Scala analysis: 166_C6
Chromatic tetrachord 40/39 * 169/160 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 13/12 138.572661 tridecimal 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 40/39 43.8311 tridecimal minor diesis 2: 169/160 94.7416 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 169/160 94.742 cents 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 640/507 403.303 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 43.8 138.6 498.0 43.8 : 94.7 454.2 498.0 138.6: 359.5 403.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 359.4723 cents 6/5, 315.6413 cents 40/39, 43.8311 cents 2: 138.5727 .. 454.2139 cents 6/5, 315.6413 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 3.787612 Largest / Average step : 2.165300 Largest / Smallest step : 8.201317 Median interval of one step : 169/160, 94.7416 cents, amount: 1 Least squares average step : 129.65081 cents, oct.: 388.95244 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1125-tone equal temperament with octave 4/3 degrees: 99 313 1125 Least number of segments generator : 563 of 249.244 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 614 of 271.822 cents and inv. generated superset size: 27 = 24 more = 900.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.653376 Lumma stability : 0.176012 Lumma impropriety factor : 0.443534 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 40/39, 43.8311 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 507 (O: 169 U: 507) Highest odd numerator or denominator: 39 Scale harmonicity : 0.017131 Average absolute harmonicity : 0.093597 Specific harmonicity : 0.090332 Fundamental : 1/156, -7.2854 octaves, 1.6771 Hz. Guide tone : 520, 9.0224 octaves, 136045.294 Hz. Exponens Consonantiae : 8.112000E+04, 16.30777 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 55.5, average 18.50000 Mersenne's string divisions : 13825 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.46543, average 2.15514 Vogel's harmonic complexity : 17.66667 Wille's k value : 84 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.48204, average 3.24701 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 1.00000 7 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 13: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 25| Scale is weakly epimorphic with val: <6 10 18 25| Scale is weakly epimorphic with val: <6 11 15 26| Scale is weakly epimorphic with val: <6 11 18 26| Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 29| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 12 15 29| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <8 11 15 25| Scale is weakly epimorphic with val: <8 11 15 30| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 12 18 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.8566 c. M: 43.8311 c. 4: 0 1 3 N G T3 SD: 26.5762 c. M: 43.8311 c. 7: 1 1 5 N M DE S SD: 15.9182 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 13.3814 c. M:-18.4246 c. 10: 1 2 7 N T3 SD: 7.1462 c. M:-10.8408 c. 11: 1 2 8 N T3 SD: 1.7898 c. M: 2.7422 c. 32: 3 6 23 N T3 SD: 1.8656 c. M:-2.8607 c. 36: 3 7 26 N T3 SD: 1.3500 c. M: 2.3273 c. 46: 4 9 33 N T3 SD: 1.2939 c. M:-2.1792 c. 47: 4 9 34 N T3 SD: 0.9576 c. M: 1.4442 c. 57: 5 11 41 N T3 SD: 0.7146 c. M:-1.2294 c. 58: 5 11 42 N T3 SD: 0.8559 c. M: 1.1809 c. 68: 6 13 49 N T3 SD: 0.3452 c. M:-0.5870 c. 79: 7 15 57 N T3 SD: 0.1870 c. M:-0.2995 c. 183: 16 35 132 N T3 SD: 0.2108 c. M: 0.2861 c. 194: 17 37 140 N T3 SD: 0.1136 c. M: 0.1879 c. 205: 18 39 148 N T3 SD: 0.0785 c. M: 0.1003 c. 273: 24 52 197 N T3 SD: 0.0522 c. M:-0.0772 c. 284: 25 54 205 N T3 SD: 0.0195 c. M: 0.0320 c. 557: 49 106 402 N T3 SD: 0.0160 c. M:-0.0215 c. 841: 74 160 607 N T3 SD: 0.0049 c. M: 0.0078 c. 1125: 99 214 812 N T3 SD: 0.0036 c. M: 0.0055 c. 1966: 173 374 1419 N T3 SD: 0.0031 c. M: 0.0051 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 98.0918 cents 6 x 7:8 S SD: 64.1491 cents 7 x 8:9 S SD: 55.9891 cents 8 x 9:11 SD: 42.1514 cents 9 x 10:12 S SD: 21.9155 cents 10 x 11:13 SD: 25.5919 cents 11 x 12:15 S SD: 20.3667 cents 12 x 13:16 SD: 0.0000 cents 13 x 14:17 SD: 17.5761 cents 14 x 15:19 SD: 18.0616 cents 15 x 16:20 S SD: 13.4207 cents 16 x 17:21 SD: 21.6417 cents 17 x 18:23 SD: 23.4966 cents 18 x 20:24 S SD: 21.9155 cents 19:20:21:25 SD: 20.4174 cents 20:21:22:27 SD: 17.6775 cents 21:22:23:28 SD: 13.7652 cents 22:23:24:29 SD: 13.4756 cents 23:24:25:31 SD: 11.9010 cents 24:25:26:32 SD: 8.9471 cents 27:28:29:36 SD: 8.0745 cents 32:33:35:43 SD: 7.7827 cents 33:34:36:44 SD: 4.7981 cents 35:36:38:47 SD: 4.6028 cents 36:37:39:48 SD: 1.2010 cents 84:86:91:112 SD: 1.0314 cents 120:123:130:160 SD: 0.3608 cents 156:160:169:208 SD: 0.0000 cents