Scala analysis: 267_C18
Chromatic tetrachord 19/18 * 16/15 * 45/38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 152/135 205.334300 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 45/38 292.7107 1: 19/18 93.6030 undevicesimal semitone 2: 16/15 111.7313 minor diatonic semitone 3: 45/38 292.7107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 45/38 292.711 cents 2: 1 152/135 205.334 cents 2: 1 5/4 386.314 cents major third 2: 1 24/19 404.442 cents smaller undevicesimal 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 : 93.6 205.3 498.0 93.6 : 111.7 404.4 498.0 205.3: 292.7 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 292.7107 cents 405/361, 199.1077 cents 19/18, 93.6030 cents 2: 205.3343 .. 404.4420 cents 405/361, 199.1077 cents 5776/6075,-87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 45/38, 292.7107 cents Average / Smallest step : 1.773607 Largest / Average step : 1.763158 Largest / Smallest step : 3.127150 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 142.74333 cents, oct.: 428.22999 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1676-tone equal temperament with octave 4/3 degrees: 315 691 1676 Least number of segments generator : 839 of 249.320 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1483 of 440.693 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 87.37640 cents Scale diversity : 1.104990 Lumma stability : 0.375882 Lumma impropriety factor : 0.175439 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 : 96/95, 18.1283 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 180.9794 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.019046 Average absolute harmonicity : 0.086143 Specific harmonicity : 0.081513 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 152, 7.2479 octaves, 39767.086 Hz. Exponens Consonantiae : 4.104000E+04, 15.32474 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 165.5, average 55.16667 Mersenne's string divisions : 10619 Sum of van Prooijen's expressibility: 3.88621, average 1.29540 Sum of Tenney's harmonic distance : 7.92538, average 2.64179 Vogel's harmonic complexity : 21.33333 Wille's k value : 142 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 19.36271, average 3.22712 Lattice compactness (without 2's) : 11.83061, average 1.97177 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -3 ..-1 -2.00000 6 1 5: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 30| Scale is weakly epimorphic with val: <6 10 16 29| Scale is weakly epimorphic with val: <6 10 18 33| Scale is weakly epimorphic with val: <6 10 19 29| Scale is weakly epimorphic with val: <6 11 15 33| Scale is weakly epimorphic with val: <6 11 17 31| Scale is weakly epimorphic with val: <7 10 16 30| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 11 15 28| Scale is weakly epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 34| Scale is JI-epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 12 15 34| Scale is weakly epimorphic with val: <7 12 18 34| Scale is weakly epimorphic with val: <8 11 16 28| Scale is weakly epimorphic with val: <8 11 17 33| Scale is weakly epimorphic with val: <8 11 19 31| Scale is weakly epimorphic with val: <8 12 16 31| Scale is weakly epimorphic with val: <8 12 19 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 58.6161 c. M: 93.6030 c. 4: 1 1 2 P M ME S SD: 30.8976 c. M:-43.6882 c. 5: 1 1 3 N M DE S SD: 4.9491 c. M: 6.1163 c. 17: 3 4 10 N T3 SD: 3.3016 c. M: 5.7127 c. 22: 4 5 13 N T3 SD: 1.9851 c. M: 3.0494 c. 27: 5 6 16 N T3 SD: 1.6098 c. M: 2.4271 c. 48: 9 11 28 N T3 SD: 1.2675 c. M:-2.1844 c. 49: 9 11 29 N T3 SD: 1.7051 c. M: 2.1254 c. 53: 10 12 31 N T3 SD: 0.8365 c. M:-1.4014 c. 58: 11 13 34 N T3 SD: 0.6574 c. M:-0.8538 c. 75: 14 17 44 N T3 SD: 0.4753 c. M: 0.6346 c. 80: 15 18 47 N T3 SD: 0.1416 c. M: 0.2196 c. 165: 31 37 97 N T3 SD: 0.0492 c. M: 0.0794 c. 410: 77 92 241 N T3 SD: 0.0462 c. M: 0.0677 c. 468: 88 105 275 N T3 SD: 0.0420 c. M:-0.0561 c. 548: 103 123 322 N T3 SD: 0.0371 c. M:-0.0638 c. 553: 104 124 325 N T3 SD: 0.0360 c. M:-0.0619 c. 633: 119 142 372 N T3 SD: 0.0193 c. M:-0.0263 c. 713: 134 160 419 N T3 SD: 0.0177 c. M:-0.0307 c. 798: 150 179 469 N T3 SD: 0.0084 c. M:-0.0145 c. 878: 165 197 516 N T3 SD: 0.0070 c. M:-0.0100 c. 1043: 196 234 613 N T3 SD: 0.0066 c. M: 0.0107 c. 1676: 315 376 985 N T3 SD: 0.0036 c. M:-0.0053 c. 1841: 346 413 1082 N T3 SD: 0.0014 c. M: 0.0023 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: 69.4664 cents 6 x 7:8 S SD: 30.7683 cents 7 x 8:9 S SD: 34.0286 cents 8 x 9:11 SD: 26.6460 cents 9 x 10:12 S SD: 11.4653 cents 10 x 11:13 SD: 29.7812 cents 11 x 12:15 S SD: 33.5613 cents 12:13:14:16 S SD: 25.4056 cents 13:14:15:17 SD: 21.4274 cents 14:15:16:19 SD: 15.8966 cents 15:16:17:20 SD: 7.1298 cents 31:33:35:41 SD: 6.9396 cents 32:34:36:43 SD: 5.8918 cents 33:35:37:44 SD: 3.6673 cents 39:41:44:52 SD: 2.6158 cents 54:57:61:72 SD: 1.8952 cents 72:76:81:96 SD: 0.4748 cents 198:209:223:264 SD: 0.1725 cents 270:285:304:360 SD: 0.0000 cents