Scala analysis: xen12-wilson-09-4C2-hexany-14
7-9-11-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 11/9 347.407941 undecimal neutral third 3: 55/42 466.850749 4: 11/7 782.492036 undecimal augmented fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 15/14 119.4428 major diatonic semitone 2: 154/135 227.9651 3: 15/14 119.4428 major diatonic semitone 4: 6/5 315.6413 minor third 5: 35/33 101.8667 6: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/33 101.867 cents 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 154/135 227.965 cents 1: 2 6/5 315.641 cents minor third 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: 1 55/42 466.851 cents 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 2 22/15 663.049 cents undecimal diminished fifth 3: 1 84/55 733.149 cents 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 5/3 884.359 cents major sixth, BP sixth 5: 1 135/77 972.035 cents 5: 2 28/15 1080.557 cents grave major seventh 5: 1 66/35 1098.133 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 : 119.4 347.4 466.9 782.5 884.4 1200.0 119.4 : 228.0 347.4 663.0 764.9 1080.6 1200.0 347.4 : 119.4 435.1 537.0 852.6 972.0 1200.0 466.9 : 315.6 417.5 733.1 852.6 1080.6 1200.0 782.5 : 101.9 417.5 537.0 764.9 884.4 1200.0 884.4 : 315.6 435.1 663.0 782.5 1098.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8667 .. 315.6413 cents 198/175, 213.7746 cents 35/33, 101.8667 cents 2: 347.4079 .. 435.0841 cents 81/77, 87.6762 cents 55/54, 31.7667 cents 3: 466.8507 .. 733.1493 cents 3528/3025, 266.2985 cents 55/54, 31.7667 cents 4: 764.9159 .. 852.5921 cents 81/77, 87.6762 cents 55/54, 31.7667 cents 5: 884.3587 .. 1098.1333 cents 198/175, 213.7746 cents 55/54, 31.7667 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 35/33, 101.8667 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.963351 Largest / Average step : 1.578206 Largest / Smallest step : 3.098573 Median interval of one step : 173.70397 cents, amount: 0 Least squares average step : 186.44585 cents, oct.: 1118.67512 cents Scale is strictly proper Step pattern alph. order: ABACDC Step pattern size order : BCBDAD Scale is a Constant Structure, by a margin of 31.76665 cents Scale diversity : 1.485763 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.275667 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 : 99/98, 17.5761 cents Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 : 135 (O: 135 U: 135) Highest odd numerator or denominator: 55 Scale harmonicity : 0.022288 Average absolute harmonicity : 0.210505 Specific harmonicity : 0.098312 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 4.158000E+04, 15.34360 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 87.5, average 14.58333 Mersenne's string divisions : 1012680 Sum of van Prooijen's expressibility: 5.69821, average 0.94970 Sum of Tenney's harmonic distance : 11.04508, average 1.84085 Vogel's harmonic complexity : 16.83333 Wille's k value : 82 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 43.41166, average 2.06722 Lattice compactness (without 2's) : 37.78998, average 1.79952 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.16667 3 1 3: -2 .. 1 -0.50000 5 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 : 0 / 6 = 0.00000 Average absolute exponent except 2's: 14 / 6 = 2.33333 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 weakly epimorphic with val: <6 10 13 18 22| Scale is weakly epimorphic with val: <6 10 13 19 21| Scale is weakly epimorphic with val: <6 10 14 15 22| Scale is weakly epimorphic with val: <6 10 14 16 19| Scale is weakly epimorphic with val: <6 10 14 16 21| Scale is weakly epimorphic with val: <6 10 14 16 23| Scale is weakly epimorphic with val: <6 10 14 17 22| Scale is weakly epimorphic with val: <6 10 14 19 22| Scale is weakly epimorphic with val: <6 10 15 15 23| Scale is weakly epimorphic with val: <6 10 15 17 21| Scale is JI-epimorphic with val: <6 10 15 18 22| Scale is weakly epimorphic with val: <6 11 13 15 20| Scale is weakly epimorphic with val: <6 11 13 17 20| Scale is weakly epimorphic with val: <6 11 13 19 20| Scale is weakly epimorphic with val: <6 11 14 15 23| Scale is weakly epimorphic with val: <6 11 14 17 21| Scale is weakly epimorphic with val: <6 11 14 18 20| Scale is weakly epimorphic with val: <6 11 15 18 19| Scale is weakly epimorphic with val: <6 11 15 18 21| Scale is weakly epimorphic with val: <6 11 15 18 23|
FIT/MODE
6: 1 1 0 2 0 2 N T3 SD: 59.3680 c. M: 84.3587 c. 7: 1 1 1 2 0 2 P D3 SD: 43.3719 c. M:-74.6508 c. 8: 1 1 1 2 1 2 P D3 SD: 28.1827 c. M: 47.4079 c. 11: 1 2 1 3 1 3 P G SD: 17.9484 c. M: 30.4871 c. 18: 2 3 2 5 1 5 P SD: 12.9783 c. M: 17.6920 c. 20: 2 4 2 5 2 5 SP SD: 9.8542 c. M:-15.6413 c. 23: 2 5 2 6 2 6 SP SD: 9.6537 c. M:-17.8095 c. 28: 3 5 3 7 3 7 SP SD: 9.0558 c. M:-15.6413 c. 31: 3 6 3 8 3 8 SP SD: 4.5060 c. M: 8.2985 c. 38: 4 7 4 10 3 10 SP SD: 4.8768 c. M:-6.9816 c. 41: 4 8 4 11 3 11 SP SD: 4.5116 c. M:-7.7519 c. 49: 5 9 5 13 4 13 SP SD: 2.6128 c. M: 4.5508 c. 69: 7 13 7 18 6 18 SP SD: 1.8064 c. M:-2.7145 c. 72: 7 14 7 19 6 19 SP SD: 1.6441 c. M: 2.7761 c. 80: 8 15 8 21 7 21 SP SD: 1.6409 c. M: 2.4920 c. 118: 12 22 12 31 10 31 SP SD: 1.3402 c. M:-2.5911 c. 121: 12 23 12 32 10 32 SP SD: 0.8866 c. M: 1.7141 c. 141: 14 27 14 37 12 37 SP SD: 0.8889 c. M:-1.5282 c. 152: 15 29 15 40 13 40 SP SD: 0.7103 c. M: 1.0613 c. 190: 19 36 19 50 16 50 SP SD: 0.4174 c. M:-0.6659 c. 221: 22 42 22 58 19 58 SP SD: 0.3824 c. M:-0.7092 c. 342: 34 65 34 90 29 90 SP SD: 0.1152 c. M: 0.1841 c. 753: 75 143 75 198 64 198 SP SD: 0.0634 c. M:-0.1034 c. 1095: 109 208 109 288 93 288 SP SD: 0.0159 c. M: 0.0263 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 x 5:6 S SD: 10.3981 cents 4 x 5 x 6:7:8 S SD: 30.7557 cents 5 x 6:7:8 x 10 S SD: 30.9836 cents 6 x 7:8:9:10:12 S SD: 23.6182 cents 7:8 x 9:11:12:14 SD: 25.1965 cents 8:9:10 x x 13:16 SD: 25.7021 cents 9:10:11:12:14:15:18 S SD: 12.0716 cents 12:13:15:16:19:20:24 SD: 9.1643 cents 13:14:16:17:20:22:26 SD: 7.9509 cents 14:15:17:18:22:23:28 SD: 6.9858 cents 19:20:23:25:30:32:38 SD: 6.8339 cents 23:25:28:30:36:38:46 SD: 5.2445 cents 26:28:32:34:41:43:52 SD: 3.5161 cents 39:42:48:51:61:65:78 SD: 2.8640 cents 42:45:51:55:66:70:84 SD: 1.8797 cents 45:48:55:59:71:75:90 SD: 1.7685 cents 54:58:66:71:85:90:108 SD: 1.4476 cents 58:62:71:76:91:97:116 SD: 1.3672 cents 68:73:83:89:107:113:136 SD: 1.1676 cents 72:77:88:94:113:120:144 SD: 1.0889 cents 81:87:99:106:127:135:162 SD: 0.9821 cents 84:90:103:110:132:140:168 SD: 0.9353 cents 100:107:122:131:157:167:200 SD: 0.9144 cents 112:120:137:147:176:187:224 SD: 0.8654 cents 126:135:154:165:198:210:252 SD: 0.0000 cents