Scala analysis: 181_C8
Chromatic tetrachord 78/77 * 14/13 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78/77 22.338814 tridecimal minor third comma 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 78/77 22.3388 tridecimal minor third comma 2: 14/13 128.2982 2/3-tone 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78/77 22.339 cents tridecimal minor third comma 1: 1 14/13 128.298 cents 2/3-tone 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 26/21 369.747 cents 2: 1 154/117 475.706 cents 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 : 22.3 150.6 498.0 22.3 : 128.3 475.7 498.0 150.6: 347.4 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.3388 .. 347.4079 cents 847/702, 325.0691 cents 78/77, 22.3388 cents 2: 150.6371 .. 475.7062 cents 847/702, 325.0691 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 78/77, 22.3388 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 7.431684 Largest / Average step : 2.092630 Largest / Smallest step : 15.551763 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 129.83914 cents, oct.: 389.51741 cents Scale is not proper Scale has trivalence property Scale is a mode of a 691-tone equal temperament with octave 4/3 degrees: 31 209 691 Least number of segments generator : 346 of 249.383 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 631 of 454.799 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 22.33881 cents Scale diversity : 0.553536 Lumma stability : 0.089706 Lumma impropriety factor : 0.395087 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 : 78/77, 22.3388 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 77 U: 117) Highest odd numerator or denominator: 77 Scale harmonicity : 0.017255 Average absolute harmonicity : 0.092157 Specific harmonicity : 0.081752 Fundamental : 1/231, -7.8517 octaves, 1.1326 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 3.603600E+04, 15.13715 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 92.5, average 30.83333 Mersenne's string divisions : 24955 Sum of van Prooijen's expressibility: 3.40500, average 1.13500 Sum of Tenney's harmonic distance : 6.97834, average 2.32611 Vogel's harmonic complexity : 18.33333 Wille's k value : 58 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.71817, average 2.28636 Lattice compactness (without 2's) : 10.71025, average 1.78504 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.33333 3 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.66667 2 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 24 29| Scale is weakly epimorphic with val: <6 10 19 24 30| Scale is weakly epimorphic with val: <6 11 18 24 28| Scale is weakly epimorphic with val: <6 11 19 24 29| Scale is weakly epimorphic with val: <6 11 20 24 30| Scale is weakly epimorphic with val: <7 10 18 25 29| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 11 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is JI-epimorphic with val: <7 11 19 23 25| Scale is weakly epimorphic with val: <7 11 19 23 28| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is JI-epimorphic with val: <7 11 20 23 26| Scale is weakly epimorphic with val: <7 11 20 23 29| Scale is weakly epimorphic with val: <7 11 20 24 25| Scale is weakly epimorphic with val: <7 11 20 24 28| Scale is weakly epimorphic with val: <7 11 20 26 26| Scale is weakly epimorphic with val: <7 11 20 26 29| Scale is weakly epimorphic with val: <7 11 20 27 28| Scale is JI-epimorphic with val: <7 11 21 23 27| Scale is weakly epimorphic with val: <7 11 21 23 30| Scale is weakly epimorphic with val: <7 11 21 24 26| Scale is weakly epimorphic with val: <7 11 21 24 29| Scale is weakly epimorphic with val: <7 11 21 26 27| Scale is weakly epimorphic with val: <7 11 21 26 30| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 22 23 25| Scale is JI-epimorphic with val: <7 11 22 23 28| Scale is weakly epimorphic with val: <7 11 22 24 27| Scale is weakly epimorphic with val: <7 11 22 24 30| Scale is weakly epimorphic with val: <7 11 22 26 28| Scale is weakly epimorphic with val: <7 11 22 27 27| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 12 18 23 26| Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 18 25 27| Scale is weakly epimorphic with val: <7 12 19 23 27| Scale is weakly epimorphic with val: <7 12 19 23 30| Scale is weakly epimorphic with val: <7 12 19 25 28| Scale is weakly epimorphic with val: <7 12 20 23 25| Scale is weakly epimorphic with val: <7 12 20 23 28| Scale is weakly epimorphic with val: <7 12 20 25 29| Scale is weakly epimorphic with val: <7 12 21 23 26| Scale is weakly epimorphic with val: <7 12 21 23 29| Scale is weakly epimorphic with val: <7 12 21 25 30| Scale is weakly epimorphic with val: <7 12 22 23 27| Scale is weakly epimorphic with val: <7 12 22 23 30| Scale is weakly epimorphic with val: <8 11 18 23 25| Scale is weakly epimorphic with val: <8 11 18 24 27| Scale is weakly epimorphic with val: <8 11 18 24 30| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 19 23 26| Scale is weakly epimorphic with val: <8 11 19 24 25| Scale is weakly epimorphic with val: <8 11 19 24 28| Scale is weakly epimorphic with val: <8 11 19 26 29| Scale is weakly epimorphic with val: <8 11 20 23 27| Scale is weakly epimorphic with val: <8 11 20 24 26| Scale is weakly epimorphic with val: <8 11 20 24 29| Scale is weakly epimorphic with val: <8 11 20 26 30| Scale is weakly epimorphic with val: <8 11 21 23 28| Scale is weakly epimorphic with val: <8 11 21 24 27| Scale is weakly epimorphic with val: <8 11 21 24 30| Scale is weakly epimorphic with val: <8 11 22 23 29| Scale is weakly epimorphic with val: <8 11 22 24 25| Scale is weakly epimorphic with val: <8 11 22 24 28| Scale is weakly epimorphic with val: <8 12 18 25 25| Scale is weakly epimorphic with val: <8 12 18 25 28| Scale is weakly epimorphic with val: <8 12 18 26 27| Scale is weakly epimorphic with val: <8 12 19 23 25| Scale is weakly epimorphic with val: <8 12 19 25 26| Scale is weakly epimorphic with val: <8 12 19 25 29| Scale is weakly epimorphic with val: <8 12 19 26 28| Scale is weakly epimorphic with val: <8 12 20 23 26| Scale is weakly epimorphic with val: <8 12 20 25 27| Scale is weakly epimorphic with val: <8 12 20 25 30| Scale is weakly epimorphic with val: <8 12 20 26 29| Scale is weakly epimorphic with val: <8 12 21 23 27| Scale is weakly epimorphic with val: <8 12 21 25 25| Scale is weakly epimorphic with val: <8 12 21 25 28| Scale is weakly epimorphic with val: <8 12 21 26 30| Scale is weakly epimorphic with val: <8 12 22 23 28| Scale is weakly epimorphic with val: <8 12 22 25 26| Scale is weakly epimorphic with val: <8 12 22 25 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 15.6578 c. M: 22.3388 c. 7: 0 2 5 N G T3 SD: 13.7665 c. M: 22.3388 c. 10: 0 3 7 N G T3 SD: 12.9167 c. M: 22.3388 c. 13: 1 3 9 N T3 SD: 9.3437 c. M:-15.9723 c. 14: 1 3 10 N T3 SD: 9.0318 c. M:-13.2358 c. 16: 1 4 11 N T3 SD: 5.8386 c. M:-8.7890 c. 17: 1 4 12 N T3 SD: 4.6784 c. M:-6.9580 c. 19: 1 5 13 N T3 SD: 4.4386 c. M:-6.6403 c. 20: 1 5 14 N T3 SD: 1.6399 c. M:-2.5634 c. 23: 1 6 16 N T3 SD: 0.6723 c. M:-0.9419 c. 43: 2 11 30 N T3 SD: 0.4784 c. M:-0.8261 c. 66: 3 17 46 N T3 SD: 0.2390 c. M:-0.2996 c. 155: 7 40 108 N T3 SD: 0.2383 c. M:-0.3830 c. 179: 8 46 125 N T3 SD: 0.2292 c. M: 0.3888 c. 202: 9 52 141 N T3 SD: 0.1617 c. M: 0.2373 c. 225: 10 58 157 N T3 SD: 0.1355 c. M: 0.2035 c. 245: 11 63 171 N T3 SD: 0.1203 c. M: 0.2071 c. 268: 12 69 187 N T3 SD: 0.0664 c. M: 0.1085 c. 291: 13 75 203 N T3 SD: 0.0537 c. M: 0.0894 c. 334: 15 86 233 N T3 SD: 0.0241 c. M: 0.0306 c. 357: 16 92 249 N T3 SD: 0.0211 c. M:-0.0320 c. 625: 28 161 436 N T3 SD: 0.0223 c. M: 0.0283 c. 691: 31 178 482 N T3 SD: 0.0029 c. M:-0.0047 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: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12 x 13:16 SD: 6.0322 cents 13 x 14:17 SD: 20.1813 cents 14 x 15:19 SD: 21.8633 cents 15 x 16:20 S SD: 19.4529 cents 16 x 17:21 SD: 26.5995 cents 17 x 19:23 SD: 24.4750 cents 18 x 20:24 S SD: 15.8833 cents 19 x 21:25 SD: 16.1087 cents 29:30:32:39 SD: 14.6584 cents 30:31:33:40 SD: 12.4352 cents 31:32:34:41 SD: 12.2343 cents 32:33:35:43 SD: 11.3466 cents 33:34:36:44 SD: 9.7812 cents 36:37:39:48 SD: 9.2815 cents 40:41:44:53 SD: 9.0725 cents 41:42:45:55 SD: 8.1452 cents 42:43:46:56 SD: 6.5447 cents 44:45:48:59 SD: 6.4176 cents 45:46:49:60 SD: 5.3454 cents 51:52:56:68 SD: 5.3167 cents 52:53:57:69 SD: 5.2886 cents 53:54:58:71 SD: 4.6709 cents 54:55:59:72 SD: 3.2662 cents 57:58:62:76 SD: 3.0926 cents 63:64:69:84 SD: 2.8140 cents 65:66:71:87 SD: 2.7047 cents 66:67:72:88 SD: 1.2318 cents 78:79:85:104 SD: 0.6241 cents 144:146:157:192 SD: 0.6126 cents 153:155:167:204 SD: 0.3179 cents 231:234:252:308 SD: 0.0000 cents