Scala analysis: 240_C16
Chromatic tetrachord 20/19 * 19/16 * 16/15, Kornerup
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 20/19 88.8007 small undevicesimal semitone 2: 19/16 297.5130 19th harmonic 3: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 5/4 386.314 cents major third 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 386.3 498.0 88.8 : 297.5 409.2 498.0 386.3: 111.7 200.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 297.5130 cents 361/320, 208.7123 cents 20/19, 88.8007 cents 2: 200.5320 .. 409.2443 cents 361/320, 208.7123 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 1.869524 Largest / Average step : 1.792085 Largest / Smallest step : 3.350345 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 168.25451 cents, oct.: 504.76353 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1520-tone equal temperament with octave 4/3 degrees: 271 1179 1520 Least number of segments generator : 761 of 249.350 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 913 of 299.155 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 : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 88.80070 cents Scale diversity : 1.087136 Lumma stability : 0.356597 Lumma impropriety factor : 0.194723 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 : 76/75, 22.9306 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 19 Odd number limit : 57 (O: 19 U: 57) Highest odd numerator or denominator: 19 Scale harmonicity : 0.021199 Average absolute harmonicity : 0.118953 Specific harmonicity : 0.106726 Fundamental : 1/228, -7.8329 octaves, 1.1475 Hz. Guide tone : 20, 4.3219 octaves, 5232.511 Hz. Exponens Consonantiae : 4.560000E+03, 12.15482 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 27.5, average 9.16667 Mersenne's string divisions : 819 Sum of van Prooijen's expressibility: 2.45484, average 0.81828 Sum of Tenney's harmonic distance : 4.95999, average 1.65333 Vogel's harmonic complexity : 20.66667 Wille's k value : 142 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 17.01942, average 2.83657 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.66667 6 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 15 29| Scale is weakly epimorphic with val: <6 10 15 32| Scale is weakly epimorphic with val: <6 10 19 28| Scale is weakly epimorphic with val: <6 11 15 28| Scale is weakly epimorphic with val: <6 11 15 31| Scale is weakly epimorphic with val: <6 11 15 34| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 17 32| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| Scale is JI-epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 17 33| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <8 11 17 30| Scale is weakly epimorphic with val: <8 11 19 28| Scale is weakly epimorphic with val: <8 11 19 31| Scale is weakly epimorphic with val: <8 11 19 34| Scale is weakly epimorphic with val: <8 12 15 28| Scale is weakly epimorphic with val: <8 12 18 31| Scale is weakly epimorphic with val: <8 12 19 30| Scale is weakly epimorphic with val: <8 12 19 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 60.0896 c. M: 88.8007 c. 4: 1 2 1 P M ME I SD: 21.8980 c. M:-35.7106 c. 5: 1 3 1 N M DE I SD: 9.3767 c. M:-12.1223 c. 12: 2 7 3 N T3 SD: 8.1012 c. M: 12.7800 c. 13: 2 8 3 N T3 SD: 7.2702 c. M: 12.1784 c. 17: 3 10 4 N T3 SD: 3.1934 c. M: 5.4558 c. 22: 4 13 5 N T3 SD: 1.3174 c. M:-1.7529 c. 40: 7 24 9 N T3 SD: 0.9673 c. M: 1.6428 c. 45: 8 27 10 N T3 SD: 0.6270 c. M:-1.0546 c. 62: 11 37 14 N T3 SD: 0.4917 c. M: 0.7305 c. 67: 12 40 15 N T3 SD: 0.2667 c. M:-0.4014 c. 107: 19 64 24 N T3 SD: 0.2098 c. M: 0.3628 c. 129: 23 77 29 N T3 SD: 0.1341 c. M: 0.2323 c. 174: 31 104 39 N T3 SD: 0.0702 c. M:-0.1005 c. 303: 54 181 68 N T3 SD: 0.0332 c. M: 0.0412 c. 370: 66 221 83 N T3 SD: 0.0234 c. M:-0.0398 c. 544: 97 325 122 N T3 SD: 0.0218 c. M:-0.0374 c. 673: 120 402 151 N T3 SD: 0.0085 c. M: 0.0143 c. 847: 151 506 190 N T3 SD: 0.0083 c. M: 0.0111 c. 1217: 217 727 273 N T3 SD: 0.0057 c. M:-0.0088 c. 1520: 271 908 341 N T3 SD: 0.0027 c. M: 0.0045 c. 1890: 337 1129 424 N T3 SD: 0.0024 c. M:-0.0042 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 5 x S SD: 0.0000 cents 5 x 6:7 S SD: 55.0665 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 75.2475 cents 8:9:10:11 H SD: 42.2797 cents 9:10:11:12 H SD: 33.7889 cents 10:11 x 13 SD: 43.9549 cents 11:12:14:15 S SD: 26.4795 cents 12:13:15:16 SD: 16.5907 cents 15:16:19:20 SD: 10.8096 cents 16:17:20:21 SD: 10.5636 cents 19:20:24:25 S SD: 9.7436 cents 20:21:25:27 SD: 7.3128 cents 21:22:26:28 SD: 6.1712 cents 24:25:30:32 S SD: 6.0428 cents 33:35:41:44 SD: 5.5925 cents 36:38:45:48 SD: 1.6008 cents 60:63:75:80 SD: 1.4445 cents 93:98:116:124 SD: 1.3886 cents 96:101:120:128 SD: 0.3006 cents 132:139:165:176 SD: 0.2185 cents 228:240:285:304 SD: 0.0000 cents