Scala analysis: xen12-wilson-09-4C2-hexany-08
1-7-11-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 165/112 670.760751 4: 11/7 782.492036 undecimal augmented fifth 5: 15/8 1088.268715 classic major seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 77/60 431.8751 3: 15/14 119.4428 major diatonic semitone 4: 16/15 111.7313 minor diatonic semitone 5: 105/88 305.7767 6: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 105/88 305.777 cents 1: 1 77/60 431.875 cents 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: 1 224/165 529.239 cents 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 2 22/15 663.049 cents undecimal diminished fifth 3: 1 165/112 670.761 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: 1 120/77 768.125 cents 5: 1 176/105 894.223 cents 5: 2 28/15 1080.557 cents grave major seventh 5: 2 15/8 1088.269 cents classic major seventh 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 : 119.4 551.3 670.8 782.5 1088.3 1200.0 119.4 : 431.9 551.3 663.0 968.8 1080.6 1200.0 551.3 : 119.4 231.2 537.0 648.7 768.1 1200.0 670.8 : 111.7 417.5 529.2 648.7 1080.6 1200.0 782.5 : 305.8 417.5 537.0 968.8 1088.3 1200.0 1088.3: 111.7 231.2 663.0 782.5 894.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 431.8751 cents 77/64, 320.1438 cents 16/15, 111.7313 cents 2: 231.1741 .. 551.3179 cents 77/64, 320.1438 cents 480/539,-200.7010 cents 3: 529.2392 .. 670.7608 cents 27225/25088, 141.5215 cents 1792/1815,-22.0787 cents 4: 648.6821 .. 968.8259 cents 77/64, 320.1438 cents 1792/1815,-22.0787 cents 5: 768.1249 .. 1088.2687 cents 77/64, 320.1438 cents 480/539,-200.7010 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 77/60, 431.8751 cents Average / Smallest step : 1.790009 Largest / Average step : 2.159376 Largest / Smallest step : 3.865302 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 208.85355 cents, oct.: 1253.12127 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : BDBACA Scale is a Constant Structure, by a margin of 14.36717 cents Scale diversity : 1.408005 Lumma stability : 0.186219 Lumma impropriety factor : 0.371300 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 : 225/224, 7.7115 cents Number of recognisable fifths : 0 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% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 11 Odd number limit : 165 (O: 165 U: 165) Highest odd numerator or denominator: 165 Scale harmonicity : 0.023510 Average absolute harmonicity : 0.206403 Specific harmonicity : 0.098312 Fundamental : 1/112, -6.8074 octaves, 2.3359 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 3.696000E+04, 15.17368 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 184.5, average 30.75000 Mersenne's string divisions : 63187578 Sum of van Prooijen's expressibility: 6.65245, average 1.10874 Sum of Tenney's harmonic distance : 12.80011, average 2.13335 Vogel's harmonic complexity : 15.33333 Wille's k value : 82 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 60.19531, average 2.86644 Lattice compactness (without 2's) : 30.14554, average 1.43550 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.66667 12 1 3: 0 .. 1 0.50000 3 5: 0 .. 1 0.50000 3 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 9 13 15 20| Scale is weakly epimorphic with val: <6 9 13 17 20| Scale is weakly epimorphic with val: <6 9 13 19 20| Scale is weakly epimorphic with val: <6 9 14 15 19| Scale is JI-epimorphic with val: <6 9 14 16 20| Scale is weakly epimorphic with val: <6 9 14 19 21| Scale is weakly epimorphic with val: <6 10 13 15 19| Scale is JI-epimorphic with val: <6 10 13 16 20| Scale is weakly epimorphic with val: <6 10 13 19 21| Scale is weakly epimorphic with val: <6 10 15 15 23| Scale is weakly epimorphic with val: <6 10 15 16 20| Scale is weakly epimorphic with val: <6 10 15 17 21| Scale is weakly epimorphic with val: <6 11 14 15 23| Scale is weakly epimorphic with val: <6 11 14 16 20| Scale is weakly epimorphic with val: <6 11 14 17 21| Scale is weakly epimorphic with val: <6 11 15 15 22| Scale is weakly epimorphic with val: <6 11 15 16 19| Scale is weakly epimorphic with val: <6 11 15 16 21| Scale is weakly epimorphic with val: <6 11 15 16 23| Scale is weakly epimorphic with val: <6 11 15 17 22| Scale is weakly epimorphic with val: <6 11 15 19 22|
FIT/MODE
6: 1 2 0 1 1 1 N T3 SD: 60.5040 c. M: 88.2687 c. 7: 1 2 1 1 1 1 P M ME SD: 47.3181 c. M:-74.6508 c. 8: 1 3 0 1 2 1 N SD: 42.4872 c. M: 70.7608 c. 9: 1 3 1 1 2 1 N D3 SD: 14.7554 c. M: 21.6020 c. 11: 1 4 1 1 3 1 N G D3 SD: 11.3062 c. M: 18.8557 c. 20: 2 7 2 2 5 2 N G D3 SD: 7.2891 c. M: 11.3179 c. 31: 3 11 3 3 8 3 N G D3 SD: 7.6203 c. M: 12.6962 c. 32: 3 12 3 3 8 3 N D3 SD: 6.0122 c. M:-11.1821 c. 41: 4 15 4 4 10 4 N D3 SD: 4.5258 c. M:-7.7519 c. 43: 4 16 4 4 11 4 N D3 SD: 4.2780 c. M: 7.8149 c. 52: 5 19 5 5 13 5 N D3 SD: 2.6788 c. M: 4.0582 c. 63: 6 23 6 6 16 6 N D3 SD: 2.9828 c. M: 5.1571 c. 72: 7 26 7 7 18 7 N D3 SD: 2.9232 c. M: 4.9354 c. 83: 8 30 8 8 21 8 N D3 SD: 3.3926 c. M: 5.7005 c. 87: 9 31 9 8 22 8 N SD: 3.2648 c. M:-5.1013 c. 89: 9 32 9 8 23 8 N SD: 2.3295 c. M:-3.8661 c. 98: 10 35 10 9 25 9 N SD: 1.8344 c. M:-3.0062 c. 109: 11 39 11 10 28 10 N SD: 1.1196 c. M:-1.6581 c. 141: 14 51 14 13 36 13 N SD: 1.1198 c. M:-1.8735 c. 150: 15 54 15 14 38 14 N SD: 0.8811 c. M:-1.5080 c. 152: 15 55 15 14 39 14 N SD: 0.9256 c. M:-1.3136 c. 161: 16 58 16 15 41 15 N SD: 0.1362 c. M:-0.2349 c. 592: 59 213 59 55 151 55 N SD: 0.1426 c. M:-0.2448 c. 753: 75 271 75 70 192 70 N SD: 0.1067 c. M:-0.1775 c. 914: 91 329 91 85 233 85 N SD: 0.0899 c. M:-0.1364 c. 934: 93 336 93 87 238 87 N SD: 0.0771 c. M: 0.1402 c. 1075: 107 387 107 100 274 100 N SD: 0.0832 c. M:-0.1239 c. 1095: 109 394 109 102 279 102 N SD: 0.0520 c. M: 0.0851 c. 1256: 125 452 125 117 320 117 N SD: 0.0379 c. M: 0.0601 c. 1417: 141 510 141 132 361 132 N SD: 0.0334 c. M: 0.0542 c. 1848: 184 665 184 172 471 172 N SD: 0.0276 c. M:-0.0430 c. 2009: 200 723 200 187 512 187 N SD: 0.0189 c. M:-0.0339 c. 2170: 216 781 216 202 553 202 N SD: 0.0162 c. M:-0.0262 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 15.5971 cents 3 x 4 x 5 x 6 S SD: 38.3186 cents 4 x x 6 x x 8 S SD: 15.5971 cents 5:6:7 x 8:9:10 S SD: 42.6308 cents 6:7:8:9 x 11:12 SD: 32.8997 cents 7:8 x 10:11:13:14 SD: 24.9771 cents 8:9:11:12:13:15:16 SD: 17.8543 cents 9:10:12:13:14:17:18 SD: 15.3116 cents 10:11:14:15:16:19:20 SD: 12.3838 cents 11:12:15:16:17:21:22 SD: 9.8215 cents 13:14:18:19:20:24:26 SD: 8.3025 cents 14:15:19:21:22:26:28 SD: 6.9915 cents 16:17:22:24:25:30:32 SD: 5.9635 cents 23:25:32:34:36:43:46 SD: 5.6379 cents 24:26:33:35:38:45:48 SD: 4.8465 cents 25:27:34:37:39:47:50 SD: 4.6997 cents 26:28:36:38:41:49:52 SD: 3.8321 cents 30:32:41:44:47:56:60 SD: 2.9663 cents 40:43:55:59:63:75:80 SD: 1.2138 cents 70:75:96:103:110:131:140 SD: 0.9941 cents 72:77:99:106:113:135:144 SD: 0.6758 cents 112:120:154:165:176:210:224 SD: 0.0000 cents