala analysis: xen12-wilson-39-4C2-hexany-07
1-5-7-11 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: 11/8 551.317942 undecimal semi-augmented fourth 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 7/4 968.825906 harmonic seventh 5: 77/40 1133.830135 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80/77 66.1699 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 5/4 386.3137 major third 3: 56/55 31.1943 undecimal diesis, konbini comma 4: 5/4 386.3137 major third 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 80/77 66.1699
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 80/77 66.170 cents 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 5/4 386.314 cents major third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 44/35 396.178 cents 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 35/22 803.822 cents 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 11/7 782.492 cents undecimal augmented fifth 4: 2 7/4 968.826 cents harmonic seventh 5: 2 8/5 813.686 cents minor sixth 5: 2 20/11 1034.996 cents large minor seventh 5: 1 77/40 1133.830 cents 5: 1 55/28 1168.806 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 : 165.0 551.3 582.5 968.8 1133.8 1200.0 165.0 : 386.3 417.5 803.8 968.8 1035.0 1200.0 551.3 : 31.2 417.5 582.5 648.7 813.7 1200.0 582.5 : 386.3 551.3 617.5 782.5 1168.8 1200.0 968.8 : 165.0 231.2 396.2 782.5 813.7 1200.0 1133.8: 66.2 231.2 617.5 648.7 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 386.3137 cents 275/224, 355.1195 cents 56/55, 31.1943 cents 2: 231.1741 .. 551.3179 cents 77/64, 320.1438 cents 32/35,-155.1396 cents 3: 396.1783 .. 803.8217 cents 1225/968, 407.6434 cents 32/35,-155.1396 cents 4: 648.6821 .. 968.8259 cents 77/64, 320.1438 cents 32/35,-155.1396 cents 5: 813.6863 .. 1168.8057 cents 275/224, 355.1195 cents 32/35,-155.1396 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 6.411438 Largest / Average step : 1.931569 Largest / Smallest step : 12.384132 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 217.13880 cents, oct.: 1302.83281 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : CDADCB Scale is a Constant Structure, by a margin of 9.86461 cents Scale diversity : 1.382651 Lumma stability : 0.051990 Lumma impropriety factor : 0.517132 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 : 176/175, 9.8646 cents Number of recognisable fifths : 0 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 n-1 differentially coherent in interval class 1 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 77 Scale harmonicity : 0.025728 Average absolute harmonicity : 0.209005 Specific harmonicity : 0.106891 Fundamental : 1/40, -5.3219 octaves, 6.5406 Hz. Guide tone : 154, 7.2668 octaves, 40290.337 Hz. Exponens Consonantiae : 6.160000E+03, 12.58871 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 91.5, average 15.25000 Mersenne's string divisions : 684684 Sum of van Prooijen's expressibility: 5.65947, average 0.94325 Sum of Tenney's harmonic distance : 10.76668, average 1.79445 Vogel's harmonic complexity : 13.16667 Wille's k value : 38 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 50.77948, average 2.41807 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 -1.33333 10 1 5: -1 .. 0 -0.50000 3 7: 0 .. 1 0.50000 3 2 11: 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 13 15 23| Scale is JI-epimorphic with val: <6 13 16 20| Scale is weakly epimorphic with val: <6 13 17 21| Scale is weakly epimorphic with val: <6 14 15 22| Scale is weakly epimorphic with val: <6 14 16 19| Scale is weakly epimorphic with val: <6 14 16 21| Scale is weakly epimorphic with val: <6 14 16 23| Scale is weakly epimorphic with val: <6 14 17 22| Scale is weakly epimorphic with val: <6 14 19 22| Scale is weakly epimorphic with val: <6 15 16 20| Scale is weakly epimorphic with val: <6 15 17 19| Scale is weakly epimorphic with val: <6 15 19 23|
FIT/MODE
6: 1 2 0 2 1 0 N T3 SD: 39.2656 c. M:-66.1699 c. 11: 1 4 0 4 1 1 N SD: 33.0277 c. M: 55.9133 c. 13: 2 4 0 4 2 1 N SD: 25.7840 c. M: 45.7490 c. 14: 2 4 1 4 2 1 N T3 SD: 21.5052 c. M: 37.0322 c. 15: 2 5 0 5 2 1 N SD: 12.0857 c. M: 22.5122 c. 20: 3 6 1 6 3 1 N T3 SD: 11.3634 c. M:-17.4878 c. 21: 3 7 0 7 3 1 N SD: 10.4628 c. M:-20.1106 c. 22: 3 7 1 7 3 1 N T3 SD: 10.3763 c. M:-17.4878 c. 29: 4 9 1 9 4 2 N SD: 11.2352 c. M: 17.1018 c. 30: 4 10 1 9 4 2 N SD: 10.6098 c. M:-17.4878 c. 31: 4 10 1 10 4 2 N SD: 7.3323 c. M: 11.2495 c. 35: 5 11 1 11 5 2 N SD: 4.7010 c. M: 8.8259 c. 37: 5 12 1 12 5 2 N SD: 2.1831 c. M:-4.1471 c. 72: 10 23 2 23 10 4 N SD: 1.2964 c. M: 2.1592 c. 109: 15 35 3 35 15 6 N SD: 0.5352 c. M:-0.9740 c. 233: 32 75 6 75 32 13 N SD: 0.4733 c. M: 0.7829 c. 270: 37 87 7 87 37 15 N SD: 0.3394 c. M: 0.5598 c. 342: 47 110 9 110 47 19 N SD: 0.3206 c. M: 0.4968 c. 379: 52 122 10 122 52 21 N SD: 0.2567 c. M: 0.3945 c. 472: 65 152 12 152 65 26 N SD: 0.2372 c. M:-0.3770 c. 509: 70 164 13 164 70 28 N SD: 0.1847 c. M:-0.3520 c. 581: 80 187 15 187 80 32 N SD: 0.1332 c. M:-0.2281 c. 618: 85 199 16 199 85 34 N SD: 0.0959 c. M:-0.1504 c. 851: 117 274 22 274 117 47 N SD: 0.0804 c. M: 0.1385 c. 888: 122 286 23 286 122 49 N SD: 0.0793 c. M: 0.1394 c. 960: 132 309 25 309 132 53 N SD: 0.0532 c. M: 0.0801 c. 1469: 202 473 38 473 202 81 N SD: 0.0442 c. M:-0.0776 c. 1578: 217 508 41 508 217 87 N SD: 0.0093 c. M:-0.0148 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 59.7214 cents 3 x 4 x 5 x 6 S SD: 33.2878 cents 4 x x 6:7 x 8 S SD: 39.8143 cents 5:6 x 7:9 x 10 SD: 39.5838 cents 6:7:8 x 11 x 12 SD: 35.0901 cents 7:8 x 10:12:13:14 S SD: 20.7229 cents 8:9:11 x 14:15:16 SD: 11.9825 cents 10:11 x 14:18:19:20 SD: 10.7531 cents 11:12:15 x 19:21:22 SD: 6.7273 cents 12:13 x 17:21:23:24 SD: 6.8551 cents 13:14:18 x 23:25:26 SD: 8.6113 cents 15:17 x 21:26:29:30 SD: 10.9571 cents 16:18:22 x 28:31:32 SD: 8.0975 cents 17:19:23:24:30:33:34 SD: 7.7689 cents 18:20 x 25:32:35:36 SD: 7.8463 cents 19:21:26:27:33:37:38 SD: 6.1817 cents 20:22 x 28:35:39:40 SD: 4.4678 cents 21:23:29 x 37:40:42 SD: 4.8369 cents 23:25 x 32:40:44:46 SD: 5.5696 cents 26:29:36 x 46:50:52 SD: 6.5870 cents 27:30:37:38:47:52:54 SD: 3.7466 cents 28:31 x 39:49:54:56 SD: 2.9276 cents 31:34:43 x 54:60:62 SD: 4.0406 cents 32:35:44:45:56:62:64 SD: 2.8005 cents 36:40 x 50:63:69:72 SD: 4.6881 cents 37:41:51:52:65:71:74 SD: 2.8806 cents 40:44:55:56:70:77:80 SD: 0.0000 cents