Scala analysis: 218_C14
Chromatic tetrachord 65/63 * 14/13 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65/63 54.105467 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: 65/63 54.1055 2: 14/13 128.2982 2/3-tone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/63 54.105 cents 1: 1 14/13 128.298 cents 2/3-tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 26/21 369.747 cents 2: 1 84/65 443.940 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 : 54.1 182.4 498.0 54.1 : 128.3 443.9 498.0 182.4: 315.6 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.1055 .. 315.6413 cents 378/325, 261.5358 cents 65/63, 54.1055 cents 2: 182.4037 .. 443.9395 cents 378/325, 261.5358 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 65/63, 54.1055 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 3.068359 Largest / Average step : 1.901282 Largest / Smallest step : 5.833815 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 136.64628 cents, oct.: 409.93883 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1611-tone equal temperament with octave 4/3 degrees: 175 590 1611 Least number of segments generator : 806 of 249.177 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1292 of 399.425 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 54.10547 cents Scale diversity : 0.884952 Lumma stability : 0.217271 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 : 65/63, 54.1055 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 65 (O: 65 U: 65) Highest odd numerator or denominator: 65 Scale harmonicity : 0.021658 Average absolute harmonicity : 0.105152 Specific harmonicity : 0.107682 Fundamental : 1/63, -5.9773 octaves, 4.1528 Hz. Guide tone : 260, 8.0224 octaves, 68022.647 Hz. Exponens Consonantiae : 1.638000E+04, 13.99965 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 77.0, average 25.66667 Mersenne's string divisions : 17024 Sum of van Prooijen's expressibility: 3.24428, average 1.08143 Sum of Tenney's harmonic distance : 6.64568, average 2.21523 Vogel's harmonic complexity : 14.33333 Wille's k value : 32 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.62384, average 2.27064 Lattice compactness (without 2's) : 10.71025, average 1.78504 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -2 ..-1 -1.66667 5 1 5: 0 .. 1 0.66667 2 1 7: -1 .. 0 -0.33333 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 18 26| Scale is weakly epimorphic with val: <6 10 15 19 27| Scale is weakly epimorphic with val: <6 10 15 20 28| Scale is weakly epimorphic with val: <6 10 15 21 29| Scale is weakly epimorphic with val: <6 10 15 22 30| Scale is weakly epimorphic with val: <6 10 17 18 25| Scale is weakly epimorphic with val: <6 10 17 18 28| Scale is weakly epimorphic with val: <6 10 17 19 26| Scale is weakly epimorphic with val: <6 10 17 19 29| Scale is weakly epimorphic with val: <6 10 17 20 27| Scale is weakly epimorphic with val: <6 10 17 20 30| Scale is weakly epimorphic with val: <6 10 17 21 25| Scale is weakly epimorphic with val: <6 10 17 21 28| Scale is weakly epimorphic with val: <6 10 17 22 26| Scale is weakly epimorphic with val: <6 10 17 22 29| Scale is weakly epimorphic with val: <6 10 18 20 25| Scale is weakly epimorphic with val: <6 10 18 21 26| Scale is weakly epimorphic with val: <6 10 18 22 27| 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 20 30| Scale is weakly epimorphic with val: <6 11 18 18 25| Scale is weakly epimorphic with val: <6 11 18 19 26| Scale is weakly epimorphic with val: <6 11 18 20 27| Scale is weakly epimorphic with val: <6 11 18 21 28| Scale is weakly epimorphic with val: <6 11 18 22 29| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <6 11 19 19 30| Scale is weakly epimorphic with val: <6 11 19 20 25| Scale is weakly epimorphic with val: <6 11 19 20 28| Scale is weakly epimorphic with val: <6 11 19 21 26| Scale is weakly epimorphic with val: <6 11 19 21 29| Scale is weakly epimorphic with val: <6 11 19 22 27| Scale is weakly epimorphic with val: <6 11 19 22 30| Scale is weakly epimorphic with val: <7 10 15 18 26| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 15 20 28| Scale is weakly epimorphic with val: <7 10 15 21 29| Scale is weakly epimorphic with val: <7 10 15 22 30| Scale is weakly epimorphic with val: <7 10 16 18 27| Scale is weakly epimorphic with val: <7 10 16 18 30| Scale is weakly epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 19 28| Scale is weakly epimorphic with val: <7 10 16 20 26| Scale is weakly epimorphic with val: <7 10 16 20 29| Scale is weakly epimorphic with val: <7 10 16 21 27| Scale is weakly epimorphic with val: <7 10 16 21 30| Scale is weakly epimorphic with val: <7 10 16 22 25| Scale is weakly epimorphic with val: <7 10 16 22 28| Scale is weakly epimorphic with val: <7 10 18 20 25| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 18 22 27| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 17 18 27| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is JI-epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 19 28| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is JI-epimorphic with val: <7 11 17 21 27| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is JI-epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 12 15 18 30| Scale is weakly epimorphic with val: <7 12 18 18 27| Scale is weakly epimorphic with val: <7 12 18 19 28| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 18 21 30| Scale is weakly epimorphic with val: <8 11 15 18 28| Scale is weakly epimorphic with val: <8 11 15 19 29| Scale is weakly epimorphic with val: <8 11 15 20 30| Scale is weakly epimorphic with val: <8 11 17 18 27| Scale is weakly epimorphic with val: <8 11 17 18 30| Scale is weakly epimorphic with val: <8 11 17 19 25| Scale is weakly epimorphic with val: <8 11 17 19 28| Scale is weakly epimorphic with val: <8 11 17 20 26| Scale is weakly epimorphic with val: <8 11 17 20 29| Scale is weakly epimorphic with val: <8 11 17 21 27| Scale is weakly epimorphic with val: <8 11 17 21 30| Scale is weakly epimorphic with val: <8 11 17 22 25| Scale is weakly epimorphic with val: <8 11 17 22 28| Scale is weakly epimorphic with val: <8 11 18 18 25| Scale is weakly epimorphic with val: <8 11 18 19 26| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 18 21 28| Scale is weakly epimorphic with val: <8 11 18 22 29| Scale is weakly epimorphic with val: <8 12 15 18 30| Scale is weakly epimorphic with val: <8 12 18 18 27| Scale is weakly epimorphic with val: <8 12 18 19 28| Scale is weakly epimorphic with val: <8 12 18 20 29| Scale is weakly epimorphic with val: <8 12 18 21 30| Scale is weakly epimorphic with val: <8 12 19 19 26| Scale is weakly epimorphic with val: <8 12 19 19 29| Scale is weakly epimorphic with val: <8 12 19 20 27| Scale is weakly epimorphic with val: <8 12 19 20 30| Scale is weakly epimorphic with val: <8 12 19 21 25| Scale is weakly epimorphic with val: <8 12 19 21 28| Scale is weakly epimorphic with val: <8 12 19 22 26| Scale is weakly epimorphic with val: <8 12 19 22 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.6394 c. M: 54.1055 c. 5: 1 1 3 N M DE S SD: 28.0077 c. M:-45.5035 c. 6: 1 1 4 N M DE S SD: 19.1826 c. M:-28.9020 c. 7: 1 2 4 N T3 SD: 20.4469 c. M:-31.0441 c. 8: 1 2 5 N T3 SD: 5.3374 c. M:-8.1502 c. 11: 1 3 7 N T3 SD: 5.1519 c. M: 8.8286 c. 17: 2 4 11 N T3 SD: 4.6191 c. M: 6.6231 c. 19: 2 5 12 N T3 SD: 1.1550 c. M: 1.6797 c. 27: 3 7 17 N T3 SD: 1.3848 c. M:-2.0574 c. 46: 5 12 29 N T3 SD: 0.9565 c. M:-1.6564 c. 55: 6 14 35 N T3 SD: 0.7599 c. M: 1.2964 c. 63: 7 16 40 N T3 SD: 0.7861 c. M:-1.2329 c. 74: 8 19 47 N T3 SD: 0.4234 c. M: 0.6846 c. 82: 9 21 52 N T3 SD: 0.3407 c. M:-0.5580 c. 93: 10 24 59 N T3 SD: 0.3693 c. M: 0.5522 c. 101: 11 26 64 N T3 SD: 0.0839 c. M:-0.1371 c. 221: 24 57 140 N T3 SD: 0.0802 c. M:-0.1377 c. 295: 32 76 187 N T3 SD: 0.0610 c. M: 0.0802 c. 396: 43 102 251 N T3 SD: 0.0266 c. M: 0.0388 c. 497: 54 128 315 N T3 SD: 0.0130 c. M: 0.0210 c. 1013: 110 261 642 N T3 SD: 0.0136 c. M: 0.0236 c. 1095: 119 282 694 N T3 SD: 0.0143 c. M:-0.0200 c. 1114: 121 287 706 N T3 SD: 0.0057 c. M: 0.0090 c. 1215: 132 313 770 N T3 SD: 0.0049 c. M:-0.0078 c. 1611: 175 415 1021 N T3 SD: 0.0030 c. M: 0.0037 c. 1712: 186 441 1085 N T3 SD: 0.0027 c. M:-0.0046 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 x 14:17 SD: 31.8493 cents 14 x 16:19 SD: 28.7988 cents 15:16:17:20 SD: 22.3509 cents 16:17:18:21 S SD: 20.5252 cents 17:18:19:23 SD: 17.4907 cents 18:19:20:24 S SD: 13.1658 cents 21:22:23:28 SD: 12.1067 cents 24:25:27:32 SD: 9.0492 cents 25:26:28:33 SD: 8.7135 cents 26:27:29:35 SD: 7.0300 cents 27:28:30:36 S SD: 2.9518 cents 36:37:40:48 SD: 2.2238 cents 63:65:70:84 SD: 0.0000 cents