Scala analysis: 515_M23
Miscellaneous tetrachord 68/53 * 53/52 * 52/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/53 431.450864 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/51 33.6173 1: 68/53 431.4509 2: 53/52 32.9769 3: 52/51 33.6173
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 53/52 32.977 cents 1: 1 52/51 33.617 cents 1: 1 68/53 431.451 cents 2: 1 53/51 66.594 cents 2: 1 17/13 464.428 cents 2: 1 208/159 465.068 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 : 431.5 464.4 498.0 431.5: 33.0 66.6 498.0 464.4: 33.6 465.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.9769 .. 431.4509 cents 3536/2809, 398.4740 cents 53/52, 32.9769 cents 2: 66.5941 .. 465.0681 cents 3536/2809, 398.4740 cents 2809/3468,-364.8567 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 53/52, 32.9769 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 68/53, 431.4509 cents Average / Smallest step : 5.034284 Largest / Average step : 2.598867 Largest / Smallest step : 13.083433 Median interval of one step : 52/51, 33.6173 cents, amount: 1 Least squares average step : 203.88867 cents, oct.: 611.66601 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2296-tone equal temperament with octave 4/3 degrees: 1989 2141 2296 Least number of segments generator : 1149 of 249.239 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2143 of 464.856 cents and inv. generated superset size: 30 = 27 more = 1000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 32.97688 cents Scale diversity : 0.181829 Lumma stability : 0.132425 Lumma impropriety factor : 0.732578 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 : 2704/2703, 0.6404 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest subharmonic part : 2 at degree 1 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 398.4740 cents: 1 -- Rational properties -- Prime limit : 53 Odd number limit : 159 (O: 53 U: 159) Highest odd numerator or denominator: 53 Scale harmonicity : 0.017563 Fundamental : 1/2067, -11.0133 octaves, 0.1266 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.405560E+05, 17.10079 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 79.0, average 26.33333 Mersenne's string divisions : 25410 Sum of van Prooijen's expressibility: 3.43185, average 1.14395 Sum of Tenney's harmonic distance : 6.98036, average 2.32679 Vogel's harmonic complexity : 58.66667 Wille's k value : 1351 Wilson's harmonic complexity : 86 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.18238, average 2.03040 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 53: -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 42| Scale is weakly epimorphic with val: <6 10 25 32 41| Scale is weakly epimorphic with val: <6 10 26 29 40| Scale is weakly epimorphic with val: <6 10 26 33 42| Scale is weakly epimorphic with val: <6 10 27 30 41| Scale is weakly epimorphic with val: <6 10 27 31 40| Scale is weakly epimorphic with val: <6 10 28 31 42| Scale is weakly epimorphic with val: <6 10 28 32 41| Scale is weakly epimorphic with val: <6 10 29 32 40| Scale is weakly epimorphic with val: <6 10 29 33 42| Scale is weakly epimorphic with val: <6 10 30 31 40| Scale is weakly epimorphic with val: <6 10 30 33 41| Scale is weakly epimorphic with val: <6 11 25 28 41| Scale is weakly epimorphic with val: <6 11 25 33 42| Scale is weakly epimorphic with val: <6 11 26 29 42| Scale is weakly epimorphic with val: <6 11 26 31 40| Scale is weakly epimorphic with val: <6 11 27 30 40| Scale is weakly epimorphic with val: <6 11 27 32 41| Scale is weakly epimorphic with val: <6 11 28 31 41| Scale is weakly epimorphic with val: <6 11 28 33 42| Scale is weakly epimorphic with val: <6 11 29 31 40| Scale is weakly epimorphic with val: <6 11 29 32 42| Scale is weakly epimorphic with val: <6 11 30 32 41| Scale is weakly epimorphic with val: <6 11 30 33 40| Scale is weakly epimorphic with val: <7 10 25 28 40| Scale is weakly epimorphic with val: <7 10 25 30 41| Scale is weakly epimorphic with val: <7 10 26 29 41| Scale is weakly epimorphic with val: <7 10 26 31 42| Scale is weakly epimorphic with val: <7 10 27 29 40| Scale is weakly epimorphic with val: <7 10 27 30 42| Scale is weakly epimorphic with val: <7 10 28 30 41| Scale is weakly epimorphic with val: <7 10 28 31 40| Scale is weakly epimorphic with val: <7 10 29 31 42| Scale is weakly epimorphic with val: <7 10 29 32 41| Scale is weakly epimorphic with val: <7 10 30 33 42| Scale is JI-epimorphic with val: <7 11 25 27 40| Scale is weakly epimorphic with val: <7 11 25 29 41| Scale is weakly epimorphic with val: <7 11 25 30 40| Scale is weakly epimorphic with val: <7 11 25 32 41| Scale is weakly epimorphic with val: <7 11 25 33 40| Scale is weakly epimorphic with val: <7 11 26 27 42| Scale is JI-epimorphic with val: <7 11 26 28 41| Scale is weakly epimorphic with val: <7 11 26 30 42| Scale is weakly epimorphic with val: <7 11 26 31 41| Scale is weakly epimorphic with val: <7 11 26 33 42| Scale is weakly epimorphic with val: <7 11 27 28 40| Scale is JI-epimorphic with val: <7 11 27 29 42| Scale is weakly epimorphic with val: <7 11 27 31 40| Scale is weakly epimorphic with val: <7 11 27 32 42| Scale is weakly epimorphic with val: <7 11 28 29 41| Scale is weakly epimorphic with val: <7 11 28 30 40| Scale is weakly epimorphic with val: <7 11 28 32 41| Scale is weakly epimorphic with val: <7 11 28 33 40| Scale is weakly epimorphic with val: <7 11 29 30 42| Scale is weakly epimorphic with val: <7 11 29 31 41| Scale is weakly epimorphic with val: <7 11 29 33 42| Scale is weakly epimorphic with val: <7 11 30 31 40| Scale is weakly epimorphic with val: <7 11 30 32 42| Scale is weakly epimorphic with val: <7 12 25 28 41| Scale is weakly epimorphic with val: <7 12 25 29 40| Scale is weakly epimorphic with val: <7 12 26 29 42| Scale is weakly epimorphic with val: <7 12 26 30 41| Scale is weakly epimorphic with val: <7 12 27 30 40| Scale is weakly epimorphic with val: <7 12 27 31 42| Scale is weakly epimorphic with val: <7 12 28 29 40| Scale is weakly epimorphic with val: <7 12 28 31 41| Scale is weakly epimorphic with val: <7 12 29 30 41| Scale is weakly epimorphic with val: <7 12 29 32 42| Scale is weakly epimorphic with val: <7 12 30 31 42| Scale is weakly epimorphic with val: <7 12 30 33 40| Scale is weakly epimorphic with val: <8 11 25 28 40| Scale is weakly epimorphic with val: <8 11 25 29 42| Scale is weakly epimorphic with val: <8 11 26 27 40| Scale is weakly epimorphic with val: <8 11 26 29 41| Scale is weakly epimorphic with val: <8 11 27 28 41| Scale is weakly epimorphic with val: <8 11 27 30 42| Scale is weakly epimorphic with val: <8 11 28 29 42| Scale is weakly epimorphic with val: <8 11 28 31 40| Scale is weakly epimorphic with val: <8 11 29 32 41| Scale is weakly epimorphic with val: <8 11 30 33 42| Scale is weakly epimorphic with val: <8 12 25 27 40| Scale is weakly epimorphic with val: <8 12 25 28 42| Scale is weakly epimorphic with val: <8 12 26 28 41| Scale is weakly epimorphic with val: <8 12 26 29 40| Scale is weakly epimorphic with val: <8 12 27 29 42| Scale is weakly epimorphic with val: <8 12 27 30 41| Scale is weakly epimorphic with val: <8 12 28 31 42| Scale is weakly epimorphic with val: <8 12 29 32 40| Scale is weakly epimorphic with val: <8 12 30 33 41|
FIT/MODE
3: 3 0 0 N M DE S SD: 43.0693 c. M:-66.5941 c. 4: 4 0 0 N M DE S SD: 43.0693 c. M:-66.5941 c. 5: 4 0 1 N G T3 SD: 42.6024 c. M: 65.9917 c. 6: 5 0 1 N G T3 SD: 30.0488 c. M: 49.3902 c. 7: 6 0 1 N G T3 SD: 21.8281 c. M: 37.5320 c. 8: 7 0 1 N G T3 SD: 16.7230 c. M: 28.6384 c. 9: 8 0 1 N G T3 SD: 14.1244 c. M: 21.7211 c. 10: 9 0 1 N G T3 SD: 13.4650 c. M:-16.7896 c. 11: 9 1 1 N M DE S SD: 15.3840 c. M: 23.9595 c. 12: 10 1 1 N M DE S SD: 10.5134 c. M: 16.4134 c. 13: 11 1 1 N M DE S SD: 6.3926 c. M: 10.0282 c. 14: 12 1 1 N M DE S SD: 2.8624 c. M: 4.5552 c. 15: 13 1 1 N M DE S SD: 0.2627 c. M:-0.4143 c. 119: 103 8 8 N M DE S SD: 0.2274 c. M: 0.3699 c. 134: 116 9 9 N M DE S SD: 0.2018 c. M: 0.3074 c. 149: 129 10 10 N M DE S SD: 0.1853 c. M: 0.2575 c. 164: 142 11 11 N M DE S SD: 0.1750 c. M: 0.2168 c. 179: 155 12 12 N M DE S SD: 0.1691 c. M:-0.2288 c. 194: 168 13 13 N M DE S SD: 0.1662 c. M:-0.2431 c. 209: 181 14 14 N M DE S SD: 0.1653 c. M:-0.2554 c. 224: 194 15 15 N M DE S SD: 0.1658 c. M:-0.2660 c. 239: 207 16 16 N M DE S SD: 0.1672 c. M:-0.2753 c. 254: 220 17 17 N M DE S SD: 0.1691 c. M:-0.2835 c. 269: 233 18 18 N M DE S SD: 0.1713 c. M:-0.2908 c. 284: 246 19 19 N M DE S SD: 0.1737 c. M:-0.2973 c. 299: 259 20 20 N M DE S SD: 0.1761 c. M:-0.3032 c. 314: 272 21 21 N M DE S SD: 0.1786 c. M:-0.3085 c. 329: 285 22 22 N M DE S SD: 0.1811 c. M:-0.3133 c. 343: 297 23 23 N M DE S SD: 0.1716 c. M:-0.2206 c. 344: 298 23 23 N M DE S SD: 0.1835 c. M:-0.3177 c. 359: 311 24 24 N M DE S SD: 0.1858 c. M:-0.3218 c. 373: 323 25 25 N M DE S SD: 0.1673 c. M:-0.2362 c. 396: 343 26 27 N T3 SD: 0.1999 c. M: 0.3404 c. 397: 344 26 27 N T3 SD: 0.1590 c. M: 0.2548 c. 411: 356 27 28 N T3 SD: 0.1833 c. M: 0.3128 c. 412: 357 27 28 N T3 SD: 0.1468 c. M: 0.2305 c. 426: 369 28 29 N T3 SD: 0.1679 c. M: 0.2872 c. 427: 370 28 29 N T3 SD: 0.1359 c. M: 0.2078 c. 441: 382 29 30 N T3 SD: 0.1536 c. M: 0.2634 c. 442: 383 29 30 N T3 SD: 0.1260 c. M: 0.1867 c. 456: 395 30 31 N T3 SD: 0.1403 c. M: 0.2411 c. 457: 396 30 31 N T3 SD: 0.1172 c. M: 0.1670 c. 471: 408 31 32 N T3 SD: 0.1278 c. M: 0.2202 c. 472: 409 31 32 N T3 SD: 0.1094 c. M: 0.1485 c. 486: 421 32 33 N T3 SD: 0.1162 c. M: 0.2006 c. 487: 422 32 33 N T3 SD: 0.1026 c. M: 0.1312 c. 501: 434 33 34 N T3 SD: 0.1054 c. M: 0.1822 c. 502: 435 33 34 N T3 SD: 0.0967 c. M:-0.1220 c. 516: 447 34 35 N T3 SD: 0.0952 c. M: 0.1649 c. 517: 448 34 35 N T3 SD: 0.0918 c. M:-0.1239 c. 531: 460 35 36 N T3 SD: 0.0857 c. M: 0.1485 c. 546: 473 36 37 N T3 SD: 0.0769 c. M: 0.1331 c. 561: 486 37 38 N T3 SD: 0.0686 c. M: 0.1184 c. 576: 499 38 39 N T3 SD: 0.0610 c. M: 0.1045 c. 591: 512 39 40 N T3 SD: 0.0540 c. M: 0.0914 c. 606: 525 40 41 N T3 SD: 0.0476 c. M: 0.0789 c. 621: 538 41 42 N T3 SD: 0.0418 c. M: 0.0670 c. 636: 551 42 43 N T3 SD: 0.0369 c. M: 0.0556 c. 651: 564 43 44 N T3 SD: 0.0329 c. M: 0.0448 c. 666: 577 44 45 N T3 SD: 0.0299 c. M:-0.0386 c. 681: 590 45 46 N T3 SD: 0.0280 c. M:-0.0419 c. 696: 603 46 47 N T3 SD: 0.0274 c. M:-0.0450 c. 740: 641 49 50 N T3 SD: 0.0289 c. M: 0.0362 c. 755: 654 50 51 N T3 SD: 0.0235 c. M: 0.0318 c. 770: 667 51 52 N T3 SD: 0.0186 c. M: 0.0275 c. 785: 680 52 53 N T3 SD: 0.0144 c. M: 0.0233 c. 800: 693 53 54 N T3 SD: 0.0112 c. M: 0.0194 c. 815: 706 54 55 N T3 SD: 0.0098 c. M: 0.0156 c. 830: 719 55 56 N T3 SD: 0.0107 c. M:-0.0142 c. 1466: 1270 97 99 N T3 SD: 0.0101 c. M: 0.0161 c. 1481: 1283 98 100 N T3 SD: 0.0085 c. M: 0.0117 c. 1496: 1296 99 101 N T3 SD: 0.0075 c. M:-0.0106 c. 1511: 1309 100 102 N T3 SD: 0.0074 c. M:-0.0123 c. 1526: 1322 101 103 N T3 SD: 0.0081 c. M:-0.0141 c. 2251: 1950 149 152 N T3 SD: 0.0081 c. M: 0.0135 c. 2266: 1963 150 153 N T3 SD: 0.0063 c. M: 0.0107 c. 2281: 1976 151 154 N T3 SD: 0.0046 c. M: 0.0079 c. 2296: 1989 152 155 N T3 SD: 0.0030 c. M: 0.0051 c. 2311: 2002 153 156 N T3 SD: 0.0016 c. M: 0.0024 c. 2326: 2015 154 157 N T3 SD: 0.0015 c. M:-0.0026 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 4:5 x x S SD: 45.1372 cents 5:6 x 7 S SD: 71.6704 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 3.6332 cents 8:10 x 11 S SD: 34.9119 cents 9 x x 12 S SD: 0.0000 cents 10 x 13 x SD: 10.2138 cents 11:14 x 15 SD: 20.6644 cents 12:15 x 16 S SD: 22.5686 cents 13 x 17 x SD: 0.0000 cents 14:18 x 19 SD: 15.4284 cents 15:19 x 20 SD: 11.1033 cents 16 x 21 x SD: 6.3532 cents 17:22 x 23 SD: 14.6725 cents 18:23 x 24 SD: 3.5433 cents 19:24:25 x SD: 14.5231 cents 20 x 26:27 SD: 11.9042 cents 21:27 x 28 SD: 1.8166 cents 22:28:29 x SD: 9.8198 cents 23 x 30:31 SD: 9.6171 cents 24:31 x 32 SD: 5.8149 cents 25:32:33 x SD: 8.3613 cents 26:33:34:35 SD: 8.3291 cents 27 x 35:36 SD: 7.5766 cents 28:36 x 37 SD: 7.9731 cents 29:37:38:39 SD: 6.0270 cents 31:40 x 41 SD: 8.5599 cents 32:41:42:43 SD: 5.0286 cents 34:44 x 45 SD: 9.8184 cents 35:45:46:47 SD: 5.1730 cents 36:46:47:48 SD: 2.5437 cents 39:50:51:52 SD: 0.4354 cents 120:154:157:160 SD: 0.3162 cents 159:204:208:212 SD: 0.2135 cents 198:254:259:264 SD: 0.1917 cents 537:689:702:716 SD: 0.1903 cents 540:693:706:720 SD: 0.1892 cents 576:739:753:768 SD: 0.1774 cents 579:743:757:772 SD: 0.1558 cents