Scala analysis: 136_C2
Chromatic tetrachord 21/20 * 40/39 * 26/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 14/13 128.298245 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 26/21 369.7468 1: 21/20 84.4672 minor semitone 2: 40/39 43.8311 tridecimal minor diesis 3: 26/21 369.7468
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 21/20 84.467 cents minor semitone 1: 1 26/21 369.747 cents 2: 1 14/13 128.298 cents 2/3-tone 2: 1 80/63 413.578 cents wide major third 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 84.5 128.3 498.0 84.5 : 43.8 413.6 498.0 128.3: 369.7 454.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 369.7468 cents 169/140, 325.9157 cents 40/39, 43.8311 cents 2: 128.2982 .. 454.2139 cents 169/140, 325.9157 cents 147/169,-241.4485 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 26/21, 369.7468 cents Average / Smallest step : 3.787612 Largest / Average step : 2.227189 Largest / Smallest step : 8.435726 Median interval of one step : 21/20, 84.4672 cents, amount: 1 Least squares average step : 131.08562 cents, oct.: 393.25686 cents Scale is not proper Scale has trivalence property Scale is a mode of a 625-tone equal temperament with octave 4/3 degrees: 106 161 625 Least number of segments generator : 313 of 249.421 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 511 of 407.202 cents and inv. generated superset size: 27 = 24 more = 900.000% 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 43.83105 cents Scale diversity : 0.597791 Lumma stability : 0.176012 Lumma impropriety factor : 0.484793 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 : 819/800, 40.6361 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 class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.020759 Average absolute harmonicity : 0.097007 Specific harmonicity : 0.102692 Fundamental : 1/780, -9.6073 octaves, 0.3354 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 6.552000E+04, 15.99965 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 37.5, average 12.50000 Mersenne's string divisions : 7749 Sum of van Prooijen's expressibility: 2.91328, average 0.97109 Sum of Tenney's harmonic distance : 5.96250, average 1.98750 Vogel's harmonic complexity : 22.00000 Wille's k value : 409 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.76839, average 2.79473 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 20 25| Scale is weakly epimorphic with val: <6 10 15 20 28| Scale is weakly epimorphic with val: <6 10 16 21 26| Scale is weakly epimorphic with val: <6 10 16 21 29| Scale is weakly epimorphic with val: <6 10 16 22 25| Scale is weakly epimorphic with val: <6 10 17 22 27| Scale is weakly epimorphic with val: <6 10 17 22 30| Scale is weakly epimorphic with val: <6 10 19 22 25| Scale is weakly epimorphic with val: <6 11 15 19 26| Scale is weakly epimorphic with val: <6 11 15 19 29| Scale is weakly epimorphic with val: <6 11 16 20 27| Scale is weakly epimorphic with val: <6 11 16 20 30| Scale is weakly epimorphic with val: <6 11 16 22 25| Scale is weakly epimorphic with val: <6 11 17 21 25| Scale is weakly epimorphic with val: <6 11 17 21 28| Scale is weakly epimorphic with val: <6 11 18 22 26| Scale is weakly epimorphic with val: <6 11 18 22 29| Scale is weakly epimorphic with val: <6 11 19 22 25| Scale is weakly epimorphic with val: <7 10 15 21 25| Scale is weakly epimorphic with val: <7 10 15 22 27| Scale is weakly epimorphic with val: <7 10 15 22 30| Scale is weakly epimorphic with val: <7 10 16 22 26| Scale is weakly epimorphic with val: <7 10 18 21 25| Scale is weakly epimorphic with val: <7 10 19 22 26| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 19 30| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 20 29| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is weakly epimorphic with val: <7 11 16 18 30| Scale is JI-epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 21 30| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 18 29| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 19 28| Scale is JI-epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 21 29| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 19 30| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 20 29| Scale is JI-epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 11 19 21 30| Scale is weakly epimorphic with val: <7 12 15 20 26| Scale is weakly epimorphic with val: <7 12 15 20 29| Scale is weakly epimorphic with val: <7 12 15 21 25| Scale is weakly epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 21 30| Scale is weakly epimorphic with val: <7 12 16 22 26| Scale is weakly epimorphic with val: <7 12 17 22 25| Scale is weakly epimorphic with val: <7 12 17 22 28| Scale is weakly epimorphic with val: <7 12 18 21 25| Scale is weakly epimorphic with val: <7 12 19 22 26| Scale is weakly epimorphic with val: <8 11 15 21 26| Scale is weakly epimorphic with val: <8 11 16 22 27| Scale is weakly epimorphic with val: <8 11 17 20 25| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 19 22 27| Scale is weakly epimorphic with val: <8 12 15 21 26| Scale is weakly epimorphic with val: <8 12 15 22 25| Scale is weakly epimorphic with val: <8 12 15 22 28| Scale is weakly epimorphic with val: <8 12 16 22 27| Scale is weakly epimorphic with val: <8 12 17 20 25| Scale is weakly epimorphic with val: <8 12 18 21 26| Scale is weakly epimorphic with val: <8 12 19 22 27|
FIT/MODE
3: 1 0 2 N G T3 SD: 51.8736 c. M:-81.5478 c. 4: 1 0 3 N G T3 SD: 23.2226 c. M:-40.0441 c. 5: 1 0 4 N G T3 SD: 18.7292 c. M: 28.6892 c. 6: 1 1 4 N M DE S SD: 21.7921 c. M:-37.7168 c. 7: 1 1 5 N M DE S SD: 11.1561 c. M:-14.0003 c. 8: 1 1 6 N M DE S SD: 13.0089 c. M: 22.2116 c. 10: 2 1 7 N T3 SD: 15.0014 c. M:-21.1153 c. 11: 2 1 8 N T3 SD: 5.5910 c. M:-7.5322 c. 12: 2 1 9 N T3 SD: 2.3432 c. M: 3.7870 c. 23: 4 2 17 N T3 SD: 1.5562 c. M:-2.1493 c. 35: 6 3 26 N T3 SD: 0.5429 c. M:-0.9119 c. 82: 14 7 61 N T3 SD: 0.5422 c. M: 0.7501 c. 89: 15 8 66 N T3 SD: 0.3855 c. M: 0.5270 c. 101: 17 9 75 N T3 SD: 0.3718 c. M: 0.6378 c. 124: 21 11 92 N T3 SD: 0.1498 c. M:-0.2295 c. 136: 23 12 101 N T3 SD: 0.1557 c. M: 0.2390 c. 159: 27 14 118 N T3 SD: 0.0963 c. M:-0.1285 c. 171: 29 15 127 N T3 SD: 0.0845 c. M: 0.1463 c. 295: 50 26 219 N T3 SD: 0.0312 c. M: 0.0528 c. 330: 56 29 245 N T3 SD: 0.0297 c. M:-0.0495 c. 454: 77 40 337 N T3 SD: 0.0304 c. M:-0.0526 c. 466: 79 41 346 N T3 SD: 0.0334 c. M: 0.0463 c. 625: 106 55 464 N T3 SD: 0.0013 c. M: 0.0019 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: 69.2863 cents 7 x 8:9 S SD: 60.3065 cents 8 x 9:11 SD: 46.2470 cents 9 x 10:12 S SD: 27.0527 cents 10 x 11:13 SD: 28.5854 cents 11 x 12:15 S SD: 22.4315 cents 12 x 13:16 SD: 5.1372 cents 13 x 14:17 SD: 16.8086 cents 14 x 15:19 SD: 15.9480 cents 15 x 16:20 S SD: 8.2835 cents 16:17 x 21 SD: 17.0521 cents 17:18 x 23 SD: 14.5659 cents 18:19 x 24 SD: 4.5679 cents 19:20 x 25 S SD: 11.6682 cents 21:22:23:28 SD: 9.8195 cents 23:24:25:31 SD: 8.9716 cents 24:25:26:32 SD: 5.7335 cents 30 x 32:40 S SD: 8.2835 cents 31 x 33:41 SD: 12.2367 cents 32:34 x 43 SD: 12.2605 cents 33:35:36:44 SD: 9.4385 cents 34:36:37:45 SD: 8.8216 cents 35:37:38:47 SD: 7.3613 cents 36:38:39:48 SD: 4.5829 cents 38:40:41:51 SD: 4.1929 cents 39:41:42:52 SD: 0.7042 cents 141:148:152:188 SD: 0.6160 cents 180:189:194:240 SD: 0.4578 cents 219:230:236:292 SD: 0.3967 cents 222:233:239:296 SD: 0.3095 cents 261:274:281:348 SD: 0.1898 cents 300:315:323:400 SD: 0.1374 cents 441:463:475:588 SD: 0.1123 cents 480:504:517:640 SD: 0.0859 cents