Scala analysis: 258_C17
Chromatic tetrachord 243/229 * 229/216 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 243/229 102.730459 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: 243/229 102.7305 2: 229/216 101.1795 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 229/216 101.180 cents 1: 1 243/229 102.730 cents 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 916/729 395.315 cents 2: 1 288/229 396.865 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 : 102.7 203.9 498.0 102.7: 101.2 395.3 498.0 203.9: 294.1 396.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.1795 .. 294.1350 cents 256/229, 192.9555 cents 229/216, 101.1795 cents 2: 203.9100 .. 396.8655 cents 256/229, 192.9555 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 229/216, 101.1795 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.640796 Largest / Average step : 1.771737 Largest / Smallest step : 2.907060 Median interval of one step : 243/229, 102.7305 cents, amount: 1 Least squares average step : 143.19182 cents, oct.: 429.57546 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1275-tone equal temperament with octave 4/3 degrees: 263 522 1275 Least number of segments generator : 638 of 249.218 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1106 of 432.030 cents and inv. generated superset size: 90 = 87 more = 3000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.088561 Lumma stability : 0.406307 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 : 52488/52441, 1.5509 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 192.9555 cents: 2 -- Rational properties -- Prime limit : 229 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.047619 Fundamental : 1/5496, -12.4242 octaves, 0.0476 Hz. Guide tone : 972, 9.9248 octaves, 254300.049 Hz. Exponens Consonantiae : 5.342112E+06, 22.34898 octaves Euler's gradus suavitatis : 246 Sum of Mann's harmonic distance : 248.0, average 82.66667 Mersenne's string divisions : 56168 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.68196, average 2.56065 Vogel's harmonic complexity : 164.33333 Wille's k value : 3091 Wilson's harmonic complexity : 247 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 27.23977, average 4.53996 Lattice compactness (without 2's) : 20.00000, average 3.33333 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.33333 5 3: -1 .. 5 2.00000 8 2 229: -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 weakly epimorphic with val: <7 11 56| Scale is weakly epimorphic with val: <7 12 56|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.2181 c. M: 102.7305 c. 4: 1 1 2 P M ME S SD: 28.9225 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 3.2536 c. M: 4.6920 c. 24: 5 5 14 N M DE S SD: 2.1665 c. M:-3.6087 c. 29: 6 6 17 N M DE S SD: 1.2702 c. M:-2.1776 c. 34: 7 7 20 N M DE S SD: 0.6830 c. M:-1.1674 c. 39: 8 8 23 N M DE S SD: 0.4062 c. M: 0.5674 c. 83: 17 17 49 N M DE S SD: 0.4211 c. M: 0.7212 c. 122: 25 25 72 N M DE S SD: 0.4060 c. M: 0.6721 c. 127: 26 26 75 N M DE S SD: 0.4438 c. M: 0.7685 c. 151: 31 31 89 N M DE S SD: 0.4381 c. M:-0.5853 c. 159: 33 32 94 N T3 SD: 0.4084 c. M:-0.6374 c. 161: 33 33 95 N M DE S SD: 0.4019 c. M: 0.6467 c. 164: 34 33 97 N T3 SD: 0.3946 c. M:-0.5228 c. 183: 38 37 108 N T3 SD: 0.4152 c. M:-0.6887 c. 188: 39 38 111 N T3 SD: 0.3420 c. M:-0.5874 c. 193: 40 39 114 N T3 SD: 0.2850 c. M:-0.4913 c. 198: 41 40 117 N T3 SD: 0.2497 c. M:-0.4001 c. 203: 42 41 120 N T3 SD: 0.2410 c. M:-0.3133 c. 227: 47 46 134 N T3 SD: 0.2377 c. M:-0.3890 c. 232: 48 47 137 N T3 SD: 0.1818 c. M:-0.3133 c. 237: 49 48 140 N T3 SD: 0.1446 c. M:-0.2409 c. 242: 50 49 143 N T3 SD: 0.1371 c. M:-0.1714 c. 271: 56 55 160 N T3 SD: 0.1187 c. M:-0.1866 c. 276: 57 56 163 N T3 SD: 0.0731 c. M:-0.1267 c. 281: 58 57 166 N T3 SD: 0.0626 c. M: 0.0838 c. 315: 65 64 186 N T3 SD: 0.0378 c. M:-0.0513 c. 320: 66 65 189 N T3 SD: 0.0141 c. M: 0.0228 c. 635: 131 129 375 N T3 SD: 0.0122 c. M:-0.0158 c. 955: 197 194 564 N T3 SD: 0.0045 c. M:-0.0076 c. 1275: 263 259 753 N T3 SD: 0.0033 c. M: 0.0045 c. 2230: 460 453 1317 N T3 SD: 0.0032 c. M:-0.0053 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 11:12 x 15 S SD: 30.8573 cents 12:13:14:16 S SD: 24.1494 cents 13:14:15:17 SD: 20.2895 cents 14:15:16:19 SD: 14.7632 cents 15:16:17:20 SD: 5.2096 cents 32:34:36:43 SD: 4.5517 cents 33:35:37:44 SD: 1.9675 cents 48:51:54:64 SD: 0.7417 cents 129:137:145:172 SD: 0.6901 cents 177:188:199:236 SD: 0.6585 cents 216:229:243:288 SD: 0.5170 cents 231:245:260:308 SD: 0.3999 cents 264:280:297:352 SD: 0.2879 cents 279:296:314:372 SD: 0.2550 cents 312:331:351:416 SD: 0.1294 cents 360:382:405:480 SD: 0.0132 cents