Scala analysis: 290_C21
Chromatic tetrachord 28/27 * 153/140 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 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: 28/27 62.9609 Archytas' 1/3-tone 2: 153/140 153.7258 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 153/140 153.726 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 560/459 344.319 cents 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 216.7 498.0 63.0 : 153.7 435.1 498.0 216.7: 281.4 344.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 281.3583 cents 135/119, 218.3974 cents 28/27, 62.9609 cents 2: 216.6867 .. 435.0841 cents 135/119, 218.3974 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 2.636795 Largest / Average step : 1.694776 Largest / Smallest step : 4.468778 Median interval of one step : 153/140, 153.7258 cents, amount: 1 Least squares average step : 142.17638 cents, oct.: 426.52913 cents Scale is not proper Scale has trivalence property Scale is a mode of a 878-tone equal temperament with octave 4/3 degrees: 111 382 878 Least number of segments generator : 441 of 250.157 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 687 of 389.700 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 62.96090 cents Scale diversity : 0.977985 Lumma stability : 0.252832 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 : 28/27, 62.9609 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% -- Rational properties -- Prime limit : 17 Odd number limit : 459 (O: 153 U: 459) Highest odd numerator or denominator: 27 Scale harmonicity : 0.017605 Average absolute harmonicity : 0.096367 Specific harmonicity : 0.092802 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 476, 8.8948 octaves, 124533.769 Hz. Exponens Consonantiae : 6.426000E+04, 15.97163 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 47.0, average 15.66667 Mersenne's string divisions : 12320 Sum of van Prooijen's expressibility: 3.13893, average 1.04631 Sum of Tenney's harmonic distance : 6.36424, average 2.12141 Vogel's harmonic complexity : 16.66667 Wille's k value : 76 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.71196, average 2.61866 Lattice compactness (without 2's) : 12.19036, average 2.03173 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -3 ..-1 -1.66667 5 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.33333 1 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 19 28| Scale is weakly epimorphic with val: <6 10 15 21 29| Scale is weakly epimorphic with val: <6 10 15 21 32| Scale is weakly epimorphic with val: <6 10 15 22 28| Scale is weakly epimorphic with val: <6 10 16 19 29| Scale is weakly epimorphic with val: <6 10 16 21 27| Scale is weakly epimorphic with val: <6 10 16 21 30| Scale is weakly epimorphic with val: <6 10 16 21 33| Scale is weakly epimorphic with val: <6 10 16 22 29| Scale is weakly epimorphic with val: <6 10 17 19 30| Scale is weakly epimorphic with val: <6 10 17 21 28| Scale is weakly epimorphic with val: <6 10 17 21 31| Scale is weakly epimorphic with val: <6 10 17 22 30| Scale is weakly epimorphic with val: <6 10 18 19 31| Scale is weakly epimorphic with val: <6 10 18 21 29| Scale is weakly epimorphic with val: <6 10 18 21 32| Scale is weakly epimorphic with val: <6 10 18 22 31| Scale is weakly epimorphic with val: <6 10 19 19 32| Scale is weakly epimorphic with val: <6 10 19 21 27| Scale is weakly epimorphic with val: <6 10 19 21 30| Scale is weakly epimorphic with val: <6 10 19 21 33| Scale is weakly epimorphic with val: <6 10 19 22 32| Scale is weakly epimorphic with val: <6 11 15 20 29| Scale is weakly epimorphic with val: <6 11 16 20 30| Scale is weakly epimorphic with val: <6 11 17 20 31| Scale is weakly epimorphic with val: <6 11 18 20 32| Scale is weakly epimorphic with val: <6 11 19 20 33| Scale is weakly epimorphic with val: <7 10 15 18 28| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 15 19 33| Scale is weakly epimorphic with val: <7 10 15 21 28| Scale is weakly epimorphic with val: <7 10 16 18 29| Scale is weakly epimorphic with val: <7 10 16 19 28| Scale is weakly epimorphic with val: <7 10 16 19 31| Scale is weakly epimorphic with val: <7 10 16 21 29| Scale is weakly epimorphic with val: <7 10 17 18 30| Scale is weakly epimorphic with val: <7 10 17 19 29| Scale is weakly epimorphic with val: <7 10 17 19 32| Scale is weakly epimorphic with val: <7 10 17 21 30| Scale is weakly epimorphic with val: <7 10 18 18 31| Scale is weakly epimorphic with val: <7 10 18 19 27| Scale is weakly epimorphic with val: <7 10 18 19 30| Scale is weakly epimorphic with val: <7 10 18 19 33| Scale is weakly epimorphic with val: <7 10 18 21 31| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 19 31| Scale is weakly epimorphic with val: <7 10 19 21 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 20 28| Scale is weakly epimorphic with val: <7 11 15 20 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 16 18 28| Scale is weakly epimorphic with val: <7 11 16 18 31| Scale is JI-epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 16 21 31| Scale is weakly epimorphic with val: <7 11 17 18 29| Scale is weakly epimorphic with val: <7 11 17 18 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 21 29| Scale is weakly epimorphic with val: <7 11 17 21 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 20 28| Scale is JI-epimorphic with val: <7 11 18 20 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 19 20 29| Scale is JI-epimorphic with val: <7 11 19 20 32| Scale is weakly epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 11 19 21 31| Scale is weakly epimorphic with val: <7 12 15 20 30| Scale is weakly epimorphic with val: <7 12 16 20 31| Scale is weakly epimorphic with val: <7 12 17 20 32| Scale is weakly epimorphic with val: <7 12 18 20 33| Scale is weakly epimorphic with val: <8 11 15 18 29| Scale is weakly epimorphic with val: <8 11 15 20 27| Scale is weakly epimorphic with val: <8 11 15 20 30| Scale is weakly epimorphic with val: <8 11 15 20 33| Scale is weakly epimorphic with val: <8 11 15 21 29| Scale is weakly epimorphic with val: <8 11 16 18 30| Scale is weakly epimorphic with val: <8 11 16 20 28| Scale is weakly epimorphic with val: <8 11 16 20 31| Scale is weakly epimorphic with val: <8 11 16 21 30| Scale is weakly epimorphic with val: <8 11 17 18 31| Scale is weakly epimorphic with val: <8 11 17 20 29| Scale is weakly epimorphic with val: <8 11 17 20 32| Scale is weakly epimorphic with val: <8 11 17 21 31| Scale is weakly epimorphic with val: <8 11 18 18 32| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 18 20 30| Scale is weakly epimorphic with val: <8 11 18 20 33| Scale is weakly epimorphic with val: <8 11 18 21 32| Scale is weakly epimorphic with val: <8 11 19 20 28| Scale is weakly epimorphic with val: <8 11 19 20 31| Scale is weakly epimorphic with val: <8 11 19 21 33| Scale is weakly epimorphic with val: <8 12 15 19 30| Scale is weakly epimorphic with val: <8 12 15 22 30| Scale is weakly epimorphic with val: <8 12 16 19 31| Scale is weakly epimorphic with val: <8 12 16 22 31| Scale is weakly epimorphic with val: <8 12 17 19 32| Scale is weakly epimorphic with val: <8 12 17 22 32| Scale is weakly epimorphic with val: <8 12 18 19 33| Scale is weakly epimorphic with val: <8 12 18 22 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 46.6608 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 23.4396 c. M:-36.6481 c. 6: 1 2 3 P T3 SD: 21.9657 c. M:-32.3358 c. 7: 1 2 4 N T3 SD: 5.0840 c. M:-8.1884 c. 9: 1 3 5 N T3 SD: 5.1601 c. M: 7.6226 c. 16: 2 5 9 N T3 SD: 0.8076 c. M:-1.2080 c. 39: 5 12 22 N T3 SD: 0.5662 c. M:-0.8910 c. 55: 7 17 31 N T3 SD: 0.4451 c. M:-0.6420 c. 94: 12 29 53 N T3 SD: 0.4766 c. M:-0.6193 c. 126: 16 39 71 N T3 SD: 0.4434 c. M:-0.7139 c. 149: 19 46 84 N T3 SD: 0.4613 c. M:-0.5813 c. 159: 20 49 90 N T3 SD: 0.3676 c. M: 0.5540 c. 175: 22 54 99 N T3 SD: 0.3036 c. M: 0.3929 c. 182: 23 56 103 N T3 SD: 0.2903 c. M: 0.5023 c. 191: 24 59 108 N T3 SD: 0.2651 c. M: 0.3793 c. 198: 25 61 112 N T3 SD: 0.2148 c. M: 0.3641 c. 214: 27 66 121 N T3 SD: 0.1592 c. M: 0.2466 c. 230: 29 71 130 N T3 SD: 0.1265 c. M: 0.1639 c. 246: 31 76 139 N T3 SD: 0.1196 c. M: 0.1991 c. 253: 32 78 143 N T3 SD: 0.0861 c. M: 0.1454 c. 269: 34 83 152 N T3 SD: 0.0380 c. M: 0.0649 c. 285: 36 88 161 N T3 SD: 0.0291 c. M: 0.0500 c. 554: 70 171 313 N T3 SD: 0.0242 c. M: 0.0310 c. 593: 75 183 335 N T3 SD: 0.0171 c. M:-0.0296 c. 609: 77 188 344 N T3 SD: 0.0196 c. M:-0.0324 c. 862: 109 266 487 N T3 SD: 0.0150 c. M: 0.0198 c. 878: 111 271 496 N T3 SD: 0.0026 c. M:-0.0038 c. 2041: 258 630 1153 N T3 SD: 0.0028 c. M: 0.0037 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: 30.2501 cents 13:14:15:17 SD: 26.5904 cents 14:15:16:19 SD: 21.9571 cents 15:16:17:20 SD: 16.2568 cents 18:19:20:24 S SD: 15.3270 cents 20:21:23:27 SD: 13.1817 cents 21:22:24:28 S SD: 7.5924 cents 23:24:26:31 SD: 7.3399 cents 24:25:27:32 SD: 4.9745 cents 30:31:34:40 SD: 2.0647 cents 54:56:61:72 SD: 1.8890 cents 75:78:85:100 SD: 1.6464 cents 81:84:92:108 SD: 1.2559 cents 105:109:119:140 SD: 0.5886 cents 135:140:153:180 SD: 0.0000 cents