Scala analysis: 343_C28
Chromatic tetrachord 19/18 * 12/11 * 22/19, Schlesinger
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 38/33 244.240073 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/19 253.8049 Godzilla third 1: 19/18 93.6030 undevicesimal semitone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 22/19 253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 22/19 253.805 cents Godzilla third 2: 1 38/33 244.240 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 24/19 404.442 cents smaller undevicesimal major 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 : 93.6 244.2 498.0 93.6 : 150.6 404.4 498.0 244.2: 253.8 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 253.8049 cents 396/361, 160.2019 cents 19/18, 93.6030 cents 2: 244.2401 .. 404.4420 cents 396/361, 160.2019 cents 361/363,-9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/19, 253.8049 cents Average / Smallest step : 1.773607 Largest / Average step : 1.528807 Largest / Smallest step : 2.711504 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 148.30130 cents, oct.: 444.90389 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 9.56485 cents Scale diversity : 1.126172 Lumma stability : 0.375882 Lumma impropriety factor : 0.019205 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 : 363/361, 9.5649 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 19 Odd number limit : 33 (O: 19 U: 33) Highest odd numerator or denominator: 33 Scale harmonicity : 0.016496 Average absolute harmonicity : 0.085628 Specific harmonicity : 0.073744 Fundamental : 1/198, -7.6294 octaves, 1.3213 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 1.504800E+04, 13.87728 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 57.5, average 19.16667 Mersenne's string divisions : 18389 Sum of van Prooijen's expressibility: 3.27439, average 1.09146 Sum of Tenney's harmonic distance : 6.71150, average 2.23717 Vogel's harmonic complexity : 23.66667 Wille's k value : 104 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 14.18372, average 2.36395 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -2 ..-1 -1.33333 4 1 11: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 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 23 30| Scale is weakly epimorphic with val: <6 10 24 29| Scale is weakly epimorphic with val: <6 10 26 33| Scale is weakly epimorphic with val: <6 10 27 29| Scale is weakly epimorphic with val: <6 11 24 31| Scale is weakly epimorphic with val: <6 11 25 33| Scale is weakly epimorphic with val: <6 11 27 31| Scale is weakly epimorphic with val: <7 10 23 29| Scale is weakly epimorphic with val: <7 10 25 30| Scale is weakly epimorphic with val: <7 10 26 32| Scale is weakly epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 31| Scale is weakly epimorphic with val: <7 11 23 34| Scale is JI-epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 24 33| Scale is weakly epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 34| Scale is weakly epimorphic with val: <7 11 27 30| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 12 24 32| Scale is weakly epimorphic with val: <7 12 25 34| Scale is weakly epimorphic with val: <8 11 23 33| Scale is weakly epimorphic with val: <8 11 25 31| Scale is weakly epimorphic with val: <8 11 26 33| Scale is weakly epimorphic with val: <8 12 24 31| Scale is weakly epimorphic with val: <8 12 27 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 70.4289 c. M: 93.6030 c. 4: 1 1 2 P M ME S SD: 18.0572 c. M:-30.9082 c. 6: 1 2 3 P T3 SD: 6.7116 c. M: 10.5955 c. 10: 2 3 5 P T3 SD: 4.4326 c. M:-6.0060 c. 16: 3 5 8 P T3 SD: 2.7640 c. M:-4.7824 c. 26: 5 8 13 P T3 SD: 3.0332 c. M:-4.7824 c. 27: 5 8 14 N T3 SD: 2.6835 c. M: 4.4406 c. 31: 6 9 16 N T3 SD: 2.4743 c. M: 3.2506 c. 33: 6 10 17 N T3 SD: 2.3760 c. M: 3.0494 c. 37: 7 11 19 N T3 SD: 1.1805 c. M: 1.9479 c. 43: 8 13 22 N T3 SD: 0.7975 c. M: 1.0088 c. 53: 10 16 27 N T3 SD: 0.2178 c. M:-0.3677 c. 112: 21 34 57 N T3 SD: 0.2315 c. M:-0.3356 c. 149: 28 45 76 N T3 SD: 0.1338 c. M: 0.2314 c. 202: 38 61 103 N T3 SD: 0.0999 c. M: 0.1487 c. 255: 48 77 130 N T3 SD: 0.1026 c. M:-0.1466 c. 261: 49 79 133 N T3 SD: 0.0583 c. M: 0.1003 c. 314: 59 95 160 N T3 SD: 0.0185 c. M:-0.0240 c. 681: 128 206 347 N T3 SD: 0.0174 c. M:-0.0287 c. 777: 146 235 396 N T3 SD: 0.0182 c. M: 0.0250 c. 830: 156 251 423 N T3 SD: 0.0109 c. M: 0.0180 c. 1144: 215 346 583 N T3 SD: 0.0039 c. M: 0.0065 c. 1458: 274 441 743 N T3 SD: 0.0035 c. M: 0.0061 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: 55.3011 cents 6 x 7:8 S SD: 11.3154 cents 7 x 8:9 S SD: 32.1512 cents 8 x 9:11 SD: 33.4085 cents 9 x 10:12 S SD: 30.9182 cents 11:12:13:15 SD: 27.4647 cents 12:13:14:16 S SD: 16.7810 cents 13:14:15:17 SD: 16.1456 cents 14:15:16:19 SD: 14.0529 cents 15:16:17:20 SD: 10.9941 cents 18:19:21:24 SD: 7.5436 cents 21:22:24:28 S SD: 6.1594 cents 33:35:38:44 SD: 2.7546 cents 39:41:45:52 SD: 2.6158 cents 54:57:62:72 SD: 1.6898 cents 72:76:83:96 SD: 0.6324 cents 126:133:145:168 SD: 0.3617 cents 198:209:228:264 SD: 0.0000 cents