Scala analysis: 292_C21
Chromatic tetrachord 68/65 * 13/12 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/65 78.114034 Valentine semitone 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: 68/65 78.1140 Valentine semitone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/65 78.114 cents Valentine semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 65/51 419.931 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 : 78.1 216.7 498.0 78.1 : 138.6 419.9 498.0 216.7: 281.4 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.1140 .. 281.3583 cents 325/289, 203.2443 cents 68/65, 78.1140 cents 2: 216.6867 .. 419.9310 cents 325/289, 203.2443 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/65, 78.1140 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 2.125290 Largest / Average step : 1.694776 Largest / Smallest step : 3.601892 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 143.25874 cents, oct.: 429.77623 cents Scale is not proper Scale has trivalence property Scale is a mode of a 593-tone equal temperament with octave 4/3 degrees: 93 258 593 Least number of segments generator : 297 of 249.442 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 428 of 359.466 cents and inv. generated superset size: 22 = 19 more = 733.333% 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 : 1.085589 Lumma stability : 0.313683 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 : 845/816, 60.4586 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 : 65 (O: 65 U: 65) Highest odd numerator or denominator: 65 Scale harmonicity : 0.015788 Average absolute harmonicity : 0.085429 Specific harmonicity : 0.069204 Fundamental : 1/195, -7.6073 octaves, 1.3417 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.326000E+04, 13.69479 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 86.0, average 28.66667 Mersenne's string divisions : 4256 Sum of van Prooijen's expressibility: 3.52048, average 1.17349 Sum of Tenney's harmonic distance : 7.13114, average 2.37705 Vogel's harmonic complexity : 24.00000 Wille's k value : 110 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.51285, average 2.25214 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.66667 2 13: -1 .. 0 -0.33333 1 17: 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 15 26 32| Scale is weakly epimorphic with val: <6 10 15 27 28| Scale is weakly epimorphic with val: <6 10 16 26 33| Scale is weakly epimorphic with val: <6 10 16 27 29| Scale is weakly epimorphic with val: <6 10 17 27 30| Scale is weakly epimorphic with val: <6 10 17 30 30| Scale is weakly epimorphic with val: <6 10 18 27 31| Scale is weakly epimorphic with val: <6 10 18 30 31| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 10 19 30 32| Scale is weakly epimorphic with val: <6 11 15 25 31| Scale is weakly epimorphic with val: <6 11 15 27 29| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 16 27 30| Scale is weakly epimorphic with val: <6 11 16 30 30| Scale is weakly epimorphic with val: <6 11 17 25 33| Scale is weakly epimorphic with val: <6 11 17 27 31| Scale is weakly epimorphic with val: <6 11 17 30 31| Scale is weakly epimorphic with val: <6 11 18 27 32| Scale is weakly epimorphic with val: <6 11 18 30 32| Scale is weakly epimorphic with val: <6 11 19 27 33| Scale is weakly epimorphic with val: <6 11 19 30 33| Scale is weakly epimorphic with val: <7 10 15 25 28| Scale is weakly epimorphic with val: <7 10 15 26 30| Scale is weakly epimorphic with val: <7 10 15 28 28| Scale is weakly epimorphic with val: <7 10 15 29 33| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 16 28 29| Scale is weakly epimorphic with val: <7 10 17 25 30| Scale is weakly epimorphic with val: <7 10 17 26 32| Scale is weakly epimorphic with val: <7 10 17 28 30| Scale is weakly epimorphic with val: <7 10 18 25 31| Scale is weakly epimorphic with val: <7 10 18 26 33| Scale is weakly epimorphic with val: <7 10 18 28 31| Scale is weakly epimorphic with val: <7 10 19 25 32| Scale is weakly epimorphic with val: <7 10 19 28 32| Scale is JI-epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 15 29 31| Scale is weakly epimorphic with val: <7 11 15 30 30| Scale is weakly epimorphic with val: <7 11 15 30 33| Scale is JI-epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 16 27 31| Scale is weakly epimorphic with val: <7 11 16 29 29| Scale is weakly epimorphic with val: <7 11 16 29 32| Scale is weakly epimorphic with val: <7 11 16 30 31| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is JI-epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 17 27 32| Scale is weakly epimorphic with val: <7 11 17 29 30| Scale is weakly epimorphic with val: <7 11 17 29 33| Scale is weakly epimorphic with val: <7 11 17 30 32| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is JI-epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is JI-epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 29 29| Scale is weakly epimorphic with val: <7 11 19 29 32| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <7 12 15 25 30| Scale is weakly epimorphic with val: <7 12 15 27 31| Scale is weakly epimorphic with val: <7 12 15 28 30| Scale is weakly epimorphic with val: <7 12 16 25 31| Scale is weakly epimorphic with val: <7 12 16 27 32| Scale is weakly epimorphic with val: <7 12 16 28 31| Scale is weakly epimorphic with val: <7 12 17 25 32| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 17 28 32| Scale is weakly epimorphic with val: <7 12 18 25 33| Scale is weakly epimorphic with val: <7 12 18 28 33| Scale is weakly epimorphic with val: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 15 26 29| Scale is weakly epimorphic with val: <8 11 15 28 30| Scale is weakly epimorphic with val: <8 11 15 29 29| Scale is weakly epimorphic with val: <8 11 16 25 28| Scale is weakly epimorphic with val: <8 11 16 26 30| Scale is weakly epimorphic with val: <8 11 16 28 31| Scale is weakly epimorphic with val: <8 11 16 29 30| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 26 31| Scale is weakly epimorphic with val: <8 11 17 28 32| Scale is weakly epimorphic with val: <8 11 17 29 31| Scale is weakly epimorphic with val: <8 11 18 25 30| Scale is weakly epimorphic with val: <8 11 18 26 32| Scale is weakly epimorphic with val: <8 11 18 28 33| Scale is weakly epimorphic with val: <8 11 18 29 32| Scale is weakly epimorphic with val: <8 11 19 25 31| Scale is weakly epimorphic with val: <8 11 19 26 33| Scale is weakly epimorphic with val: <8 11 19 29 33| Scale is weakly epimorphic with val: <8 12 15 26 30| Scale is weakly epimorphic with val: <8 12 15 27 29| Scale is weakly epimorphic with val: <8 12 15 29 30| Scale is weakly epimorphic with val: <8 12 15 30 32| Scale is weakly epimorphic with val: <8 12 16 26 31| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 16 29 31| Scale is weakly epimorphic with val: <8 12 16 30 33| Scale is weakly epimorphic with val: <8 12 17 26 32| Scale is weakly epimorphic with val: <8 12 17 27 31| Scale is weakly epimorphic with val: <8 12 17 29 32| Scale is weakly epimorphic with val: <8 12 18 26 33| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 18 29 33| Scale is weakly epimorphic with val: <8 12 19 27 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.7569 c. M: 78.1140 c. 4: 1 1 2 P M ME S SD: 32.6512 c. M:-46.3972 c. 5: 1 1 3 N M DE S SD: 15.9915 c. M:-21.4950 c. 6: 1 2 3 P T3 SD: 18.8817 c. M:-32.3358 c. 7: 1 2 4 N T3 SD: 4.4346 c. M: 6.9647 c. 18: 3 5 10 N T3 SD: 3.9040 c. M:-4.8935 c. 25: 4 7 14 N T3 SD: 1.6825 c. M:-2.4531 c. 32: 5 9 18 N T3 SD: 0.7179 c. M:-1.2080 c. 69: 11 19 39 N T3 SD: 0.7463 c. M:-1.2844 c. 71: 11 20 40 N T3 SD: 0.7068 c. M: 0.9521 c. 76: 12 21 43 N T3 SD: 0.3918 c. M:-0.5247 c. 83: 13 23 47 N T3 SD: 0.3901 c. M: 0.6672 c. 108: 17 30 61 N T3 SD: 0.1659 c. M:-0.2819 c. 115: 18 32 65 N T3 SD: 0.1245 c. M: 0.1592 c. 223: 35 62 126 N T3 SD: 0.0420 c. M:-0.0545 c. 338: 53 94 191 N T3 SD: 0.0481 c. M: 0.0813 c. 370: 58 103 209 N T3 SD: 0.0299 c. M: 0.0421 c. 478: 75 133 270 N T3 SD: 0.0274 c. M:-0.0358 c. 593: 93 165 335 N T3 SD: 0.0034 c. M: 0.0058 c. 2002: 314 557 1131 N T3 SD: 0.0028 c. M: 0.0048 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: 26.1910 cents 13:14:15:17 SD: 22.6396 cents 14:15:16:19 SD: 17.8166 cents 15:16:17:20 SD: 11.2058 cents 21:22:24:28 S SD: 4.8962 cents 39:41:44:52 SD: 3.8487 cents 44:46:50:59 SD: 3.6350 cents 45:47:51:60 SD: 0.9437 cents 105:110:119:140 SD: 0.8077 cents 150:157:170:200 SD: 0.2828 cents 195:204:221:260 SD: 0.0000 cents