Scala analysis: 286_C21
Chromatic tetrachord 51/49 * 49/45 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51/49 69.258597 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 51/49 69.2586 2: 49/45 147.4281 BP minor semitone 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 51/49 69.259 cents 1: 1 49/45 147.428 cents BP minor semitone 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 60/49 350.617 cents smaller approximation to neutral third 2: 1 196/153 428.786 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 : 69.3 216.7 498.0 69.3 : 147.4 428.8 498.0 216.7: 281.4 350.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.2586 .. 281.3583 cents 980/867, 212.0997 cents 51/49, 69.2586 cents 2: 216.6867 .. 428.7864 cents 980/867, 212.0997 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 51/49, 69.2586 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 2.397031 Largest / Average step : 1.694776 Largest / Smallest step : 4.062431 Median interval of one step : 49/45, 147.4281 cents, amount: 1 Least squares average step : 142.62621 cents, oct.: 427.87864 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1733-tone equal temperament with octave 4/3 degrees: 241 754 1733 Least number of segments generator : 867 of 249.166 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1461 of 419.875 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 64.67161 cents Scale diversity : 1.028744 Lumma stability : 0.278122 Lumma impropriety factor : 0.129851 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 : 300/289, 64.6716 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.015523 Average absolute harmonicity : 0.086182 Specific harmonicity : 0.070780 Fundamental : 1/735, -9.5216 octaves, 0.3560 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 1.499400E+05, 17.19403 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 69.5, average 23.16667 Mersenne's string divisions : 5600 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 6.88349, average 2.29450 Vogel's harmonic complexity : 26.66667 Wille's k value : 416 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.47265, average 2.57877 Lattice compactness (without 2's) : 12.59575, average 2.09929 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 7: -2 .. 0 -0.66667 2 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 18 29| Scale is weakly epimorphic with val: <6 10 15 20 28| Scale is weakly epimorphic with val: <6 10 16 19 29| Scale is weakly epimorphic with val: <6 10 16 20 33| Scale is weakly epimorphic with val: <6 10 16 22 29| Scale is weakly epimorphic with val: <6 10 17 18 30| Scale is weakly epimorphic with val: <6 10 17 19 31| Scale is weakly epimorphic with val: <6 10 17 21 30| Scale is weakly epimorphic with val: <6 10 18 18 29| Scale is weakly epimorphic with val: <6 10 18 20 31| Scale is weakly epimorphic with val: <6 10 19 19 32| Scale is weakly epimorphic with val: <6 10 19 20 33| Scale is weakly epimorphic with val: <6 10 19 22 32| Scale is weakly epimorphic with val: <6 11 15 18 28| Scale is weakly epimorphic with val: <6 11 15 19 29| Scale is weakly epimorphic with val: <6 11 15 22 29| Scale is weakly epimorphic with val: <6 11 16 18 30| Scale is weakly epimorphic with val: <6 11 16 20 32| Scale is weakly epimorphic with val: <6 11 16 21 30| Scale is weakly epimorphic with val: <6 11 17 19 30| Scale is weakly epimorphic with val: <6 11 17 20 31| Scale is weakly epimorphic with val: <6 11 18 18 28| Scale is weakly epimorphic with val: <6 11 18 19 32| Scale is weakly epimorphic with val: <6 11 18 22 32| Scale is weakly epimorphic with val: <6 11 19 20 32| Scale is weakly epimorphic with val: <6 11 19 21 33| Scale is weakly epimorphic with val: <7 10 15 18 28| Scale is weakly epimorphic with val: <7 10 15 20 33| Scale is weakly epimorphic with val: <7 10 15 21 28| Scale is weakly epimorphic with val: <7 10 16 19 31| Scale is weakly epimorphic with val: <7 10 16 20 29| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is weakly epimorphic with val: <7 10 17 19 30| Scale is weakly epimorphic with val: <7 10 17 22 30| Scale is weakly epimorphic with val: <7 10 18 18 31| Scale is weakly epimorphic with val: <7 10 18 20 33| Scale is weakly epimorphic with val: <7 10 18 21 31| Scale is weakly epimorphic with val: <7 10 19 19 31| Scale is weakly epimorphic with val: <7 10 19 20 32| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 18 33| Scale is JI-epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 15 21 33| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 20 31| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 17 19 29| Scale is weakly epimorphic with val: <7 11 17 19 32| Scale is weakly epimorphic with val: <7 11 17 20 27| Scale is JI-epimorphic with val: <7 11 17 20 30| = patent Scale is weakly epimorphic with val: <7 11 17 20 33| Scale is weakly epimorphic with val: <7 11 17 22 29| Scale is weakly epimorphic with val: <7 11 17 22 32| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 18 33| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 18 21 33| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 20 31| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is JI-epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 12 15 19 30| Scale is weakly epimorphic with val: <7 12 15 20 31| Scale is weakly epimorphic with val: <7 12 15 22 30| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 19 29| Scale is weakly epimorphic with val: <7 12 16 21 31| Scale is weakly epimorphic with val: <7 12 17 18 27| Scale is weakly epimorphic with val: <7 12 17 20 32| Scale is weakly epimorphic with val: <7 12 17 21 33| Scale is weakly epimorphic with val: <7 12 18 19 33| Scale is weakly epimorphic with val: <7 12 18 20 31| Scale is weakly epimorphic with val: <7 12 18 22 33| Scale is weakly epimorphic with val: <7 12 19 19 29| Scale is weakly epimorphic with val: <8 11 15 18 29| Scale is weakly epimorphic with val: <8 11 15 19 30| Scale is weakly epimorphic with val: <8 11 15 21 29| Scale is weakly epimorphic with val: <8 11 16 18 28| Scale is weakly epimorphic with val: <8 11 16 20 30| Scale is weakly epimorphic with val: <8 11 17 19 31| Scale is weakly epimorphic with val: <8 11 17 20 32| Scale is weakly epimorphic with val: <8 11 17 22 31| Scale is weakly epimorphic with val: <8 11 18 18 32| Scale is weakly epimorphic with val: <8 11 18 19 30| Scale is weakly epimorphic with val: <8 11 18 21 32| Scale is weakly epimorphic with val: <8 11 19 20 33| Scale is weakly epimorphic with val: <8 12 15 19 29| Scale is weakly epimorphic with val: <8 12 15 20 30| Scale is weakly epimorphic with val: <8 12 16 18 27| Scale is weakly epimorphic with val: <8 12 16 19 31| Scale is weakly epimorphic with val: <8 12 16 21 33| Scale is weakly epimorphic with val: <8 12 16 22 31| Scale is weakly epimorphic with val: <8 12 17 18 32| Scale is weakly epimorphic with val: <8 12 17 20 31| Scale is weakly epimorphic with val: <8 12 17 21 32| Scale is weakly epimorphic with val: <8 12 18 19 29| Scale is weakly epimorphic with val: <8 12 18 20 33| Scale is weakly epimorphic with val: <8 12 19 21 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.5459 c. M: 69.2586 c. 4: 1 1 2 P M ME S SD: 36.9615 c. M:-55.2527 c. 5: 1 1 3 N M DE S SD: 20.2180 c. M:-30.3504 c. 6: 1 2 3 P T3 SD: 20.2866 c. M:-32.3358 c. 7: 1 2 4 N T3 SD: 2.1652 c. M: 3.2388 c. 23: 3 7 13 N T3 SD: 2.4818 c. M: 4.2962 c. 30: 4 9 17 N T3 SD: 1.7214 c. M: 2.8526 c. 37: 5 11 21 N T3 SD: 1.3607 c. M: 1.9552 c. 44: 6 13 25 N T3 SD: 1.2159 c. M: 1.6218 c. 51: 7 15 29 N T3 SD: 1.1844 c. M: 1.8438 c. 57: 8 17 32 N T3 SD: 1.0785 c. M:-1.7541 c. 64: 9 19 36 N T3 SD: 0.8299 c. M:-1.2080 c. 71: 10 21 40 N T3 SD: 0.6787 c. M:-0.8886 c. 78: 11 23 44 N T3 SD: 0.6125 c. M:-0.9785 c. 85: 12 25 48 N T3 SD: 0.6116 c. M:-1.0536 c. 87: 12 26 49 N T3 SD: 0.5886 c. M:-0.8502 c. 94: 13 28 53 N T3 SD: 0.3839 c. M:-0.5457 c. 101: 14 30 57 N T3 SD: 0.2081 c. M:-0.2834 c. 108: 15 32 61 N T3 SD: 0.0588 c. M: 0.0857 c. 223: 31 66 126 N T3 SD: 0.0310 c. M: 0.0483 c. 331: 46 98 187 N T3 SD: 0.0267 c. M: 0.0439 c. 554: 77 164 313 N T3 SD: 0.0263 c. M: 0.0357 c. 777: 108 230 439 N T3 SD: 0.0270 c. M: 0.0339 c. 885: 123 262 500 N T3 SD: 0.0260 c. M: 0.0388 c. 1064: 148 315 601 N T3 SD: 0.0242 c. M:-0.0378 c. 1071: 149 317 605 N T3 SD: 0.0200 c. M:-0.0306 c. 1179: 164 349 666 N T3 SD: 0.0163 c. M:-0.0199 c. 1287: 179 381 727 N T3 SD: 0.0147 c. M:-0.0229 c. 1294: 180 383 731 N T3 SD: 0.0126 c. M:-0.0212 c. 1402: 195 415 792 N T3 SD: 0.0091 c. M:-0.0130 c. 1510: 210 447 853 N T3 SD: 0.0079 c. M:-0.0124 c. 1625: 226 481 918 N T3 SD: 0.0047 c. M:-0.0080 c. 1733: 241 513 979 N T3 SD: 0.0029 c. M:-0.0046 c. 1956: 272 579 1105 N T3 SD: 0.0010 c. M: 0.0015 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10 x 11:13 SD: 33.8830 cents 11 x 12:15 S SD: 38.3282 cents 12:13:14:16 S SD: 28.5246 cents 13:14:15:17 SD: 24.9002 cents 14:15:16:19 SD: 20.1860 cents 15:16:17:20 SD: 14.1576 cents 18:19:20:24 S SD: 14.0158 cents 20:21:23:27 SD: 12.1682 cents 21:22:24:28 S SD: 6.1200 cents 24:25:27:32 SD: 4.2849 cents 30:31:34:40 SD: 4.1639 cents 45:47:51:60 SD: 2.0081 cents 75:78:85:100 SD: 0.4528 cents 195:203:221:260 SD: 0.1160 cents 270:281:306:360 SD: 0.0419 cents 465:484:527:620 SD: 0.0243 cents