Scala analysis: 282_C20
Chromatic tetrachord 16/15 * 35/33 * 33/28
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 112/99 213.597962 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 16/15 111.7313 minor diatonic semitone 2: 35/33 101.8667 3: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/33 101.867 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 5/4 386.314 cents major third 2: 1 44/35 396.178 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 : 111.7 213.6 498.0 111.7: 101.9 386.3 498.0 213.6: 284.4 396.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8667 .. 284.4470 cents 1089/980, 182.5804 cents 35/33, 101.8667 cents 2: 213.5980 .. 396.1783 cents 1089/980, 182.5804 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 35/33, 101.8667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 1.629728 Largest / Average step : 1.713382 Largest / Smallest step : 2.792346 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 145.21873 cents, oct.: 435.65619 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1413-tone equal temperament with octave 4/3 degrees: 317 606 1413 Least number of segments generator : 707 of 249.199 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1240 of 437.067 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 70.84907 cents Scale diversity : 1.122851 Lumma stability : 0.409066 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 : 176/175, 9.8646 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 182.5804 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 35 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.105756 Specific harmonicity : 0.118868 Fundamental : 1/495, -8.9513 octaves, 0.5285 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 5.544000E+04, 15.75864 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 124.5, average 41.50000 Mersenne's string divisions : 45787 Sum of van Prooijen's expressibility: 3.64885, average 1.21628 Sum of Tenney's harmonic distance : 7.50425, average 2.50142 Vogel's harmonic complexity : 18.33333 Wille's k value : 82 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 18.05094, average 3.00849 Lattice compactness (without 2's) : 9.59575, average 1.59929 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.33333 10 3: -2 ..-1 -1.33333 4 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 16 22 23| Scale is weakly epimorphic with val: <6 10 19 22 23| Scale is weakly epimorphic with val: <7 10 15 18 24| Scale is weakly epimorphic with val: <7 10 15 18 27| Scale is weakly epimorphic with val: <7 10 15 19 25| Scale is weakly epimorphic with val: <7 10 15 20 23| Scale is weakly epimorphic with val: <7 10 15 20 26| Scale is weakly epimorphic with val: <7 10 15 21 24| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 15 22 25| Scale is weakly epimorphic with val: <7 10 16 18 23| Scale is weakly epimorphic with val: <7 10 16 19 24| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 16 21 26| Scale is weakly epimorphic with val: <7 10 16 22 27| Scale is weakly epimorphic with val: <7 10 19 19 24| Scale is weakly epimorphic with val: <7 10 19 20 25| Scale is weakly epimorphic with val: <7 10 19 21 26| Scale is weakly epimorphic with val: <7 10 19 22 27| Scale is weakly epimorphic with val: <7 11 15 18 23| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 19 24| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 21 23| Scale is weakly epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 16 18 25| Scale is JI-epimorphic with val: <7 11 16 19 23| Scale is weakly epimorphic with val: <7 11 16 19 26| Scale is JI-epimorphic with val: <7 11 16 20 24| Scale is weakly epimorphic with val: <7 11 16 20 27| Scale is JI-epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 16 22 23| Scale is JI-epimorphic with val: <7 11 16 22 26| Scale is weakly epimorphic with val: <7 11 18 18 23| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 19 24| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 21 23| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 18 22 24| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 19 19 23| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 20 24| Scale is weakly epimorphic with val: <7 11 19 20 27| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is weakly epimorphic with val: <7 11 19 22 23| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 12 15 22 23| Scale is weakly epimorphic with val: <7 12 18 22 23| Scale is weakly epimorphic with val: <8 11 17 18 25| Scale is weakly epimorphic with val: <8 11 17 19 26| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 18 18 24| Scale is weakly epimorphic with val: <8 11 18 18 27| Scale is weakly epimorphic with val: <8 11 18 19 25| Scale is weakly epimorphic with val: <8 11 18 20 23| Scale is weakly epimorphic with val: <8 11 18 20 26| Scale is weakly epimorphic with val: <8 11 18 21 24| Scale is weakly epimorphic with val: <8 11 18 21 27| Scale is weakly epimorphic with val: <8 11 18 22 25| Scale is weakly epimorphic with val: <8 12 15 18 23| Scale is weakly epimorphic with val: <8 12 15 19 24| Scale is weakly epimorphic with val: <8 12 15 20 25| Scale is weakly epimorphic with val: <8 12 15 21 26| Scale is weakly epimorphic with val: <8 12 15 22 27| Scale is weakly epimorphic with val: <8 12 17 18 24| Scale is weakly epimorphic with val: <8 12 17 18 27| Scale is weakly epimorphic with val: <8 12 17 19 25| Scale is weakly epimorphic with val: <8 12 17 20 23| Scale is weakly epimorphic with val: <8 12 17 20 26| Scale is weakly epimorphic with val: <8 12 17 21 24| Scale is weakly epimorphic with val: <8 12 17 21 27| Scale is weakly epimorphic with val: <8 12 17 22 25| Scale is weakly epimorphic with val: <8 12 18 18 23| Scale is weakly epimorphic with val: <8 12 18 19 24| Scale is weakly epimorphic with val: <8 12 18 20 25| Scale is weakly epimorphic with val: <8 12 18 21 26| Scale is weakly epimorphic with val: <8 12 18 22 27|
FIT/MODE
3: 1 0 2 N G T3 SD: 41.6768 c. M:-54.2837 c. 4: 1 1 2 P M ME S SD: 21.7426 c. M:-35.4245 c. 5: 1 1 3 N M DE S SD: 10.8587 c. M: 14.3800 c. 9: 2 2 5 N M DE S SD: 4.5188 c. M:-7.7554 c. 14: 3 3 8 N M DE S SD: 2.8923 c. M: 5.0074 c. 23: 5 5 13 N M DE S SD: 2.6229 c. M: 3.4606 c. 26: 6 5 15 N T3 SD: 2.4891 c. M:-3.2022 c. 30: 7 6 17 N T3 SD: 2.8867 c. M:-4.4792 c. 31: 7 6 18 N T3 SD: 2.7692 c. M: 4.7404 c. 35: 8 7 20 N T3 SD: 1.2199 c. M:-2.1076 c. 40: 9 8 23 N T3 SD: 1.1297 c. M: 1.9288 c. 44: 10 9 25 N T3 SD: 1.1952 c. M:-1.4669 c. 49: 11 10 28 N T3 SD: 0.0968 c. M: 0.1501 c. 205: 46 42 117 N T3 SD: 0.1146 c. M:-0.1970 c. 254: 57 52 145 N T3 SD: 0.0777 c. M:-0.1300 c. 303: 68 62 173 N T3 SD: 0.0544 c. M:-0.0847 c. 352: 79 72 201 N T3 SD: 0.0400 c. M:-0.0520 c. 401: 90 82 229 N T3 SD: 0.0326 c. M:-0.0494 c. 450: 101 92 257 N T3 SD: 0.0305 c. M:-0.0521 c. 660: 148 135 377 N T3 SD: 0.0371 c. M: 0.0485 c. 709: 159 145 405 N T3 SD: 0.0368 c. M: 0.0498 c. 753: 169 154 430 N T3 SD: 0.0355 c. M:-0.0477 c. 767: 172 157 438 N T3 SD: 0.0329 c. M: 0.0445 c. 816: 183 167 466 N T3 SD: 0.0257 c. M: 0.0374 c. 865: 194 177 494 N T3 SD: 0.0197 c. M: 0.0310 c. 914: 205 187 522 N T3 SD: 0.0150 c. M: 0.0254 c. 963: 216 197 550 N T3 SD: 0.0118 c. M: 0.0203 c. 1012: 227 207 578 N T3 SD: 0.0106 c. M: 0.0157 c. 1315: 295 269 751 N T3 SD: 0.0072 c. M:-0.0122 c. 1364: 306 279 779 N T3 SD: 0.0037 c. M:-0.0064 c. 1413: 317 289 807 N T3 SD: 0.0017 c. M:-0.0028 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: 27.5105 cents 12:13:14:16 S SD: 19.8843 cents 13:14:15:17 SD: 16.8995 cents 14:15:16:19 SD: 12.0523 cents 15:16:17:20 SD: 1.0296 cents 138:147:156:184 SD: 0.9036 cents 153:163:173:204 SD: 0.7698 cents 168:179:190:224 SD: 0.6702 cents 183:195:207:244 SD: 0.5976 cents 198:211:224:264 SD: 0.5467 cents 213:227:241:284 SD: 0.5134 cents 228:243:258:304 SD: 0.4937 cents 243:259:275:324 SD: 0.4846 cents 252:269:285:336 SD: 0.4670 cents 267:285:302:356 SD: 0.4213 cents 282:301:319:376 SD: 0.3875 cents 297:317:336:396 SD: 0.3642 cents 312:333:353:416 SD: 0.3502 cents 327:349:370:436 SD: 0.3440 cents 375:400:424:500 SD: 0.3299 cents 390:416:441:520 SD: 0.2775 cents 405:432:458:540 SD: 0.2290 cents 420:448:475:560 SD: 0.1840 cents 435:464:492:580 SD: 0.1422 cents 450:480:509:600 SD: 0.1031 cents 465:496:526:620 SD: 0.0665 cents 480:512:543:640 SD: 0.0322 cents 495:528:560:660 SD: 0.0000 cents