Scala analysis: 055_E4
Enharmonic tetrachord 44/43 * 43/42 * 14/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/43 39.800237 2: 22/21 80.537035 undecimal minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 44/43 39.8002 2: 43/42 40.7368 3: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44/43 39.800 cents 1: 1 43/42 40.737 cents 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 22/21 80.537 cents undecimal minor semitone 2: 1 56/43 457.308 cents 2: 1 43/33 458.245 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 : 39.8 80.5 498.0 39.8 : 40.7 458.2 498.0 80.5 : 417.5 457.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.8002 .. 417.5080 cents 301/242, 377.7077 cents 44/43, 39.8002 cents 2: 80.5370 .. 458.2448 cents 301/242, 377.7077 cents 121/147,-336.9709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 44/43, 39.8002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 4.171206 Largest / Average step : 2.514881 Largest / Smallest step : 10.490087 Median interval of one step : 43/42, 40.7368 cents, amount: 1 Least squares average step : 121.07209 cents, oct.: 363.21628 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2115-tone equal temperament with octave 4/3 degrees: 169 342 2115 Least number of segments generator : 1058 of 249.140 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1372 of 323.082 cents and inv. generated superset size: 24 = 21 more = 800.000% 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 39.80024 cents Scale diversity : 0.283958 Lumma stability : 0.159826 Lumma impropriety factor : 0.676587 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 : 1849/1848, 0.9366 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 376.7712 cents: 2 -- Rational properties -- Prime limit : 43 Odd number limit : 43 (O: 43 U: 43) Highest odd numerator or denominator: 43 Scale harmonicity : 0.030180 Fundamental : 1/903, -9.8186 octaves, 0.2897 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 3.973200E+04, 15.27801 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 26187 Sum of van Prooijen's expressibility: 3.43281, average 1.14427 Sum of Tenney's harmonic distance : 7.02074, average 2.34025 Vogel's harmonic complexity : 43.33333 Wille's k value : 236 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.35045, average 1.89174 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 43: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 25 36| Scale is weakly epimorphic with val: <6 10 18 25 39| Scale is weakly epimorphic with val: <6 10 18 25 42| Scale is weakly epimorphic with val: <6 10 19 26 37| Scale is weakly epimorphic with val: <6 10 19 26 40| Scale is weakly epimorphic with val: <6 10 19 27 36| Scale is weakly epimorphic with val: <6 10 20 27 38| Scale is weakly epimorphic with val: <6 10 20 27 41| Scale is weakly epimorphic with val: <6 10 22 27 36| Scale is weakly epimorphic with val: <6 11 18 26 36| Scale is weakly epimorphic with val: <6 11 18 26 39| Scale is weakly epimorphic with val: <6 11 18 26 42| Scale is weakly epimorphic with val: <6 11 19 27 37| Scale is weakly epimorphic with val: <6 11 19 27 40| Scale is weakly epimorphic with val: <6 11 20 27 36| Scale is weakly epimorphic with val: <7 10 18 24 36| Scale is weakly epimorphic with val: <7 10 18 24 39| Scale is weakly epimorphic with val: <7 10 18 24 42| Scale is weakly epimorphic with val: <7 10 18 26 37| Scale is weakly epimorphic with val: <7 10 19 25 37| Scale is weakly epimorphic with val: <7 10 19 25 40| Scale is weakly epimorphic with val: <7 10 19 27 38| Scale is weakly epimorphic with val: <7 10 20 25 36| Scale is weakly epimorphic with val: <7 10 20 26 38| Scale is weakly epimorphic with val: <7 10 20 26 41| Scale is weakly epimorphic with val: <7 10 21 26 37| Scale is weakly epimorphic with val: <7 10 21 27 36| Scale is weakly epimorphic with val: <7 10 21 27 39| Scale is weakly epimorphic with val: <7 10 21 27 42| Scale is weakly epimorphic with val: <7 10 22 27 38| Scale is weakly epimorphic with val: <7 11 18 23 38| Scale is weakly epimorphic with val: <7 11 18 23 41| Scale is JI-epimorphic with val: <7 11 18 24 37| Scale is weakly epimorphic with val: <7 11 18 24 40| Scale is weakly epimorphic with val: <7 11 18 26 38| Scale is weakly epimorphic with val: <7 11 18 26 41| Scale is weakly epimorphic with val: <7 11 18 27 37| Scale is weakly epimorphic with val: <7 11 18 27 40| Scale is weakly epimorphic with val: <7 11 19 24 36| Scale is weakly epimorphic with val: <7 11 19 24 39| Scale is weakly epimorphic with val: <7 11 19 24 42| Scale is JI-epimorphic with val: <7 11 19 25 38| Scale is weakly epimorphic with val: <7 11 19 25 41| Scale is weakly epimorphic with val: <7 11 19 27 36| Scale is weakly epimorphic with val: <7 11 19 27 39| Scale is weakly epimorphic with val: <7 11 19 27 42| Scale is weakly epimorphic with val: <7 11 20 23 36| Scale is weakly epimorphic with val: <7 11 20 23 39| Scale is weakly epimorphic with val: <7 11 20 23 42| Scale is weakly epimorphic with val: <7 11 20 25 37| Scale is weakly epimorphic with val: <7 11 20 25 40| Scale is weakly epimorphic with val: <7 11 20 26 36| Scale is JI-epimorphic with val: <7 11 20 26 39| Scale is weakly epimorphic with val: <7 11 20 26 42| Scale is weakly epimorphic with val: <7 11 21 23 38| Scale is weakly epimorphic with val: <7 11 21 23 41| Scale is weakly epimorphic with val: <7 11 21 24 37| Scale is weakly epimorphic with val: <7 11 21 24 40| Scale is weakly epimorphic with val: <7 11 21 26 38| Scale is weakly epimorphic with val: <7 11 21 26 41| Scale is weakly epimorphic with val: <7 11 21 27 37| Scale is JI-epimorphic with val: <7 11 21 27 40| Scale is weakly epimorphic with val: <7 11 22 24 36| Scale is weakly epimorphic with val: <7 11 22 24 39| Scale is weakly epimorphic with val: <7 11 22 24 42| Scale is weakly epimorphic with val: <7 11 22 25 38| Scale is weakly epimorphic with val: <7 11 22 25 41| Scale is weakly epimorphic with val: <7 11 22 27 36| Scale is weakly epimorphic with val: <7 11 22 27 39| Scale is weakly epimorphic with val: <7 11 22 27 42| Scale is weakly epimorphic with val: <7 12 18 26 36| Scale is weakly epimorphic with val: <7 12 18 26 39| Scale is weakly epimorphic with val: <7 12 18 26 42| Scale is weakly epimorphic with val: <7 12 18 27 38| Scale is weakly epimorphic with val: <7 12 19 25 36| Scale is weakly epimorphic with val: <7 12 19 27 37| Scale is weakly epimorphic with val: <7 12 19 27 40| Scale is weakly epimorphic with val: <7 12 20 26 37| Scale is weakly epimorphic with val: <7 12 21 27 38| Scale is weakly epimorphic with val: <7 12 22 25 36| Scale is weakly epimorphic with val: <8 11 18 24 36| Scale is weakly epimorphic with val: <8 11 18 24 39| Scale is weakly epimorphic with val: <8 11 18 24 42| Scale is weakly epimorphic with val: <8 11 18 25 38| Scale is weakly epimorphic with val: <8 11 19 23 36| Scale is weakly epimorphic with val: <8 11 19 25 37| Scale is weakly epimorphic with val: <8 11 19 25 40| Scale is weakly epimorphic with val: <8 11 19 26 39| Scale is weakly epimorphic with val: <8 11 20 24 37| Scale is weakly epimorphic with val: <8 11 20 26 38| Scale is weakly epimorphic with val: <8 11 20 26 41| Scale is weakly epimorphic with val: <8 11 20 27 40| Scale is weakly epimorphic with val: <8 11 21 25 38| Scale is weakly epimorphic with val: <8 11 21 27 36| Scale is weakly epimorphic with val: <8 11 21 27 39| Scale is weakly epimorphic with val: <8 11 21 27 42| Scale is weakly epimorphic with val: <8 11 22 23 36| Scale is weakly epimorphic with val: <8 11 22 26 39| Scale is weakly epimorphic with val: <8 12 18 24 37| Scale is weakly epimorphic with val: <8 12 18 25 36| Scale is weakly epimorphic with val: <8 12 18 25 39| Scale is weakly epimorphic with val: <8 12 18 25 42| Scale is weakly epimorphic with val: <8 12 18 27 40| Scale is weakly epimorphic with val: <8 12 19 25 38| Scale is weakly epimorphic with val: <8 12 19 26 37| Scale is weakly epimorphic with val: <8 12 19 26 40| Scale is weakly epimorphic with val: <8 12 20 23 36| Scale is weakly epimorphic with val: <8 12 20 26 39| Scale is weakly epimorphic with val: <8 12 20 27 38| Scale is weakly epimorphic with val: <8 12 20 27 41| Scale is weakly epimorphic with val: <8 12 21 24 37| Scale is weakly epimorphic with val: <8 12 21 27 40| Scale is weakly epimorphic with val: <8 12 22 25 38|
FIT/MODE
3: 0 0 3 N M DE S SD: 51.8661 c. M: 80.5370 c. 5: 0 1 4 N G T3 SD: 25.4807 c. M: 39.8002 c. 6: 0 1 5 N G T3 SD: 23.0229 c. M: 39.8002 c. 7: 0 1 6 N G T3 SD: 23.6092 c. M: 39.8002 c. 8: 0 1 7 N G T3 SD: 25.2868 c. M: 39.8002 c. 9: 1 0 8 N G T3 SD: 17.0920 c. M: 25.1987 c. 10: 1 1 8 N M DE S SD: 12.4342 c. M:-19.0720 c. 11: 1 1 9 N M DE S SD: 6.5910 c. M:-10.0166 c. 12: 1 1 10 N M DE S SD: 1.7325 c. M:-2.4705 c. 25: 2 2 21 N M DE S SD: 0.4913 c. M: 0.8498 c. 37: 3 3 31 N M DE S SD: 0.3606 c. M:-0.5818 c. 62: 5 5 52 N M DE S SD: 0.2422 c. M:-0.3647 c. 99: 8 8 83 N M DE S SD: 0.2587 c. M:-0.4458 c. 136: 11 11 114 N M DE S SD: 0.2793 c. M:-0.4828 c. 149: 12 12 125 N M DE S SD: 0.2555 c. M: 0.3150 c. 161: 13 13 135 N M DE S SD: 0.2473 c. M:-0.4146 c. 223: 18 18 187 N M DE S SD: 0.2442 c. M:-0.4007 c. 235: 19 19 197 N M DE S SD: 0.2698 c. M:-0.4672 c. 236: 19 19 198 N M DE S SD: 0.2620 c. M: 0.3433 c. 260: 21 21 218 N M DE S SD: 0.2509 c. M:-0.4265 c. 265: 21 22 222 N T3 SD: 0.2502 c. M: 0.3325 c. 273: 22 22 229 N M DE S SD: 0.2471 c. M:-0.3353 c. 278: 22 23 233 N T3 SD: 0.2281 c. M: 0.3866 c. 290: 23 24 243 N T3 SD: 0.2022 c. M: 0.3001 c. 302: 24 25 253 N T3 SD: 0.2020 c. M:-0.2716 c. 303: 24 25 254 N T3 SD: 0.2027 c. M: 0.3511 c. 315: 25 26 264 N T3 SD: 0.1675 c. M: 0.2729 c. 327: 26 27 274 N T3 SD: 0.1578 c. M: 0.2003 c. 328: 26 27 275 N T3 SD: 0.1886 c. M: 0.3211 c. 339: 27 28 284 N T3 SD: 0.1721 c. M:-0.2667 c. 340: 27 28 285 N T3 SD: 0.1451 c. M: 0.2496 c. 352: 28 29 295 N T3 SD: 0.1240 c. M: 0.1830 c. 365: 29 30 306 N T3 SD: 0.1337 c. M: 0.2295 c. 377: 30 31 316 N T3 SD: 0.1010 c. M: 0.1680 c. 389: 31 32 326 N T3 SD: 0.0955 c. M:-0.1232 c. 402: 32 33 337 N T3 SD: 0.0895 c. M: 0.1549 c. 414: 33 34 347 N T3 SD: 0.0692 c. M: 0.1010 c. 439: 35 36 368 N T3 SD: 0.0540 c. M: 0.0928 c. 451: 36 37 378 N T3 SD: 0.0519 c. M:-0.0778 c. 464: 37 38 389 N T3 SD: 0.0531 c. M: 0.0854 c. 476: 38 39 399 N T3 SD: 0.0287 c. M: 0.0403 c. 501: 40 41 420 N T3 SD: 0.0226 c. M: 0.0362 c. 538: 43 44 451 N T3 SD: 0.0038 c. M:-0.0063 c. 2115: 169 173 1773 N T3 SD: 0.0025 c. M: 0.0037 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: 93.1669 cents 7 x 8:9 S SD: 81.6327 cents 8 x 9:11 SD: 67.1917 cents 9 x 10:12 S SD: 50.9333 cents 10 x 11:13 SD: 47.5812 cents 11 x 12:15 S SD: 40.0864 cents 12 x 13:16 SD: 29.0178 cents 13 x 14:17 SD: 29.2030 cents 14 x 15:19 SD: 24.7619 cents 15 x 16:20 S SD: 15.5971 cents 16 x 17:21 SD: 18.3002 cents 17 x 18:23 SD: 15.6363 cents 18 x 19:24 SD: 6.5330 cents 19 x 20:25 S SD: 12.1871 cents 20 x 21:27 SD: 10.9312 cents 21 x 22:28 SD: 0.0000 cents 22 x 23:29 SD: 10.0536 cents 23 x 24:31 SD: 9.9663 cents 24 x 25:32 SD: 4.9323 cents 25 x 26:33 SD: 10.7521 cents 26 x 27:35 SD: 11.2416 cents 27 x 28:36 SD: 8.7881 cents 28 x 29:37 SD: 12.5754 cents 29:30 x 39 SD: 12.0178 cents 30:31 x 40 SD: 8.4833 cents 31:32 x 41 SD: 10.3255 cents 32:33:34:43 SD: 10.3241 cents 33:34:35:44 SD: 8.1387 cents 35:36:37:47 SD: 7.2859 cents 36:37:38:48 SD: 5.0442 cents 38:39:40:51 SD: 4.9876 cents 39:40:41:52 SD: 2.4212 cents 42:43:44:56 SD: 0.3122 cents 339:347:355:452 SD: 0.3022 cents 381:390:399:508 SD: 0.2921 cents 423:433:443:564 SD: 0.2858 cents 465:476:487:620 SD: 0.2820 cents 480:491:503:640 SD: 0.2519 cents 522:534:547:696 SD: 0.2132 cents 564:577:591:752 SD: 0.1816 cents