Scala analysis: xen12-wilson-39-4C2-hexany-08
1-5-9-11 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: 9/8 203.910002 major whole tone 3: 99/80 368.914230 4: 11/8 551.317942 undecimal semi-augmented fourth 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: 45/44 38.9058 1/5-tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 10/9 182.4037 minor whole tone 5: 72/55 466.2783 undecimal semi-diminished fourth 6: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 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 72/55 466.278 cents undecimal semi-diminished fourth 2: 2 9/8 203.910 cents major whole tone 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 99/80 368.914 cents 3: 2 5/4 386.314 cents major third 3: 2 8/5 813.686 cents minor sixth 3: 1 160/99 831.086 cents 4: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 2 18/11 852.592 cents undecimal neutral sixth 4: 2 16/9 996.090 cents Pythagorean minor seventh 5: 1 55/36 733.722 cents undecimal semi-augmented fifth 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 5: 2 20/11 1034.996 cents large minor seventh 5: 1 88/45 1161.094 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 : 165.0 203.9 368.9 551.3 1017.6 1200.0 165.0 : 38.9 203.9 386.3 852.6 1035.0 1200.0 203.9 : 165.0 347.4 813.7 996.1 1161.1 1200.0 368.9 : 182.4 648.7 831.1 996.1 1035.0 1200.0 551.3 : 466.3 648.7 813.7 852.6 1017.6 1200.0 1017.6: 182.4 347.4 386.3 551.3 733.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 466.2783 cents 32/25, 427.3726 cents 45/44, 38.9058 cents 2: 203.9100 .. 648.6821 cents 128/99, 444.7721 cents 55/64,-262.3683 cents 3: 368.9142 .. 831.0858 cents 12800/9801, 462.1715 cents 1089/1280,-279.7678 cents 4: 551.3179 .. 996.0900 cents 128/99, 444.7721 cents 1089/1280,-279.7678 cents 5: 733.7217 .. 1161.0942 cents 32/25, 427.3726 cents 55/64,-262.3683 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 72/55, 466.2783 cents Average / Smallest step : 5.140625 Largest / Average step : 2.331392 Largest / Smallest step : 11.984811 Median interval of one step : 173.70397 cents, amount: 0 Least squares average step : 177.72330 cents, oct.: 1066.33979 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : BABCDC Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.406711 Lumma stability : 0.064843 Lumma impropriety factor : 0.660150 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 : 100/99, 17.3995 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% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined 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 : 0.028641 Average absolute harmonicity : 0.220168 Specific harmonicity : 0.120398 Fundamental : 1/80, -6.3219 octaves, 3.2703 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.584000E+04, 13.95128 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 126.5, average 21.08333 Mersenne's string divisions : 2428314 Sum of van Prooijen's expressibility: 5.98691, average 0.99782 Sum of Tenney's harmonic distance : 11.69618, average 1.94936 Vogel's harmonic complexity : 13.33333 Wille's k value : 49 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 64.51771, average 3.07227 Lattice compactness (without 2's) : 36.22094, average 1.72481 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.66667 12 1 3: 0 .. 2 1.00000 6 1 5: -1 .. 0 -0.50000 3 1 11: 0 .. 1 0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 12 / 6 = 2.00000 Scale is weakly epimorphic with val: <6 10 13 22| Scale is JI-epimorphic with val: <6 10 15 22| Scale is weakly epimorphic with val: <6 11 13 20| Scale is weakly epimorphic with val: <6 11 14 19| Scale is weakly epimorphic with val: <6 11 14 21| Scale is weakly epimorphic with val: <6 11 14 23| Scale is weakly epimorphic with val: <6 11 15 20|
FIT/MODE
6: 1 0 1 1 2 1 N D3 SD: 28.5362 c. M:-48.6821 c. 7: 1 0 1 1 3 1 N D3 SD: 23.3350 c. M: 37.0322 c. 13: 2 0 2 2 5 2 N D3 SD: 11.3156 c. M:-19.6112 c. 22: 3 1 3 3 9 3 N D3 SD: 11.2447 c. M:-18.7673 c. 24: 3 1 3 4 9 4 N SD: 12.3121 c. M: 18.9142 c. 26: 4 0 4 4 10 4 N D3 SD: 11.3156 c. M:-19.6112 c. 27: 4 1 3 4 11 4 N SD: 13.0499 c. M:-18.3122 c. 28: 4 1 4 4 11 4 N D3 SD: 9.8789 c. M:-16.8001 c. 29: 4 1 4 4 12 4 N D3 SD: 8.9981 c. M:-16.8865 c. 32: 4 1 5 5 12 5 N SD: 10.6651 c. M: 16.4100 c. 33: 5 1 4 5 13 5 N SD: 9.5653 c. M:-16.8140 c. 35: 5 1 5 5 14 5 N D3 SD: 6.3277 c. M:-10.9751 c. 41: 6 1 6 6 16 6 N D3 SD: 7.2614 c. M:-11.5736 c. 42: 6 1 6 6 17 6 N D3 SD: 6.5182 c. M:-10.9751 c. 45: 6 2 6 7 17 7 N SD: 6.1498 c. M:-9.4233 c. 46: 6 2 6 7 18 7 N SD: 4.4862 c. M: 8.4825 c. 52: 7 2 7 8 20 8 N SD: 2.5067 c. M:-3.7823 c. 59: 8 2 8 9 23 9 N SD: 1.7580 c. M: 2.8125 c. 65: 9 2 9 10 25 10 N SD: 1.4944 c. M:-2.5282 c. 124: 17 4 17 19 48 19 N SD: 0.8486 c. M: 1.4673 c. 159: 22 5 22 24 62 24 N SD: 0.7798 c. M:-1.2716 c. 205: 28 7 28 31 80 31 N SD: 0.8373 c. M: 1.1018 c. 211: 29 7 29 32 82 32 N SD: 0.5081 c. M:-0.8293 c. 218: 30 7 30 33 85 33 N SD: 0.4815 c. M: 0.8592 c. 270: 37 9 37 41 105 41 N SD: 0.3355 c. M: 0.5598 c. 283: 39 9 39 43 110 43 N SD: 0.2191 c. M: 0.3764 c. 335: 46 11 46 51 130 51 N SD: 0.2277 c. M:-0.3238 c. 494: 68 16 68 75 192 75 N SD: 0.1863 c. M:-0.3165 c. 553: 76 18 76 84 215 84 N SD: 0.0897 c. M: 0.1425 c. 618: 85 20 85 94 240 94 N SD: 0.0782 c. M:-0.1384 c. 836: 115 27 115 127 325 127 N SD: 0.0794 c. M: 0.1218 c. 1112: 153 36 153 169 432 169 N SD: 0.0923 c. M:-0.1505 c. 1171: 161 38 161 178 455 178 N SD: 0.0106 c. M:-0.0183 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 75.3185 cents 3 x x x 4:5:6 S SD: 47.8310 cents 4 x x 5:6:7:8 S SD: 39.8221 cents 5 x x 6:7:9:10 SD: 15.4335 cents 6 x 7 x 8:11:12 SD: 22.0953 cents 7 x 8:9:10:13:14 SD: 22.2959 cents 8 x 9:10:11:14:16 SD: 10.3562 cents 9:10 x 11:12:16:18 S SD: 12.7527 cents 10:11 x 12:14:18:20 SD: 12.3468 cents 11:12 x 14:15:20:22 S SD: 11.0940 cents 13:14:15:16:18:23:26 SD: 11.0481 cents 15 x 17:19:21:27:30 SD: 10.5125 cents 16 x 18:20:22:29:32 SD: 4.2251 cents 17 x 19:21:23:31:34 SD: 7.5575 cents 18:20 x 22:25:32:36 SD: 7.8244 cents 19:21 x 24:26:34:38 SD: 7.7526 cents 21:23:24:26:29:38:42 SD: 5.1094 cents 25 x 28:31:34:45:50 SD: 4.1583 cents 26 x 29:32:36:47:52 SD: 4.5168 cents 27:30 x 33:37:49:54 SD: 6.3269 cents 29:32:33:36:40:52:58 SD: 3.8142 cents 30:33:34:37:41:54:60 SD: 2.9254 cents 35 x 39:43:48:63:70 SD: 4.2516 cents 37:41:42:46:51:67:74 SD: 4.0569 cents 38:42:43:47:52:68:76 SD: 3.0871 cents 39:43:44:48:54:70:78 SD: 2.8848 cents 41:45:46:51:56:74:82 SD: 2.7493 cents 48:53:54:59:66:86:96 SD: 2.6046 cents 49:54:55:61:67:88:98 SD: 2.5875 cents 50:55:56:62:69:90:100 SD: 1.7572 cents 70:77:79:87:96:126:140 SD: 1.7184 cents 71:78:80:88:98:128:142 SD: 1.4040 cents 72:79:81:89:99:130:144 SD: 1.1949 cents 80:88:90:99:110:144:160 SD: 0.0000 cents