Scala analysis: 161_C6
Chromatic tetrachord 26/25 * 25/24 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/25 67.900234 tridecimal 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: 26/25 67.9002 tridecimal 1/3-tone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 50/39 430.145 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 : 67.9 138.6 498.0 67.9 : 70.7 430.1 498.0 138.6: 359.5 427.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9002 .. 359.4723 cents 200/169, 291.5721 cents 26/25, 67.9002 cents 2: 138.5727 .. 430.1448 cents 200/169, 291.5721 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 26/25, 67.9002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 2.444984 Largest / Average step : 2.165300 Largest / Smallest step : 5.294125 Median interval of one step : 25/24, 70.6724 cents, amount: 1 Least squares average step : 131.37004 cents, oct.: 394.11012 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1621-tone equal temperament with octave 4/3 degrees: 221 451 1621 Least number of segments generator : 811 of 249.176 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 940 of 288.811 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 67.90023 cents Scale diversity : 0.719154 Lumma stability : 0.272667 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 : 625/624, 2.7722 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 : 2 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 Limited inverse transpositions with margin 288.7999 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 25 U: 39) Highest odd numerator or denominator: 25 Scale harmonicity : 0.024027 Average absolute harmonicity : 0.093128 Specific harmonicity : 0.106183 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 52, 5.7004 octaves, 13604.529 Hz. Exponens Consonantiae : 1.560000E+04, 13.92926 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 41.5, average 13.83333 Mersenne's string divisions : 8925 Sum of van Prooijen's expressibility: 2.98900, average 0.99633 Sum of Tenney's harmonic distance : 6.08522, average 2.02841 Vogel's harmonic complexity : 18.66667 Wille's k value : 162 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 17.64556, average 2.94093 Lattice compactness (without 2's) : 10.33584, average 1.72264 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -0.66667 2 13: 0 .. 1 0.66667 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 16 29| 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 26| Scale is weakly epimorphic with val: <7 10 16 27| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 19 29| Scale is weakly epimorphic with val: <8 11 15 25| Scale is weakly epimorphic with val: <8 11 17 30| Scale is weakly epimorphic with val: <8 12 16 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.2829 c. M: 67.9002 c. 4: 0 1 3 N G T3 SD: 40.0340 c. M: 67.9002 c. 5: 1 0 4 N G T3 SD: 29.0035 c. M: 38.9637 c. 6: 1 1 4 N M DE S SD: 18.0860 c. M:-27.4423 c. 7: 1 1 5 N M DE S SD: 2.8542 c. M:-3.7259 c. 22: 3 3 16 N M DE S SD: 1.5832 c. M: 2.7422 c. 29: 4 4 21 N M DE S SD: 0.8221 c. M: 1.1809 c. 36: 5 5 26 N M DE S SD: 0.7464 c. M:-1.2727 c. 65: 9 9 47 N M DE S SD: 0.7186 c. M:-1.0598 c. 79: 11 11 57 N M DE S SD: 0.8389 c. M:-1.4478 c. 94: 13 13 68 N M DE S SD: 0.7354 c. M:-0.9783 c. 97: 13 14 70 N T3 SD: 0.6659 c. M: 1.1519 c. 104: 14 15 75 N T3 SD: 0.5245 c. M: 0.8557 c. 111: 15 16 80 N T3 SD: 0.4574 c. M: 0.5969 c. 118: 16 17 85 N T3 SD: 0.4625 c. M:-0.7111 c. 126: 17 18 91 N T3 SD: 0.4269 c. M: 0.7037 c. 133: 18 19 96 N T3 SD: 0.2864 c. M: 0.4956 c. 140: 19 20 101 N T3 SD: 0.2029 c. M: 0.3084 c. 162: 22 23 117 N T3 SD: 0.2012 c. M: 0.2645 c. 169: 23 24 122 N T3 SD: 0.0777 c. M: 0.1190 c. 176: 24 25 127 N T3 SD: 0.0513 c. M:-0.0876 c. 345: 47 49 249 N T3 SD: 0.0303 c. M: 0.0506 c. 521: 71 74 376 N T3 SD: 0.0277 c. M:-0.0387 c. 550: 75 78 397 N T3 SD: 0.0171 c. M: 0.0256 c. 726: 99 103 524 N T3 SD: 0.0087 c. M:-0.0150 c. 895: 122 127 646 N T3 SD: 0.0085 c. M: 0.0104 c. 1071: 146 152 773 N T3 SD: 0.0048 c. M: 0.0061 c. 1621: 221 230 1170 N T3 SD: 0.0029 c. M: 0.0049 c. 1797: 245 255 1297 N T3 SD: 0.0028 c. M:-0.0041 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: 20.0196 cents 18:19:20:24 S SD: 16.9371 cents 19:20:21:25 SD: 15.5149 cents 20:21:22:27 SD: 12.6298 cents 21:22:23:28 SD: 7.5842 cents 23:24:25:31 SD: 6.8079 cents 24:25:26:32 SD: 0.9241 cents 156:162:169:208 SD: 0.8543 cents 177:184:192:236 SD: 0.7926 cents 180:187:195:240 SD: 0.6169 cents 204:212:221:272 SD: 0.4354 cents 228:237:247:304 SD: 0.2921 cents 252:262:273:336 SD: 0.1762 cents 276:287:299:368 SD: 0.0804 cents 300:312:325:400 SD: 0.0000 cents