Scala analysis: 241_C16
Chromatic tetrachord 256/243 * 81/76 * 19/16, Boethius
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 256/243 90.2250 limma, Pythagorean minor second 2: 81/76 110.3070 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 81/76 110.307 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 304/243 387.738 cents 2: 1 81/64 407.820 cents Pythagorean major third 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 : 90.2 200.5 498.0 90.2 : 110.3 407.8 498.0 200.5: 297.5 387.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 297.5130 cents 4617/4096, 207.2880 cents 256/243, 90.2250 cents 2: 200.5320 .. 407.8200 cents 4617/4096, 207.2880 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 1.840011 Largest / Average step : 1.792085 Largest / Smallest step : 3.297457 Median interval of one step : 81/76, 110.3070 cents, amount: 1 Least squares average step : 141.81600 cents, oct.: 425.44799 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2208-tone equal temperament with octave 4/3 degrees: 400 889 2208 Least number of segments generator : 1105 of 249.248 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2045 of 461.278 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 90.22500 cents Scale diversity : 1.087803 Lumma stability : 0.362317 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 : 19683/19456, 20.0820 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 187.2060 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.018038 Average absolute harmonicity : 0.094846 Specific harmonicity : 0.093943 Fundamental : 1/4617, -12.1727 octaves, 0.0567 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 1.181952E+06, 20.17274 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 313.5, average 104.50000 Mersenne's string divisions : 422653 Sum of van Prooijen's expressibility: 4.61860, average 1.53953 Sum of Tenney's harmonic distance : 9.43508, average 3.14503 Vogel's harmonic complexity : 26.00000 Wille's k value : 769 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 33.75125, average 5.62521 Lattice compactness (without 2's) : 16.53732, average 2.75622 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 5.33333 16 3: -5 ..-1 -2.33333 7 2 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-8 / 3 =-2.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 11 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 55.7733 c. M: 90.2250 c. 4: 1 1 2 P M ME S SD: 34.2874 c. M:-48.4905 c. 5: 1 1 3 N M DE S SD: 5.4707 c. M:-9.3840 c. 12: 2 3 7 N T3 SD: 5.7996 c. M: 7.2175 c. 17: 3 4 10 N T3 SD: 2.9502 c. M:-4.5454 c. 22: 4 5 13 N T3 SD: 1.8651 c. M:-3.2137 c. 27: 5 6 16 N T3 SD: 1.7948 c. M:-2.3752 c. 45: 8 10 27 N T3 SD: 1.2331 c. M: 1.6837 c. 50: 9 11 30 N T3 SD: 0.8285 c. M: 1.3140 c. 55: 10 12 33 N T3 SD: 0.7820 c. M: 1.3140 c. 67: 12 15 40 N T3 SD: 0.5989 c. M: 1.0229 c. 72: 13 16 43 N T3 SD: 0.1779 c. M: 0.3002 c. 77: 14 17 46 N T3 SD: 0.1901 c. M:-0.3286 c. 149: 27 33 89 N T3 SD: 0.0195 c. M:-0.0248 c. 668: 121 148 399 N T3 SD: 0.0172 c. M:-0.0281 c. 817: 148 181 488 N T3 SD: 0.0158 c. M:-0.0271 c. 966: 175 214 577 N T3 SD: 0.0153 c. M:-0.0265 c. 1115: 202 247 666 N T3 SD: 0.0152 c. M:-0.0260 c. 1264: 229 280 755 N T3 SD: 0.0153 c. M:-0.0257 c. 1314: 238 291 785 N T3 SD: 0.0173 c. M: 0.0253 c. 1391: 252 308 831 N T3 SD: 0.0146 c. M: 0.0250 c. 1463: 265 324 874 N T3 SD: 0.0136 c. M: 0.0204 c. 1540: 279 341 920 N T3 SD: 0.0121 c. M: 0.0204 c. 1612: 292 357 963 N T3 SD: 0.0106 c. M: 0.0163 c. 1689: 306 374 1009 N T3 SD: 0.0104 c. M: 0.0165 c. 1761: 319 390 1052 N T3 SD: 0.0082 c. M: 0.0130 c. 1910: 346 423 1141 N T3 SD: 0.0062 c. M: 0.0102 c. 2059: 373 456 1230 N T3 SD: 0.0046 c. M: 0.0078 c. 2208: 400 489 1319 N T3 SD: 0.0033 c. M: 0.0057 c. 2357: 427 522 1408 N T3 SD: 0.0025 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: 24.1738 cents 13:14:15:17 SD: 23.1142 cents 14:15:16:19 SD: 17.4214 cents 15:16:17:20 SD: 8.9660 cents 18:19:20:24 S SD: 6.1468 cents 33:35:37:44 SD: 3.9663 cents 39:41:44:52 SD: 3.0227 cents 56:59:63:75 SD: 2.8066 cents 57:60:64:76 SD: 0.4748 cents 186:196:209:248 SD: 0.4597 cents 204:215:229:272 SD: 0.2672 cents 261:275:293:348 SD: 0.1296 cents 318:335:357:424 SD: 0.0877 cents