Scala analysis: 318_C24
Chromatic tetrachord 14/13 * 7/6 * 52/49
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 49/39 395.169150 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/49 102.8758 1: 14/13 128.2982 2/3-tone 2: 7/6 266.8709 septimal minor third 3: 52/49 102.8758
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/49 102.876 cents 1: 1 14/13 128.298 cents 2/3-tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 26/21 369.747 cents 2: 1 49/39 395.169 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 : 128.3 395.2 498.0 128.3: 266.9 369.7 498.0 395.2: 102.9 231.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 102.8758 .. 266.8709 cents 343/312, 163.9951 cents 52/49, 102.8758 cents 2: 231.1741 .. 395.1692 cents 343/312, 163.9951 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/49, 102.8758 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.613741 Largest / Average step : 1.607511 Largest / Smallest step : 2.594106 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 172.34082 cents, oct.: 517.02247 cents Scale is not proper Scale has trivalence property Scale is a mode of a 823-tone equal temperament with octave 4/3 degrees: 212 653 823 Least number of segments generator : 412 of 249.325 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 446 of 269.900 cents and inv. generated superset size: 31 = 28 more = 1033.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.153719 Lumma stability : 0.413119 Lumma impropriety factor : 0.071674 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 : 343/338, 25.4224 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 13 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.021101 Average absolute harmonicity : 0.088740 Specific harmonicity : 0.089745 Fundamental : 1/39, -5.2854 octaves, 6.7083 Hz. Guide tone : 196, 7.6147 octaves, 51278.611 Hz. Exponens Consonantiae : 7.644000E+03, 12.90011 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 61.0, average 20.33333 Mersenne's string divisions : 16632 Sum of van Prooijen's expressibility: 3.28126, average 1.09375 Sum of Tenney's harmonic distance : 6.62051, average 2.20684 Vogel's harmonic complexity : 13.33333 Wille's k value : 24 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.14966, average 2.19161 Lattice compactness (without 2's) : 10.24604, average 1.70767 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 .. 0 -0.66667 2 1 7: 0 .. 2 1.00000 3 13: -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 21 29| Scale is weakly epimorphic with val: <6 11 21 28| Scale is weakly epimorphic with val: <6 11 22 25| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 22 26| Scale is JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 20 25| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 22 25| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <8 11 20 25| Scale is weakly epimorphic with val: <8 11 21 28| Scale is weakly epimorphic with val: <8 12 21 27| Scale is weakly epimorphic with val: <8 12 22 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 42.4622 c. M: 63.1392 c. 4: 1 2 1 P M ME I SD: 12.6811 c. M: 21.6354 c. 9: 2 5 2 N M DE I SD: 11.1261 c. M: 17.6216 c. 11: 3 6 2 N T3 SD: 8.3381 c. M:-12.3222 c. 15: 4 8 3 N T3 SD: 3.2169 c. M:-4.5138 c. 19: 5 10 4 N T3 SD: 1.9626 c. M:-2.7662 c. 24: 6 13 5 N T3 SD: 2.2451 c. M: 3.7870 c. 34: 9 18 7 N T3 SD: 2.0515 c. M:-3.5372 c. 35: 9 19 7 N T3 SD: 1.8908 c. M:-3.2668 c. 39: 10 21 8 N T3 SD: 0.5358 c. M:-0.7128 c. 58: 15 31 12 N T3 SD: 0.3081 c. M:-0.5065 c. 97: 25 52 20 N T3 SD: 0.1136 c. M:-0.1862 c. 237: 61 127 49 N T3 SD: 0.0839 c. M: 0.1094 c. 295: 76 158 61 N T3 SD: 0.0637 c. M: 0.1097 c. 334: 86 179 69 N T3 SD: 0.0350 c. M: 0.0591 c. 392: 101 210 81 N T3 SD: 0.0254 c. M: 0.0365 c. 431: 111 231 89 N T3 SD: 0.0256 c. M: 0.0314 c. 489: 126 262 101 N T3 SD: 0.0192 c. M:-0.0324 c. 726: 187 389 150 N T3 SD: 0.0170 c. M: 0.0260 c. 823: 212 441 170 N T3 SD: 0.0028 c. M: 0.0048 c. 2135: 550 1144 441 N T3 SD: 0.0022 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 5 x S SD: 8.8554 cents 5 x 6:7 S SD: 58.0073 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 55.1739 cents 8:9:10:11 H SD: 30.9723 cents 9:10:11:12 H SD: 24.0567 cents 10:11 x 13 SD: 28.5854 cents 11:12:14:15 S SD: 16.7056 cents 12:13:15:16 SD: 4.5213 cents 27:29:34:36 SD: 2.0113 cents 39:42:49:52 SD: 0.0000 cents