Scala analysis: 199_C11
Chromatic tetrachord 35/34 * 16/15 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/34 50.184211 septendecimal 1/4-tone 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 35/34 50.1842 septendecimal 1/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/34 50.184 cents septendecimal 1/4-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 5/4 386.314 cents major third 2: 1 136/105 447.861 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 : 50.2 161.9 498.0 50.2 : 111.7 447.9 498.0 161.9: 336.1 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.1842 .. 336.1295 cents 289/245, 285.9453 cents 35/34, 50.1842 cents 2: 161.9155 .. 447.8608 cents 289/245, 285.9453 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 35/34, 50.1842 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 3.308112 Largest / Average step : 2.024694 Largest / Smallest step : 6.697913 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 133.43930 cents, oct.: 400.31790 cents Scale is not proper Scale has trivalence property Scale is a mode of a 526-tone equal temperament with octave 4/3 degrees: 53 171 526 Least number of segments generator : 265 of 250.916 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 473 of 447.862 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 50.18421 cents Scale diversity : 0.794395 Lumma stability : 0.201525 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 : 35/34, 50.1842 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 : 105 (O: 35 U: 105) Highest odd numerator or denominator: 51 Scale harmonicity : 0.018702 Average absolute harmonicity : 0.085636 Specific harmonicity : 0.077866 Fundamental : 1/102, -6.6724 octaves, 2.5650 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 2.856000E+04, 14.80171 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 91.5, average 30.50000 Mersenne's string divisions : 51681 Sum of van Prooijen's expressibility: 3.72876, average 1.24292 Sum of Tenney's harmonic distance : 7.61049, average 2.53683 Vogel's harmonic complexity : 15.33333 Wille's k value : 52 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 17.28041, average 2.88007 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.66667 2 17: -1 .. 0 -0.66667 2 2 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 15 22 27| Scale is weakly epimorphic with val: <6 10 16 20 27| Scale is weakly epimorphic with val: <6 10 16 21 28| Scale is weakly epimorphic with val: <6 10 16 22 29| Scale is weakly epimorphic with val: <6 10 18 22 27| Scale is weakly epimorphic with val: <6 10 19 19 29| Scale is weakly epimorphic with val: <6 10 19 20 30| Scale is weakly epimorphic with val: <6 10 19 21 31| Scale is weakly epimorphic with val: <6 10 19 22 32| Scale is weakly epimorphic with val: <6 11 17 19 27| Scale is weakly epimorphic with val: <6 11 17 20 28| Scale is weakly epimorphic with val: <6 11 17 21 29| Scale is weakly epimorphic with val: <6 11 17 22 30| Scale is weakly epimorphic with val: <7 10 16 21 27| Scale is weakly epimorphic with val: <7 10 16 22 28| Scale is weakly epimorphic with val: <7 10 17 19 27| Scale is weakly epimorphic with val: <7 10 17 20 28| Scale is weakly epimorphic with val: <7 10 17 21 29| Scale is weakly epimorphic with val: <7 10 17 22 30| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 20 29| Scale is weakly epimorphic with val: <7 10 19 21 30| Scale is weakly epimorphic with val: <7 10 19 22 31| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 18 33| Scale is weakly epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is weakly epimorphic with val: <7 11 15 20 29| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 15 21 33| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is JI-epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 19 33| Scale is JI-epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 20 31| Scale is JI-epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is JI-epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 16 22 33| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 18 33| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 29| Scale is weakly epimorphic with val: <7 11 18 20 32| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 18 21 33| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 19 33| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 20 31| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 11 19 22 33| Scale is weakly epimorphic with val: <7 12 15 22 27| Scale is weakly epimorphic with val: <7 12 17 21 27| Scale is weakly epimorphic with val: <7 12 17 22 28| Scale is weakly epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 18 21 29| Scale is weakly epimorphic with val: <7 12 18 22 30| Scale is weakly epimorphic with val: <8 11 16 18 28| Scale is weakly epimorphic with val: <8 11 16 19 29| Scale is weakly epimorphic with val: <8 11 16 20 30| Scale is weakly epimorphic with val: <8 11 16 21 31| Scale is weakly epimorphic with val: <8 11 16 22 32| Scale is weakly epimorphic with val: <8 11 17 21 27| Scale is weakly epimorphic with val: <8 11 17 22 28| Scale is weakly epimorphic with val: <8 11 19 19 29| Scale is weakly epimorphic with val: <8 11 19 20 30| Scale is weakly epimorphic with val: <8 11 19 21 31| Scale is weakly epimorphic with val: <8 11 19 22 32| Scale is weakly epimorphic with val: <8 12 16 18 27| Scale is weakly epimorphic with val: <8 12 16 19 28| Scale is weakly epimorphic with val: <8 12 16 20 29| Scale is weakly epimorphic with val: <8 12 16 21 30| Scale is weakly epimorphic with val: <8 12 16 22 31| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 18 21 28| Scale is weakly epimorphic with val: <8 12 18 22 29| Scale is weakly epimorphic with val: <8 12 19 19 28| Scale is weakly epimorphic with val: <8 12 19 20 29| Scale is weakly epimorphic with val: <8 12 19 21 30| Scale is weakly epimorphic with val: <8 12 19 22 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.0704 c. M: 50.1842 c. 6: 1 1 4 N M DE S SD: 19.0978 c. M:-32.8233 c. 7: 1 1 5 N M DE S SD: 16.5767 c. M:-20.9651 c. 8: 1 2 5 N T3 SD: 15.9511 c. M:-24.8514 c. 9: 1 2 6 N T3 SD: 3.8022 c. M:-5.1541 c. 19: 2 4 13 N T3 SD: 2.9742 c. M: 4.6381 c. 21: 2 5 14 N T3 SD: 2.8505 c. M:-4.0995 c. 28: 3 6 19 N T3 SD: 2.1170 c. M:-3.1778 c. 30: 3 7 20 N T3 SD: 2.3770 c. M:-4.0995 c. 31: 3 7 21 N T3 SD: 1.3568 c. M: 1.9863 c. 40: 4 9 27 N T3 SD: 0.2212 c. M: 0.3797 c. 89: 9 20 60 N T3 SD: 0.2369 c. M:-0.3688 c. 129: 13 29 87 N T3 SD: 0.1379 c. M:-0.2387 c. 169: 17 38 114 N T3 SD: 0.1098 c. M:-0.1702 c. 209: 21 47 141 N T3 SD: 0.1101 c. M: 0.1414 c. 277: 28 62 187 N T3 SD: 0.1075 c. M:-0.1597 c. 308: 31 69 208 N T3 SD: 0.1270 c. M: 0.2126 c. 317: 32 71 214 N T3 SD: 0.0742 c. M:-0.0916 c. 357: 36 80 241 N T3 SD: 0.0543 c. M: 0.0857 c. 397: 40 89 268 N T3 SD: 0.0475 c. M: 0.0822 c. 437: 44 98 295 N T3 SD: 0.0508 c. M: 0.0794 c. 446: 45 100 301 N T3 SD: 0.0388 c. M:-0.0670 c. 486: 49 109 328 N T3 SD: 0.0174 c. M:-0.0302 c. 526: 53 118 355 N T3 SD: 0.0021 c. M: 0.0035 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: 24.7358 cents 17:18:19:23 SD: 20.9663 cents 18:19:20:24 S SD: 16.0033 cents 19:20:21:25 SD: 15.4414 cents 20:21:22:27 SD: 13.5293 cents 21:22:23:28 SD: 10.2244 cents 27:28:30:36 S SD: 8.0485 cents 28:29:31:37 SD: 7.8674 cents 29:30:32:39 SD: 6.3734 cents 30:31:33:40 SD: 2.4238 cents 63:65:69:84 SD: 1.9701 cents 69:71:76:92 SD: 1.8053 cents 72:74:79:96 SD: 1.0124 cents 102:105:112:136 SD: 0.0000 cents