Scala analysis: xen12-wilson-25-6C5-hexany
1.3.5.7.9.11 6C5 Hexany, Figure 25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 10/7 617.487807 Euler's tritone 4: 5/3 884.358713 major sixth, BP sixth 5: 20/11 1034.995772 large minor seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 8/7 231.1741 septimal whole tone 4: 7/6 266.8709 septimal minor third 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 4/3 498.045 cents perfect fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 3/2 701.955 cents perfect fifth 4: 1 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 11/7 782.492 cents undecimal augmented fifth 4: 1 8/5 813.686 cents minor sixth 4: 1 18/11 852.592 cents undecimal neutral sixth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 7/4 968.826 cents harmonic seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 5: 1 20/11 1034.996 cents large minor seventh 5: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 182.4 386.3 617.5 884.4 1035.0 1200.0 182.4 : 203.9 435.1 702.0 852.6 1017.6 1200.0 386.3 : 231.2 498.0 648.7 813.7 996.1 1200.0 617.5 : 266.9 417.5 582.5 764.9 968.8 1200.0 884.4 : 150.6 315.6 498.0 702.0 933.1 1200.0 1035.0: 165.0 347.4 551.3 782.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 266.8709 cents 77/72, 116.2338 cents 12/11, 150.6371 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 36/35, 48.7704 cents 3: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 5: 933.1291 .. 1049.3629 cents 77/72, 116.2338 cents 36/35, 48.7704 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.327695 Largest / Average step : 1.334355 Largest / Smallest step : 1.771615 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 205.71328 cents, oct.: 1234.27967 cents Scale is proper Step pattern alph. order: ABCDEF Step pattern size order : CDEFAB Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.609657 Rothenberg stability : 0.866667 = 13/15 Lumma stability : 0.332346 Rothenberg efficiency : 0.355556 redundancy: 0.644444 Efficiency x scale size : 2.133333 Number of different interval sizes : 28 = 5.60000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 121/120, 14.3672 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Scale is subharmonic, base degree is: 4 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Limited inverse transpositions with margin 182.4037 cents: 5 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.233673 Specific harmonicity : 0.159364 Fundamental : 1/2772, -11.4367 octaves, 0.0944 Hz. Guide tone : 20, 4.3219 octaves, 5232.511 Hz. Exponens Consonantiae : 5.544000E+04, 15.75864 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 43.5, average 7.25000 Mersenne's string divisions : 720936 Sum of van Prooijen's expressibility: 4.23867, average 0.70645 Sum of Tenney's harmonic distance : 8.91991, average 1.48665 Vogel's harmonic complexity : 26.16667 Wille's k value : 1732 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 46.69834, average 2.22373 Lattice compactness (without 2's) : 29.67219, average 1.41296 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.50000 7 1 3: -2 .. 0 -0.50000 3 5: 0 .. 1 0.83333 5 3 7: -1 .. 0 -0.16667 1 1 11: -1 .. 0 -0.16667 1 1 Average exponent except 2's : 0 / 6 = 0.00000 Average absolute exponent except 2's: 10 / 6 = 1.66667 Scale is weakly epimorphic with val: <6 10 13 15 23| Scale is weakly epimorphic with val: <6 10 13 17 21| Scale is weakly epimorphic with val: <6 10 15 17 19| Scale is weakly epimorphic with val: <6 10 15 19 23| Scale is weakly epimorphic with val: <6 11 13 15 20| Scale is weakly epimorphic with val: <6 11 14 15 19| Scale is weakly epimorphic with val: <6 11 14 19 21| Scale is weakly epimorphic with val: <6 11 15 19 20|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 39.0382 c. M: 84.3587 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 2 1 1 1 P M ME SD: 35.2272 c. M:-68.2265 c. 8: 1 2 1 2 1 1 P D3 SD: 31.3091 c. M:-63.6863 c. 9: 1 2 2 2 1 1 N SD: 37.4507 c. M:-49.1789 c. 12: 2 2 2 3 1 2 P T3 SD: 19.4599 c. M: 34.9958 c. Prometheus (Scriabin), Mystic, Raga Barbara 14: 2 2 3 3 2 2 P D3 I SD: 22.7183 c. M: 43.4566 c. 15: 2 3 3 3 2 2 P SD: 14.3764 c. M:-22.5122 c. 19: 3 3 4 4 2 3 P SD: 12.2582 c. M: 24.4695 c. 22: 3 4 4 5 3 3 P SD: 11.6577 c. M: 18.7673 c. 27: 4 5 5 6 3 4 P SD: 8.3148 c. M:-13.6863 c. 31: 5 5 6 7 4 4 P SD: 6.6734 c. M:-11.1447 c. 35: 5 6 7 8 4 5 N SD: 7.0230 c. M: 10.9751 c. 37: 6 6 7 8 5 5 SP SD: 6.3505 c. M:-12.1909 c. 41: 6 7 8 9 5 6 P SD: 6.3316 c. M: 10.6055 c. 46: 7 8 9 10 6 6 P SD: 5.4405 c. M:-8.5991 c. 50: 8 8 10 11 6 7 P SD: 5.1975 c. M:-9.5963 c. 52: 8 9 10 11 7 7 SP SD: 4.8194 c. M: 7.4356 c. 53: 8 9 10 12 7 7 P SD: 3.7828 c. M:-6.5137 c. 58: 9 10 11 13 7 8 P SD: 4.0647 c. M:-6.7897 c. 60: 9 10 12 13 8 8 P SD: 3.9998 c. M: 6.3137 c. 65: 10 11 12 15 8 9 P SD: 3.6404 c. M: 8.2570 c. 66: 10 11 13 15 8 9 N SD: 3.3119 c. M:-6.5504 c. 68: 10 12 13 15 9 9 P SD: 3.6775 c. M:-6.1807 c. 72: 11 12 14 16 9 10 P SD: 1.5404 c. M: 2.9804 c. 111: 17 19 21 25 14 15 P SD: 2.0164 c. M:-2.8755 c. 118: 18 20 23 26 15 16 P SD: 1.5258 c. M:-2.8512 c. 130: 20 22 25 29 16 18 P SD: 1.4309 c. M:-2.2117 c. 152: 23 26 29 34 19 21 P SD: 0.8643 c. M: 1.6983 c. 159: 24 27 31 35 20 22 P SD: 1.1809 c. M: 1.4081 c. 183: 28 31 35 41 23 25 P SD: 0.9039 c. M:-1.2028 c. 190: 29 32 37 42 24 26 P SD: 0.8617 c. M:-1.4596 c. 224: 34 38 43 50 28 31 P SD: 0.7914 c. M: 1.4164 c. 239: 36 41 46 53 30 33 P SD: 0.7904 c. M: 1.6506 c. 255: 39 43 49 57 32 35 P SD: 0.6705 c. M:-1.1257 c. 270: 41 46 52 60 34 37 P SD: 0.3061 c. M:-0.5598 c. 342: 52 58 66 76 43 47 P SD: 0.1623 c. M: 0.3488 c. 612: 93 104 118 136 77 84 P SD: 0.1417 c. M:-0.2983 c. 764: 116 130 147 170 96 105 P SD: 0.1309 c. M: 0.2103 c. 836: 127 142 161 186 105 115 P SD: 0.1544 c. M: 0.2629 c. 954: 145 162 184 212 120 131 P SD: 0.1257 c. M:-0.2244 c. 1034: 157 176 199 230 130 142 P SD: 0.1360 c. M:-0.2073 c. 1053: 160 179 203 234 132 145 P SD: 0.1245 c. M: 0.2379 c. 1106: 168 188 213 246 139 152 P SD: 0.0921 c. M: 0.1280 c. 1236: 188 210 238 275 155 170 P SD: 0.0785 c. M:-0.1206 c. 1506: 229 256 290 335 189 207 P SD: 0.0824 c. M:-0.1405 c. 1578: 240 268 304 351 198 217 P SD: 0.0485 c. M:-0.1058 c. 1848: 281 314 356 411 232 254 P SD: 0.0526 c. M:-0.0692 c. 1920: 292 326 370 427 241 264 P SD: 0.0479 c. M:-0.0963 c. 2190: 333 372 422 487 275 301 P SD: 0.0448 c. M:-0.0727 c. 2342: 356 398 451 521 294 322 P SD: 0.0302 c. M: 0.0668 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 42.2336 cents 3 x 4 x 5 x 6 S SD: 37.2438 cents 4 x 5:6 x 7:8 S SD: 26.8248 cents 5 x 6:7:8:9:10 S SD: 21.4618 cents 7:8:9:10:12:13:14 S SD: 15.3505 cents 9:10:11:13:15:16:18 SD: 9.7086 cents 12:13:15:17:20:22:24 SD: 8.0579 cents 16:18:20:23:27:29:32 SD: 5.4537 cents 21:23:26:30:35:38:42 SD: 5.1728 cents 24:27:30:34:40:44:48 SD: 4.9408 cents 27:30:34:39:45:49:54 SD: 3.8712 cents 28:31:35:40:47:51:56 SD: 2.3555 cents 44:49:55:63:73:80:88 SD: 1.6081 cents 56:62:70:80:93:102:112 SD: 1.5481 cents 63:70:79:90:105:115:126 SD: 1.4636 cents 72:80:90:103:120:131:144 SD: 0.4478 cents 180:200:225:257:300:327:360 SD: 0.2891 cents 252:280:315:360:420:458:504 SD: 0.1145 cents 324:360:405:463:540:589:648 SD: 0.0996 cents 576:640:720:823:960:1047:1152 SD: 0.0903 cents