Scala analysis: 212_C14
Chromatic tetrachord 20/19 * 19/18 * 6/5, Eratosthenes
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: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 20/19 88.8007 small undevicesimal semitone 2: 19/18 93.6030 undevicesimal semitone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 24/19 404.442 cents smaller undevicesimal 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 : 88.8 182.4 498.0 88.8 : 93.6 409.2 498.0 182.4: 315.6 404.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 315.6413 cents 57/50, 226.8406 cents 20/19, 88.8007 cents 2: 182.4037 .. 409.2443 cents 57/50, 226.8406 cents 25/27,-133.2376 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 : 6/5, 315.6413 cents Average / Smallest step : 1.869524 Largest / Average step : 1.901282 Largest / Smallest step : 3.554491 Median interval of one step : 19/18, 93.6030 cents, amount: 1 Least squares average step : 139.12451 cents, oct.: 417.37353 cents Scale is not proper Scale has trivalence property 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 88.80070 cents Scale diversity : 1.002278 Lumma stability : 0.356597 Lumma impropriety factor : 0.267521 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 : 361/360, 4.8023 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Limited inverse transpositions with margin 222.0383 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 19 (O: 19 U: 19) Highest odd numerator or denominator: 19 Scale harmonicity : 0.020904 Average absolute harmonicity : 0.105448 Specific harmonicity : 0.104178 Fundamental : 1/171, -7.4179 octaves, 1.5300 Hz. Guide tone : 20, 4.3219 octaves, 5232.511 Hz. Exponens Consonantiae : 3.420000E+03, 11.73978 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 32.5, average 10.83333 Mersenne's string divisions : 5187 Sum of van Prooijen's expressibility: 2.71012, average 0.90337 Sum of Tenney's harmonic distance : 5.61321, average 1.87107 Vogel's harmonic complexity : 20.66667 Wille's k value : 47 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.04864, average 2.17477 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.66667 2 1 19: -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: <6 10 17 28| Scale is weakly epimorphic with val: <6 10 17 31| Scale is weakly epimorphic with val: <6 10 17 34| Scale is weakly epimorphic with val: <6 11 19 29| Scale is weakly epimorphic with val: <6 11 19 32| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 16 34| Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 34| Scale is JI-epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 17 29| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 18 31| 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 1 2 N G T3 SD: 52.1349 c. M: 88.8007 c. 4: 1 1 2 P M ME S SD: 43.6398 c. M:-66.6188 c. 5: 1 1 3 N M DE S SD: 11.5404 c. M:-16.8143 c. 6: 1 1 4 N M DE S SD: 10.0358 c. M: 16.3887 c. 11: 2 2 7 N M DE S SD: 1.2588 c. M:-1.7529 c. 57: 10 11 36 N T3 SD: 1.0343 c. M: 1.4244 c. 63: 11 12 40 N T3 SD: 1.1137 c. M: 1.8405 c. 68: 12 13 43 N T3 SD: 0.6634 c. M: 0.9104 c. 79: 14 15 50 N T3 SD: 0.3958 c. M: 0.5396 c. 90: 16 17 57 N T3 SD: 0.1937 c. M: 0.2594 c. 101: 18 19 64 N T3 SD: 0.0363 c. M:-0.0484 c. 213: 38 40 135 N T3 SD: 0.0326 c. M:-0.0524 c. 314: 56 59 199 N T3 SD: 0.0131 c. M:-0.0226 c. 415: 74 78 263 N T3 SD: 0.0085 c. M:-0.0128 c. 1144: 204 215 725 N T3 SD: 0.0087 c. M:-0.0115 c. 1559: 278 293 988 N T3 SD: 0.0085 c. M:-0.0105 c. 1974: 352 371 1251 N T3 SD: 0.0085 c. M:-0.0109 c. 2389: 426 449 1514 N T3 SD: 0.0084 c. M:-0.0113 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13:14 x 17 SD: 25.9335 cents 14:15:16:19 SD: 21.7471 cents 15:16:17:20 SD: 13.7483 cents 16:17:18:21 S SD: 12.7664 cents 17:18:19:23 SD: 9.6895 cents 18:19:20:24 S SD: 1.6008 cents 99:104:110:132 SD: 1.1670 cents 117:123:130:156 SD: 0.7403 cents 135:142:150:180 SD: 0.4276 cents 153:161:170:204 SD: 0.1886 cents 171:180:190:228 S SD: 0.0000 cents