Scala analysis: 167_C6
Chromatic tetrachord 28/27 * 117/112 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 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: 28/27 62.9609 Archytas' 1/3-tone 2: 117/112 75.6118 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 117/112 75.612 cents 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 448/351 422.433 cents 2: 1 9/7 435.084 cents septimal major third, BP third 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 : 63.0 138.6 498.0 63.0 : 75.6 435.1 498.0 138.6: 359.5 422.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 359.4723 cents 108/91, 296.5114 cents 28/27, 62.9609 cents 2: 138.5727 .. 435.0841 cents 108/91, 296.5114 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 2.636795 Largest / Average step : 2.165300 Largest / Smallest step : 5.709453 Median interval of one step : 117/112, 75.6118 cents, amount: 1 Least squares average step : 131.01723 cents, oct.: 393.05169 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1851-tone equal temperament with octave 4/3 degrees: 234 515 1851 Least number of segments generator : 926 of 249.157 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1687 of 453.918 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 62.96090 cents Scale diversity : 0.714337 Lumma stability : 0.252832 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 : 3159/3136, 12.6509 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% Limited inverse transpositions with margin 283.8606 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 351 (O: 117 U: 351) Highest odd numerator or denominator: 27 Scale harmonicity : 0.022502 Average absolute harmonicity : 0.100288 Specific harmonicity : 0.118239 Fundamental : 1/108, -6.7549 octaves, 2.4225 Hz. Guide tone : 364, 8.5078 octaves, 95231.706 Hz. Exponens Consonantiae : 3.931200E+04, 15.26268 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 1925 Sum of van Prooijen's expressibility: 3.02243, average 1.00748 Sum of Tenney's harmonic distance : 6.15083, average 2.05028 Vogel's harmonic complexity : 13.33333 Wille's k value : 58 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 19.47680, average 3.24613 Lattice compactness (without 2's) : 11.26205, average 1.87701 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.66667 6 3: -3 ..-1 -1.66667 5 1 7: 0 .. 1 0.33333 1 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 25| Scale is weakly epimorphic with val: <6 10 21 26| Scale is weakly epimorphic with val: <6 10 21 29| Scale is weakly epimorphic with val: <6 10 22 25| Scale is weakly epimorphic with val: <6 11 20 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 10 19 26| Scale is weakly epimorphic with val: <7 10 19 29| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 29| Scale is JI-epimorphic with val: <7 11 20 27| = patent Scale is weakly epimorphic with val: <7 11 20 30| Scale is weakly epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 12 20 29| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 11 20 25| Scale is weakly epimorphic with val: <8 11 20 28| Scale is weakly epimorphic with val: <8 11 21 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 39.6533 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 37.2460 c. M: 62.9609 c. 5: 1 0 4 N G T3 SD: 30.8828 c. M: 38.9637 c. 6: 1 1 4 N M DE S SD: 19.6210 c. M:-27.4423 c. 7: 1 1 5 N M DE S SD: 5.1940 c. M:-8.1884 c. 15: 2 2 11 N M DE S SD: 3.8753 c. M: 5.7607 c. 22: 3 3 16 N M DE S SD: 3.2693 c. M:-4.9543 c. 25: 3 4 18 N T3 SD: 1.9136 c. M: 3.1955 c. 32: 4 5 23 N T3 SD: 0.9583 c. M:-1.5025 c. 40: 5 6 29 N T3 SD: 1.0150 c. M: 1.6103 c. 47: 6 7 34 N T3 SD: 0.5912 c. M: 0.8155 c. 72: 9 11 52 N T3 SD: 0.4277 c. M: 0.7053 c. 79: 10 12 57 N T3 SD: 0.0858 c. M:-0.1234 c. 277: 35 42 200 N T3 SD: 0.0754 c. M: 0.1269 c. 309: 39 47 223 N T3 SD: 0.0630 c. M: 0.1009 c. 356: 45 54 257 N T3 SD: 0.0413 c. M: 0.0714 c. 388: 49 59 280 N T3 SD: 0.0498 c. M: 0.0635 c. 435: 55 66 314 N T3 SD: 0.0216 c. M: 0.0360 c. 514: 65 78 371 N T3 SD: 0.0140 c. M:-0.0214 c. 902: 114 137 651 N T3 SD: 0.0138 c. M:-0.0186 c. 1179: 149 179 851 N T3 SD: 0.0141 c. M: 0.0188 c. 1258: 159 191 908 N T3 SD: 0.0082 c. M: 0.0125 c. 1337: 169 203 965 N T3 SD: 0.0040 c. M: 0.0068 c. 1851: 234 281 1336 N T3 SD: 0.0016 c. M: 0.0026 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 17:18 x 23 SD: 21.9904 cents 18:19:20:24 S SD: 17.8266 cents 19:20:21:25 SD: 16.3206 cents 20:21:22:27 SD: 13.4316 cents 21:22:23:28 SD: 8.6082 cents 23:24:25:31 SD: 7.4433 cents 24:25:26:32 SD: 2.5705 cents 60:62:65:80 SD: 2.0647 cents 81:84:88:108 SD: 1.6418 cents 84:87:91:112 SD: 0.7365 cents 108:112:117:144 SD: 0.0000 cents