Scala analysis: 054_E3
Enharmonic tetrachord 240/233 * 466/459 * 51/40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 240/233 51.245341 2: 160/153 77.448303 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 51/40 420.5967 septendecimal diminished fourth 1: 240/233 51.2453 2: 466/459 26.2030 3: 51/40 420.5967 septendecimal diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 466/459 26.203 cents 1: 1 240/233 51.245 cents 1: 1 51/40 420.597 cents septendecimal diminished fourth 2: 1 160/153 77.448 cents 2: 1 233/180 446.800 cents 2: 1 306/233 471.842 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 : 51.2 77.4 498.0 51.2 : 26.2 446.8 498.0 77.4 : 420.6 471.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.2030 .. 420.5967 cents 23409/18640, 394.3937 cents 466/459, 26.2030 cents 2: 77.4483 .. 471.8420 cents 23409/18640, 394.3937 cents 6400/7803,-343.1484 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 466/459, 26.2030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 51/40, 420.5967 cents Average / Smallest step : 6.335734 Largest / Average step : 2.533486 Largest / Smallest step : 16.051495 Median interval of one step : 240/233, 51.2453 cents, amount: 1 Least squares average step : 121.44835 cents, oct.: 364.34506 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2148-tone equal temperament with octave 4/3 degrees: 221 334 2148 Least number of segments generator : 1075 of 249.254 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2035 of 471.844 cents and inv. generated superset size: 99 = 96 more = 3300.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 26.20296 cents Scale diversity : 0.236173 Lumma stability : 0.105223 Lumma impropriety factor : 0.688991 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 : 55080/54289, 25.0424 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 394.3937 cents: 2 -- Rational properties -- Prime limit : 233 Odd number limit : 459 (O: 233 U: 459) Highest odd numerator or denominator: 233 Scale harmonicity : 0.020195 Fundamental : 1/35649, -15.1216 octaves, 0.0073 Hz. Guide tone : 480, 8.9069 octaves, 125580.271 Hz. Exponens Consonantiae : 1.711152E+07, 24.02846 octaves Euler's gradus suavitatis : 264 Sum of Mann's harmonic distance : 396.5, average 132.16667 Mersenne's string divisions : 1036343 Sum of van Prooijen's expressibility: 5.02917, average 1.67639 Sum of Tenney's harmonic distance : 10.21556, average 3.40519 Vogel's harmonic complexity : 177.66667 Wille's k value : 5941 Wilson's harmonic complexity : 264 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 21.82720, average 3.63787 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 233: -1 .. 0 -0.33333 1 1 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: <7 10 15 27 57| Scale is weakly epimorphic with val: <7 10 16 28 58| Scale is weakly epimorphic with val: <7 10 17 29 56| Scale is weakly epimorphic with val: <7 10 18 30 57| Scale is weakly epimorphic with val: <7 10 19 31 58| Scale is weakly epimorphic with val: <7 11 15 27 58| Scale is weakly epimorphic with val: <7 11 15 29 56| Scale is weakly epimorphic with val: <7 11 15 30 58| Scale is weakly epimorphic with val: <7 11 15 32 56| Scale is weakly epimorphic with val: <7 11 15 33 58| Scale is weakly epimorphic with val: <7 11 16 27 57| Scale is weakly epimorphic with val: <7 11 16 28 56| Scale is weakly epimorphic with val: <7 11 16 30 57| Scale is weakly epimorphic with val: <7 11 16 31 56| Scale is weakly epimorphic with val: <7 11 16 33 57| Scale is weakly epimorphic with val: <7 11 17 28 58| Scale is weakly epimorphic with val: <7 11 17 29 57| Scale is weakly epimorphic with val: <7 11 17 31 58| Scale is weakly epimorphic with val: <7 11 17 32 57| Scale is weakly epimorphic with val: <7 11 18 27 58| Scale is JI-epimorphic with val: <7 11 18 29 56| Scale is weakly epimorphic with val: <7 11 18 30 58| Scale is weakly epimorphic with val: <7 11 18 32 56| Scale is weakly epimorphic with val: <7 11 18 33 58| Scale is weakly epimorphic with val: <7 11 19 27 57| Scale is weakly epimorphic with val: <7 11 19 28 56| Scale is JI-epimorphic with val: <7 11 19 30 57| Scale is weakly epimorphic with val: <7 11 19 31 56| Scale is weakly epimorphic with val: <7 11 19 33 57| Scale is weakly epimorphic with val: <7 12 19 27 58| Scale is weakly epimorphic with val: <7 12 19 29 56| Scale is weakly epimorphic with val: <7 12 19 32 56| Scale is weakly epimorphic with val: <8 11 15 30 57| Scale is weakly epimorphic with val: <8 11 16 27 56| Scale is weakly epimorphic with val: <8 11 16 30 56| Scale is weakly epimorphic with val: <8 11 16 31 58| Scale is weakly epimorphic with val: <8 11 16 33 56| Scale is weakly epimorphic with val: <8 11 17 28 57| Scale is weakly epimorphic with val: <8 11 17 31 57| Scale is weakly epimorphic with val: <8 11 17 32 56| Scale is weakly epimorphic with val: <8 11 18 29 58| Scale is weakly epimorphic with val: <8 11 18 32 58| Scale is weakly epimorphic with val: <8 11 18 33 57| Scale is weakly epimorphic with val: <8 12 15 28 57| Scale is weakly epimorphic with val: <8 12 15 29 56| Scale is weakly epimorphic with val: <8 12 15 32 56| Scale is weakly epimorphic with val: <8 12 16 27 57| Scale is weakly epimorphic with val: <8 12 16 29 58| Scale is weakly epimorphic with val: <8 12 16 30 57| Scale is weakly epimorphic with val: <8 12 16 33 57| Scale is weakly epimorphic with val: <8 12 17 28 58| Scale is weakly epimorphic with val: <8 12 17 30 56| Scale is weakly epimorphic with val: <8 12 17 31 58| Scale is weakly epimorphic with val: <8 12 18 31 57| Scale is weakly epimorphic with val: <8 12 19 32 58|
FIT/MODE
3: 0 0 3 N M DE S SD: 53.6169 c. M: 77.4483 c. 4: 0 1 3 N G T3 SD: 40.1705 c. M: 51.2453 c. 5: 1 0 4 N G T3 SD: 30.7145 c. M:-48.3637 c. 6: 1 0 5 N G T3 SD: 18.6167 c. M:-31.7622 c. 7: 1 0 6 N G T3 SD: 12.0533 c. M:-19.9039 c. 8: 1 0 7 N G T3 SD: 10.8327 c. M: 15.1927 c. 11: 1 1 9 N M DE S SD: 8.3141 c. M:-13.1053 c. 12: 1 1 10 N M DE S SD: 6.4757 c. M: 9.7416 c. 13: 1 1 11 N M DE S SD: 7.4828 c. M: 12.9342 c. 17: 2 1 14 N T3 SD: 7.3718 c. M:-10.4420 c. 18: 2 1 15 N T3 SD: 3.9857 c. M:-5.5592 c. 19: 2 1 16 N T3 SD: 0.9679 c. M:-1.1904 c. 39: 4 2 33 N T3 SD: 0.4862 c. M: 0.8260 c. 58: 6 3 49 N T3 SD: 0.1861 c. M:-0.2766 c. 193: 20 10 163 N T3 SD: 0.2119 c. M:-0.3655 c. 213: 22 11 180 N T3 SD: 0.2003 c. M: 0.2864 c. 225: 23 12 190 N T3 SD: 0.1934 c. M: 0.3341 c. 244: 25 13 206 N T3 SD: 0.1416 c. M: 0.2161 c. 263: 27 14 222 N T3 SD: 0.1301 c. M:-0.1937 c. 283: 29 15 239 N T3 SD: 0.1209 c. M: 0.2089 c. 302: 31 16 255 N T3 SD: 0.0788 c. M: 0.1215 c. 321: 33 17 271 N T3 SD: 0.0787 c. M:-0.1288 c. 341: 35 18 288 N T3 SD: 0.0764 c. M: 0.1264 c. 360: 37 19 304 N T3 SD: 0.0362 c. M: 0.0574 c. 418: 43 22 353 N T3 SD: 0.0064 c. M: 0.0110 c. 1312: 135 69 1108 N T3 SD: 0.0049 c. M: 0.0084 c. 1730: 178 91 1461 N T3 SD: 0.0039 c. M: 0.0066 c. 2148: 221 113 1814 N T3 SD: 0.0037 c. M: 0.0056 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 94.7113 cents 7 x 8:9 S SD: 83.0598 cents 8 x 9:11 SD: 68.6123 cents 9 x 10:12 S SD: 52.4777 cents 10 x 11:13 SD: 48.9571 cents 11 x 12:15 S SD: 41.4435 cents 12 x 13:16 SD: 30.5622 cents 13 x 14:17 SD: 30.4788 cents 14 x 15:19 SD: 25.9927 cents 15 x 16:20 S SD: 17.1415 cents 16 x 17:21 SD: 19.3647 cents 17 x 18:23 SD: 16.5929 cents 18 x 19:24 SD: 8.0774 cents 19 x 20:25 S SD: 12.7934 cents 20 x 21:27 SD: 11.3113 cents 21 x 22:28 SD: 1.5444 cents 22 x 23:29 SD: 9.8959 cents 23 x 24:31 SD: 9.5458 cents 24 x 25:32 SD: 3.3879 cents 25 x 26:33 SD: 9.9236 cents 26 x 27:35 SD: 10.2608 cents 27:28 x 36 SD: 5.8578 cents 28:29 x 37 SD: 9.1028 cents 29:30 x 39 SD: 8.3108 cents 30:31 x 40 SD: 2.7608 cents 31:32 x 41 SD: 7.2516 cents 32:33 x 43 SD: 6.8122 cents 36:37:38:48 SD: 5.5327 cents 39:40:41:52 SD: 3.9208 cents 42:43:44:56 SD: 3.6510 cents 50 x 52:67 SD: 6.4367 cents 51 x 53:68 SD: 5.4271 cents 52 x 54:69 SD: 7.3533 cents 53:55 x 71 SD: 7.6209 cents 54:56 x 72 SD: 5.8578 cents 57:59:60:76 SD: 4.7190 cents 59:61:62:79 SD: 4.2978 cents 60:62:63:80 SD: 2.9768 cents 63:65:66:84 SD: 1.4032 cents 66:68:69:88 SD: 0.2194 cents 369:380:386:492 SD: 0.2189 cents 435:448:455:580 SD: 0.1526 cents 501:516:524:668 SD: 0.1038 cents 567:584:593:756 SD: 0.0665 cents