Scala analysis: 553_M61
Miscellaneous tetrachord 90/83 * 166/159 * 53/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90/83 140.176398 2: 60/53 214.764169 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 53/45 283.2808 1: 90/83 140.1764 2: 166/159 74.5878 3: 53/45 283.2808
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 166/159 74.588 cents 1: 1 90/83 140.176 cents 1: 1 53/45 283.281 cents 2: 1 60/53 214.764 cents 2: 1 166/135 357.869 cents 2: 1 106/83 423.457 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 : 140.2 214.8 498.0 140.2: 74.6 357.9 498.0 214.8: 283.3 423.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.5878 .. 283.2808 cents 2809/2490, 208.6931 cents 166/159, 74.5878 cents 2: 214.7642 .. 423.4572 cents 2809/2490, 208.6931 cents 2700/2809,-68.5167 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 166/159, 74.5878 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 53/45, 283.2808 cents Average / Smallest step : 2.225767 Largest / Average step : 1.706357 Largest / Smallest step : 3.797953 Median interval of one step : 90/83, 140.1764 cents, amount: 1 Least squares average step : 147.41712 cents, oct.: 442.25137 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2050-tone equal temperament with octave 4/3 degrees: 577 884 2050 Least number of segments generator : 1027 of 249.508 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1203 of 292.267 cents and inv. generated superset size: 29 = 26 more = 966.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 68.51666 cents Scale diversity : 1.065185 Lumma stability : 0.299522 Lumma impropriety factor : 0.137571 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 : 7155/6889, 65.5886 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 83 Odd number limit : 159 (O: 83 U: 159) Highest odd numerator or denominator: 83 Scale harmonicity : 0.060976 Fundamental : 1/13197, -13.6879 octaves, 0.0198 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.375460E+06, 21.17978 octaves Euler's gradus suavitatis : 147 Sum of Mann's harmonic distance : 146.5, average 48.83333 Mersenne's string divisions : 136843 Sum of van Prooijen's expressibility: 4.12048, average 1.37349 Sum of Tenney's harmonic distance : 8.45493, average 2.81831 Vogel's harmonic complexity : 100.66667 Wille's k value : 3577 Wilson's harmonic complexity : 150 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.10195, average 2.35033 Lattice compactness (without 2's) : 11.04863, average 1.84144 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 53: -1 .. 0 -0.33333 1 1 83: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 19 40 47| Scale is weakly epimorphic with val: <7 11 15 41 46| Scale is weakly epimorphic with val: <7 11 15 42 45| Scale is weakly epimorphic with val: <7 11 16 40 46| Scale is weakly epimorphic with val: <7 11 16 42 47| Scale is JI-epimorphic with val: <7 11 17 40 45| Scale is weakly epimorphic with val: <7 11 17 41 47| Scale is JI-epimorphic with val: <7 11 18 41 46| Scale is weakly epimorphic with val: <7 11 18 42 45| Scale is weakly epimorphic with val: <7 11 19 40 46| Scale is JI-epimorphic with val: <7 11 19 42 47| Scale is weakly epimorphic with val: <7 12 17 40 47| Scale is weakly epimorphic with val: <7 12 17 42 45| Scale is weakly epimorphic with val: <7 12 18 40 46| Scale is weakly epimorphic with val: <7 12 18 41 45| Scale is weakly epimorphic with val: <7 12 19 41 47| Scale is weakly epimorphic with val: <7 12 19 42 46| Scale is weakly epimorphic with val: <8 11 16 40 45| Scale is weakly epimorphic with val: <8 11 17 41 46| Scale is weakly epimorphic with val: <8 11 18 41 45| Scale is weakly epimorphic with val: <8 11 18 42 47| Scale is weakly epimorphic with val: <8 11 19 42 46| Scale is weakly epimorphic with val: <8 12 15 40 45| Scale is weakly epimorphic with val: <8 12 16 41 46| Scale is weakly epimorphic with val: <8 12 16 42 45| Scale is weakly epimorphic with val: <8 12 17 40 46| Scale is weakly epimorphic with val: <8 12 17 42 47| Scale is weakly epimorphic with val: <8 12 18 41 47|
FIT/MODE
3: 1 0 2 N G T3 SD: 31.8544 c. M: 48.7492 c. 4: 1 1 2 P M ME S SD: 21.7488 c. M:-34.2583 c. 5: 1 1 3 N M DE S SD: 25.0825 c. M: 40.5674 c. 6: 2 1 3 P T3 SD: 24.7741 c. M:-34.2583 c. 7: 2 1 4 N T3 SD: 1.4418 c. M:-2.1222 c. 39: 11 6 22 N T3 SD: 1.3575 c. M:-2.3324 c. 46: 13 7 26 N T3 SD: 1.0785 c. M:-1.7771 c. 53: 15 8 30 N T3 SD: 0.9094 c. M:-1.3686 c. 60: 17 9 34 N T3 SD: 0.8146 c. M:-1.0553 c. 67: 19 10 38 N T3 SD: 0.7695 c. M:-1.0602 c. 74: 21 11 42 N T3 SD: 0.7561 c. M:-1.1607 c. 86: 24 13 49 N T3 SD: 0.7412 c. M: 1.1871 c. 93: 26 14 53 N T3 SD: 0.6282 c. M: 0.9380 c. 100: 28 15 57 N T3 SD: 0.5446 c. M: 0.7238 c. 107: 30 16 61 N T3 SD: 0.4876 c. M: 0.6514 c. 114: 32 17 65 N T3 SD: 0.4543 c. M: 0.6922 c. 121: 34 18 69 N T3 SD: 0.4409 c. M: 0.7283 c. 132: 37 20 75 N T3 SD: 0.3735 c. M: 0.5729 c. 139: 39 21 79 N T3 SD: 0.2824 c. M: 0.4372 c. 146: 41 22 83 N T3 SD: 0.2001 c. M: 0.3144 c. 153: 43 23 87 N T3 SD: 0.1257 c. M: 0.2030 c. 160: 45 24 91 N T3 SD: 0.0593 c. M: 0.1012 c. 167: 47 25 95 N T3 SD: 0.0225 c. M: 0.0382 c. 494: 139 74 281 N T3 SD: 0.0249 c. M: 0.0382 c. 661: 186 99 376 N T3 SD: 0.0227 c. M: 0.0306 c. 828: 233 124 471 N T3 SD: 0.0218 c. M: 0.0274 c. 995: 280 149 566 N T3 SD: 0.0215 c. M: 0.0292 c. 1162: 327 174 661 N T3 SD: 0.0213 c. M: 0.0305 c. 1215: 342 182 691 N T3 SD: 0.0194 c. M:-0.0305 c. 1222: 344 183 695 N T3 SD: 0.0200 c. M:-0.0261 c. 1375: 387 206 782 N T3 SD: 0.0168 c. M:-0.0291 c. 1382: 389 207 786 N T3 SD: 0.0144 c. M:-0.0222 c. 1389: 391 208 790 N T3 SD: 0.0155 c. M:-0.0220 c. 1542: 434 231 877 N T3 SD: 0.0126 c. M:-0.0218 c. 1549: 436 232 881 N T3 SD: 0.0105 c. M:-0.0157 c. 1709: 481 256 972 N T3 SD: 0.0092 c. M:-0.0159 c. 1716: 483 257 976 N T3 SD: 0.0075 c. M:-0.0105 c. 1876: 528 281 1067 N T3 SD: 0.0065 c. M:-0.0111 c. 1883: 530 282 1071 N T3 SD: 0.0051 c. M:-0.0062 c. 2043: 575 306 1162 N T3 SD: 0.0043 c. M:-0.0071 c. 2050: 577 307 1166 N T3 SD: 0.0033 c. M:-0.0050 c. 2210: 622 331 1257 N T3 SD: 0.0026 c. M:-0.0037 c. 2217: 624 332 1261 N T3 SD: 0.0024 c. M:-0.0041 c. 2377: 669 356 1352 N T3 SD: 0.0018 c. M: 0.0030 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: 65.7854 cents 6 x 7:8 S SD: 26.0534 cents 7 x 8:9 S SD: 32.5321 cents 8 x 9:11 SD: 27.1837 cents 9 x 10:12 S SD: 16.1802 cents 10:11 x 13 SD: 25.1872 cents 11:12 x 15 S SD: 20.1438 cents 12:13:14:16 S SD: 17.3771 cents 13:14:15:17 SD: 16.1888 cents 14:15:16:19 SD: 13.4912 cents 15:16:17:20 SD: 9.5033 cents 18 x 20:24 S SD: 16.1802 cents 20:22:23:27 SD: 14.2150 cents 21:23:24:28 SD: 7.9524 cents 22:24:25:29 SD: 7.7728 cents 23:25:26:31 SD: 6.4468 cents 24:26:27:32 SD: 3.6573 cents 36:39:41:48 SD: 3.5038 cents 45:49:51:60 SD: 2.5007 cents 60:65:68:80 SD: 0.8345 cents 84:91:95:112 SD: 0.7835 cents 129:140:146:172 SD: 0.5187 cents 189:205:214:252 SD: 0.1978 cents 273:296:309:364 SD: 0.1157 cents 462:501:523:616 SD: 0.0465 cents