Scala analysis: 281_C20
Chromatic tetrachord 56/55 * 10/9 * 33/28
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/55 31.194250 undecimal diesis, konbini comma 2: 112/99 213.597962 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 56/55 31.1943 undecimal diesis, konbini comma 2: 10/9 182.4037 minor whole tone 3: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 10/9 182.404 cents minor whole tone 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 6/5 315.641 cents minor third 2: 1 55/42 466.851 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 : 31.2 213.6 498.0 31.2 : 182.4 466.9 498.0 213.6: 284.4 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 284.4470 cents 1815/1568, 253.2528 cents 56/55, 31.1943 cents 2: 213.5980 .. 466.8507 cents 1815/1568, 253.2528 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 5.321974 Largest / Average step : 1.713382 Largest / Smallest step : 9.118573 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 139.46608 cents, oct.: 418.39825 cents Scale is not proper Scale has trivalence property Scale is a mode of a 942-tone equal temperament with octave 4/3 degrees: 59 404 942 Least number of segments generator : 473 of 250.080 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 799 of 422.439 cents and inv. generated superset size: 17 = 14 more = 566.667% 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 31.19425 cents Scale diversity : 0.650832 Lumma stability : 0.125267 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 : 56/55, 31.1943 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 55 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.089049 Specific harmonicity : 0.097124 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 : 164.5, average 54.83333 Mersenne's string divisions : 163947 Sum of van Prooijen's expressibility: 4.21312, average 1.40437 Sum of Tenney's harmonic distance : 8.61259, average 2.87086 Vogel's harmonic complexity : 17.66667 Wille's k value : 82 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 17.72189, average 2.95365 Lattice compactness (without 2's) : 11.14966, average 1.85828 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 11: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 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 20 23| Scale is weakly epimorphic with val: <7 10 15 21 24| Scale is weakly epimorphic with val: <7 10 15 22 25| Scale is weakly epimorphic with val: <7 10 17 18 23| Scale is weakly epimorphic with val: <7 10 17 19 24| Scale is weakly epimorphic with val: <7 10 17 20 25| Scale is weakly epimorphic with val: <7 10 17 21 26| Scale is weakly epimorphic with val: <7 10 17 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 17 18 23| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 19 24| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is weakly epimorphic with val: <7 11 17 20 25| = patent Scale is weakly epimorphic with val: <7 11 17 21 23| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 22 24| Scale is weakly epimorphic with val: <7 11 17 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 20 23| Scale is weakly epimorphic with val: <7 12 15 21 24| Scale is weakly epimorphic with val: <7 12 15 22 25| Scale is weakly epimorphic with val: <7 12 16 22 23| Scale is weakly epimorphic with val: <7 12 19 22 23| Scale is weakly epimorphic with val: <8 11 15 18 24| Scale is weakly epimorphic with val: <8 11 15 19 25| Scale is weakly epimorphic with val: <8 11 15 20 26| Scale is weakly epimorphic with val: <8 11 15 21 27| Scale is weakly epimorphic with val: <8 11 16 18 25| Scale is weakly epimorphic with val: <8 11 16 19 26| Scale is weakly epimorphic with val: <8 11 16 20 27| Scale is weakly epimorphic with val: <8 11 18 20 23| Scale is weakly epimorphic with val: <8 11 18 21 24| Scale is weakly epimorphic with val: <8 11 18 22 25| Scale is weakly epimorphic with val: <8 11 19 19 26| Scale is weakly epimorphic with val: <8 11 19 20 27| Scale is weakly epimorphic with val: <8 12 15 18 24| Scale is weakly epimorphic with val: <8 12 15 19 25| Scale is weakly epimorphic with val: <8 12 15 20 26| Scale is weakly epimorphic with val: <8 12 15 21 27| Scale is weakly epimorphic with val: <8 12 17 18 23| Scale is weakly epimorphic with val: <8 12 17 19 24| Scale is weakly epimorphic with val: <8 12 17 20 25| Scale is weakly epimorphic with val: <8 12 17 21 26| Scale is weakly epimorphic with val: <8 12 17 22 27| Scale is weakly epimorphic with val: <8 12 18 20 23| Scale is weakly epimorphic with val: <8 12 18 21 24| Scale is weakly epimorphic with val: <8 12 18 22 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.8492 c. M: 47.5830 c. 4: 0 2 2 P M DE S SD: 27.2518 c. M:-35.4245 c. 5: 0 2 3 N G T3 SD: 19.8315 c. M: 31.1943 c. 7: 0 3 4 N G T3 SD: 18.0102 c. M: 31.1943 c. 9: 1 3 5 N T3 SD: 14.6411 c. M:-24.1441 c. 11: 1 4 6 N T3 SD: 10.9819 c. M:-14.0826 c. 12: 1 4 7 N T3 SD: 6.9100 c. M:-10.3095 c. 14: 1 5 8 N T3 SD: 2.5305 c. M:-4.3804 c. 16: 1 6 9 N T3 SD: 2.4810 c. M:-4.2967 c. 30: 2 11 17 N T3 SD: 1.7292 c. M:-2.2215 c. 33: 2 12 19 N T3 SD: 1.4535 c. M: 2.3061 c. 47: 3 17 27 N T3 SD: 1.0204 c. M: 1.6639 c. 49: 3 18 28 N T3 SD: 0.4143 c. M: 0.7017 c. 63: 4 23 36 N T3 SD: 0.2617 c. M:-0.4277 c. 112: 7 41 64 N T3 SD: 0.0948 c. M: 0.1501 c. 240: 15 88 137 N T3 SD: 0.0928 c. M:-0.1463 c. 287: 18 105 164 N T3 SD: 0.0900 c. M: 0.1501 c. 303: 19 111 173 N T3 SD: 0.0532 c. M:-0.0847 c. 352: 22 129 201 N T3 SD: 0.0487 c. M: 0.0664 c. 415: 26 152 237 N T3 SD: 0.0133 c. M:-0.0213 c. 527: 33 193 301 N T3 SD: 0.0097 c. M: 0.0151 c. 942: 59 345 538 N T3 SD: 0.0006 c. M:-0.0010 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 x 12:15 S SD: 37.0059 cents 12 x 14:16 S SD: 26.6365 cents 13 x 15:17 SD: 23.9576 cents 18:19:20:24 S SD: 23.2569 cents 20:21:23:27 SD: 21.3567 cents 21:22:24:28 S SD: 17.4599 cents 22:23:25:29 SD: 16.8164 cents 23:24:26:31 SD: 15.4819 cents 24:25:27:32 SD: 13.5498 cents 28:29:32:37 SD: 12.5770 cents 29:30:33:39 SD: 10.9489 cents 30:31:34:40 SD: 8.5862 cents 33:34:37:44 SD: 8.5690 cents 36:37:41:48 SD: 6.6436 cents 37:38:42:49 SD: 6.6341 cents 38:39:43:51 SD: 5.9517 cents 39:40:44:52 SD: 4.5015 cents 45:46:51:60 SD: 2.5067 cents 54:55:61:72 SD: 0.8803 cents 114:116:129:152 SD: 0.3863 cents 168:171:190:224 SD: 0.2603 cents 327:333:370:436 SD: 0.1337 cents 381:388:431:508 SD: 0.1155 cents 441:449:499:588 SD: 0.1077 cents 495:504:560:660 SD: 0.0000 cents