Scala analysis: 052_E3
Enharmonic tetrachord 320/313 * 313/306 * 51/40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 320/313 38.291098 2: 160/153 77.448303 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 51/40 420.5967 septendecimal diminished fourth 1: 320/313 38.2911 2: 313/306 39.1572 3: 51/40 420.5967 septendecimal diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 320/313 38.291 cents 1: 1 313/306 39.157 cents 1: 1 51/40 420.597 cents septendecimal diminished fourth 2: 1 160/153 77.448 cents 2: 1 408/313 458.888 cents 2: 1 313/240 459.754 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 : 38.3 77.4 498.0 38.3 : 39.2 459.8 498.0 77.4 : 420.6 458.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.2911 .. 420.5967 cents 15963/12800, 382.3056 cents 320/313, 38.2911 cents 2: 77.4483 .. 459.7539 cents 15963/12800, 382.3056 cents 6400/7803,-343.1484 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 320/313, 38.2911 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 51/40, 420.5967 cents Average / Smallest step : 4.335603 Largest / Average step : 2.533486 Largest / Smallest step : 10.984190 Median interval of one step : 313/306, 39.1572 cents, amount: 1 Least squares average step : 120.52305 cents, oct.: 361.56915 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1704-tone equal temperament with octave 4/3 degrees: 131 265 1704 Least number of segments generator : 853 of 249.315 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1573 of 459.756 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 38.29110 cents Scale diversity : 0.261141 Lumma stability : 0.153766 Lumma impropriety factor : 0.688991 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 : 97969/97920, 0.8661 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 381.4395 cents: 2 -- Rational properties -- Prime limit : 313 Odd number limit : 313 (O: 313 U: 313) Highest odd numerator or denominator: 313 Scale harmonicity : 0.020898 Fundamental : 1/47889, -15.5474 octaves, 0.0055 Hz. Guide tone : 320, 8.3219 octaves, 83720.181 Hz. Exponens Consonantiae : 1.532448E+07, 23.86933 octaves Euler's gradus suavitatis : 343 Sum of Mann's harmonic distance : 476.5, average 158.83333 Mersenne's string divisions : 1386903 Sum of van Prooijen's expressibility: 5.15736, average 1.71912 Sum of Tenney's harmonic distance : 10.46869, average 3.48956 Vogel's harmonic complexity : 230.66667 Wille's k value : 7981 Wilson's harmonic complexity : 341 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 24.04283, average 4.00714 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.33333 13 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 313: -1 .. 0 -0.33333 1 1 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: <7 10 15 27 61| Scale is weakly epimorphic with val: <7 10 16 28 59| Scale is weakly epimorphic with val: <7 10 17 29 60| Scale is weakly epimorphic with val: <7 10 18 30 61| Scale is weakly epimorphic with val: <7 10 19 31 59| Scale is weakly epimorphic with val: <7 11 15 27 61| Scale is weakly epimorphic with val: <7 11 15 29 59| Scale is weakly epimorphic with val: <7 11 15 30 61| Scale is weakly epimorphic with val: <7 11 15 32 59| Scale is weakly epimorphic with val: <7 11 15 33 61| Scale is weakly epimorphic with val: <7 11 16 27 60| Scale is weakly epimorphic with val: <7 11 16 28 59| Scale is weakly epimorphic with val: <7 11 16 30 60| Scale is weakly epimorphic with val: <7 11 16 31 59| Scale is weakly epimorphic with val: <7 11 16 33 60| Scale is weakly epimorphic with val: <7 11 17 28 61| Scale is weakly epimorphic with val: <7 11 17 29 60| Scale is weakly epimorphic with val: <7 11 17 31 61| Scale is weakly epimorphic with val: <7 11 17 32 60| Scale is weakly epimorphic with val: <7 11 18 27 61| Scale is JI-epimorphic with val: <7 11 18 29 59| Scale is weakly epimorphic with val: <7 11 18 30 61| Scale is weakly epimorphic with val: <7 11 18 32 59| Scale is weakly epimorphic with val: <7 11 18 33 61| Scale is weakly epimorphic with val: <7 11 19 27 60| Scale is weakly epimorphic with val: <7 11 19 28 59| Scale is JI-epimorphic with val: <7 11 19 30 60| Scale is weakly epimorphic with val: <7 11 19 31 59| Scale is weakly epimorphic with val: <7 11 19 33 60| Scale is weakly epimorphic with val: <7 12 19 27 60| Scale is weakly epimorphic with val: <8 11 15 29 60| Scale is weakly epimorphic with val: <8 11 15 30 59| Scale is weakly epimorphic with val: <8 11 15 32 60| Scale is weakly epimorphic with val: <8 11 16 27 61| Scale is weakly epimorphic with val: <8 11 16 30 61| Scale is weakly epimorphic with val: <8 11 16 31 60| Scale is weakly epimorphic with val: <8 11 16 33 61| Scale is weakly epimorphic with val: <8 11 17 32 61| Scale is weakly epimorphic with val: <8 11 18 33 59| Scale is weakly epimorphic with val: <8 12 15 28 61| Scale is weakly epimorphic with val: <8 12 15 29 60| Scale is weakly epimorphic with val: <8 12 15 32 60| Scale is weakly epimorphic with val: <8 12 16 27 61| Scale is weakly epimorphic with val: <8 12 16 29 59| Scale is weakly epimorphic with val: <8 12 16 30 61| Scale is weakly epimorphic with val: <8 12 16 33 61| Scale is weakly epimorphic with val: <8 12 17 30 60| Scale is weakly epimorphic with val: <8 12 18 31 61| Scale is weakly epimorphic with val: <8 12 19 32 59|
FIT/MODE
3: 0 0 3 N M DE S SD: 49.8814 c. M: 77.4483 c. 5: 0 1 4 N G T3 SD: 25.5428 c. M: 38.2911 c. 6: 0 1 5 N G T3 SD: 22.3391 c. M: 38.2911 c. 7: 0 1 6 N G T3 SD: 22.4045 c. M: 38.2911 c. 8: 0 1 7 N G T3 SD: 23.7839 c. M: 38.2911 c. 9: 1 0 8 N G T3 SD: 16.1189 c. M: 22.1100 c. 10: 1 1 8 N M DE S SD: 14.4182 c. M:-22.1607 c. 11: 1 1 9 N M DE S SD: 8.5742 c. M:-13.1053 c. 12: 1 1 10 N M DE S SD: 3.7070 c. M:-5.5592 c. 13: 1 1 11 N M DE S SD: 0.4770 c. M: 0.8260 c. 51: 4 4 43 N M DE S SD: 0.5923 c. M:-0.7713 c. 64: 5 5 54 N M DE S SD: 0.4166 c. M:-0.6187 c. 77: 6 6 65 N M DE S SD: 0.3144 c. M:-0.5176 c. 90: 7 7 76 N M DE S SD: 0.2578 c. M:-0.4457 c. 103: 8 8 87 N M DE S SD: 0.2312 c. M:-0.3920 c. 116: 9 9 98 N M DE S SD: 0.2237 c. M:-0.3503 c. 129: 10 10 109 N M DE S SD: 0.2268 c. M:-0.3170 c. 142: 11 11 120 N M DE S SD: 0.2353 c. M:-0.2899 c. 219: 17 17 185 N M DE S SD: 0.2257 c. M:-0.3699 c. 245: 19 19 207 N M DE S SD: 0.2243 c. M:-0.3328 c. 283: 22 22 239 N M DE S SD: 0.2462 c. M:-0.4262 c. 289: 22 23 244 N T3 SD: 0.2258 c. M: 0.3776 c. 302: 23 24 255 N T3 SD: 0.2112 c. M: 0.3605 c. 314: 24 25 265 N T3 SD: 0.2035 c. M:-0.2721 c. 315: 24 25 266 N T3 SD: 0.1996 c. M: 0.3448 c. 327: 25 26 276 N T3 SD: 0.1808 c. M:-0.2284 c. 328: 25 26 277 N T3 SD: 0.1908 c. M: 0.3304 c. 340: 26 27 287 N T3 SD: 0.1608 c. M: 0.2053 c. 341: 26 27 288 N T3 SD: 0.1844 c. M: 0.3170 c. 353: 27 28 298 N T3 SD: 0.1432 c. M: 0.1970 c. 366: 28 29 309 N T3 SD: 0.1282 c. M: 0.1893 c. 379: 29 30 320 N T3 SD: 0.1157 c. M: 0.1821 c. 392: 30 31 331 N T3 SD: 0.1059 c. M: 0.1754 c. 405: 31 32 342 N T3 SD: 0.0987 c. M: 0.1691 c. 418: 32 33 353 N T3 SD: 0.0943 c. M: 0.1633 c. 430: 33 34 363 N T3 SD: 0.0975 c. M:-0.1541 c. 431: 33 34 364 N T3 SD: 0.0923 c. M: 0.1577 c. 443: 34 35 374 N T3 SD: 0.0819 c. M:-0.1253 c. 444: 34 35 375 N T3 SD: 0.0926 c. M: 0.1525 c. 456: 35 36 385 N T3 SD: 0.0677 c. M:-0.0982 c. 469: 36 37 396 N T3 SD: 0.0550 c. M:-0.0726 c. 482: 37 38 407 N T3 SD: 0.0442 c. M: 0.0594 c. 495: 38 39 418 N T3 SD: 0.0362 c. M: 0.0573 c. 508: 39 40 429 N T3 SD: 0.0320 c. M: 0.0554 c. 521: 40 41 440 N T3 SD: 0.0324 c. M: 0.0535 c. 534: 41 42 451 N T3 SD: 0.0366 c. M: 0.0517 c. 572: 44 45 483 N T3 SD: 0.0283 c. M:-0.0447 c. 585: 45 46 494 N T3 SD: 0.0187 c. M:-0.0254 c. 598: 46 47 505 N T3 SD: 0.0122 c. M:-0.0201 c. 611: 47 48 516 N T3 SD: 0.0132 c. M:-0.0201 c. 1093: 84 86 923 N T3 SD: 0.0123 c. M:-0.0152 c. 1106: 85 87 934 N T3 SD: 0.0090 c. M: 0.0146 c. 1119: 86 88 945 N T3 SD: 0.0086 c. M: 0.0142 c. 1132: 87 89 956 N T3 SD: 0.0112 c. M: 0.0138 c. 1678: 129 132 1417 N T3 SD: 0.0110 c. M:-0.0188 c. 1691: 130 133 1428 N T3 SD: 0.0072 c. M:-0.0123 c. 1704: 131 134 1439 N T3 SD: 0.0037 c. M:-0.0059 c. 1717: 132 135 1450 N T3 SD: 0.0013 c. M: 0.0023 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: 94.7113 cents 7 x 8:9 S SD: 83.0598 cents 8 x 9:11 SD: 68.6123 cents 9 x 10:12 S SD: 52.4777 cents 10 x 11:13 SD: 48.9571 cents 11 x 12:15 S SD: 41.4435 cents 12 x 13:16 SD: 30.5622 cents 13 x 14:17 SD: 30.4788 cents 14 x 15:19 SD: 25.9927 cents 15 x 16:20 S SD: 17.1415 cents 16 x 17:21 SD: 19.3647 cents 17 x 18:23 SD: 16.5929 cents 18 x 19:24 SD: 8.0774 cents 19 x 20:25 S SD: 12.7934 cents 20 x 21:27 SD: 11.3113 cents 21 x 22:28 SD: 1.5444 cents 22 x 23:29 SD: 9.8959 cents 23 x 24:31 SD: 9.5458 cents 24 x 25:32 SD: 3.3879 cents 25 x 26:33 SD: 9.9236 cents 26 x 27:35 SD: 10.2608 cents 27 x 28:36 SD: 7.2437 cents 28 x 29:37 SD: 11.4004 cents 29 x 30:39 SD: 11.9651 cents 30:31 x 40 SD: 9.2379 cents 31:32 x 41 SD: 10.8916 cents 32:33 x 43 SD: 10.0743 cents 33:34:35:44 SD: 9.2831 cents 34:35:36:45 S SD: 9.2329 cents 35:36:37:47 SD: 8.2559 cents 36:37:38:48 SD: 6.1875 cents 38:39:40:51 SD: 5.7961 cents 39:40:41:52 SD: 3.5602 cents 42:43:44:56 SD: 1.3133 cents 45:46:47:60 SD: 0.7262 cents 87:89:91:116 SD: 0.3736 cents 132:135:138:176 SD: 0.2624 cents 351:359:367:468 SD: 0.2585 cents 483:494:505:644 SD: 0.2571 cents 501:512:524:668 SD: 0.2461 cents 543:555:568:724 SD: 0.2185 cents 588:601:615:784 SD: 0.1710 cents