Scala analysis: 237_C16
Chromatic tetrachord 128/121 * 121/114 * 19/16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128/121 97.364115 undecimal semitone 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 128/121 97.3641 undecimal semitone 2: 121/114 103.1679 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/121 97.364 cents undecimal semitone 1: 1 121/114 103.168 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 152/121 394.877 cents 2: 1 121/96 400.681 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 : 97.4 200.5 498.0 97.4 : 103.2 400.7 498.0 200.5: 297.5 394.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.3641 .. 297.5130 cents 2299/2048, 200.1489 cents 128/121, 97.3641 cents 2: 200.5320 .. 400.6809 cents 2299/2048, 200.1489 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/121, 97.3641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 1.705094 Largest / Average step : 1.792085 Largest / Smallest step : 3.055674 Median interval of one step : 121/114, 103.1679 cents, amount: 1 Least squares average step : 142.32593 cents, oct.: 426.97780 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1284-tone equal temperament with octave 4/3 degrees: 251 517 1284 Least number of segments generator : 643 of 249.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1027 of 398.358 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 96.98103 cents Scale diversity : 1.082268 Lumma stability : 0.390985 Lumma impropriety factor : 0.194723 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 : 14641/14592, 5.8038 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 194.3451 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012479 Average absolute harmonicity : 0.086908 Specific harmonicity : 0.064758 Fundamental : 1/6897, -12.7518 octaves, 0.0379 Hz. Guide tone : 128, 7.0000 octaves, 33488.072 Hz. Exponens Consonantiae : 8.828160E+05, 19.75175 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 188.5, average 62.83333 Mersenne's string divisions : 210903 Sum of van Prooijen's expressibility: 4.31578, average 1.43859 Sum of Tenney's harmonic distance : 8.83123, average 2.94374 Vogel's harmonic complexity : 33.33333 Wille's k value : 1149 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 27.92667, average 4.65445 Lattice compactness (without 2's) : 10.09977, average 1.68330 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 7 5.00000 15 3: -1 .. 0 -0.66667 2 1 11: -2 .. 0 -0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 23 30| Scale is weakly epimorphic with val: <7 10 23 33| Scale is weakly epimorphic with val: <7 10 25 29| Scale is JI-epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 24 32| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 12 23 29| Scale is weakly epimorphic with val: <7 12 23 32| Scale is weakly epimorphic with val: <8 11 23 34| Scale is weakly epimorphic with val: <8 11 26 34| Scale is weakly epimorphic with val: <8 12 24 33| Scale is weakly epimorphic with val: <8 12 27 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 59.6411 c. M: 97.3641 c. 4: 1 1 2 P M ME S SD: 32.0848 c. M:-48.4905 c. 5: 1 1 3 N M DE S SD: 1.5018 c. M:-2.2449 c. 47: 9 10 28 N T3 SD: 1.2415 c. M: 1.9938 c. 52: 10 11 31 N T3 SD: 0.9795 c. M: 1.5862 c. 57: 11 12 34 N T3 SD: 0.7640 c. M: 1.2502 c. 62: 12 13 37 N T3 SD: 0.5840 c. M: 0.9683 c. 67: 13 14 40 N T3 SD: 0.4323 c. M: 0.7285 c. 72: 14 15 43 N T3 SD: 0.3041 c. M: 0.5220 c. 77: 15 16 46 N T3 SD: 0.1980 c. M: 0.3424 c. 82: 16 17 49 N T3 SD: 0.1210 c. M: 0.1846 c. 87: 17 18 52 N T3 SD: 0.1010 c. M: 0.1691 c. 169: 33 35 101 N T3 SD: 0.1016 c. M: 0.1352 c. 256: 50 53 153 N T3 SD: 0.0993 c. M: 0.1467 c. 343: 67 71 205 N T3 SD: 0.0989 c. M: 0.1524 c. 420: 82 87 251 N T3 SD: 0.1041 c. M: 0.1282 c. 425: 83 88 254 N T3 SD: 0.0999 c. M: 0.1421 c. 430: 84 89 257 N T3 SD: 0.0990 c. M: 0.1557 c. 675: 132 140 403 N T3 SD: 0.0951 c. M:-0.1617 c. 680: 133 141 406 N T3 SD: 0.0913 c. M:-0.1509 c. 685: 134 142 409 N T3 SD: 0.0889 c. M:-0.1402 c. 690: 135 143 412 N T3 SD: 0.0878 c. M:-0.1296 c. 695: 136 144 415 N T3 SD: 0.0880 c. M:-0.1192 c. 700: 137 145 418 N T3 SD: 0.0896 c. M:-0.1104 c. 747: 146 155 446 N T3 SD: 0.0891 c. M:-0.1528 c. 752: 147 156 449 N T3 SD: 0.0827 c. M:-0.1431 c. 757: 148 157 452 N T3 SD: 0.0772 c. M:-0.1334 c. 762: 149 158 455 N T3 SD: 0.0727 c. M:-0.1239 c. 767: 150 159 458 N T3 SD: 0.0695 c. M:-0.1146 c. 772: 151 160 461 N T3 SD: 0.0677 c. M:-0.1053 c. 777: 152 161 464 N T3 SD: 0.0672 c. M:-0.0962 c. 782: 153 162 467 N T3 SD: 0.0681 c. M:-0.0872 c. 839: 164 174 501 N T3 SD: 0.0642 c. M:-0.1107 c. 844: 165 175 504 N T3 SD: 0.0591 c. M:-0.1023 c. 849: 166 176 507 N T3 SD: 0.0550 c. M:-0.0939 c. 854: 167 177 510 N T3 SD: 0.0522 c. M:-0.0857 c. 859: 168 178 513 N T3 SD: 0.0508 c. M:-0.0775 c. 864: 169 179 516 N T3 SD: 0.0509 c. M:-0.0695 c. 869: 170 180 519 N T3 SD: 0.0525 c. M:-0.0670 c. 926: 181 192 553 N T3 SD: 0.0494 c. M:-0.0844 c. 931: 182 193 556 N T3 SD: 0.0444 c. M:-0.0769 c. 936: 183 194 559 N T3 SD: 0.0405 c. M:-0.0695 c. 941: 184 195 562 N T3 SD: 0.0380 c. M:-0.0621 c. 946: 185 196 565 N T3 SD: 0.0372 c. M:-0.0549 c. 951: 186 197 568 N T3 SD: 0.0380 c. M:-0.0477 c. 1013: 198 210 605 N T3 SD: 0.0374 c. M:-0.0626 c. 1018: 199 211 608 N T3 SD: 0.0324 c. M:-0.0559 c. 1023: 200 212 611 N T3 SD: 0.0286 c. M:-0.0492 c. 1028: 201 213 614 N T3 SD: 0.0263 c. M:-0.0426 c. 1033: 202 214 617 N T3 SD: 0.0260 c. M:-0.0360 c. 1105: 216 229 660 N T3 SD: 0.0226 c. M:-0.0382 c. 1110: 217 230 663 N T3 SD: 0.0185 c. M:-0.0321 c. 1115: 218 231 666 N T3 SD: 0.0164 c. M:-0.0260 c. 1120: 219 232 669 N T3 SD: 0.0170 c. M:-0.0215 c. 1192: 233 247 712 N T3 SD: 0.0148 c. M:-0.0231 c. 1197: 234 248 715 N T3 SD: 0.0101 c. M:-0.0175 c. 1202: 235 249 718 N T3 SD: 0.0081 c. M:-0.0119 c. 1284: 251 266 767 N T3 SD: 0.0040 c. M: 0.0049 c. 1289: 252 267 770 N T3 SD: 0.0022 c. M:-0.0039 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: 71.3878 cents 6 x 7:8 S SD: 33.1695 cents 7 x 8:9 S SD: 35.0108 cents 8 x 9:11 SD: 26.6900 cents 9 x 10:12 S SD: 9.0641 cents 10 x 11:13 SD: 28.2107 cents 11 x 12:15 S SD: 31.6353 cents 12:13 x 16 SD: 20.6043 cents 14:15:16:19 SD: 16.2116 cents 15:16:17:20 SD: 7.2064 cents 18:19:20:24 S SD: 6.1714 cents 32:34:36:43 SD: 5.2763 cents 33:35:37:44 SD: 1.7104 cents 72:76:81:96 SD: 1.6851 cents 90:95:101:120 SD: 1.2892 cents 105:111:118:140 SD: 0.6440 cents 138:146:155:184 SD: 0.2066 cents 294:311:330:392 SD: 0.1847 cents 399:422:448:532 SD: 0.1130 cents 432:457:485:576 SD: 0.0635 cents 570:603:640:760 SD: 0.0237 cents