Scala analysis: 197_C11
Chromatic tetrachord 52/51 * 14/13 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 52/51 33.6173 2: 14/13 128.2982 2/3-tone 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 14/13 128.298 cents 2/3-tone 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 26/21 369.747 cents 2: 1 17/13 464.428 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 : 33.6 161.9 498.0 33.6 : 128.3 464.4 498.0 161.9: 336.1 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 336.1295 cents 867/728, 302.5123 cents 52/51, 33.6173 cents 2: 161.9155 .. 464.4277 cents 867/728, 302.5123 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 4.938387 Largest / Average step : 2.024694 Largest / Smallest step : 9.998721 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 132.25595 cents, oct.: 396.76784 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 71 342 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 981 of 464.432 cents and inv. generated superset size: 12 = 9 more = 400.000% 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 33.61725 cents Scale diversity : 0.675563 Lumma stability : 0.134997 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 : 52/51, 33.6173 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 : 17 Odd number limit : 51 (O: 17 U: 51) Highest odd numerator or denominator: 51 Scale harmonicity : 0.014658 Average absolute harmonicity : 0.084518 Specific harmonicity : 0.068146 Fundamental : 1/51, -5.6724 octaves, 5.1299 Hz. Guide tone : 728, 9.5078 octaves, 190463.412 Hz. Exponens Consonantiae : 3.712800E+04, 15.18022 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 108.5, average 36.16667 Mersenne's string divisions : 77147 Sum of van Prooijen's expressibility: 3.89226, average 1.29742 Sum of Tenney's harmonic distance : 7.95851, average 2.65284 Vogel's harmonic complexity : 14.66667 Wille's k value : 8 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 13.22424, average 2.20404 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 ..-1 -1.00000 3 1 7: 0 .. 1 0.33333 1 13: 0 .. 1 0.33333 1 17: -1 .. 0 -0.66667 2 2 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 26 27| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 19 25 27| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is weakly epimorphic with val: <7 10 20 26 28| Scale is weakly epimorphic with val: <7 10 20 28 29| Scale is weakly epimorphic with val: <7 10 21 26 27| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 21 29 30| Scale is weakly epimorphic with val: <7 10 22 25 30| Scale is weakly epimorphic with val: <7 10 22 27 28| Scale is weakly epimorphic with val: <7 10 22 28 30| Scale is weakly epimorphic with val: <7 10 22 30 31| Scale is weakly epimorphic with val: <7 11 18 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 26 33| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 29 30| Scale is weakly epimorphic with val: <7 11 18 29 33| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is JI-epimorphic with val: <7 11 19 25 27| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 28 30| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <7 11 20 25 29| Scale is weakly epimorphic with val: <7 11 20 25 32| Scale is JI-epimorphic with val: <7 11 20 26 28| Scale is weakly epimorphic with val: <7 11 20 26 31| Scale is weakly epimorphic with val: <7 11 20 28 29| Scale is weakly epimorphic with val: <7 11 20 28 32| Scale is weakly epimorphic with val: <7 11 20 29 31| Scale is weakly epimorphic with val: <7 11 21 26 27| Scale is weakly epimorphic with val: <7 11 21 26 30| Scale is weakly epimorphic with val: <7 11 21 26 33| Scale is JI-epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 21 27 32| Scale is weakly epimorphic with val: <7 11 21 29 30| Scale is weakly epimorphic with val: <7 11 21 29 33| Scale is weakly epimorphic with val: <7 11 21 30 32| Scale is weakly epimorphic with val: <7 11 22 25 27| Scale is weakly epimorphic with val: <7 11 22 25 30| Scale is weakly epimorphic with val: <7 11 22 25 33| Scale is weakly epimorphic with val: <7 11 22 27 28| Scale is weakly epimorphic with val: <7 11 22 27 31| Scale is JI-epimorphic with val: <7 11 22 28 30| Scale is weakly epimorphic with val: <7 11 22 28 33| Scale is weakly epimorphic with val: <7 11 22 30 31| Scale is weakly epimorphic with val: <7 12 21 26 27| Scale is weakly epimorphic with val: <7 12 22 27 28| Scale is weakly epimorphic with val: <8 11 18 25 27| Scale is weakly epimorphic with val: <8 11 18 27 28| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 19 25 29| Scale is weakly epimorphic with val: <8 11 19 26 28| Scale is weakly epimorphic with val: <8 11 19 28 29| Scale is weakly epimorphic with val: <8 11 19 29 31| Scale is weakly epimorphic with val: <8 11 20 26 30| Scale is weakly epimorphic with val: <8 11 20 27 29| Scale is weakly epimorphic with val: <8 11 20 29 30| Scale is weakly epimorphic with val: <8 11 20 30 32| Scale is weakly epimorphic with val: <8 11 21 25 27| Scale is weakly epimorphic with val: <8 11 21 27 31| Scale is weakly epimorphic with val: <8 11 21 28 30| Scale is weakly epimorphic with val: <8 11 21 30 31| Scale is weakly epimorphic with val: <8 11 22 25 32| Scale is weakly epimorphic with val: <8 11 22 26 28| Scale is weakly epimorphic with val: <8 11 22 28 32| Scale is weakly epimorphic with val: <8 11 22 29 31| Scale is weakly epimorphic with val: <8 12 18 25 27| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 18 30 31| Scale is weakly epimorphic with val: <8 12 19 26 28| Scale is weakly epimorphic with val: <8 12 19 28 29| Scale is weakly epimorphic with val: <8 12 20 26 27| Scale is weakly epimorphic with val: <8 12 20 27 29| Scale is weakly epimorphic with val: <8 12 20 29 30| Scale is weakly epimorphic with val: <8 12 21 25 30| Scale is weakly epimorphic with val: <8 12 21 27 28| Scale is weakly epimorphic with val: <8 12 21 28 30| Scale is weakly epimorphic with val: <8 12 21 30 31| Scale is weakly epimorphic with val: <8 12 22 26 31| Scale is weakly epimorphic with val: <8 12 22 28 29| Scale is weakly epimorphic with val: <8 12 22 29 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 19.5527 c. M: 33.6173 c. 7: 0 2 5 N G T3 SD: 22.4718 c. M: 33.6173 c. 9: 1 2 6 N T3 SD: 12.7621 c. M:-21.7211 c. 10: 1 2 7 N T3 SD: 11.8086 c. M:-16.1872 c. 11: 1 3 7 N T3 SD: 12.9649 c. M:-19.1918 c. 12: 1 3 8 N T3 SD: 5.1317 c. M:-7.8865 c. 15: 1 4 10 N T3 SD: 2.3789 c. M:-4.0995 c. 27: 2 7 18 N T3 SD: 3.0294 c. M:-4.0995 c. 28: 2 7 19 N T3 SD: 1.5469 c. M:-1.9574 c. 31: 2 8 21 N T3 SD: 1.1230 c. M: 1.4853 c. 43: 3 11 29 N T3 SD: 0.6668 c. M:-1.1301 c. 74: 5 19 50 N T3 SD: 0.2245 c. M: 0.3874 c. 89: 6 23 60 N T3 SD: 0.2143 c. M:-0.3688 c. 132: 9 34 89 N T3 SD: 0.2723 c. M:-0.3404 c. 163: 11 42 110 N T3 SD: 0.0153 c. M:-0.0255 c. 563: 38 145 380 N T3 SD: 0.0166 c. M: 0.0288 c. 726: 49 187 490 N T3 SD: 0.0097 c. M: 0.0166 c. 889: 60 229 600 N T3 SD: 0.0055 c. M: 0.0089 c. 1052: 71 271 710 N T3 SD: 0.0031 c. M: 0.0039 c. 1215: 82 313 820 N T3 SD: 0.0025 c. M: 0.0043 c. 2267: 153 584 1530 N T3 SD: 0.0025 c. M: 0.0042 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 x 18:21 S SD: 25.0343 cents 17 x 19:23 SD: 19.8602 cents 20:21:22:27 SD: 18.4324 cents 21:22:23:28 SD: 15.7092 cents 24:25:26:32 SD: 14.5982 cents 27:28:30:36 S SD: 11.9295 cents 28:29:31:37 SD: 11.4584 cents 29:30:32:39 SD: 10.1211 cents 30:31:33:40 SD: 7.7849 cents 33:34:36:44 SD: 7.0989 cents 38:39:42:51 SD: 6.5543 cents 39:40:43:52 SD: 4.1501 cents 42:43:46:56 SD: 2.7937 cents 51:52:56:68 SD: 0.0000 cents