Scala analysis: 185_C8
Chromatic tetrachord 40/39 * 117/110 * 11/9
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: 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: 40/39 43.8311 tridecimal minor diesis 2: 117/110 106.8060 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 117/110 106.806 cents 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 440/351 391.239 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 : 43.8 150.6 498.0 43.8 : 106.8 454.2 498.0 150.6: 347.4 391.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 347.4079 cents 143/120, 303.5769 cents 40/39, 43.8311 cents 2: 150.6371 .. 454.2139 cents 143/120, 303.5769 cents 108/121,-196.7709 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 : 11/9, 347.4079 cents Average / Smallest step : 3.787612 Largest / Average step : 2.092630 Largest / Smallest step : 7.926069 Median interval of one step : 117/110, 106.8060 cents, amount: 1 Least squares average step : 131.37430 cents, oct.: 394.12289 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1716-tone equal temperament with octave 4/3 degrees: 151 519 1716 Least number of segments generator : 859 of 249.313 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1379 of 400.235 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 : 0.710256 Lumma stability : 0.176012 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 : 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 : 351 (O: 117 U: 351) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018159 Average absolute harmonicity : 0.095758 Specific harmonicity : 0.095309 Fundamental : 1/429, -8.7448 octaves, 0.6098 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 5.148000E+04, 15.65172 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 54.5, average 18.16667 Mersenne's string divisions : 12719 Sum of van Prooijen's expressibility: 3.10958, average 1.03653 Sum of Tenney's harmonic distance : 6.39288, average 2.13096 Vogel's harmonic complexity : 22.00000 Wille's k value : 71 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.94621, average 2.49103 Lattice compactness (without 2's) : 10.44230, average 1.74038 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 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: <7 10 17 25 25| Scale is weakly epimorphic with val: <7 10 18 25 26| Scale is weakly epimorphic with val: <7 10 19 25 27| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| Scale is weakly epimorphic with val: <7 11 15 24 26| Scale is weakly epimorphic with val: <7 11 15 24 29| Scale is weakly epimorphic with val: <7 11 15 26 27| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is JI-epimorphic with val: <7 11 16 23 25| Scale is weakly epimorphic with val: <7 11 16 23 28| Scale is weakly epimorphic with val: <7 11 16 24 27| Scale is weakly epimorphic with val: <7 11 16 24 30| Scale is weakly epimorphic with val: <7 11 16 26 28| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is JI-epimorphic with val: <7 11 17 23 26| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 24 25| Scale is weakly epimorphic with val: <7 11 17 24 28| Scale is weakly epimorphic with val: <7 11 17 26 26| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 27 28| Scale is JI-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 weakly epimorphic with val: <7 11 19 23 25| Scale is JI-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 weakly epimorphic with val: <7 12 15 23 26| Scale is weakly epimorphic with val: <7 12 15 23 29| Scale is weakly epimorphic with val: <7 12 16 23 27| Scale is weakly epimorphic with val: <7 12 16 23 30| Scale is weakly epimorphic with val: <7 12 17 23 25| Scale is weakly epimorphic with val: <7 12 17 23 28| 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 19 23 27| Scale is weakly epimorphic with val: <7 12 19 23 30| Scale is weakly epimorphic with val: <7 12 19 25 25| Scale is weakly epimorphic with val: <8 11 15 23 25| Scale is weakly epimorphic with val: <8 11 15 24 27| Scale is weakly epimorphic with val: <8 11 15 24 30| Scale is weakly epimorphic with val: <8 11 16 23 26| Scale is weakly epimorphic with val: <8 11 16 24 25| Scale is weakly epimorphic with val: <8 11 16 24 28| Scale is weakly epimorphic with val: <8 11 16 26 26| Scale is weakly epimorphic with val: <8 11 17 23 27| Scale is weakly epimorphic with val: <8 11 17 24 26| Scale is weakly epimorphic with val: <8 11 17 24 29| Scale is weakly epimorphic with val: <8 11 17 26 27| Scale is weakly epimorphic with val: <8 11 18 23 28| 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 29| 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 12 15 25 25| Scale is weakly epimorphic with val: <8 12 15 25 28| Scale is weakly epimorphic with val: <8 12 16 23 25| Scale is weakly epimorphic with val: <8 12 16 25 26| Scale is weakly epimorphic with val: <8 12 16 25 29| Scale is weakly epimorphic with val: <8 12 17 23 26| Scale is weakly epimorphic with val: <8 12 17 25 27| Scale is weakly epimorphic with val: <8 12 17 25 30| Scale is weakly epimorphic with val: <8 12 17 26 26| Scale is weakly epimorphic with val: <8 12 18 23 27| 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 28| 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|
FIT/MODE
3: 0 1 2 N G T3 SD: 26.8182 c. M: 43.8311 c. 4: 0 1 3 N G T3 SD: 29.4602 c. M: 43.8311 c. 6: 1 1 4 N M DE S SD: 24.2987 c. M:-39.1764 c. 7: 1 1 5 N M DE S SD: 16.4906 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 18.4574 c. M: 26.1258 c. 9: 1 2 6 N T3 SD: 11.0890 c. M:-15.3779 c. 10: 1 2 7 N T3 SD: 3.5204 c. M:-5.9734 c. 13: 1 3 9 N T3 SD: 3.5246 c. M: 5.5199 c. 23: 2 5 16 N T3 SD: 0.6219 c. M:-0.9419 c. 56: 5 12 39 N T3 SD: 0.4880 c. M:-0.6373 c. 79: 7 17 55 N T3 SD: 0.4225 c. M:-0.6678 c. 126: 11 27 88 N T3 SD: 0.3218 c. M: 0.4330 c. 136: 12 29 95 N T3 SD: 0.2911 c. M: 0.4911 c. 149: 13 32 104 N T3 SD: 0.2525 c. M: 0.3775 c. 159: 14 34 111 N T3 SD: 0.1644 c. M: 0.2839 c. 182: 16 39 127 N T3 SD: 0.0792 c. M: 0.1290 c. 205: 18 44 143 N T3 SD: 0.0581 c. M: 0.1003 c. 387: 34 83 270 N T3 SD: 0.0575 c. M: 0.0752 c. 420: 37 90 293 N T3 SD: 0.0336 c. M:-0.0443 c. 443: 39 95 309 N T3 SD: 0.0115 c. M:-0.0149 c. 1068: 94 229 745 N T3 SD: 0.0069 c. M: 0.0111 c. 1091: 96 234 761 N T3 SD: 0.0065 c. M:-0.0090 c. 1511: 133 324 1054 N T3 SD: 0.0049 c. M:-0.0075 c. 1716: 151 368 1197 N T3 SD: 0.0041 c. M: 0.0054 c. 2159: 190 463 1506 N T3 SD: 0.0009 c. M: 0.0012 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 18:19:20:24 S SD: 19.6818 cents 19:20:21:25 SD: 18.4398 cents 20:21:22:27 SD: 16.0563 cents 21:22:23:28 SD: 12.4470 cents 23:24:25:31 SD: 11.9293 cents 24:25:26:32 SD: 9.8093 cents 29:30:32:39 SD: 9.6214 cents 30:31:33:40 SD: 6.4442 cents 32:33:35:43 SD: 5.6856 cents 33:34:36:44 SD: 2.6171 cents 42:43:46:56 SD: 2.5074 cents 45:46:49:60 SD: 2.2038 cents 75:77:82:100 SD: 1.4048 cents 78:80:85:104 SD: 0.6169 cents 120:123:131:160 SD: 0.5391 cents 153:157:167:204 SD: 0.4228 cents 198:203:216:264 SD: 0.2186 cents 231:237:252:308 SD: 0.1873 cents 351:360:383:468 SD: 0.1370 cents 429:440:468:572 SD: 0.0000 cents