Scala analysis: 247_C17
Chromatic tetrachord 27/26 * 13/12 * 32/27, Barbour?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/26 65.337341 tridecimal comma 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 27/26 65.3373 tridecimal comma 2: 13/12 138.5727 tridecimal 2/3-tone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/26 65.337 cents tridecimal comma 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 104/81 432.708 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 : 65.3 203.9 498.0 65.3 : 138.6 432.7 498.0 203.9: 294.1 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.3373 .. 294.1350 cents 832/729, 228.7977 cents 27/26, 65.3373 cents 2: 203.9100 .. 432.7077 cents 832/729, 228.7977 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/26, 65.3373 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.540890 Largest / Average step : 1.771737 Largest / Smallest step : 4.501790 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 140.52088 cents, oct.: 421.56264 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1700-tone equal temperament with octave 4/3 degrees: 223 696 1700 Least number of segments generator : 851 of 249.315 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 879 of 257.519 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 65.33734 cents Scale diversity : 0.999257 Lumma stability : 0.262375 Lumma impropriety factor : 0.181158 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 : 27/26, 65.3373 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 : 13 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026441 Average absolute harmonicity : 0.122128 Specific harmonicity : 0.133561 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 3.369600E+04, 15.04029 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 38.5, average 12.83333 Mersenne's string divisions : 6307 Sum of van Prooijen's expressibility: 2.86273, average 0.95424 Sum of Tenney's harmonic distance : 5.78285, average 1.92762 Vogel's harmonic complexity : 18.00000 Wille's k value : 175 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 22.53771, average 3.75628 Lattice compactness (without 2's) : 14.69960, average 2.44993 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 6 3: -1 .. 3 1.33333 6 2 13: -1 .. 0 -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: <7 11 27| = patent Scale is weakly epimorphic with val: <7 11 30| Scale is weakly epimorphic with val: <7 12 25| Scale is weakly epimorphic with val: <7 12 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.6081 c. M: 65.3373 c. 5: 1 1 3 N M DE S SD: 19.9713 c. M:-34.2717 c. 7: 1 2 4 N T3 SD: 6.4485 c. M:-9.5379 c. 15: 2 4 9 N T3 SD: 2.7783 c. M: 4.6920 c. 22: 3 6 13 N T3 SD: 1.4914 c. M:-2.5779 c. 37: 5 10 22 N T3 SD: 1.6191 c. M: 1.9999 c. 39: 5 11 23 N T3 SD: 0.8906 c. M: 1.4854 c. 54: 7 15 32 N T3 SD: 0.7320 c. M: 1.0028 c. 61: 8 17 36 N T3 SD: 0.1200 c. M:-0.2068 c. 198: 26 55 117 N T3 SD: 0.1015 c. M: 0.1643 c. 237: 31 66 140 N T3 SD: 0.1179 c. M: 0.1922 c. 259: 34 72 153 N T3 SD: 0.0509 c. M: 0.0769 c. 320: 42 89 189 N T3 SD: 0.0223 c. M:-0.0311 c. 381: 50 106 225 N T3 SD: 0.0155 c. M:-0.0229 c. 701: 92 195 414 N T3 SD: 0.0155 c. M:-0.0266 c. 1082: 142 301 639 N T3 SD: 0.0147 c. M:-0.0253 c. 1258: 165 350 743 N T3 SD: 0.0141 c. M: 0.0204 c. 1319: 173 367 779 N T3 SD: 0.0098 c. M: 0.0138 c. 1380: 181 384 815 N T3 SD: 0.0081 c. M: 0.0140 c. 1639: 215 456 968 N T3 SD: 0.0077 c. M: 0.0124 c. 1700: 223 473 1004 N T3 SD: 0.0041 c. M: 0.0056 c. 1761: 231 490 1040 N T3 SD: 0.0039 c. M: 0.0061 c. 2081: 273 579 1229 N T3 SD: 0.0007 c. M: 0.0011 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12 x 14:16 S SD: 31.4805 cents 13:14:15:17 SD: 27.9192 cents 14:15:16:19 SD: 22.6315 cents 15:16:17:20 SD: 16.0404 cents 16:17:18:21 S SD: 16.0309 cents 17:18:19:23 SD: 14.5211 cents 18:19:20:24 S SD: 11.8391 cents 21:22:24:28 S SD: 10.4049 cents 22:23:25:29 SD: 9.5987 cents 23:24:26:31 SD: 7.3750 cents 24:25:27:32 SD: 1.7784 cents 78:81:88:104 SD: 1.6418 cents 81:84:91:108 SD: 1.1203 cents 105:109:118:140 SD: 0.6440 cents 129:134:145:172 SD: 0.5241 cents 183:190:206:244 SD: 0.3692 cents 207:215:233:276 SD: 0.3264 cents 264:274:297:352 SD: 0.3239 cents 288:299:324:384 SD: 0.1484 cents 312:324:351:416 SD: 0.0000 cents