Scala analysis: 372_D2
Diatonic tetrachord 44/41 * 41/38 * 38/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/41 122.255537 2: 22/19 253.804926 Godzilla third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 38/33 244.2401 1: 44/41 122.2555 2: 41/38 131.5494 3: 38/33 244.2401
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44/41 122.256 cents 1: 1 41/38 131.549 cents 1: 1 38/33 244.240 cents 2: 1 22/19 253.805 cents Godzilla third 2: 1 152/123 366.496 cents 2: 1 41/33 375.789 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 : 122.3 253.8 498.0 122.3: 131.5 375.8 498.0 253.8: 244.2 366.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 122.2555 .. 244.2401 cents 779/726, 121.9845 cents 44/41, 122.2555 cents 2: 253.8049 .. 375.7895 cents 779/726, 121.9845 cents 363/361, 9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 44/41, 122.2555 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 38/33, 244.2401 cents Average / Smallest step : 1.357934 Largest / Average step : 1.471193 Largest / Smallest step : 1.997783 Median interval of one step : 41/38, 131.5494 cents, amount: 1 Least squares average step : 151.71431 cents, oct.: 455.14294 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1821-tone equal temperament with octave 4/3 degrees: 447 928 1821 Least number of segments generator : 911 of 249.159 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1340 of 366.491 cents and inv. generated superset size: 19 = 16 more = 633.333% 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 9.56485 cents Scale diversity : 1.162063 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.510147 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 : 1681/1672, 9.2939 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 112.6907 cents: 2 -- Rational properties -- Prime limit : 41 Odd number limit : 123 (O: 41 U: 123) Highest odd numerator or denominator: 41 Scale harmonicity : 0.017558 Fundamental : 1/2337, -11.1904 octaves, 0.1119 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 1.028280E+05, 16.64987 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 66.5, average 22.16667 Mersenne's string divisions : 24395 Sum of van Prooijen's expressibility: 3.36866, average 1.12289 Sum of Tenney's harmonic distance : 6.95659, average 2.31886 Vogel's harmonic complexity : 51.00000 Wille's k value : 676 Wilson's harmonic complexity : 74 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.03261, average 1.83877 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.33333 1 1 11: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 41: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 25 28 36| Scale is weakly epimorphic with val: <6 10 25 28 39| Scale is weakly epimorphic with val: <6 10 25 28 42| Scale is weakly epimorphic with val: <6 10 26 29 37| Scale is weakly epimorphic with val: <6 10 26 29 40| Scale is weakly epimorphic with val: <6 10 27 29 36| Scale is weakly epimorphic with val: <6 10 27 30 38| Scale is weakly epimorphic with val: <6 10 27 30 41| Scale is weakly epimorphic with val: <6 10 27 32 36| Scale is weakly epimorphic with val: <6 11 25 28 38| Scale is weakly epimorphic with val: <6 11 25 28 41| Scale is weakly epimorphic with val: <6 11 26 29 36| Scale is weakly epimorphic with val: <6 11 26 29 39| Scale is weakly epimorphic with val: <6 11 26 29 42| Scale is weakly epimorphic with val: <6 11 27 28 36| Scale is weakly epimorphic with val: <6 11 27 30 37| Scale is weakly epimorphic with val: <6 11 27 30 40| Scale is weakly epimorphic with val: <6 11 27 31 36| Scale is weakly epimorphic with val: <6 11 27 34 36| Scale is weakly epimorphic with val: <7 10 24 28 36| Scale is weakly epimorphic with val: <7 10 24 28 39| Scale is weakly epimorphic with val: <7 10 24 28 42| Scale is weakly epimorphic with val: <7 10 25 29 37| Scale is weakly epimorphic with val: <7 10 25 29 40| Scale is weakly epimorphic with val: <7 10 25 30 36| Scale is weakly epimorphic with val: <7 10 25 33 36| Scale is weakly epimorphic with val: <7 10 26 28 37| Scale is weakly epimorphic with val: <7 10 26 30 38| Scale is weakly epimorphic with val: <7 10 26 30 41| Scale is weakly epimorphic with val: <7 10 26 31 37| Scale is weakly epimorphic with val: <7 10 26 34 37| Scale is weakly epimorphic with val: <7 10 27 29 38| Scale is weakly epimorphic with val: <7 10 27 31 36| Scale is weakly epimorphic with val: <7 10 27 31 39| Scale is weakly epimorphic with val: <7 10 27 31 42| Scale is weakly epimorphic with val: <7 10 27 32 38| Scale is JI-epimorphic with val: <7 11 23 28 36| Scale is weakly epimorphic with val: <7 11 23 28 39| Scale is weakly epimorphic with val: <7 11 23 28 42| Scale is weakly epimorphic with val: <7 11 23 29 38| Scale is weakly epimorphic with val: <7 11 23 29 41| Scale is weakly epimorphic with val: <7 11 23 31 36| Scale is weakly epimorphic with val: <7 11 23 31 39| Scale is weakly epimorphic with val: <7 11 23 31 42| Scale is weakly epimorphic with val: <7 11 23 32 38| Scale is weakly epimorphic with val: <7 11 23 32 41| Scale is weakly epimorphic with val: <7 11 23 34 36| Scale is weakly epimorphic with val: <7 11 23 34 39| Scale is weakly epimorphic with val: <7 11 23 34 42| Scale is JI-epimorphic with val: <7 11 24 29 37| Scale is weakly epimorphic with val: <7 11 24 29 40| Scale is weakly epimorphic with val: <7 11 24 30 36| Scale is weakly epimorphic with val: <7 11 24 30 39| Scale is weakly epimorphic with val: <7 11 24 30 42| Scale is weakly epimorphic with val: <7 11 24 32 37| Scale is weakly epimorphic with val: <7 11 24 32 40| Scale is weakly epimorphic with val: <7 11 24 33 36| Scale is weakly epimorphic with val: <7 11 24 33 39| Scale is weakly epimorphic with val: <7 11 24 33 42| Scale is weakly epimorphic with val: <7 11 25 28 37| Scale is weakly epimorphic with val: <7 11 25 28 40| Scale is JI-epimorphic with val: <7 11 25 30 38| Scale is weakly epimorphic with val: <7 11 25 30 41| Scale is weakly epimorphic with val: <7 11 25 31 37| Scale is weakly epimorphic with val: <7 11 25 31 40| Scale is weakly epimorphic with val: <7 11 25 33 38| Scale is weakly epimorphic with val: <7 11 25 33 41| Scale is weakly epimorphic with val: <7 11 25 34 37| Scale is weakly epimorphic with val: <7 11 25 34 40| Scale is weakly epimorphic with val: <7 11 26 28 36| Scale is weakly epimorphic with val: <7 11 26 28 39| Scale is weakly epimorphic with val: <7 11 26 28 42| Scale is weakly epimorphic with val: <7 11 26 29 38| Scale is weakly epimorphic with val: <7 11 26 29 41| Scale is weakly epimorphic with val: <7 11 26 31 36| Scale is JI-epimorphic with val: <7 11 26 31 39| Scale is weakly epimorphic with val: <7 11 26 31 42| Scale is weakly epimorphic with val: <7 11 26 32 38| Scale is weakly epimorphic with val: <7 11 26 32 41| Scale is weakly epimorphic with val: <7 11 26 34 36| Scale is weakly epimorphic with val: <7 11 26 34 39| Scale is weakly epimorphic with val: <7 11 26 34 42| Scale is weakly epimorphic with val: <7 11 27 29 37| Scale is weakly epimorphic with val: <7 11 27 29 40| Scale is weakly epimorphic with val: <7 11 27 30 36| Scale is weakly epimorphic with val: <7 11 27 30 39| Scale is weakly epimorphic with val: <7 11 27 30 42| Scale is weakly epimorphic with val: <7 11 27 32 37| Scale is JI-epimorphic with val: <7 11 27 32 40| Scale is weakly epimorphic with val: <7 11 27 33 36| Scale is weakly epimorphic with val: <7 11 27 33 39| Scale is weakly epimorphic with val: <7 11 27 33 42| Scale is weakly epimorphic with val: <7 12 24 28 37| Scale is weakly epimorphic with val: <7 12 24 28 40| Scale is weakly epimorphic with val: <7 12 25 28 36| Scale is weakly epimorphic with val: <7 12 25 29 38| Scale is weakly epimorphic with val: <7 12 25 29 41| Scale is weakly epimorphic with val: <7 12 25 31 36| Scale is weakly epimorphic with val: <7 12 25 34 36| Scale is weakly epimorphic with val: <7 12 26 29 37| Scale is weakly epimorphic with val: <7 12 26 30 36| Scale is weakly epimorphic with val: <7 12 26 30 39| Scale is weakly epimorphic with val: <7 12 26 30 42| Scale is weakly epimorphic with val: <7 12 26 32 37| Scale is weakly epimorphic with val: <7 12 27 30 38| Scale is weakly epimorphic with val: <7 12 27 31 37| Scale is weakly epimorphic with val: <7 12 27 31 40| Scale is weakly epimorphic with val: <7 12 27 33 38| Scale is weakly epimorphic with val: <8 11 23 28 38| Scale is weakly epimorphic with val: <8 11 23 28 41| Scale is weakly epimorphic with val: <8 11 23 30 36| Scale is weakly epimorphic with val: <8 11 23 33 36| Scale is weakly epimorphic with val: <8 11 24 28 37| Scale is weakly epimorphic with val: <8 11 24 29 36| Scale is weakly epimorphic with val: <8 11 24 29 39| Scale is weakly epimorphic with val: <8 11 24 29 42| Scale is weakly epimorphic with val: <8 11 24 31 37| Scale is weakly epimorphic with val: <8 11 24 34 37| Scale is weakly epimorphic with val: <8 11 25 29 38| Scale is weakly epimorphic with val: <8 11 25 30 37| Scale is weakly epimorphic with val: <8 11 25 30 40| Scale is weakly epimorphic with val: <8 11 25 32 38| Scale is weakly epimorphic with val: <8 11 26 30 39| Scale is weakly epimorphic with val: <8 11 26 31 38| Scale is weakly epimorphic with val: <8 11 26 31 41| Scale is weakly epimorphic with val: <8 11 26 33 39| Scale is weakly epimorphic with val: <8 11 27 28 40| Scale is weakly epimorphic with val: <8 11 27 31 40| Scale is weakly epimorphic with val: <8 11 27 32 36| Scale is weakly epimorphic with val: <8 11 27 32 39| Scale is weakly epimorphic with val: <8 11 27 32 42| Scale is weakly epimorphic with val: <8 11 27 34 40| Scale is weakly epimorphic with val: <8 12 23 28 37| Scale is weakly epimorphic with val: <8 12 23 28 40| Scale is weakly epimorphic with val: <8 12 23 29 36| Scale is weakly epimorphic with val: <8 12 23 32 36| Scale is weakly epimorphic with val: <8 12 24 29 38| Scale is weakly epimorphic with val: <8 12 24 29 41| Scale is weakly epimorphic with val: <8 12 24 30 37| Scale is weakly epimorphic with val: <8 12 24 33 37| Scale is weakly epimorphic with val: <8 12 25 28 38| Scale is weakly epimorphic with val: <8 12 25 30 36| Scale is weakly epimorphic with val: <8 12 25 30 39| Scale is weakly epimorphic with val: <8 12 25 30 42| Scale is weakly epimorphic with val: <8 12 25 31 38| Scale is weakly epimorphic with val: <8 12 25 34 38| Scale is weakly epimorphic with val: <8 12 26 29 39| Scale is weakly epimorphic with val: <8 12 26 31 37| Scale is weakly epimorphic with val: <8 12 26 31 40| Scale is weakly epimorphic with val: <8 12 26 32 39| Scale is weakly epimorphic with val: <8 12 27 30 40| Scale is weakly epimorphic with val: <8 12 27 32 38| Scale is weakly epimorphic with val: <8 12 27 32 41| Scale is weakly epimorphic with val: <8 12 27 33 40|
FIT/MODE
3: 0 1 2 N G T3 SD: 86.8974 c. M: 122.2555 c. 4: 1 1 2 P M ME S SD: 3.0529 c. M: 4.7824 c. 29: 7 8 14 SP T3 SD: 2.4918 c. M:-3.8046 c. 33: 8 9 16 SP T3 SD: 1.8203 c. M:-2.7637 c. 37: 9 10 18 SP T3 SD: 1.2943 c. M:-1.9479 c. 41: 10 11 20 SP T3 SD: 0.8713 c. M:-1.2913 c. 45: 11 12 22 SP T3 SD: 0.5247 c. M:-0.7514 c. 49: 12 13 24 SP T3 SD: 0.2389 c. M:-0.2997 c. 53: 13 14 26 SP T3 SD: 0.0725 c. M: 0.0936 c. 367: 90 97 180 SP T3 SD: 0.0713 c. M: 0.1192 c. 420: 103 111 206 SP T3 SD: 0.0706 c. M: 0.1159 c. 473: 116 125 232 SP T3 SD: 0.0703 c. M: 0.1134 c. 526: 129 139 258 SP T3 SD: 0.0701 c. M: 0.1114 c. 579: 142 153 284 SP T3 SD: 0.0700 c. M: 0.1098 c. 632: 155 167 310 SP T3 SD: 0.0700 c. M: 0.1084 c. 920: 226 243 451 SP T3 SD: 0.0735 c. M:-0.0903 c. 924: 227 244 453 SP T3 SD: 0.0699 c. M:-0.0997 c. 928: 228 245 455 SP T3 SD: 0.0687 c. M:-0.1090 c. 973: 239 257 477 SP T3 SD: 0.0656 c. M:-0.0803 c. 977: 240 258 479 SP T3 SD: 0.0622 c. M:-0.0892 c. 981: 241 259 481 SP T3 SD: 0.0613 c. M:-0.0980 c. 1026: 252 271 503 SP T3 SD: 0.0584 c. M:-0.0718 c. 1030: 253 272 505 SP T3 SD: 0.0553 c. M:-0.0798 c. 1034: 254 273 507 SP T3 SD: 0.0546 c. M:-0.0882 c. 1079: 265 285 529 SP T3 SD: 0.0520 c. M:-0.0642 c. 1083: 266 286 531 SP T3 SD: 0.0491 c. M:-0.0713 c. 1087: 267 287 533 SP T3 SD: 0.0487 c. M:-0.0793 c. 1132: 278 299 555 SP T3 SD: 0.0462 c. M:-0.0572 c. 1136: 279 300 557 SP T3 SD: 0.0434 c. M:-0.0636 c. 1140: 280 301 559 SP T3 SD: 0.0433 c. M:-0.0713 c. 1185: 291 313 581 SP T3 SD: 0.0409 c. M:-0.0509 c. 1189: 292 314 583 SP T3 SD: 0.0383 c. M:-0.0566 c. 1238: 304 327 607 SP T3 SD: 0.0360 c. M:-0.0452 c. 1242: 305 328 609 SP T3 SD: 0.0336 c. M:-0.0502 c. 1291: 317 341 633 SP T3 SD: 0.0316 c. M:-0.0399 c. 1295: 318 342 635 SP T3 SD: 0.0294 c. M:-0.0443 c. 1344: 330 355 659 SP T3 SD: 0.0275 c. M:-0.0350 c. 1348: 331 356 661 SP T3 SD: 0.0254 c. M:-0.0389 c. 1397: 343 369 685 SP T3 SD: 0.0237 c. M:-0.0305 c. 1401: 344 370 687 SP T3 SD: 0.0218 c. M:-0.0339 c. 1450: 356 383 711 SP T3 SD: 0.0202 c. M:-0.0263 c. 1454: 357 384 713 SP T3 SD: 0.0185 c. M:-0.0292 c. 1503: 369 397 737 SP T3 SD: 0.0170 c. M:-0.0224 c. 1507: 370 398 739 SP T3 SD: 0.0154 c. M:-0.0249 c. 1556: 382 411 763 SP T3 SD: 0.0139 c. M:-0.0188 c. 1560: 383 412 765 SP T3 SD: 0.0126 c. M:-0.0209 c. 1609: 395 425 789 SP T3 SD: 0.0111 c. M:-0.0154 c. 1613: 396 426 791 SP T3 SD: 0.0101 c. M:-0.0171 c. 1662: 408 439 815 SP T3 SD: 0.0085 c. M:-0.0122 c. 1666: 409 440 817 SP T3 SD: 0.0079 c. M:-0.0136 c. 1715: 421 453 841 SP T3 SD: 0.0061 c. M:-0.0093 c. 1719: 422 454 843 SP T3 SD: 0.0061 c. M:-0.0103 c. 1768: 434 467 867 SP T3 SD: 0.0039 c. M:-0.0065 c. 1821: 447 481 893 SP T3 SD: 0.0022 c. M:-0.0038 c. 1874: 460 495 919 SP T3 SD: 0.0021 c. M: 0.0033 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: 52.3413 cents 6 x 7:8 S SD: 6.5330 cents 7 x 8:9 S SD: 33.4523 cents 8 x 9:11 SD: 36.4949 cents 9:10 x 12 S SD: 30.0741 cents 10:11:12:13 H SD: 29.0064 cents 11:12:13:15 SD: 19.9239 cents 12:13:14:16 S SD: 6.9679 cents 25:27:29:33 SD: 6.9381 cents 26:28:30:35 S SD: 6.2160 cents 27:29:31:36 SD: 4.9022 cents 38:41:44:51 SD: 4.8905 cents 39:42:45:52 SD: 2.8536 cents 57:61:66:76 SD: 1.6129 cents 69:74:80:92 SD: 0.8497 cents 96:103:111:128 SD: 0.8316 cents 108:116:125:144 SD: 0.5429 cents 165:177:191:220 SD: 0.2866 cents 177:190:205:236 SD: 0.2096 cents 273:293:316:364 SD: 0.1981 cents 342:367:396:456 SD: 0.0384 cents