Scala analysis: 264_C18
Chromatic tetrachord 304/287 * 287/270 * 45/38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 304/287 99.624704 2: 152/135 205.334300 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 45/38 292.7107 1: 304/287 99.6247 2: 287/270 105.7096 3: 45/38 292.7107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 304/287 99.625 cents 1: 1 287/270 105.710 cents 1: 1 45/38 292.711 cents 2: 1 152/135 205.334 cents 2: 1 360/287 392.335 cents 2: 1 287/228 398.420 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 : 99.6 205.3 498.0 99.6 : 105.7 398.4 498.0 205.3: 292.7 392.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.6247 .. 292.7107 cents 12915/11552, 193.0860 cents 304/287, 99.6247 cents 2: 205.3343 .. 398.4203 cents 12915/11552, 193.0860 cents 5776/6075,-87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 304/287, 99.6247 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 45/38, 292.7107 cents Average / Smallest step : 1.666404 Largest / Average step : 1.763158 Largest / Smallest step : 2.938134 Median interval of one step : 287/270, 105.7096 cents, amount: 1 Least squares average step : 143.17345 cents, oct.: 429.52035 cents Scale is not proper Scale has trivalence property 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 : 1.098069 Lumma stability : 0.400063 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 : 82369/82080, 6.0849 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 187.0011 cents: 2 -- Rational properties -- Prime limit : 41 Odd number limit : 287 (O: 287 U: 287) Highest odd numerator or denominator: 287 Scale harmonicity : 0.015926 Fundamental : 1/38745, -15.2417 octaves, 0.0068 Hz. Guide tone : 304, 8.2479 octaves, 79534.172 Hz. Exponens Consonantiae : 1.177848E+07, 23.48965 octaves Euler's gradus suavitatis : 79 Sum of Mann's harmonic distance : 442.5, average 147.50000 Mersenne's string divisions : 169617 Sum of van Prooijen's expressibility: 5.06534, average 1.68845 Sum of Tenney's harmonic distance : 10.33211, average 3.44404 Vogel's harmonic complexity : 56.00000 Wille's k value : 6457 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 19.70645, average 3.28441 Lattice compactness (without 2's) : 13.22900, average 2.20483 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -3 .. 0 -1.33333 4 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 1 41: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is JI-epimorphic with val: <7 11 16 19 30 38| Scale is weakly epimorphic with val: <7 11 16 19 30 41| Scale is weakly epimorphic with val: <7 11 16 19 32 39| Scale is JI-epimorphic with val: <7 11 16 20 30 37| Scale is weakly epimorphic with val: <7 11 16 20 30 40| Scale is weakly epimorphic with val: <7 11 16 20 32 38| Scale is weakly epimorphic with val: <7 11 16 20 32 41| Scale is weakly epimorphic with val: <7 11 16 21 30 39| Scale is weakly epimorphic with val: <7 11 16 21 32 37| Scale is weakly epimorphic with val: <7 11 16 21 32 40| Scale is weakly epimorphic with val: <7 11 17 19 30 37| Scale is weakly epimorphic with val: <7 11 17 19 30 40| Scale is JI-epimorphic with val: <7 11 17 19 31 39| Scale is weakly epimorphic with val: <7 11 17 20 30 39| Scale is JI-epimorphic with val: <7 11 17 20 31 38| Scale is weakly epimorphic with val: <7 11 17 20 31 41| Scale is weakly epimorphic with val: <7 11 17 21 30 38| Scale is weakly epimorphic with val: <7 11 17 21 30 41| Scale is JI-epimorphic with val: <7 11 17 21 31 37| Scale is weakly epimorphic with val: <7 11 17 21 31 40| Scale is weakly epimorphic with val: <7 11 18 19 31 38| Scale is weakly epimorphic with val: <7 11 18 19 31 41| Scale is weakly epimorphic with val: <7 11 18 19 32 37| Scale is JI-epimorphic with val: <7 11 18 19 32 40| Scale is weakly epimorphic with val: <7 11 18 20 31 37| Scale is weakly epimorphic with val: <7 11 18 20 31 40| Scale is JI-epimorphic with val: <7 11 18 20 32 39| Scale is weakly epimorphic with val: <7 11 18 21 31 39| Scale is JI-epimorphic with val: <7 11 18 21 32 38| Scale is weakly epimorphic with val: <7 11 18 21 32 41| Scale is weakly epimorphic with val: <7 12 16 19 32 38| Scale is weakly epimorphic with val: <7 12 16 20 32 37| Scale is weakly epimorphic with val: <7 12 18 19 31 37|
FIT/MODE
3: 0 1 2 N G T3 SD: 61.8360 c. M: 99.6247 c. 4: 1 1 2 P M ME S SD: 29.0287 c. M:-43.6882 c. 5: 1 1 3 N M DE S SD: 3.5313 c. M: 6.1163 c. 19: 4 4 11 N M DE S SD: 3.9331 c. M:-5.2269 c. 24: 5 5 14 N M DE S SD: 2.6998 c. M:-4.1347 c. 29: 6 6 17 N M DE S SD: 2.0214 c. M:-3.4191 c. 34: 7 7 20 N M DE S SD: 1.6889 c. M:-2.9140 c. 36: 7 8 21 N T3 SD: 2.0424 c. M: 2.7826 c. 39: 8 8 23 N M DE S SD: 1.5769 c. M:-2.5384 c. 41: 8 9 24 N T3 SD: 1.5656 c. M: 2.4452 c. 44: 9 9 26 N M DE S SD: 1.5893 c. M:-2.2481 c. 46: 9 10 27 N T3 SD: 1.2782 c. M: 2.1811 c. 49: 10 10 29 N M DE S SD: 1.6607 c. M: 2.0506 c. 51: 10 11 30 N T3 SD: 1.1463 c. M: 1.9688 c. 56: 11 12 33 N T3 SD: 1.1297 c. M: 1.7944 c. 61: 12 13 36 N T3 SD: 1.1833 c. M: 1.6486 c. 65: 13 14 38 N T3 SD: 0.8926 c. M:-1.5459 c. 70: 14 15 41 N T3 SD: 0.5766 c. M:-0.9986 c. 75: 15 16 44 N T3 SD: 0.3028 c. M:-0.5243 c. 80: 16 17 47 N T3 SD: 0.0637 c. M:-0.1093 c. 165: 33 35 97 N T3 SD: 0.0467 c. M: 0.0794 c. 245: 49 52 144 N T3 SD: 0.0137 c. M: 0.0178 c. 325: 65 69 191 N T3 SD: 0.0120 c. M: 0.0157 c. 570: 114 121 335 N T3 SD: 0.0091 c. M: 0.0157 c. 815: 163 173 479 N T3 SD: 0.0096 c. M: 0.0157 c. 895: 179 190 526 N T3 SD: 0.0095 c. M: 0.0157 c. 1060: 212 225 623 N T3 SD: 0.0102 c. M: 0.0157 c. 1220: 244 259 717 N T3 SD: 0.0100 c. M: 0.0157 c. 1385: 277 294 814 N T3 SD: 0.0092 c. M: 0.0157 c. 1465: 293 311 861 N T3 SD: 0.0092 c. M: 0.0157 c. 1955: 391 415 1149 N T3 SD: 0.0092 c. M: 0.0157 c. 2035: 407 432 1196 N T3 SD: 0.0092 c. M: 0.0157 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 11:12 x 15 S SD: 32.0777 cents 12:13:14:16 S SD: 24.2755 cents 13:14:15:17 SD: 20.4141 cents 14:15:16:19 SD: 14.9049 cents 15:16:17:20 SD: 5.5322 cents 32:34:36:43 SD: 4.8529 cents 33:35:37:44 SD: 2.5338 cents 48:51:54:64 SD: 1.8392 cents 87:92:98:116 SD: 0.9959 cents 102:108:115:136 SD: 0.8124 cents 120:127:135:160 SD: 0.6827 cents 135:143:152:180 SD: 0.0141 cents