Scala analysis: 278_C20
Chromatic tetrachord 224/211 * 211/198 * 33/28
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 224/211 103.506880 2: 112/99 213.597962 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 224/211 103.5069 2: 211/198 110.0911 3: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 224/211 103.507 cents 1: 1 211/198 110.091 cents 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 264/211 387.954 cents 2: 1 211/168 394.538 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 : 103.5 213.6 498.0 103.5: 110.1 394.5 498.0 213.6: 284.4 388.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.5069 .. 284.4470 cents 6963/6272, 180.9402 cents 224/211, 103.5069 cents 2: 213.5980 .. 394.5381 cents 6963/6272, 180.9402 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 224/211, 103.5069 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 1.603903 Largest / Average step : 1.713382 Largest / Smallest step : 2.748098 Median interval of one step : 211/198, 110.0911 cents, amount: 1 Least squares average step : 144.63127 cents, oct.: 433.89381 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1891-tone equal temperament with octave 4/3 degrees: 393 811 1891 Least number of segments generator : 946 of 249.154 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1056 of 278.126 cents and inv. generated superset size: 45 = 42 more = 1500.000% 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 70.84907 cents Scale diversity : 1.119282 Lumma stability : 0.415653 Lumma impropriety factor : 0.142254 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 : 44521/44352, 6.5842 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 174.3560 cents: 2 -- Rational properties -- Prime limit : 211 Odd number limit : 211 (O: 211 U: 211) Highest odd numerator or denominator: 211 Scale harmonicity : 0.025773 Fundamental : 1/20889, -14.3505 octaves, 0.0125 Hz. Guide tone : 224, 7.8074 octaves, 58604.127 Hz. Exponens Consonantiae : 4.679136E+06, 22.15781 octaves Euler's gradus suavitatis : 236 Sum of Mann's harmonic distance : 326.5, average 108.83333 Mersenne's string divisions : 642495 Sum of van Prooijen's expressibility: 4.79704, average 1.59901 Sum of Tenney's harmonic distance : 9.79856, average 3.26619 Vogel's harmonic complexity : 159.33333 Wille's k value : 3481 Wilson's harmonic complexity : 235 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 20.43737, average 3.40623 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -2 .. 0 -1.00000 3 1 7: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 1 211: -1 .. 0 -0.33333 1 1 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 22 23 57| Scale is weakly epimorphic with val: <7 10 18 23 57| Scale is weakly epimorphic with val: <7 10 19 24 55| Scale is weakly epimorphic with val: <7 10 20 25 56| Scale is weakly epimorphic with val: <7 10 21 26 57| Scale is weakly epimorphic with val: <7 10 22 27 55| Scale is weakly epimorphic with val: <7 11 18 23 57| Scale is weakly epimorphic with val: <7 11 18 25 55| Scale is weakly epimorphic with val: <7 11 18 26 57| Scale is weakly epimorphic with val: <7 11 19 23 56| Scale is weakly epimorphic with val: <7 11 19 24 55| Scale is weakly epimorphic with val: <7 11 19 26 56| Scale is weakly epimorphic with val: <7 11 19 27 55| Scale is weakly epimorphic with val: <7 11 20 24 57| Scale is weakly epimorphic with val: <7 11 20 25 56| = patent Scale is weakly epimorphic with val: <7 11 20 27 57| Scale is weakly epimorphic with val: <7 11 21 23 57| Scale is JI-epimorphic with val: <7 11 21 25 55| Scale is weakly epimorphic with val: <7 11 21 26 57| Scale is weakly epimorphic with val: <7 11 22 23 56| Scale is weakly epimorphic with val: <7 11 22 24 55| Scale is JI-epimorphic with val: <7 11 22 26 56| Scale is weakly epimorphic with val: <7 11 22 27 55| Scale is weakly epimorphic with val: <7 12 22 23 56| Scale is weakly epimorphic with val: <8 11 18 24 55| Scale is weakly epimorphic with val: <8 11 18 25 57| Scale is weakly epimorphic with val: <8 11 18 27 55| Scale is weakly epimorphic with val: <8 11 19 25 56| Scale is weakly epimorphic with val: <8 11 19 26 55| Scale is weakly epimorphic with val: <8 11 20 23 57| Scale is weakly epimorphic with val: <8 11 20 26 57| Scale is weakly epimorphic with val: <8 11 20 27 56| Scale is weakly epimorphic with val: <8 12 18 23 56| Scale is weakly epimorphic with val: <8 12 18 24 55| Scale is weakly epimorphic with val: <8 12 18 27 55| Scale is weakly epimorphic with val: <8 12 19 24 57| Scale is weakly epimorphic with val: <8 12 19 25 56| Scale is weakly epimorphic with val: <8 12 20 23 57| Scale is weakly epimorphic with val: <8 12 20 25 55| Scale is weakly epimorphic with val: <8 12 20 26 57| Scale is weakly epimorphic with val: <8 12 21 26 56| Scale is weakly epimorphic with val: <8 12 22 27 57|
FIT/MODE
3: 0 1 2 N G T3 SD: 65.7719 c. M: 103.5069 c. 4: 1 1 2 P M ME S SD: 23.7773 c. M:-35.4245 c. 5: 1 1 3 N M DE S SD: 8.6019 c. M: 14.3800 c. 9: 2 2 5 N M DE S SD: 6.0979 c. M:-7.7554 c. 14: 3 3 8 N M DE S SD: 1.8594 c. M:-3.2170 c. 33: 7 7 19 N M DE S SD: 1.8160 c. M: 2.3061 c. 44: 9 10 25 N T3 SD: 1.2678 c. M: 1.6340 c. 49: 10 11 28 N T3 SD: 1.0803 c. M: 1.8650 c. 58: 12 13 33 N T3 SD: 0.6766 c. M:-1.0766 c. 63: 13 14 36 N T3 SD: 0.4335 c. M: 0.7357 c. 77: 16 17 44 N T3 SD: 0.0872 c. M: 0.1501 c. 289: 60 64 165 N T3 SD: 0.0828 c. M: 0.1065 c. 303: 63 67 173 N T3 SD: 0.0559 c. M:-0.0847 c. 380: 79 84 217 N T3 SD: 0.0291 c. M:-0.0371 c. 457: 95 101 261 N T3 SD: 0.0150 c. M:-0.0255 c. 534: 111 118 305 N T3 SD: 0.0148 c. M:-0.0193 c. 900: 187 199 514 N T3 SD: 0.0147 c. M: 0.0242 c. 977: 203 216 558 N T3 SD: 0.0139 c. M: 0.0236 c. 991: 206 219 566 N T3 SD: 0.0133 c. M:-0.0222 c. 1054: 219 233 602 N T3 SD: 0.0160 c. M: 0.0231 c. 1280: 266 283 731 N T3 SD: 0.0104 c. M:-0.0167 c. 1357: 282 300 775 N T3 SD: 0.0060 c. M: 0.0075 c. 1434: 298 317 819 N T3 SD: 0.0047 c. M: 0.0080 c. 1814: 377 401 1036 N T3 SD: 0.0039 c. M:-0.0068 c. 1891: 393 418 1080 N T3 SD: 0.0002 c. M:-0.0004 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: 66.2336 cents 6 x 7:8 S SD: 26.6365 cents 7 x 8:9 S SD: 32.6841 cents 8 x 9:11 SD: 27.0733 cents 9 x 10:12 S SD: 15.5971 cents 10 x 11:13 SD: 32.7205 cents 11:12 x 15 S SD: 30.5570 cents 12:13:14:16 S SD: 21.2593 cents 13:14:15:17 SD: 17.9830 cents 14:15:16:19 SD: 12.9177 cents 15:16:17:20 SD: 2.9284 cents 63:67:71:84 SD: 2.4368 cents 69:73:78:92 SD: 2.0323 cents 83:88:94:111 SD: 1.9882 cents 84:89:95:112 SD: 1.1507 cents 99:105:112:132 SD: 0.5467 cents 114:121:129:152 SD: 0.1765 cents 357:379:404:476 SD: 0.1733 cents 471:500:533:628 SD: 0.1655 cents 519:551:587:692 SD: 0.1510 cents