Scala analysis: xen12-wilson-09-4C2-hexany-06
1-7-9-11 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 9/7 435.084095 septimal major third, BP third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 11/7 782.492036 undecimal augmented fifth 5: 99/56 986.402038 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112/99 213.5980 1: 9/8 203.9100 major whole tone 2: 8/7 231.1741 septimal whole tone 3: 77/72 116.2338 undecimal secor 4: 8/7 231.1741 septimal whole tone 5: 9/8 203.9100 major whole tone 6: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 77/72 116.234 cents undecimal secor 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 2 8/7 231.174 cents septimal whole tone 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 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 88/63 578.582 cents 3: 1 63/44 621.418 cents 3: 2 16/11 648.682 cents undecimal semi-diminished fifth 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: 2 7/4 968.826 cents harmonic seventh 5: 1 99/56 986.402 cents 5: 2 16/9 996.090 cents Pythagorean minor seventh 5: 1 144/77 1083.766 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 : 203.9 435.1 551.3 782.5 986.4 1200.0 203.9 : 231.2 347.4 578.6 782.5 996.1 1200.0 435.1 : 116.2 347.4 551.3 764.9 968.8 1200.0 551.3 : 231.2 435.1 648.7 852.6 1083.8 1200.0 782.5 : 203.9 417.5 621.4 852.6 968.8 1200.0 986.4 : 213.6 417.5 648.7 764.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.2338 .. 231.1741 cents 576/539, 114.9402 cents 77/72, 116.2338 cents 2: 347.4079 .. 435.0841 cents 81/77, 87.6762 cents 77/72, 116.2338 cents 3: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 77/72, 116.2338 cents 4: 764.9159 .. 852.5921 cents 81/77, 87.6762 cents 77/72, 116.2338 cents 5: 968.8259 .. 1083.7662 cents 576/539, 114.9402 cents 77/72, 116.2338 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 77/72, 116.2338 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.720669 Largest / Average step : 1.155870 Largest / Smallest step : 1.988871 Median interval of one step : 208.75398 cents, amount: 0 Least squares average step : 197.69242 cents, oct.: 1186.15453 cents Scale is strictly proper Step pattern alph. order: ABCBAD Step pattern size order : BDADBC Scale is a Constant Structure, by a margin of 116.23385 cents Scale diversity : 1.430318 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.581169 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 : 896/891, 9.6880 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 16.6667% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.215589 Specific harmonicity : 0.109470 Fundamental : 1/56, -5.8074 octaves, 4.6719 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 114.0, average 19.00000 Mersenne's string divisions : 7209360 Sum of van Prooijen's expressibility: 5.98691, average 0.99782 Sum of Tenney's harmonic distance : 11.53250, average 1.92208 Vogel's harmonic complexity : 13.66667 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 61.71906, average 2.93900 Lattice compactness (without 2's) : 36.22094, average 1.72481 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.33333 10 1 3: 0 .. 2 1.00000 6 1 7: -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 15 22| Scale is weakly epimorphic with val: <6 10 16 19| Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 10 16 23| Scale is weakly epimorphic with val: <6 10 17 22| Scale is weakly epimorphic with val: <6 10 19 22| Scale is weakly epimorphic with val: <6 11 15 20| Scale is weakly epimorphic with val: <6 11 17 20| Scale is weakly epimorphic with val: <6 11 19 20|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 26.1647 c. M:-48.6821 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 11: 2 2 1 2 2 2 SP M ME SD: 10.1345 c. M: 18.8557 c. Machine-6 17: 3 3 2 3 3 3 SP M ME SD: 8.3073 c. M:-13.3879 c. Machine-6 28: 5 5 3 5 5 5 SP M DE SD: 7.1516 c. M: 11.0635 c. Machine-6 35: 6 7 3 7 6 6 SP SD: 6.0952 c. M:-10.6302 c. 41: 7 8 4 8 7 7 SP SD: 5.4073 c. M:-8.7199 c. 46: 8 9 4 9 8 8 SP SD: 4.6476 c. M:-8.3942 c. 52: 9 10 5 10 9 9 SP SD: 3.4518 c. M:-5.9057 c. 63: 11 12 6 12 11 11 SP SD: 3.1802 c. M:-5.6138 c. 69: 12 13 7 13 12 12 SP SD: 3.5147 c. M:-5.2038 c. 72: 12 14 7 14 12 13 SP SD: 2.2441 c. M: 3.9100 c. 83: 14 16 8 16 14 15 SP SD: 1.8964 c. M: 3.2695 c. 100: 17 19 10 19 17 18 SP SD: 1.9133 c. M: 3.0841 c. 107: 18 21 10 21 18 19 SP SD: 1.7995 c. M:-2.5547 c. 113: 19 22 11 22 19 20 SP SD: 1.7394 c. M:-3.3487 c. 118: 20 23 11 23 20 21 SP SD: 1.2994 c. M:-2.2040 c. 124: 21 24 12 24 21 22 SP SD: 0.7187 c. M:-1.3789 c. 135: 23 26 13 26 23 24 SP SD: 0.3400 c. M:-0.5344 c. 259: 44 50 25 50 44 46 SP SD: 0.3381 c. M:-0.5195 c. 342: 58 66 33 66 58 61 SP SD: 0.3021 c. M: 0.4407 c. 394: 67 76 38 76 67 70 SP SD: 0.2735 c. M:-0.4489 c. 466: 79 90 45 90 79 83 SP SD: 0.2688 c. M: 0.4765 c. 477: 81 92 46 92 81 85 SP SD: 0.2020 c. M: 0.3745 c. 483: 82 93 47 93 82 86 SP SD: 0.1815 c. M: 0.3015 c. 601: 102 116 58 116 102 107 SP SD: 0.1816 c. M: 0.2494 c. 612: 104 118 59 118 104 109 SP SD: 0.1797 c. M: 0.3376 c. 618: 105 119 60 119 105 110 SP SD: 0.0801 c. M:-0.1384 c. 753: 128 145 73 145 128 134 SP SD: 0.0502 c. M:-0.0765 c. 1713: 291 330 166 330 291 305 SP SD: 0.0419 c. M: 0.0623 c. 1848: 314 356 179 356 314 329 SP SD: 0.0224 c. M: 0.0384 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 x 4:5 x 6 S SD: 38.3186 cents 4 x 5 x 6:7:8 S SD: 23.9448 cents 5:6 x 7:8:9:10 S SD: 24.8219 cents 6:7 x 8:9:11:12 SD: 26.2697 cents 7:8:9:10:11:12:14 S SD: 14.8696 cents 8:9:10:11:13:14:16 SD: 12.9696 cents 9:10 x 12:14:16:18 S SD: 12.1710 cents 10:11:13:14:16:18:20 SD: 11.5456 cents 13:15:17:18:20:23:26 SD: 10.8997 cents 14:16:18:19:22:25:28 SD: 6.5791 cents 17:19:22:23:27:30:34 SD: 6.2110 cents 18:20:23:25:28:32:36 SD: 5.9697 cents 21:24:27:29:33:37:42 SD: 4.8113 cents 24:27:31:33:38:42:48 SD: 3.8858 cents 31:35:40:43:49:55:62 SD: 3.5259 cents 32:36:41:44:50:57:64 SD: 2.9073 cents 38:43:49:52:60:67:76 SD: 2.8182 cents 39:44:50:54:61:69:78 SD: 2.6950 cents 42:47:54:58:66:74:84 SD: 2.2008 cents 48:54:62:66:75:85:96 SD: 2.1714 cents 49:55:63:67:77:87:98 SD: 2.1392 cents 56:63:72:77:88:99:112 SD: 0.0000 cents