Scala analysis: 283_C20
Chromatic tetrachord 34/33 * 33/28 * 56/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/51 161.9155 1: 34/33 51.6825 2: 33/28 284.4470 undecimal minor third 3: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 56/51 161.915 cents 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 17/14 336.130 cents supraminor third 2: 1 22/17 446.363 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 : 51.7 336.1 498.0 51.7 : 284.4 446.4 498.0 336.1: 161.9 213.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 284.4470 cents 1089/952, 232.7646 cents 34/33, 51.6825 cents 2: 213.5980 .. 446.3625 cents 1089/952, 232.7646 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 3.212211 Largest / Average step : 1.713382 Largest / Smallest step : 5.503743 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 158.43403 cents, oct.: 475.30210 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1378-tone equal temperament with octave 4/3 degrees: 143 930 1378 Least number of segments generator : 691 of 249.745 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 703 of 254.082 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 51.68247 cents Scale diversity : 0.875807 Lumma stability : 0.207541 Lumma impropriety factor : 0.142254 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 : 34/33, 51.6825 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% -- Rational properties -- Prime limit : 17 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.015564 Average absolute harmonicity : 0.085893 Specific harmonicity : 0.070627 Fundamental : 1/462, -8.8517 octaves, 0.5663 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 3.141600E+04, 14.93921 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 52.5, average 17.50000 Mersenne's string divisions : 14539 Sum of van Prooijen's expressibility: 3.22608, average 1.07536 Sum of Tenney's harmonic distance : 6.50575, average 2.16858 Vogel's harmonic complexity : 26.00000 Wille's k value : 280 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.81002, average 2.30167 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 0 -0.66667 2 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 17: 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 18 24 31| Scale is weakly epimorphic with val: <6 10 18 25 27| Scale is weakly epimorphic with val: <6 10 19 23 28| Scale is weakly epimorphic with val: <6 10 19 25 32| Scale is weakly epimorphic with val: <6 10 19 26 28| Scale is weakly epimorphic with val: <6 10 20 23 30| Scale is weakly epimorphic with val: <6 10 20 24 29| Scale is weakly epimorphic with val: <6 10 20 26 33| Scale is weakly epimorphic with val: <6 10 20 27 29| Scale is weakly epimorphic with val: <6 10 21 24 31| Scale is weakly epimorphic with val: <6 10 21 25 30| Scale is weakly epimorphic with val: <6 10 22 23 31| Scale is weakly epimorphic with val: <6 10 22 25 32| Scale is weakly epimorphic with val: <6 10 22 26 31| Scale is weakly epimorphic with val: <6 11 18 23 27| Scale is weakly epimorphic with val: <6 11 18 24 32| Scale is weakly epimorphic with val: <6 11 18 26 27| Scale is weakly epimorphic with val: <6 11 19 24 28| Scale is weakly epimorphic with val: <6 11 19 25 33| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <6 11 20 23 31| Scale is weakly epimorphic with val: <6 11 20 25 29| Scale is weakly epimorphic with val: <6 11 21 23 30| Scale is weakly epimorphic with val: <6 11 21 24 32| Scale is weakly epimorphic with val: <6 11 21 26 30| Scale is weakly epimorphic with val: <6 11 22 24 31| Scale is weakly epimorphic with val: <6 11 22 25 33| Scale is weakly epimorphic with val: <6 11 22 27 31| Scale is weakly epimorphic with val: <7 10 18 23 28| Scale is weakly epimorphic with val: <7 10 18 24 30| Scale is weakly epimorphic with val: <7 10 18 26 28| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 19 24 29| Scale is weakly epimorphic with val: <7 10 19 25 31| Scale is weakly epimorphic with val: <7 10 19 27 29| Scale is weakly epimorphic with val: <7 10 20 23 29| Scale is weakly epimorphic with val: <7 10 20 25 30| Scale is weakly epimorphic with val: <7 10 20 26 32| Scale is weakly epimorphic with val: <7 10 21 23 31| Scale is weakly epimorphic with val: <7 10 21 24 30| Scale is weakly epimorphic with val: <7 10 21 26 31| Scale is weakly epimorphic with val: <7 10 21 27 33| Scale is weakly epimorphic with val: <7 10 22 24 32| Scale is weakly epimorphic with val: <7 10 22 25 31| Scale is weakly epimorphic with val: <7 10 22 27 32| Scale is weakly epimorphic with val: <7 11 18 23 29| Scale is weakly epimorphic with val: <7 11 18 23 32| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 26 29| Scale is weakly epimorphic with val: <7 11 18 26 32| Scale is JI-epimorphic with val: <7 11 19 23 28| Scale is weakly epimorphic with val: <7 11 19 23 31| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 26 31| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is JI-epimorphic with val: <7 11 20 24 29| Scale is weakly epimorphic with val: <7 11 20 24 32| Scale is weakly epimorphic with val: <7 11 20 25 28| Scale is weakly epimorphic with val: <7 11 20 25 31| Scale is weakly epimorphic with val: <7 11 20 27 29| Scale is weakly epimorphic with val: <7 11 20 27 32| Scale is weakly epimorphic with val: <7 11 21 23 29| Scale is weakly epimorphic with val: <7 11 21 23 32| Scale is weakly epimorphic with val: <7 11 21 25 27| Scale is JI-epimorphic with val: <7 11 21 25 30| Scale is weakly epimorphic with val: <7 11 21 25 33| Scale is weakly epimorphic with val: <7 11 21 26 29| Scale is weakly epimorphic with val: <7 11 21 26 32| Scale is weakly epimorphic with val: <7 11 22 23 28| Scale is weakly epimorphic with val: <7 11 22 23 31| Scale is weakly epimorphic with val: <7 11 22 24 27| Scale is weakly epimorphic with val: <7 11 22 24 30| Scale is weakly epimorphic with val: <7 11 22 24 33| Scale is weakly epimorphic with val: <7 11 22 26 28| Scale is JI-epimorphic with val: <7 11 22 26 31| Scale is weakly epimorphic with val: <7 11 22 27 27| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 11 22 27 33| Scale is weakly epimorphic with val: <7 12 18 24 32| Scale is weakly epimorphic with val: <7 12 18 25 28| Scale is weakly epimorphic with val: <7 12 19 23 29| Scale is weakly epimorphic with val: <7 12 19 25 33| Scale is weakly epimorphic with val: <7 12 19 26 29| Scale is weakly epimorphic with val: <7 12 20 23 31| Scale is weakly epimorphic with val: <7 12 20 24 30| Scale is weakly epimorphic with val: <7 12 20 27 30| Scale is weakly epimorphic with val: <7 12 21 24 32| Scale is weakly epimorphic with val: <7 12 21 25 31| Scale is weakly epimorphic with val: <7 12 22 23 32| Scale is weakly epimorphic with val: <7 12 22 25 33| Scale is weakly epimorphic with val: <7 12 22 26 32| Scale is weakly epimorphic with val: <8 11 18 24 30| Scale is weakly epimorphic with val: <8 11 18 25 29| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 19 23 30| Scale is weakly epimorphic with val: <8 11 19 25 31| Scale is weakly epimorphic with val: <8 11 19 26 30| Scale is weakly epimorphic with val: <8 11 20 23 29| Scale is weakly epimorphic with val: <8 11 20 24 31| Scale is weakly epimorphic with val: <8 11 20 26 32| Scale is weakly epimorphic with val: <8 11 20 27 31| Scale is weakly epimorphic with val: <8 11 21 24 30| Scale is weakly epimorphic with val: <8 11 21 25 32| Scale is weakly epimorphic with val: <8 11 21 27 33| Scale is weakly epimorphic with val: <8 11 22 23 33| Scale is weakly epimorphic with val: <8 11 22 25 31| Scale is weakly epimorphic with val: <8 11 22 26 33| Scale is weakly epimorphic with val: <8 12 18 23 29| Scale is weakly epimorphic with val: <8 12 18 24 31| Scale is weakly epimorphic with val: <8 12 18 26 29| Scale is weakly epimorphic with val: <8 12 19 24 30| Scale is weakly epimorphic with val: <8 12 19 25 32| Scale is weakly epimorphic with val: <8 12 19 27 30| Scale is weakly epimorphic with val: <8 12 20 23 30| Scale is weakly epimorphic with val: <8 12 20 25 31| Scale is weakly epimorphic with val: <8 12 20 26 33| Scale is weakly epimorphic with val: <8 12 21 23 32| Scale is weakly epimorphic with val: <8 12 21 24 31| Scale is weakly epimorphic with val: <8 12 21 26 32| Scale is weakly epimorphic with val: <8 12 22 24 33| Scale is weakly epimorphic with val: <8 12 22 25 32| Scale is weakly epimorphic with val: <8 12 22 27 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 29.9326 c. M: 51.6825 c. 6: 1 3 2 P T3 SD: 18.2397 c. M:-31.3250 c. 7: 1 4 2 N T3 SD: 15.9560 c. M:-19.6169 c. 8: 1 4 3 P T3 SD: 15.5925 c. M: 24.8514 c. 9: 1 5 3 N T3 SD: 3.1713 c. M: 4.0995 c. 19: 2 11 6 N T3 SD: 2.7120 c. M:-4.6381 c. 28: 3 16 9 N T3 SD: 1.4339 c. M:-1.8296 c. 37: 4 21 12 N T3 SD: 1.2671 c. M:-2.1602 c. 40: 4 23 13 N T3 SD: 1.0846 c. M: 1.8780 c. 49: 5 28 16 N T3 SD: 0.6451 c. M: 0.8615 c. 68: 7 39 22 N T3 SD: 0.5113 c. M:-0.7833 c. 77: 8 44 25 N T3 SD: 0.1279 c. M:-0.2126 c. 203: 21 116 66 N T3 SD: 0.0929 c. M: 0.1606 c. 280: 29 160 91 N T3 SD: 0.0644 c. M: 0.0992 c. 289: 30 165 94 N T3 SD: 0.0464 c. M: 0.0784 c. 366: 38 209 119 N T3 SD: 0.0185 c. M:-0.0271 c. 646: 67 369 210 N T3 SD: 0.0175 c. M: 0.0276 c. 809: 84 462 263 N T3 SD: 0.0178 c. M:-0.0305 c. 935: 97 534 304 N T3 SD: 0.0120 c. M: 0.0157 c. 1012: 105 578 329 N T3 SD: 0.0046 c. M: 0.0078 c. 1378: 143 787 448 N T3 SD: 0.0021 c. M: 0.0033 c. 2390: 248 1365 777 N T3 SD: 0.0016 c. M: 0.0025 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: 50.1842 cents 5 x 6:7 S SD: 43.4582 cents 6 x 7:8 S SD: 34.6293 cents 7 x x 9 SD: 62.9609 cents 8 x 10:11 S SD: 36.5939 cents 12:13:15:16 SD: 33.4471 cents 13:14:16:17 S SD: 28.9540 cents 14:15:17:19 SD: 24.7889 cents 15:16:18:20 S SD: 21.1493 cents 17:18:21:23 SD: 20.4268 cents 18:19:22:24 SD: 14.4704 cents 22:23:27:29 SD: 12.3354 cents 23:24:28:31 SD: 9.7398 cents 24:25:29:32 SD: 6.9362 cents 27:28:33:36 SD: 5.3167 cents 32:33:39:43 SD: 4.9934 cents 33:34:40:44 SD: 1.0296 cents 102:105:124:136 SD: 0.8318 cents 126:130:153:168 SD: 0.8077 cents 135:139:164:180 SD: 0.4534 cents 168:173:204:224 SD: 0.3032 cents 261:269:317:348 SD: 0.2344 cents 294:303:357:392 SD: 0.1732 cents 396:408:481:528 SD: 0.1714 cents 429:442:521:572 SD: 0.0791 cents 462:476:561:616 SD: 0.0000 cents