Scala analysis: 196_C11
Chromatic tetrachord 168/163 * 163/153 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 168/163 52.307122 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 168/163 52.3071 2: 163/153 109.6084 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 168/163 52.307 cents 1: 1 163/153 109.608 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 204/163 388.437 cents 2: 1 163/126 445.738 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 : 52.3 161.9 498.0 52.3 : 109.6 445.7 498.0 161.9: 336.1 388.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.3071 .. 336.1295 cents 2771/2352, 283.8224 cents 168/163, 52.3071 cents 2: 161.9155 .. 445.7379 cents 2771/2352, 283.8224 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 168/163, 52.3071 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 3.173851 Largest / Average step : 2.024694 Largest / Smallest step : 6.426075 Median interval of one step : 163/153, 109.6084 cents, amount: 1 Least squares average step : 133.59094 cents, oct.: 400.77281 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1095-tone equal temperament with octave 4/3 degrees: 115 356 1095 Least number of segments generator : 548 of 249.250 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 589 of 267.898 cents and inv. generated superset size: 51 = 48 more = 1700.000% 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 52.30712 cents Scale diversity : 0.806560 Lumma stability : 0.210050 Lumma impropriety factor : 0.349796 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 : 168/163, 52.3071 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% -- Rational properties -- Prime limit : 163 Odd number limit : 163 (O: 163 U: 163) Highest odd numerator or denominator: 163 Scale harmonicity : 0.020518 Fundamental : 1/8313, -13.0212 octaves, 0.0315 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 1.396584E+06, 20.41347 octaves Euler's gradus suavitatis : 192 Sum of Mann's harmonic distance : 222.5, average 74.16667 Mersenne's string divisions : 247919 Sum of van Prooijen's expressibility: 4.39688, average 1.46563 Sum of Tenney's harmonic distance : 8.97244, average 2.99081 Vogel's harmonic complexity : 129.33333 Wille's k value : 1385 Wilson's harmonic complexity : 193 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.43440, average 2.57240 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 -0.33333 3 1 7: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 163: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 22 27 52| Scale is weakly epimorphic with val: <7 10 19 27 54| Scale is weakly epimorphic with val: <7 10 20 28 52| Scale is weakly epimorphic with val: <7 10 21 29 53| Scale is weakly epimorphic with val: <7 10 22 30 54| Scale is weakly epimorphic with val: <7 11 18 27 54| Scale is weakly epimorphic with val: <7 11 18 29 52| Scale is weakly epimorphic with val: <7 11 18 30 54| Scale is weakly epimorphic with val: <7 11 18 32 52| Scale is weakly epimorphic with val: <7 11 18 33 54| Scale is weakly epimorphic with val: <7 11 19 27 53| Scale is weakly epimorphic with val: <7 11 19 28 52| Scale is weakly epimorphic with val: <7 11 19 30 53| Scale is weakly epimorphic with val: <7 11 19 31 52| Scale is weakly epimorphic with val: <7 11 19 33 53| Scale is weakly epimorphic with val: <7 11 20 28 54| Scale is weakly epimorphic with val: <7 11 20 29 53| Scale is weakly epimorphic with val: <7 11 20 31 54| Scale is weakly epimorphic with val: <7 11 20 32 53| Scale is weakly epimorphic with val: <7 11 21 27 54| Scale is JI-epimorphic with val: <7 11 21 29 52| Scale is weakly epimorphic with val: <7 11 21 30 54| Scale is weakly epimorphic with val: <7 11 21 32 52| Scale is weakly epimorphic with val: <7 11 21 33 54| Scale is weakly epimorphic with val: <7 11 22 27 53| Scale is weakly epimorphic with val: <7 11 22 28 52| Scale is JI-epimorphic with val: <7 11 22 30 53| Scale is weakly epimorphic with val: <7 11 22 31 52| Scale is weakly epimorphic with val: <7 11 22 33 53| Scale is weakly epimorphic with val: <7 12 21 27 53| Scale is weakly epimorphic with val: <7 12 22 27 52| Scale is weakly epimorphic with val: <7 12 22 28 54| Scale is weakly epimorphic with val: <7 12 22 30 52| Scale is weakly epimorphic with val: <7 12 22 33 52| Scale is weakly epimorphic with val: <8 11 18 28 52| Scale is weakly epimorphic with val: <8 11 19 29 53| Scale is weakly epimorphic with val: <8 11 20 29 52| Scale is weakly epimorphic with val: <8 11 20 30 54| Scale is weakly epimorphic with val: <8 11 20 32 52| Scale is weakly epimorphic with val: <8 11 21 27 53| Scale is weakly epimorphic with val: <8 11 21 30 53| Scale is weakly epimorphic with val: <8 11 21 31 52| Scale is weakly epimorphic with val: <8 11 21 33 53| Scale is weakly epimorphic with val: <8 11 22 28 54| Scale is weakly epimorphic with val: <8 11 22 31 54| Scale is weakly epimorphic with val: <8 11 22 32 53| Scale is weakly epimorphic with val: <8 12 18 27 52| Scale is weakly epimorphic with val: <8 12 19 28 53| Scale is weakly epimorphic with val: <8 12 19 29 52| Scale is weakly epimorphic with val: <8 12 19 32 52| Scale is weakly epimorphic with val: <8 12 20 27 53| Scale is weakly epimorphic with val: <8 12 20 29 54| Scale is weakly epimorphic with val: <8 12 20 30 53| Scale is weakly epimorphic with val: <8 12 20 33 53| Scale is weakly epimorphic with val: <8 12 21 28 54| Scale is weakly epimorphic with val: <8 12 21 30 52| Scale is weakly epimorphic with val: <8 12 21 31 54| Scale is weakly epimorphic with val: <8 12 22 31 53|
FIT/MODE
3: 0 1 2 N G T3 SD: 30.2921 c. M: 52.3071 c. 6: 1 1 4 N M DE S SD: 17.8822 c. M:-30.7004 c. 7: 1 1 5 N M DE S SD: 15.7040 c. M: 19.6169 c. 8: 1 2 5 N T3 SD: 15.4549 c. M:-24.8514 c. 9: 1 2 6 N T3 SD: 2.9436 c. M:-4.0995 c. 19: 2 4 13 N T3 SD: 2.6787 c. M: 4.6381 c. 28: 3 6 19 N T3 SD: 1.2193 c. M: 1.8296 c. 37: 4 8 25 N T3 SD: 0.9143 c. M:-1.5356 c. 46: 5 10 31 N T3 SD: 1.0928 c. M:-1.8282 c. 49: 5 11 33 N T3 SD: 0.9513 c. M: 1.4862 c. 58: 6 13 39 N T3 SD: 0.8460 c. M:-1.2372 c. 68: 7 15 46 N T3 SD: 0.7507 c. M: 1.0378 c. 77: 8 17 52 N T3 SD: 0.3470 c. M: 0.5622 c. 86: 9 19 58 N T3 SD: 0.1748 c. M:-0.2387 c. 114: 12 25 77 N T3 SD: 0.1699 c. M: 0.2693 c. 123: 13 27 83 N T3 SD: 0.1937 c. M:-0.3318 c. 191: 20 42 129 N T3 SD: 0.1683 c. M: 0.2464 c. 200: 21 44 135 N T3 SD: 0.0302 c. M: 0.0509 c. 486: 51 107 328 N T3 SD: 0.0249 c. M: 0.0431 c. 609: 64 134 411 N T3 SD: 0.0198 c. M:-0.0326 c. 809: 85 178 546 N T3 SD: 0.0127 c. M:-0.0215 c. 895: 94 197 604 N T3 SD: 0.0108 c. M:-0.0187 c. 1009: 106 222 681 N T3 SD: 0.0117 c. M:-0.0148 c. 1095: 115 241 739 N T3 SD: 0.0035 c. M:-0.0060 c. 1295: 136 285 874 N T3 SD: 0.0023 c. M: 0.0028 c. 2390: 251 526 1613 N T3 SD: 0.0013 c. M: 0.0020 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: 87.7017 cents 6 x 7:8 S SD: 52.4777 cents 7 x 8:9 S SD: 46.7996 cents 8 x 9:11 SD: 33.9173 cents 9 x 10:12 S SD: 10.2441 cents 10 x 11:13 SD: 21.9699 cents 11 x 12:15 S SD: 20.2538 cents 12 x 13:16 SD: 11.6714 cents 13 x 14:17 SD: 23.7710 cents 14 x 15:19 SD: 26.1862 cents 15 x 16:20 S SD: 25.0921 cents 16:17:18:21 S SD: 24.2182 cents 17:18:19:23 SD: 20.4225 cents 18:19:20:24 S SD: 15.3663 cents 19:20:21:25 SD: 14.8566 cents 20:21:22:27 SD: 12.9372 cents 21:22:23:28 SD: 9.5247 cents 27:28:30:36 S SD: 7.6975 cents 28:29:31:37 SD: 7.5771 cents 29:30:32:39 SD: 6.0916 cents 30:31:33:40 SD: 1.8083 cents 63:65:69:84 SD: 1.5912 cents 93:96:102:124 SD: 1.1077 cents 102:105:112:136 SD: 0.7076 cents 132:136:145:176 SD: 0.3133 cents 225:232:247:300 SD: 0.2802 cents 327:337:359:436 SD: 0.1082 cents 357:368:392:476 SD: 0.0770 cents 489:504:537:652 SD: 0.0632 cents