Scala analysis: 195_C11
Chromatic tetrachord 84/79 * 158/153 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 84/79 106.244010 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 84/79 106.2440 2: 158/153 55.6715 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 158/153 55.671 cents 1: 1 84/79 106.244 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 79/63 391.801 cents 2: 1 102/79 442.374 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 : 106.2 161.9 498.0 106.2: 55.7 391.8 498.0 161.9: 336.1 442.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.6715 .. 336.1295 cents 2601/2212, 280.4580 cents 158/153, 55.6715 cents 2: 161.9155 .. 442.3735 cents 2601/2212, 280.4580 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 158/153, 55.6715 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 2.982047 Largest / Average step : 2.024694 Largest / Smallest step : 6.037732 Median interval of one step : 84/79, 106.2440 cents, amount: 1 Least squares average step : 137.44357 cents, oct.: 412.33071 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1861-tone equal temperament with octave 4/3 degrees: 397 605 1861 Least number of segments generator : 931 of 249.156 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1599 of 427.928 cents and inv. generated superset size: 35 = 32 more = 1166.667% 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 55.67149 cents Scale diversity : 0.824165 Lumma stability : 0.223560 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 : 6426/6241, 50.5725 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 79 Odd number limit : 153 (O: 79 U: 153) Highest odd numerator or denominator: 79 Scale harmonicity : 0.020518 Fundamental : 1/4029, -11.9762 octaves, 0.0649 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 6.768720E+05, 19.36852 octaves Euler's gradus suavitatis : 108 Sum of Mann's harmonic distance : 138.5, average 46.16667 Mersenne's string divisions : 122087 Sum of van Prooijen's expressibility: 4.08232, average 1.36077 Sum of Tenney's harmonic distance : 8.35685, average 2.78562 Vogel's harmonic complexity : 73.00000 Wille's k value : 671 Wilson's harmonic complexity : 109 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.56727, average 2.42788 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 2.33333 7 3: -1 .. 1 -0.33333 3 1 7: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 79: -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 46| Scale is weakly epimorphic with val: <7 10 19 27 47| Scale is weakly epimorphic with val: <7 10 20 28 45| Scale is weakly epimorphic with val: <7 10 21 29 46| Scale is weakly epimorphic with val: <7 10 22 30 47| Scale is weakly epimorphic with val: <7 11 18 27 47| Scale is weakly epimorphic with val: <7 11 18 29 45| Scale is weakly epimorphic with val: <7 11 18 30 47| Scale is weakly epimorphic with val: <7 11 18 32 45| Scale is weakly epimorphic with val: <7 11 18 33 47| Scale is weakly epimorphic with val: <7 11 19 27 46| Scale is weakly epimorphic with val: <7 11 19 28 45| Scale is weakly epimorphic with val: <7 11 19 30 46| Scale is weakly epimorphic with val: <7 11 19 31 45| Scale is weakly epimorphic with val: <7 11 19 33 46| Scale is weakly epimorphic with val: <7 11 20 28 47| Scale is weakly epimorphic with val: <7 11 20 29 46| Scale is weakly epimorphic with val: <7 11 20 31 47| Scale is weakly epimorphic with val: <7 11 20 32 46| Scale is weakly epimorphic with val: <7 11 21 27 47| Scale is JI-epimorphic with val: <7 11 21 29 45| Scale is weakly epimorphic with val: <7 11 21 30 47| Scale is weakly epimorphic with val: <7 11 21 32 45| Scale is weakly epimorphic with val: <7 11 21 33 47| Scale is weakly epimorphic with val: <7 11 22 27 46| Scale is weakly epimorphic with val: <7 11 22 28 45| Scale is JI-epimorphic with val: <7 11 22 30 46| Scale is weakly epimorphic with val: <7 11 22 31 45| Scale is weakly epimorphic with val: <7 11 22 33 46| Scale is weakly epimorphic with val: <7 12 21 27 46| Scale is weakly epimorphic with val: <7 12 22 27 45| Scale is weakly epimorphic with val: <7 12 22 28 47| Scale is weakly epimorphic with val: <7 12 22 30 45| Scale is weakly epimorphic with val: <7 12 22 33 45| Scale is weakly epimorphic with val: <8 11 18 28 47| Scale is weakly epimorphic with val: <8 11 19 29 45| Scale is weakly epimorphic with val: <8 11 20 30 46| Scale is weakly epimorphic with val: <8 11 21 27 45| Scale is weakly epimorphic with val: <8 11 21 30 45| Scale is weakly epimorphic with val: <8 11 21 31 47| Scale is weakly epimorphic with val: <8 11 21 33 45| Scale is weakly epimorphic with val: <8 11 22 28 46| Scale is weakly epimorphic with val: <8 11 22 31 46| Scale is weakly epimorphic with val: <8 11 22 32 45| Scale is weakly epimorphic with val: <8 12 18 27 47| Scale is weakly epimorphic with val: <8 12 19 28 45| Scale is weakly epimorphic with val: <8 12 20 27 45| Scale is weakly epimorphic with val: <8 12 20 29 46| Scale is weakly epimorphic with val: <8 12 20 30 45| Scale is weakly epimorphic with val: <8 12 20 33 45| Scale is weakly epimorphic with val: <8 12 21 28 46| Scale is weakly epimorphic with val: <8 12 21 30 47| Scale is weakly epimorphic with val: <8 12 21 31 46| Scale is weakly epimorphic with val: <8 12 22 29 47| Scale is weakly epimorphic with val: <8 12 22 31 45| Scale is weakly epimorphic with val: <8 12 22 32 47|
FIT/MODE
3: 1 0 2 N G T3 SD: 34.5899 c. M:-59.7710 c. 4: 1 0 3 N G T3 SD: 24.0331 c. M: 37.4042 c. 5: 1 1 3 N M DE S SD: 21.8746 c. M:-37.3025 c. 6: 1 1 4 N M DE S SD: 13.6228 c. M: 23.2365 c. 9: 2 1 6 N T3 SD: 3.4859 c. M:-4.4327 c. 19: 4 2 13 N T3 SD: 2.7959 c. M: 4.6381 c. 24: 5 3 16 N T3 SD: 2.7676 c. M:-4.0995 c. 28: 6 3 19 N T3 SD: 1.0921 c. M: 1.8296 c. 37: 8 4 25 N T3 SD: 0.8617 c. M:-1.4414 c. 52: 11 6 35 N T3 SD: 0.7329 c. M:-0.9069 c. 61: 13 7 41 N T3 SD: 0.7978 c. M:-1.3779 c. 71: 15 8 48 N T3 SD: 0.6782 c. M: 1.0232 c. 80: 17 9 54 N T3 SD: 0.2382 c. M: 0.4094 c. 89: 19 10 60 N T3 SD: 0.2179 c. M:-0.3688 c. 117: 25 13 79 N T3 SD: 0.1362 c. M:-0.1759 c. 169: 36 19 114 N T3 SD: 0.1316 c. M:-0.1702 c. 197: 42 22 133 N T3 SD: 0.0749 c. M: 0.1141 c. 286: 61 32 193 N T3 SD: 0.0232 c. M:-0.0362 c. 483: 103 54 326 N T3 SD: 0.0252 c. M: 0.0357 c. 689: 147 77 465 N T3 SD: 0.0090 c. M:-0.0152 c. 975: 208 109 658 N T3 SD: 0.0082 c. M:-0.0130 c. 1172: 250 131 791 N T3 SD: 0.0059 c. M: 0.0084 c. 1458: 311 163 984 N T3 SD: 0.0047 c. M: 0.0081 c. 1861: 397 208 1256 N T3 SD: 0.0026 c. M: 0.0040 c. 2147: 458 240 1449 N T3 SD: 0.0008 c. M:-0.0013 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 13:14 x 17 SD: 20.1029 cents 14:15 x 19 SD: 16.6819 cents 15:16 x 20 S SD: 2.7436 cents 24 x 26:32 SD: 11.6714 cents 25:27 x 33 SD: 16.0577 cents 26:28:29:35 SD: 12.8975 cents 27:29:30:36 SD: 8.9747 cents 28:30:31:37 SD: 8.2974 cents 29:31:32:39 SD: 6.4817 cents 30:32:33:40 SD: 2.0990 cents 63:67:69:84 SD: 1.4780 cents 81:86:89:108 SD: 0.9306 cents 111:118:122:148 SD: 0.5704 cents 174:185:191:232 SD: 0.1820 cents 285:303:313:380 SD: 0.1304 cents 459:488:504:612 SD: 0.0599 cents