Scala analysis: 219_C14
Chromatic tetrachord 22/21 * 35/33 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 22/21 80.5370 undecimal minor semitone 2: 35/33 101.8667 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 35/33 101.867 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 44/35 396.178 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 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 : 80.5 182.4 498.0 80.5 : 101.9 417.5 498.0 182.4: 315.6 396.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 315.6413 cents 63/55, 235.1043 cents 22/21, 80.5370 cents 2: 182.4037 .. 417.5080 cents 63/55, 235.1043 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.061350 Largest / Average step : 1.901282 Largest / Smallest step : 3.919207 Median interval of one step : 35/33, 101.8667 cents, amount: 1 Least squares average step : 138.53425 cents, oct.: 415.60274 cents Scale is not proper Scale has trivalence property Scale is a mode of a 841-tone equal temperament with octave 4/3 degrees: 136 308 841 Least number of segments generator : 421 of 249.319 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 705 of 417.505 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 80.53704 cents Scale diversity : 1.001380 Lumma stability : 0.323413 Lumma impropriety factor : 0.267521 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 : 245/242, 21.3296 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 Limited inverse transpositions with margin 213.7746 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 21 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.107979 Specific harmonicity : 0.126379 Fundamental : 1/63, -5.9773 octaves, 4.1528 Hz. Guide tone : 220, 7.7814 octaves, 57557.624 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 34.5, average 11.50000 Mersenne's string divisions : 5719 Sum of van Prooijen's expressibility: 2.75358, average 0.91786 Sum of Tenney's harmonic distance : 5.69807, average 1.89936 Vogel's harmonic complexity : 13.33333 Wille's k value : 17 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 12.14966, average 2.02494 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -2 ..-1 -1.33333 4 1 5: 0 .. 1 0.33333 1 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.33333 1 1 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 15 18 25| Scale is weakly epimorphic with val: <6 10 15 19 26| Scale is weakly epimorphic with val: <6 10 15 20 27| Scale is weakly epimorphic with val: <6 10 17 18 23| Scale is weakly epimorphic with val: <6 10 17 18 26| Scale is weakly epimorphic with val: <6 10 17 19 24| Scale is weakly epimorphic with val: <6 10 17 19 27| Scale is weakly epimorphic with val: <6 10 17 20 25| Scale is weakly epimorphic with val: <6 10 17 21 23| Scale is weakly epimorphic with val: <6 10 17 21 26| Scale is weakly epimorphic with val: <6 10 17 22 24| Scale is weakly epimorphic with val: <6 10 17 22 27| Scale is weakly epimorphic with val: <6 10 18 18 25| Scale is weakly epimorphic with val: <6 10 18 19 26| Scale is weakly epimorphic with val: <6 10 18 20 27| Scale is weakly epimorphic with val: <6 11 15 18 26| Scale is weakly epimorphic with val: <6 11 15 19 27| Scale is weakly epimorphic with val: <6 11 18 18 26| Scale is weakly epimorphic with val: <6 11 18 19 27| Scale is weakly epimorphic with val: <6 11 19 19 23| Scale is weakly epimorphic with val: <6 11 19 19 26| Scale is weakly epimorphic with val: <6 11 19 20 24| Scale is weakly epimorphic with val: <6 11 19 20 27| Scale is weakly epimorphic with val: <6 11 19 21 25| Scale is weakly epimorphic with val: <6 11 19 22 23| Scale is weakly epimorphic with val: <6 11 19 22 26| Scale is weakly epimorphic with val: <7 10 15 18 24| Scale is weakly epimorphic with val: <7 10 15 19 25| Scale is weakly epimorphic with val: <7 10 15 20 26| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 16 18 23| Scale is weakly epimorphic with val: <7 10 16 18 26| Scale is weakly epimorphic with val: <7 10 16 19 24| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 16 21 23| Scale is weakly epimorphic with val: <7 10 16 21 26| Scale is weakly epimorphic with val: <7 10 16 22 24| Scale is weakly epimorphic with val: <7 10 16 22 27| Scale is weakly epimorphic with val: <7 10 18 18 24| Scale is weakly epimorphic with val: <7 10 18 19 25| Scale is weakly epimorphic with val: <7 10 18 20 26| Scale is weakly epimorphic with val: <7 10 18 21 27| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is weakly epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 20 23| Scale is weakly epimorphic with val: <7 11 16 20 26| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is JI-epimorphic with val: <7 11 17 18 23| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is JI-epimorphic with val: <7 11 17 19 24| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is JI-epimorphic with val: <7 11 17 20 25| = patent Scale is weakly epimorphic with val: <7 11 17 21 23| Scale is JI-epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 22 24| Scale is JI-epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is weakly epimorphic with val: <7 11 19 20 23| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 12 15 18 26| Scale is weakly epimorphic with val: <7 12 15 19 27| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <8 11 15 18 24| Scale is weakly epimorphic with val: <8 11 15 19 25| Scale is weakly epimorphic with val: <8 11 15 20 26| Scale is weakly epimorphic with val: <8 11 15 21 27| Scale is weakly epimorphic with val: <8 11 17 18 25| Scale is weakly epimorphic with val: <8 11 17 19 23| Scale is weakly epimorphic with val: <8 11 17 19 26| Scale is weakly epimorphic with val: <8 11 17 20 24| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 17 21 25| Scale is weakly epimorphic with val: <8 11 17 22 23| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 18 18 24| Scale is weakly epimorphic with val: <8 11 18 19 25| Scale is weakly epimorphic with val: <8 11 18 20 26| Scale is weakly epimorphic with val: <8 11 18 21 27| Scale is weakly epimorphic with val: <8 12 15 18 25| Scale is weakly epimorphic with val: <8 12 15 19 26| Scale is weakly epimorphic with val: <8 12 15 20 27| Scale is weakly epimorphic with val: <8 12 18 18 25| Scale is weakly epimorphic with val: <8 12 18 19 26| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 19 19 25| Scale is weakly epimorphic with val: <8 12 19 20 23| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 21 24| Scale is weakly epimorphic with val: <8 12 19 21 27| Scale is weakly epimorphic with val: <8 12 19 22 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 47.4510 c. M: 80.5370 c. 5: 1 1 3 N M DE S SD: 14.6795 c. M:-19.0720 c. 6: 1 1 4 N M DE S SD: 9.5689 c. M: 16.3887 c. 11: 2 2 7 N M DE S SD: 5.8313 c. M:-10.0166 c. 13: 2 3 8 N T3 SD: 5.7470 c. M:-9.1521 c. 14: 2 3 9 N T3 SD: 6.0182 c. M: 9.3877 c. 17: 3 3 11 N M DE S SD: 5.7136 c. M:-7.3533 c. 19: 3 4 12 N T3 SD: 1.2628 c. M: 1.8984 c. 30: 5 6 19 N T3 SD: 1.4316 c. M:-2.4705 c. 44: 7 9 28 N T3 SD: 1.0611 c. M: 1.3026 c. 49: 8 10 31 N T3 SD: 0.5499 c. M:-0.7764 c. 68: 11 14 43 N T3 SD: 0.4051 c. M:-0.7011 c. 74: 12 15 47 N T3 SD: 0.4164 c. M: 0.6846 c. 93: 15 19 59 N T3 SD: 0.2214 c. M: 0.3227 c. 142: 23 29 90 N T3 SD: 0.0773 c. M:-0.1322 c. 161: 26 33 102 N T3 SD: 0.0886 c. M:-0.1097 c. 235: 38 48 149 N T3 SD: 0.0811 c. M: 0.1404 c. 254: 41 52 161 N T3 SD: 0.0877 c. M: 0.1439 c. 303: 49 62 192 N T3 SD: 0.0281 c. M:-0.0484 c. 396: 64 81 251 N T3 SD: 0.0342 c. M: 0.0449 c. 445: 72 91 282 N T3 SD: 0.0303 c. M:-0.0455 c. 538: 87 110 341 N T3 SD: 0.0197 c. M: 0.0341 c. 680: 110 139 431 N T3 SD: 0.0247 c. M: 0.0314 c. 699: 113 143 443 N T3 SD: 0.0135 c. M: 0.0233 c. 841: 136 172 533 N T3 SD: 0.0030 c. M: 0.0044 c. 1985: 321 406 1258 N T3 SD: 0.0028 c. M:-0.0037 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13:14 x 17 SD: 29.2030 cents 14:15:16:19 SD: 23.1688 cents 15:16:17:20 SD: 15.4503 cents 16:17:18:21 S SD: 14.1504 cents 17:18:19:23 SD: 10.9599 cents 18:19:20:24 S SD: 4.3553 cents 42:44:47:56 SD: 4.1073 cents 44:46:49:59 SD: 3.7190 cents 45:47:50:60 SD: 1.7514 cents 63:66:70:84 SD: 0.0000 cents