Scala analysis: 049_E2
Enharmonic tetrachord 46/45 * 45/44 * 88/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 23/22 76.956405 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 88/69 421.0886 1: 46/45 38.0506 23rd-partial chroma 2: 45/44 38.9058 1/5-tone 3: 88/69 421.0886
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 45/44 38.906 cents 1/5-tone 1: 1 88/69 421.089 cents 2: 1 23/22 76.956 cents 2: 1 176/135 459.139 cents 2: 1 30/23 459.994 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 : 38.1 77.0 498.0 38.1 : 38.9 460.0 498.0 77.0 : 421.1 459.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 421.0886 cents 660/529, 383.0380 cents 46/45, 38.0506 cents 2: 76.9564 .. 459.9944 cents 660/529, 383.0380 cents 1587/1936,-344.1322 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 88/69, 421.0886 cents Average / Smallest step : 4.363002 Largest / Average step : 2.536449 Largest / Smallest step : 11.066534 Median interval of one step : 45/44, 38.9058 cents, amount: 1 Least squares average step : 120.43560 cents, oct.: 361.30681 cents Scale is not proper Scale has trivalence property Scale is a mode of a 576-tone equal temperament with octave 4/3 degrees: 44 89 576 Least number of segments generator : 289 of 249.887 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 443 of 383.045 cents and inv. generated superset size: 10 = 7 more = 333.333% 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 38.05063 cents Scale diversity : 0.257517 Lumma stability : 0.152800 Lumma impropriety factor : 0.690966 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 : 2025/2024, 0.8551 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 : 2 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 Limited inverse transpositions with margin 382.1828 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.013333 Average absolute harmonicity : 0.082949 Specific harmonicity : 0.059092 Fundamental : 1/990, -9.9513 octaves, 0.2643 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 9.108000E+04, 16.47485 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 71.5, average 23.83333 Mersenne's string divisions : 4095 Sum of van Prooijen's expressibility: 3.49206, average 1.16402 Sum of Tenney's harmonic distance : 7.09930, average 2.36643 Vogel's harmonic complexity : 30.66667 Wille's k value : 517 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.24025, average 2.54004 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 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: <6 10 15 24 33| Scale is weakly epimorphic with val: <6 10 15 25 32| Scale is weakly epimorphic with val: <6 10 15 27 36| Scale is weakly epimorphic with val: <6 10 16 23 33| Scale is weakly epimorphic with val: <6 10 16 25 34| Scale is weakly epimorphic with val: <6 10 16 26 33| Scale is weakly epimorphic with val: <6 10 17 23 32| Scale is weakly epimorphic with val: <6 10 17 24 34| Scale is weakly epimorphic with val: <6 10 17 26 35| Scale is weakly epimorphic with val: <6 10 17 27 34| Scale is weakly epimorphic with val: <6 10 18 24 33| Scale is weakly epimorphic with val: <6 10 18 25 35| Scale is weakly epimorphic with val: <6 10 18 27 36| Scale is weakly epimorphic with val: <6 10 19 23 36| Scale is weakly epimorphic with val: <6 10 19 25 34| Scale is weakly epimorphic with val: <6 10 19 26 36| Scale is weakly epimorphic with val: <6 11 15 23 34| Scale is weakly epimorphic with val: <6 11 15 24 33| Scale is weakly epimorphic with val: <6 11 15 26 34| Scale is weakly epimorphic with val: <6 11 15 27 36| Scale is weakly epimorphic with val: <6 11 16 24 35| Scale is weakly epimorphic with val: <6 11 16 25 34| Scale is weakly epimorphic with val: <6 11 16 27 35| Scale is weakly epimorphic with val: <6 11 17 23 32| Scale is weakly epimorphic with val: <6 11 17 25 36| Scale is weakly epimorphic with val: <6 11 17 26 35| Scale is weakly epimorphic with val: <6 11 18 24 33| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 19 25 34| Scale is weakly epimorphic with val: <7 10 15 23 33| Scale is weakly epimorphic with val: <7 10 15 25 31| Scale is weakly epimorphic with val: <7 10 15 26 36| Scale is weakly epimorphic with val: <7 10 16 23 32| Scale is weakly epimorphic with val: <7 10 16 24 34| Scale is weakly epimorphic with val: <7 10 16 26 32| Scale is weakly epimorphic with val: <7 10 17 24 33| Scale is weakly epimorphic with val: <7 10 17 25 35| Scale is weakly epimorphic with val: <7 10 17 27 33| Scale is weakly epimorphic with val: <7 10 18 23 33| Scale is weakly epimorphic with val: <7 10 18 25 34| Scale is weakly epimorphic with val: <7 10 18 26 36| Scale is weakly epimorphic with val: <7 10 19 23 35| Scale is weakly epimorphic with val: <7 10 19 24 34| Scale is weakly epimorphic with val: <7 10 19 26 35| Scale is weakly epimorphic with val: <7 11 15 24 32| Scale is weakly epimorphic with val: <7 11 15 24 35| Scale is weakly epimorphic with val: <7 11 15 25 31| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is JI-epimorphic with val: <7 11 16 23 32| Scale is weakly epimorphic with val: <7 11 16 23 35| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 25 33| Scale is weakly epimorphic with val: <7 11 16 25 36| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 26 35| Scale is weakly epimorphic with val: <7 11 17 23 31| Scale is weakly epimorphic with val: <7 11 17 23 34| Scale is weakly epimorphic with val: <7 11 17 24 30| Scale is JI-epimorphic with val: <7 11 17 24 33| Scale is weakly epimorphic with val: <7 11 17 24 36| Scale is weakly epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 26 34| Scale is weakly epimorphic with val: <7 11 17 27 30| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 18 24 32| Scale is weakly epimorphic with val: <7 11 18 24 35| Scale is weakly epimorphic with val: <7 11 18 25 31| Scale is JI-epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 23 35| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 25 36| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is JI-epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 12 15 23 33| Scale is weakly epimorphic with val: <7 12 15 24 35| Scale is weakly epimorphic with val: <7 12 15 26 36| Scale is weakly epimorphic with val: <7 12 15 27 35| Scale is weakly epimorphic with val: <7 12 16 24 34| Scale is weakly epimorphic with val: <7 12 16 25 36| Scale is weakly epimorphic with val: <7 12 17 25 35| Scale is weakly epimorphic with val: <7 12 18 23 33| Scale is weakly epimorphic with val: <7 12 18 26 36| Scale is weakly epimorphic with val: <7 12 19 24 34| Scale is weakly epimorphic with val: <8 11 15 23 32| Scale is weakly epimorphic with val: <8 11 15 25 36| Scale is weakly epimorphic with val: <8 11 15 26 32| Scale is weakly epimorphic with val: <8 11 16 23 34| Scale is weakly epimorphic with val: <8 11 16 24 33| Scale is weakly epimorphic with val: <8 11 16 27 33| Scale is weakly epimorphic with val: <8 11 17 24 35| Scale is weakly epimorphic with val: <8 11 17 25 34| Scale is weakly epimorphic with val: <8 11 18 23 35| Scale is weakly epimorphic with val: <8 11 18 25 36| Scale is weakly epimorphic with val: <8 11 18 26 35| Scale is weakly epimorphic with val: <8 11 19 23 34| Scale is weakly epimorphic with val: <8 11 19 24 36| Scale is weakly epimorphic with val: <8 11 19 27 36| Scale is weakly epimorphic with val: <8 12 15 24 34| Scale is weakly epimorphic with val: <8 12 15 25 36| Scale is weakly epimorphic with val: <8 12 15 27 34| Scale is weakly epimorphic with val: <8 12 16 23 34| Scale is weakly epimorphic with val: <8 12 16 25 35| Scale is weakly epimorphic with val: <8 12 17 23 36| Scale is weakly epimorphic with val: <8 12 17 24 35| Scale is weakly epimorphic with val: <8 12 17 26 36| Scale is weakly epimorphic with val: <8 12 18 25 36| Scale is weakly epimorphic with val: <8 12 19 23 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 49.5652 c. M: 76.9564 c. 5: 0 1 4 N G T3 SD: 25.5668 c. M: 38.0506 c. 6: 0 1 5 N G T3 SD: 22.2446 c. M: 38.0506 c. 7: 0 1 6 N G T3 SD: 22.2229 c. M: 38.0506 c. 8: 0 1 7 N G T3 SD: 23.5511 c. M: 38.0506 c. 9: 1 0 8 N G T3 SD: 15.9813 c. M: 21.6181 c. 10: 1 1 8 N M DE S SD: 14.7342 c. M:-22.6526 c. 11: 1 1 9 N M DE S SD: 8.8901 c. M:-13.5972 c. 12: 1 1 10 N M DE S SD: 4.0224 c. M:-6.0511 c. 13: 1 1 11 N M DE S SD: 0.2446 c. M: 0.3341 c. 168: 13 13 142 N M DE S SD: 0.2907 c. M:-0.4886 c. 181: 14 14 153 N M DE S SD: 0.2774 c. M:-0.4722 c. 194: 15 15 164 N M DE S SD: 0.2668 c. M:-0.4580 c. 207: 16 16 175 N M DE S SD: 0.2581 c. M:-0.4456 c. 220: 17 17 186 N M DE S SD: 0.2511 c. M:-0.4347 c. 233: 18 18 197 N M DE S SD: 0.2454 c. M:-0.4249 c. 246: 19 19 208 N M DE S SD: 0.2407 c. M:-0.4163 c. 259: 20 20 219 N M DE S SD: 0.2368 c. M:-0.4084 c. 272: 21 21 230 N M DE S SD: 0.2337 c. M:-0.4014 c. 285: 22 22 241 N M DE S SD: 0.2311 c. M:-0.3949 c. 290: 22 23 245 N T3 SD: 0.2438 c. M:-0.3264 c. 291: 22 23 246 N T3 SD: 0.2323 c. M: 0.3977 c. 298: 23 23 252 N M DE S SD: 0.2290 c. M:-0.3891 c. 303: 23 24 256 N T3 SD: 0.2229 c. M:-0.2981 c. 304: 23 24 257 N T3 SD: 0.2149 c. M: 0.3696 c. 316: 24 25 267 N T3 SD: 0.2036 c. M:-0.2721 c. 317: 24 25 268 N T3 SD: 0.1991 c. M: 0.3438 c. 329: 25 26 278 N T3 SD: 0.1859 c. M:-0.2481 c. 330: 25 26 279 N T3 SD: 0.1849 c. M: 0.3199 c. 342: 26 27 289 N T3 SD: 0.1696 c. M:-0.2260 c. 343: 26 27 290 N T3 SD: 0.1720 c. M: 0.2979 c. 355: 27 28 300 N T3 SD: 0.1544 c. M:-0.2055 c. 356: 27 28 301 N T3 SD: 0.1604 c. M: 0.2776 c. 368: 28 29 311 N T3 SD: 0.1403 c. M:-0.1864 c. 369: 28 29 312 N T3 SD: 0.1499 c. M: 0.2586 c. 381: 29 30 322 N T3 SD: 0.1272 c. M:-0.1687 c. 382: 29 30 323 N T3 SD: 0.1404 c. M: 0.2409 c. 394: 30 31 333 N T3 SD: 0.1149 c. M:-0.1521 c. 395: 30 31 334 N T3 SD: 0.1319 c. M: 0.2244 c. 407: 31 32 344 N T3 SD: 0.1034 c. M:-0.1366 c. 420: 32 33 355 N T3 SD: 0.0927 c. M:-0.1220 c. 433: 33 34 366 N T3 SD: 0.0826 c. M:-0.1083 c. 446: 34 35 377 N T3 SD: 0.0730 c. M:-0.0954 c. 459: 35 36 388 N T3 SD: 0.0641 c. M:-0.0832 c. 472: 36 37 399 N T3 SD: 0.0556 c. M:-0.0717 c. 485: 37 38 410 N T3 SD: 0.0475 c. M:-0.0609 c. 498: 38 39 421 N T3 SD: 0.0399 c. M:-0.0506 c. 511: 39 40 432 N T3 SD: 0.0327 c. M:-0.0408 c. 524: 40 41 443 N T3 SD: 0.0259 c. M: 0.0319 c. 537: 41 42 454 N T3 SD: 0.0194 c. M: 0.0248 c. 550: 42 43 465 N T3 SD: 0.0133 c. M: 0.0181 c. 563: 43 44 476 N T3 SD: 0.0076 c. M: 0.0117 c. 576: 44 45 487 N T3 SD: 0.0033 c. M: 0.0055 c. 1165: 89 91 985 N T3 SD: 0.0034 c. M: 0.0052 c. 1741: 133 136 1472 N T3 SD: 0.0031 c. M: 0.0040 c. 2317: 177 181 1959 N T3 SD: 0.0030 c. M: 0.0040 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 94.9573 cents 7 x 8:9 S SD: 83.2874 cents 8 x 9:11 SD: 68.8390 cents 9 x 10:12 S SD: 52.7237 cents 10 x 11:13 SD: 49.1772 cents 11 x 12:15 S SD: 41.6608 cents 12 x 13:16 SD: 30.8081 cents 13 x 14:17 SD: 30.6843 cents 14 x 15:19 SD: 26.1918 cents 15 x 16:20 S SD: 17.3874 cents 16 x 17:21 SD: 19.5402 cents 17 x 18:23 SD: 16.7533 cents 18 x 19:24 SD: 8.3233 cents 19 x 20:25 S SD: 12.9044 cents 20 x 21:27 SD: 11.3900 cents 21 x 22:28 SD: 1.7903 cents 22 x 23:29 SD: 9.8929 cents 23 x 24:31 SD: 9.5004 cents 24 x 25:32 SD: 3.1420 cents 25 x 26:33 SD: 9.8076 cents 26 x 27:35 SD: 10.1176 cents 27 x 28:36 SD: 6.9978 cents 28 x 29:37 SD: 11.2215 cents 29 x 30:39 SD: 11.7733 cents 30:31 x 40 SD: 9.3581 cents 31:32 x 41 SD: 10.9839 cents 32:33 x 43 SD: 10.1641 cents 33:34:35:44 SD: 9.4654 cents 34:35:36:45 S SD: 9.3950 cents 35:36:37:47 SD: 8.4145 cents 36:37:38:48 SD: 6.3697 cents 38:39:40:51 SD: 5.9352 cents 39:40:41:52 SD: 3.7420 cents 42:43:44:56 SD: 1.4921 cents 45:46:47:60 SD: 0.5578 cents 87:89:91:116 SD: 0.5197 cents 132:135:138:176 SD: 0.2850 cents 177:181:185:236 SD: 0.2555 cents 486:497:508:648 SD: 0.2542 cents 504:515:527:672 SD: 0.2452 cents 546:558:571:728 SD: 0.2298 cents 549:561:574:732 SD: 0.2107 cents 591:604:618:788 SD: 0.1801 cents