Scala analysis: xen12-wilson-09-4C2-hexany-09
1-9-11-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/48 235.676655 undecimal semi-augmented whole tone 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 5/3 884.358713 major sixth, BP sixth 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: 55/48 235.6767 undecimal semi-augmented whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 40/33 333.0408 5: 9/8 203.9100 major whole tone 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 9/8 203.910 cents major whole tone 1: 1 55/48 235.677 cents undecimal semi-augmented whole tone 1: 1 40/33 333.041 cents 2: 2 6/5 315.641 cents minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 15/11 536.951 cents undecimal augmented fourth 3: 1 176/135 459.139 cents 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 2 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 135/88 740.861 cents 4: 2 22/15 663.049 cents undecimal diminished fifth 4: 2 18/11 852.592 cents undecimal neutral sixth 4: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 33/20 866.959 cents 5: 1 96/55 964.323 cents 5: 2 16/9 996.090 cents Pythagorean minor 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 : 235.7 347.4 551.3 884.4 1088.3 1200.0 235.7 : 111.7 315.6 648.7 852.6 964.3 1200.0 347.4 : 203.9 537.0 740.9 852.6 1088.3 1200.0 551.3 : 333.0 537.0 648.7 884.4 996.1 1200.0 884.4 : 203.9 315.6 551.3 663.0 867.0 1200.0 1088.3: 111.7 347.4 459.1 663.0 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 333.0408 cents 25/22, 221.3095 cents 16/15, 111.7313 cents 2: 315.6413 .. 536.9508 cents 25/22, 221.3095 cents 99/100,-17.3995 cents 3: 459.1392 .. 740.8608 cents 18225/15488, 281.7215 cents 1936/2025,-77.8115 cents 4: 663.0492 .. 884.3587 cents 25/22, 221.3095 cents 1936/2025,-77.8115 cents 5: 866.9592 .. 1088.2687 cents 25/22, 221.3095 cents 99/100,-17.3995 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 : 40/33, 333.0408 cents Average / Smallest step : 1.790009 Largest / Average step : 1.665204 Largest / Smallest step : 2.980730 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 206.18928 cents, oct.: 1237.13570 cents Scale is not proper Step pattern alph. order: ABCDCB Step pattern size order : CABDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.36717 cents Scale diversity : 1.462674 Lumma stability : 0.186219 Lumma impropriety factor : 0.158685 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 : 121/120, 14.3672 cents Number of recognisable fifths : 0 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 55 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.219150 Specific harmonicity : 0.120398 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 88.0, average 14.66667 Mersenne's string divisions : 5401320 Sum of van Prooijen's expressibility: 5.69821, average 0.94970 Sum of Tenney's harmonic distance : 10.91802, average 1.81967 Vogel's harmonic complexity : 15.00000 Wille's k value : 82 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 64.48560, average 3.07074 Lattice compactness (without 2's) : 34.17036, average 1.62716 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.50000 11 1 3: -2 .. 1 -0.50000 5 5: 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: 11 / 6 = 1.83333 Scale is weakly epimorphic with val: <6 10 13 22| Scale is weakly epimorphic with val: <6 10 15 22| Scale is weakly epimorphic with val: <6 11 14 20| Scale is weakly epimorphic with val: <6 11 15 19| Scale is weakly epimorphic with val: <6 11 15 21| Scale is weakly epimorphic with val: <6 11 15 23|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 59.6049 c. M: 88.2687 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 1 2 1 1 P M ME SD: 40.4648 c. M: 64.2481 c. 9: 2 1 1 3 1 1 N D3 SD: 33.9483 c. M:-52.5921 c. 10: 2 1 2 2 2 1 P D3 SD: 27.6383 c. M:-48.6821 c. 11: 2 1 2 3 2 1 N G SD: 12.1665 c. M: 20.1352 c. 20: 4 2 3 6 3 2 N SD: 10.1519 c. M:-15.6413 c. 24: 5 2 4 7 4 2 N SD: 9.9657 c. M:-15.6413 c. 30: 6 3 5 8 5 3 N SD: 7.5277 c. M:-12.5921 c. 31: 6 3 5 9 5 3 N SD: 5.0922 c. M: 9.3825 c. 35: 7 3 6 10 6 3 N SD: 5.4111 c. M:-8.8741 c. 41: 8 4 7 11 7 4 N SD: 4.2439 c. M: 6.3099 c. 42: 8 4 7 12 7 4 N SD: 5.0190 c. M: 8.4608 c. 45: 9 4 8 12 8 4 N SD: 4.8178 c. M:-8.6821 c. 52: 10 5 9 14 9 5 N SD: 4.0964 c. M: 7.4356 c. 56: 11 5 10 15 10 5 N SD: 4.2659 c. M:-5.8249 c. 61: 12 6 10 17 10 6 N SD: 3.7784 c. M:-6.6904 c. 65: 13 6 11 18 11 6 N SD: 2.5990 c. M:-4.3233 c. 72: 14 7 12 20 12 7 N SD: 2.5611 c. M: 4.9354 c. 76: 15 7 13 21 13 7 N SD: 0.8717 c. M:-1.3136 c. 183: 36 17 31 51 31 17 N SD: 0.4600 c. M:-0.8872 c. 224: 44 21 38 62 38 21 N SD: 0.5238 c. M:-0.8063 c. 235: 46 22 40 65 40 22 N SD: 0.5708 c. M: 0.9545 c. 259: 51 24 44 72 44 24 N SD: 0.4111 c. M:-0.6168 c. 270: 53 25 46 75 46 25 N SD: 0.4080 c. M: 0.7413 c. 311: 61 29 53 86 53 29 N SD: 0.3912 c. M: 0.7574 c. 342: 67 32 58 95 58 32 N SD: 0.3800 c. M: 0.5889 c. 387: 76 36 66 107 66 36 N SD: 0.3690 c. M: 0.6378 c. 407: 80 38 69 113 69 38 N SD: 0.2627 c. M:-0.5036 c. 418: 82 39 71 116 71 39 N SD: 0.1655 c. M: 0.2700 c. 494: 97 46 84 137 84 46 N SD: 0.0773 c. M: 0.1482 c. 677: 133 63 115 188 115 63 N SD: 0.0707 c. M:-0.1317 c. 1095: 215 102 186 304 186 102 N SD: 0.0484 c. M: 0.0851 c. 1171: 230 109 199 325 199 109 N SD: 0.0172 c. M:-0.0319 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 75.3185 cents 3 x x 4:5 x 6 S SD: 17.7576 cents 4 x 5:6:7 x 8 S SD: 44.2577 cents 5 x 6:7:8:9:10 S SD: 21.8828 cents 6:7 x 8:10:11:12 S SD: 14.5942 cents 8:9:10:11:13:15:16 SD: 11.1105 cents 11:13 x 15:18:21:22 SD: 14.2189 cents 12:14:15:17:20:23:24 SD: 13.5459 cents 13:15:16:18:22:24:26 SD: 7.1797 cents 14:16:17:19:23:26:28 SD: 6.5714 cents 18:21:22:25:30:34:36 SD: 6.3225 cents 19:22:23:26:32:36:38 SD: 6.0827 cents 21:24:26:29:35:39:42 SD: 4.8582 cents 22:25:27:30:37:41:44 SD: 4.7727 cents 26:30:32:36:43:49:52 SD: 4.3900 cents 27:31:33:37:45:51:54 SD: 2.4126 cents 40:46:49:55:67:75:80 SD: 1.8966 cents 48:55:59:66:80:90:96 SD: 1.6348 cents 54:62:66:74:90:101:108 SD: 1.3398 cents 81:93:99:111:135:152:162 SD: 1.1586 cents 90:103:110:124:150:169:180 SD: 0.8025 cents 104:119:127:143:173:195:208 SD: 0.7316 cents 117:134:143:161:195:219:234 SD: 0.5586 cents 144:165:176:198:240:270:288 SD: 0.0000 cents