Scala analysis: 333_C26
Chromatic tetrachord 31/29 * 29/27 * 36/31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 31/29 115.458378 2: 31/27 239.170570 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/31 258.8744 1: 31/29 115.4584 2: 29/27 123.7122 3: 36/31 258.8744
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 31/29 115.458 cents 1: 1 29/27 123.712 cents 1: 1 36/31 258.874 cents 2: 1 31/27 239.171 cents 2: 1 36/29 374.333 cents 2: 1 116/93 382.587 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 : 115.5 239.2 498.0 115.5: 123.7 382.6 498.0 239.2: 258.9 374.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 115.4584 .. 258.8744 cents 1044/961, 143.4161 cents 31/29, 115.4584 cents 2: 239.1706 .. 382.5866 cents 1044/961, 143.4161 cents 961/972,-19.7039 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 31/29, 115.4584 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 36/31, 258.8744 cents Average / Smallest step : 1.437877 Largest / Average step : 1.559344 Largest / Smallest step : 2.242145 Median interval of one step : 29/27, 123.7122 cents, amount: 1 Least squares average step : 149.13818 cents, oct.: 447.41454 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1087-tone equal temperament with octave 4/3 degrees: 252 522 1087 Least number of segments generator : 544 of 249.252 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1069 of 489.798 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 19.70386 cents Scale diversity : 1.132910 Lumma stability : 0.463646 Lumma impropriety factor : 0.039562 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 : 841/837, 8.2538 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% Limited inverse transpositions with margin 135.1622 cents: 2 -- Rational properties -- Prime limit : 31 Odd number limit : 93 (O: 31 U: 93) Highest odd numerator or denominator: 31 Scale harmonicity : 0.015608 Fundamental : 1/783, -9.6129 octaves, 0.3341 Hz. Guide tone : 124, 6.9542 octaves, 32441.570 Hz. Exponens Consonantiae : 9.709200E+04, 16.56706 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 62.5, average 20.83333 Mersenne's string divisions : 12180 Sum of van Prooijen's expressibility: 3.45984, average 1.15328 Sum of Tenney's harmonic distance : 6.95567, average 2.31856 Vogel's harmonic complexity : 45.66667 Wille's k value : 449 Wilson's harmonic complexity : 69 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.67626, average 2.44604 Lattice compactness (without 2's) : 11.57649, average 1.92942 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -3 .. 0 -1.33333 4 1 29: -1 .. 0 -0.33333 1 31: 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 32 33| Scale is weakly epimorphic with val: <6 10 34 37| Scale is weakly epimorphic with val: <6 11 32 35| Scale is weakly epimorphic with val: <6 11 34 36| Scale is weakly epimorphic with val: <6 11 35 38| Scale is weakly epimorphic with val: <7 10 32 35| Scale is weakly epimorphic with val: <7 10 35 38| Scale is weakly epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 11 32 37| Scale is JI-epimorphic with val: <7 11 34 35| Scale is weakly epimorphic with val: <7 11 34 38| Scale is weakly epimorphic with val: <7 11 35 37| Scale is weakly epimorphic with val: <7 11 37 38| Scale is weakly epimorphic with val: <7 12 32 39| Scale is weakly epimorphic with val: <7 12 34 37| Scale is weakly epimorphic with val: <7 12 35 39| Scale is weakly epimorphic with val: <7 12 38 39| Scale is weakly epimorphic with val: <8 11 32 36| Scale is weakly epimorphic with val: <8 11 34 37| Scale is weakly epimorphic with val: <8 11 35 36| Scale is weakly epimorphic with val: <8 12 32 35| Scale is weakly epimorphic with val: <8 12 34 39| Scale is weakly epimorphic with val: <8 12 35 38| Scale is weakly epimorphic with val: <8 12 37 39|
FIT/MODE
3: 1 0 2 N G T3 SD: 51.3410 c. M: 73.1556 c. 4: 1 1 2 P M ME S SD: 7.7247 c. M:-9.8519 c. 13: 3 3 7 N M DE S SD: 5.3800 c. M: 9.3036 c. 17: 4 4 9 N M DE S SD: 2.9436 c. M: 4.7965 c. 21: 5 5 11 N M DE S SD: 2.1434 c. M:-3.1238 c. 25: 6 6 13 N M DE S SD: 2.3521 c. M:-4.0724 c. 31: 7 8 16 N T3 SD: 2.0239 c. M: 2.9966 c. 35: 8 9 18 N T3 SD: 1.8361 c. M:-2.7370 c. 39: 9 10 20 N T3 SD: 2.0243 c. M:-3.4667 c. 44: 10 11 23 N T3 SD: 1.5588 c. M: 2.2663 c. 48: 11 12 25 N T3 SD: 0.8216 c. M: 1.3231 c. 52: 12 13 27 N T3 SD: 0.3419 c. M: 0.5249 c. 73: 17 18 38 N T3 SD: 0.3747 c. M:-0.5247 c. 121: 28 30 63 N T3 SD: 0.2802 c. M: 0.4383 c. 125: 29 31 65 N T3 SD: 0.0809 c. M: 0.1090 c. 177: 41 44 92 N T3 SD: 0.0532 c. M: 0.0920 c. 302: 70 75 157 N T3 SD: 0.0268 c. M: 0.0430 c. 608: 141 151 316 N T3 SD: 0.0275 c. M:-0.0422 c. 660: 153 164 343 N T3 SD: 0.0243 c. M:-0.0420 c. 781: 181 194 406 N T3 SD: 0.0273 c. M: 0.0344 c. 785: 182 195 408 N T3 SD: 0.0124 c. M:-0.0179 c. 962: 223 239 500 N T3 SD: 0.0098 c. M:-0.0153 c. 1087: 252 270 565 N T3 SD: 0.0022 c. M:-0.0038 c. 2351: 545 584 1222 N T3 SD: 0.0021 c. M: 0.0035 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: 56.9703 cents 6 x 7:8 S SD: 13.8502 cents 7 x 8:9 S SD: 31.7333 cents 8 x 9:11 SD: 31.9426 cents 9 x 10:12 S SD: 28.3834 cents 10:11 x 13 SD: 33.0755 cents 11:12:13:15 SD: 24.1641 cents 12:13:14:16 S SD: 12.0258 cents 14:15:16:19 SD: 10.6393 cents 15:16:17:20 SD: 7.5969 cents 26:28:30:35 S SD: 7.5482 cents 27:29:31:36 SD: 2.7513 cents 60:64:69:80 SD: 1.5519 cents 75:80:86:100 SD: 1.4487 cents 87:93:100:116 SD: 0.6416 cents 102:109:117:136 SD: 0.5774 cents 162:173:186:216 SD: 0.5748 cents 189:202:217:252 SD: 0.0985 cents 405:433:465:540 SD: 0.0919 cents 594:635:682:792 SD: 0.0313 cents