Scala analysis: 169_C6
Chromatic tetrachord 22/21 * 91/88 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 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: 22/21 80.5370 undecimal minor semitone 2: 91/88 58.0356 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 91/88 58.036 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 352/273 440.009 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 : 80.5 138.6 498.0 80.5 : 58.0 417.5 498.0 138.6: 359.5 440.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.0356 .. 359.4723 cents 1408/1183, 301.4367 cents 91/88, 58.0356 cents 2: 138.5727 .. 440.0094 cents 1408/1183, 301.4367 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 91/88, 58.0356 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 2.860571 Largest / Average step : 2.165300 Largest / Smallest step : 6.193994 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 132.27267 cents, oct.: 396.81800 cents Scale is not proper Scale has trivalence property Scale is a mode of a 841-tone equal temperament with octave 4/3 degrees: 136 234 841 Least number of segments generator : 421 of 249.319 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 528 of 312.685 cents and inv. generated superset size: 14 = 11 more = 466.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 58.03563 cents Scale diversity : 0.704906 Lumma stability : 0.233054 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 : 1936/1911, 22.5014 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Limited inverse transpositions with margin 301.4367 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 273 (O: 91 U: 273) Highest odd numerator or denominator: 21 Scale harmonicity : 0.017456 Average absolute harmonicity : 0.094230 Specific harmonicity : 0.092558 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 572, 9.1599 octaves, 149649.823 Hz. Exponens Consonantiae : 4.804800E+04, 15.55219 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 37.5, average 12.50000 Mersenne's string divisions : 7525 Sum of van Prooijen's expressibility: 2.91328, average 0.97109 Sum of Tenney's harmonic distance : 5.93695, average 1.97898 Vogel's harmonic complexity : 15.00000 Wille's k value : 45 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.00482, average 2.66747 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 ..-1 -1.00000 3 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.33333 1 1 13: 0 .. 1 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: <6 10 18 23 25| Scale is weakly epimorphic with val: <6 10 18 25 26| Scale is weakly epimorphic with val: <6 10 18 25 29| Scale is weakly epimorphic with val: <6 10 19 24 25| Scale is weakly epimorphic with val: <6 10 19 26 26| Scale is weakly epimorphic with val: <6 10 19 26 29| Scale is weakly epimorphic with val: <6 10 20 25 25| Scale is weakly epimorphic with val: <6 10 20 27 29| Scale is weakly epimorphic with val: <6 10 21 23 25| Scale is weakly epimorphic with val: <6 10 22 24 25| Scale is weakly epimorphic with val: <6 11 18 25 26| Scale is weakly epimorphic with val: <6 11 18 26 28| Scale is weakly epimorphic with val: <6 11 19 23 26| Scale is weakly epimorphic with val: <6 11 19 26 26| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <6 11 20 24 26| Scale is weakly epimorphic with val: <6 11 21 25 26| Scale is weakly epimorphic with val: <6 11 22 23 26| Scale is weakly epimorphic with val: <6 11 22 26 26| Scale is weakly epimorphic with val: <7 10 18 23 27| Scale is weakly epimorphic with val: <7 10 18 24 26| Scale is weakly epimorphic with val: <7 10 18 24 29| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 19 24 27| Scale is weakly epimorphic with val: <7 10 19 25 26| Scale is weakly epimorphic with val: <7 10 19 25 29| Scale is weakly epimorphic with val: <7 10 19 27 27| Scale is weakly epimorphic with val: <7 10 20 25 27| Scale is weakly epimorphic with val: <7 10 20 26 26| Scale is weakly epimorphic with val: <7 10 20 26 29| Scale is weakly epimorphic with val: <7 10 21 23 27| Scale is weakly epimorphic with val: <7 10 21 26 27| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 22 24 27| Scale is weakly epimorphic with val: <7 10 22 27 27| 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 JI-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 25 26| Scale is weakly epimorphic with val: <7 11 19 25 29| 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 11 20 23 26| Scale is weakly epimorphic with val: <7 11 20 23 29| Scale is JI-epimorphic with val: <7 11 20 25 27| = patent Scale is weakly epimorphic with val: <7 11 20 25 30| 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 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 JI-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 24 27| Scale is weakly epimorphic with val: <7 11 22 24 30| Scale is weakly epimorphic with val: <7 11 22 25 26| Scale is weakly epimorphic with val: <7 11 22 25 29| Scale is JI-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 24 29| Scale is weakly epimorphic with val: <7 12 18 26 27| Scale is weakly epimorphic with val: <7 12 18 26 30| Scale is weakly epimorphic with val: <7 12 18 27 29| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <7 12 19 27 27| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 20 23 29| Scale is weakly epimorphic with val: <7 12 20 26 29| Scale is weakly epimorphic with val: <7 12 21 24 29| Scale is weakly epimorphic with val: <7 12 21 27 29| Scale is weakly epimorphic with val: <7 12 22 25 29| Scale is weakly epimorphic with val: <8 11 18 24 25| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 25 30| Scale is weakly epimorphic with val: <8 11 19 23 30| Scale is weakly epimorphic with val: <8 11 19 25 25| Scale is weakly epimorphic with val: <8 11 19 25 28| Scale is weakly epimorphic with val: <8 11 19 26 30| Scale is weakly epimorphic with val: <8 11 20 24 30| Scale is weakly epimorphic with val: <8 11 20 26 28| Scale is weakly epimorphic with val: <8 11 20 27 30| Scale is weakly epimorphic with val: <8 11 21 25 30| Scale is weakly epimorphic with val: <8 11 21 27 28| Scale is weakly epimorphic with val: <8 11 22 23 30| Scale is weakly epimorphic with val: <8 11 22 26 30| Scale is weakly epimorphic with val: <8 12 18 25 27| Scale is weakly epimorphic with val: <8 12 18 25 30| Scale is weakly epimorphic with val: <8 12 19 26 27| Scale is weakly epimorphic with val: <8 12 19 26 30| Scale is weakly epimorphic with val: <8 12 20 27 27| Scale is weakly epimorphic with val: <8 12 20 27 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.1233 c. M: 80.5370 c. 4: 1 0 3 N G T3 SD: 26.6549 c. M:-43.9742 c. 5: 1 0 4 N G T3 SD: 25.0460 c. M: 38.9637 c. 6: 1 1 4 N M DE S SD: 15.9079 c. M:-27.4423 c. 7: 1 1 5 N M DE S SD: 5.8313 c. M: 9.3877 c. 11: 2 1 8 N T3 SD: 5.9959 c. M:-10.0166 c. 17: 3 2 12 N T3 SD: 6.2358 c. M:-7.9112 c. 18: 3 2 13 N T3 SD: 1.4323 c. M:-2.4705 c. 25: 4 3 18 N T3 SD: 0.7063 c. M:-0.8799 c. 43: 7 5 31 N T3 SD: 0.3938 c. M:-0.5401 c. 68: 11 8 49 N T3 SD: 0.3393 c. M:-0.5870 c. 111: 18 13 80 N T3 SD: 0.3281 c. M:-0.5210 c. 154: 25 18 111 N T3 SD: 0.3370 c. M:-0.4919 c. 155: 25 18 112 N T3 SD: 0.2628 c. M: 0.4053 c. 173: 28 20 125 N T3 SD: 0.2271 c. M: 0.3868 c. 180: 29 21 130 N T3 SD: 0.2155 c. M: 0.2965 c. 198: 32 23 143 N T3 SD: 0.1335 c. M: 0.2268 c. 223: 36 26 161 N T3 SD: 0.0980 c. M: 0.1352 c. 241: 39 28 174 N T3 SD: 0.0732 c. M: 0.1120 c. 266: 43 31 192 N T3 SD: 0.0185 c. M: 0.0260 c. 575: 93 67 415 N T3 SD: 0.0123 c. M:-0.0163 c. 841: 136 98 607 N T3 SD: 0.0026 c. M:-0.0035 c. 1107: 179 129 799 N T3 SD: 0.0026 c. M: 0.0040 c. 1948: 315 227 1406 N T3 SD: 0.0006 c. M: 0.0010 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 16:17 x 21 SD: 18.3002 cents 17:18 x 23 SD: 15.6363 cents 18:19:20:24 S SD: 15.2457 cents 19:20:21:25 SD: 14.1337 cents 20:21:22:27 SD: 11.4338 cents 21:22:23:28 SD: 6.3069 cents 24:25:26:32 SD: 3.2882 cents 59:62:64:79 SD: 3.1100 cents 60:63:65:80 SD: 1.3101 cents 84:88:91:112 SD: 0.0000 cents