Scala analysis: 496_M4
Miscellaneous tetrachord 21/16 * 656/651 * 124/123
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/16 470.780907 narrow fourth 2: 41/31 484.026833 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 124/123 14.0182 1: 21/16 470.7809 narrow fourth 2: 656/651 13.2459 3: 124/123 14.0182
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 656/651 13.246 cents 1: 1 124/123 14.018 cents 1: 1 21/16 470.781 cents narrow fourth 2: 1 64/63 27.264 cents septimal comma, Archytas' comma 2: 1 41/31 484.027 cents 2: 1 217/164 484.799 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 : 470.8 484.0 498.0 470.8: 13.2 27.3 498.0 484.0: 14.0 484.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.2459 .. 470.7809 cents 13671/10496, 457.5350 cents 656/651, 13.2459 cents 2: 27.2641 .. 484.7991 cents 13671/10496, 457.5350 cents 1024/1323,-443.5168 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 656/651, 13.2459 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/16, 470.7809 cents Average / Smallest step : 12.533288 Largest / Average step : 2.835773 Largest / Smallest step : 35.541563 Median interval of one step : 124/123, 14.0182 cents, amount: 1 Least squares average step : 209.49783 cents, oct.: 628.49348 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1279-tone equal temperament with octave 4/3 degrees: 1209 1243 1279 Least number of segments generator : 640 of 249.217 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1277 of 497.266 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 13.24593 cents Scale diversity :-0.092462 Lumma stability : 0.053192 Lumma impropriety factor : 0.890516 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 : 6727/6724, 0.7722 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 484.4130 cents Number of appreciable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 457.5350 cents: 1 -- Rational properties -- Prime limit : 41 Odd number limit : 651 (O: 217 U: 651) Highest odd numerator or denominator: 41 Scale harmonicity : 0.046256 Fundamental : 1/1488, -10.5392 octaves, 0.1758 Hz. Guide tone : 3444, 11.7499 octaves, 901038.447 Hz. Exponens Consonantiae : 5.124672E+06, 22.28903 octaves Euler's gradus suavitatis : 87 Sum of Mann's harmonic distance : 58.0, average 19.33333 Mersenne's string divisions : 18648 Sum of van Prooijen's expressibility: 3.41212, average 1.13737 Sum of Tenney's harmonic distance : 6.70967, average 2.23656 Vogel's harmonic complexity : 43.00000 Wille's k value : 976 Wilson's harmonic complexity : 85 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 19.36054, average 3.22676 Lattice compactness (without 2's) : 7.06450, average 1.17742 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.66667 6 3: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.33333 1 1 31: -1 .. 0 -0.33333 1 41: 0 .. 1 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 18 33 36| Scale is weakly epimorphic with val: <6 10 18 34 37| Scale is weakly epimorphic with val: <6 10 18 35 38| Scale is weakly epimorphic with val: <6 10 18 36 39| Scale is weakly epimorphic with val: <6 10 18 37 40| Scale is weakly epimorphic with val: <6 10 18 38 41| Scale is weakly epimorphic with val: <6 10 18 39 42| Scale is weakly epimorphic with val: <6 10 21 33 36| Scale is weakly epimorphic with val: <6 10 21 34 37| Scale is weakly epimorphic with val: <6 10 21 35 38| Scale is weakly epimorphic with val: <6 10 21 36 39| Scale is weakly epimorphic with val: <6 10 21 37 40| Scale is weakly epimorphic with val: <6 10 21 38 41| Scale is weakly epimorphic with val: <6 10 21 39 42| Scale is weakly epimorphic with val: <6 11 18 33 36| Scale is weakly epimorphic with val: <6 11 18 34 37| Scale is weakly epimorphic with val: <6 11 18 35 38| Scale is weakly epimorphic with val: <6 11 18 36 39| Scale is weakly epimorphic with val: <6 11 18 37 40| Scale is weakly epimorphic with val: <6 11 18 38 41| Scale is weakly epimorphic with val: <6 11 18 39 42| Scale is weakly epimorphic with val: <6 11 21 33 36| Scale is weakly epimorphic with val: <6 11 21 34 37| Scale is weakly epimorphic with val: <6 11 21 35 38| Scale is weakly epimorphic with val: <6 11 21 36 39| Scale is weakly epimorphic with val: <6 11 21 37 40| Scale is weakly epimorphic with val: <6 11 21 38 41| Scale is weakly epimorphic with val: <6 11 21 39 42| Scale is weakly epimorphic with val: <7 10 20 33 36| Scale is weakly epimorphic with val: <7 10 20 34 37| Scale is weakly epimorphic with val: <7 10 20 35 38| Scale is weakly epimorphic with val: <7 10 20 36 39| Scale is weakly epimorphic with val: <7 10 20 37 40| Scale is weakly epimorphic with val: <7 10 20 38 41| Scale is weakly epimorphic with val: <7 10 20 39 42| Scale is weakly epimorphic with val: <7 10 21 33 38| Scale is weakly epimorphic with val: <7 10 21 33 41| Scale is weakly epimorphic with val: <7 10 21 34 36| Scale is weakly epimorphic with val: <7 10 21 34 39| Scale is weakly epimorphic with val: <7 10 21 34 42| Scale is weakly epimorphic with val: <7 10 21 35 37| Scale is weakly epimorphic with val: <7 10 21 35 40| Scale is weakly epimorphic with val: <7 10 21 36 38| Scale is weakly epimorphic with val: <7 10 21 36 41| Scale is weakly epimorphic with val: <7 10 21 37 39| Scale is weakly epimorphic with val: <7 10 21 37 42| Scale is weakly epimorphic with val: <7 10 21 38 40| Scale is weakly epimorphic with val: <7 10 21 39 41| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 33 41| Scale is JI-epimorphic with val: <7 11 18 34 36| Scale is weakly epimorphic with val: <7 11 18 34 39| Scale is weakly epimorphic with val: <7 11 18 34 42| Scale is JI-epimorphic with val: <7 11 18 35 37| Scale is weakly epimorphic with val: <7 11 18 35 40| Scale is JI-epimorphic with val: <7 11 18 36 38| Scale is weakly epimorphic with val: <7 11 18 36 41| Scale is JI-epimorphic with val: <7 11 18 37 39| Scale is weakly epimorphic with val: <7 11 18 37 42| Scale is JI-epimorphic with val: <7 11 18 38 40| Scale is JI-epimorphic with val: <7 11 18 39 41| Scale is weakly epimorphic with val: <7 11 19 33 37| Scale is weakly epimorphic with val: <7 11 19 33 40| Scale is weakly epimorphic with val: <7 11 19 34 38| Scale is weakly epimorphic with val: <7 11 19 34 41| Scale is weakly epimorphic with val: <7 11 19 35 36| Scale is weakly epimorphic with val: <7 11 19 35 39| Scale is weakly epimorphic with val: <7 11 19 35 42| Scale is weakly epimorphic with val: <7 11 19 36 37| Scale is weakly epimorphic with val: <7 11 19 36 40| Scale is weakly epimorphic with val: <7 11 19 37 38| Scale is weakly epimorphic with val: <7 11 19 37 41| Scale is weakly epimorphic with val: <7 11 19 38 39| Scale is weakly epimorphic with val: <7 11 19 38 42| Scale is weakly epimorphic with val: <7 11 19 39 40| Scale is weakly epimorphic with val: <7 11 21 33 38| Scale is weakly epimorphic with val: <7 11 21 33 41| Scale is weakly epimorphic with val: <7 11 21 34 36| Scale is weakly epimorphic with val: <7 11 21 34 39| Scale is weakly epimorphic with val: <7 11 21 34 42| Scale is weakly epimorphic with val: <7 11 21 35 37| Scale is weakly epimorphic with val: <7 11 21 35 40| Scale is weakly epimorphic with val: <7 11 21 36 38| Scale is weakly epimorphic with val: <7 11 21 36 41| Scale is weakly epimorphic with val: <7 11 21 37 39| Scale is weakly epimorphic with val: <7 11 21 37 42| Scale is weakly epimorphic with val: <7 11 21 38 40| Scale is weakly epimorphic with val: <7 11 21 39 41| Scale is weakly epimorphic with val: <7 11 22 33 37| Scale is weakly epimorphic with val: <7 11 22 33 40| Scale is weakly epimorphic with val: <7 11 22 34 38| Scale is weakly epimorphic with val: <7 11 22 34 41| Scale is weakly epimorphic with val: <7 11 22 35 36| Scale is weakly epimorphic with val: <7 11 22 35 39| Scale is weakly epimorphic with val: <7 11 22 35 42| Scale is weakly epimorphic with val: <7 11 22 36 37| Scale is weakly epimorphic with val: <7 11 22 36 40| Scale is weakly epimorphic with val: <7 11 22 37 38| Scale is weakly epimorphic with val: <7 11 22 37 41| Scale is weakly epimorphic with val: <7 11 22 38 39| Scale is weakly epimorphic with val: <7 11 22 38 42| Scale is weakly epimorphic with val: <7 11 22 39 40| Scale is weakly epimorphic with val: <7 12 19 33 37| Scale is weakly epimorphic with val: <7 12 19 33 40| Scale is weakly epimorphic with val: <7 12 19 34 38| Scale is weakly epimorphic with val: <7 12 19 34 41| Scale is weakly epimorphic with val: <7 12 19 35 36| Scale is weakly epimorphic with val: <7 12 19 35 39| Scale is weakly epimorphic with val: <7 12 19 35 42| Scale is weakly epimorphic with val: <7 12 19 36 37| Scale is weakly epimorphic with val: <7 12 19 36 40| Scale is weakly epimorphic with val: <7 12 19 37 38| Scale is weakly epimorphic with val: <7 12 19 37 41| Scale is weakly epimorphic with val: <7 12 19 38 39| Scale is weakly epimorphic with val: <7 12 19 38 42| Scale is weakly epimorphic with val: <7 12 19 39 40| Scale is weakly epimorphic with val: <7 12 20 33 36| Scale is weakly epimorphic with val: <7 12 20 34 37| Scale is weakly epimorphic with val: <7 12 20 35 38| Scale is weakly epimorphic with val: <7 12 20 36 39| Scale is weakly epimorphic with val: <7 12 20 37 40| Scale is weakly epimorphic with val: <7 12 20 38 41| Scale is weakly epimorphic with val: <7 12 20 39 42| Scale is weakly epimorphic with val: <8 11 19 33 36| Scale is weakly epimorphic with val: <8 11 19 34 37| Scale is weakly epimorphic with val: <8 11 19 35 38| Scale is weakly epimorphic with val: <8 11 19 36 39| Scale is weakly epimorphic with val: <8 11 19 37 40| Scale is weakly epimorphic with val: <8 11 19 38 41| Scale is weakly epimorphic with val: <8 11 19 39 42| Scale is weakly epimorphic with val: <8 11 22 33 36| Scale is weakly epimorphic with val: <8 11 22 34 37| Scale is weakly epimorphic with val: <8 11 22 35 38| Scale is weakly epimorphic with val: <8 11 22 36 39| Scale is weakly epimorphic with val: <8 11 22 37 40| Scale is weakly epimorphic with val: <8 11 22 38 41| Scale is weakly epimorphic with val: <8 11 22 39 42| Scale is weakly epimorphic with val: <8 12 19 33 36| Scale is weakly epimorphic with val: <8 12 19 34 37| Scale is weakly epimorphic with val: <8 12 19 35 38| Scale is weakly epimorphic with val: <8 12 19 36 39| Scale is weakly epimorphic with val: <8 12 19 37 40| Scale is weakly epimorphic with val: <8 12 19 38 41| Scale is weakly epimorphic with val: <8 12 19 39 42| Scale is weakly epimorphic with val: <8 12 22 33 36| Scale is weakly epimorphic with val: <8 12 22 34 37| Scale is weakly epimorphic with val: <8 12 22 35 38| Scale is weakly epimorphic with val: <8 12 22 36 39| Scale is weakly epimorphic with val: <8 12 22 37 40| Scale is weakly epimorphic with val: <8 12 22 38 41| Scale is weakly epimorphic with val: <8 12 22 39 42|
FIT/MODE
3: 3 0 0 N M DE S SD: 17.6997 c. M:-27.2641 c. 4: 4 0 0 N M DE S SD: 17.6997 c. M:-27.2641 c. 5: 5 0 0 N M DE S SD: 17.6997 c. M:-27.2641 c. 10: 9 1 0 N G T3 SD: 15.3251 c. M: 22.5404 c. 11: 10 1 0 N G T3 SD: 13.1779 c. M: 18.0127 c. 12: 11 1 0 N G T3 SD: 11.5366 c. M: 14.2397 c. 14: 13 0 1 N G T3 SD: 13.3385 c. M: 21.5565 c. 15: 14 0 1 N G T3 SD: 11.5949 c. M: 19.1848 c. 16: 15 0 1 N G T3 SD: 10.1270 c. M: 17.1096 c. 17: 16 0 1 N G T3 SD: 8.8988 c. M: 15.2786 c. 18: 17 0 1 N G T3 SD: 7.8849 c. M: 13.6510 c. 19: 18 0 1 N G T3 SD: 7.0667 c. M: 12.1947 c. 20: 19 0 1 N G T3 SD: 6.4302 c. M: 10.8841 c. 21: 20 0 1 N G T3 SD: 5.9622 c. M: 9.6983 c. 22: 21 0 1 N G T3 SD: 5.6482 c. M: 8.6202 c. 23: 22 0 1 N G T3 SD: 5.4705 c. M: 7.6360 c. 24: 23 0 1 N G T3 SD: 5.4084 c. M: 6.7337 c. 27: 25 1 1 N M DE S SD: 6.1185 c. M: 9.6281 c. 28: 26 1 1 N M DE S SD: 5.2685 c. M: 8.3106 c. 29: 27 1 1 N M DE S SD: 4.4773 c. M: 7.0838 c. 30: 28 1 1 N M DE S SD: 3.7392 c. M: 5.9389 c. 31: 29 1 1 N M DE S SD: 3.0490 c. M: 4.8678 c. 32: 30 1 1 N M DE S SD: 2.4026 c. M: 3.8637 c. 33: 31 1 1 N M DE S SD: 1.7965 c. M: 2.9205 c. 34: 32 1 1 N M DE S SD: 1.2287 c. M: 2.0327 c. 35: 33 1 1 N M DE S SD: 0.7010 c. M: 1.1956 c. 36: 34 1 1 N M DE S SD: 0.2568 c. M: 0.4051 c. 73: 69 2 2 N M DE S SD: 0.2159 c. M:-0.3731 c. 109: 103 3 3 N M DE S SD: 0.1994 c. M:-0.3105 c. 145: 137 4 4 N M DE S SD: 0.2031 c. M:-0.2790 c. 181: 171 5 5 N M DE S SD: 0.2091 c. M:-0.2600 c. 182: 172 5 5 N M DE S SD: 0.2024 c. M:-0.3356 c. 254: 240 7 7 N M DE S SD: 0.2005 c. M:-0.2925 c. 329: 311 9 9 N M DE S SD: 0.2276 c. M:-0.3938 c. 345: 326 9 10 N T3 SD: 0.2593 c. M: 0.4179 c. 346: 327 9 10 N T3 SD: 0.2227 c. M: 0.3762 c. 347: 328 9 10 N T3 SD: 0.1933 c. M: 0.3347 c. 348: 329 9 10 N T3 SD: 0.1745 c. M: 0.2935 c. 349: 330 9 10 N T3 SD: 0.1695 c. M: 0.2525 c. 350: 331 9 10 N T3 SD: 0.1794 c. M:-0.2274 c. 382: 361 10 11 N T3 SD: 0.1983 c. M: 0.3234 c. 383: 362 10 11 N T3 SD: 0.1671 c. M: 0.2860 c. 384: 363 10 11 N T3 SD: 0.1445 c. M: 0.2487 c. 385: 364 10 11 N T3 SD: 0.1347 c. M: 0.2117 c. 386: 365 10 11 N T3 SD: 0.1401 c. M: 0.1748 c. 419: 396 11 12 N T3 SD: 0.1483 c. M: 0.2457 c. 420: 397 11 12 N T3 SD: 0.1224 c. M: 0.2117 c. 421: 398 11 12 N T3 SD: 0.1075 c. M: 0.1779 c. 422: 399 11 12 N T3 SD: 0.1081 c. M: 0.1443 c. 456: 431 12 13 N T3 SD: 0.1069 c. M: 0.1805 c. 457: 432 12 13 N T3 SD: 0.0869 c. M: 0.1494 c. 458: 433 12 13 N T3 SD: 0.0820 c. M: 0.1185 c. 492: 465 13 14 N T3 SD: 0.0970 c. M: 0.1538 c. 493: 466 13 14 N T3 SD: 0.0726 c. M: 0.1251 c. 494: 467 13 14 N T3 SD: 0.0610 c. M: 0.0965 c. 529: 500 14 15 N T3 SD: 0.0642 c. M: 0.1041 c. 530: 501 14 15 N T3 SD: 0.0453 c. M: 0.0774 c. 531: 502 14 15 N T3 SD: 0.0472 c. M:-0.0639 c. 566: 535 15 16 N T3 SD: 0.0360 c. M: 0.0608 c. 567: 536 15 16 N T3 SD: 0.0286 c. M: 0.0360 c. 602: 569 16 17 N T3 SD: 0.0343 c. M: 0.0462 c. 603: 570 16 17 N T3 SD: 0.0140 c. M: 0.0229 c. 639: 604 17 18 N T3 SD: 0.0110 c. M: 0.0154 c. 1242: 1174 33 35 N T3 SD: 0.0100 c. M: 0.0169 c. 1279: 1209 34 36 N T3 SD: 0.0034 c. M:-0.0060 c. 1315: 1243 35 37 N T3 SD: 0.0041 c. M: 0.0053 c. 1918: 1813 51 54 N T3 SD: 0.0024 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 4:5 x x S SD: 84.4672 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 35.6968 cents 8 x x 11 SD: 53.2729 cents 9 x x 12 S SD: 0.0000 cents 10:13 x x SD: 16.5670 cents 11:14 x 15 SD: 32.9836 cents 12 x x 16 S SD: 0.0000 cents 13:17 x x SD: 6.3532 cents 14:18 x 19 SD: 23.5223 cents 15 x x 20 S SD: 0.0000 cents 16:21 x x SD: 0.0000 cents 17:22 x 23 SD: 17.5715 cents 18 x x 24 S SD: 0.0000 cents 19:25 x x SD: 4.3335 cents 20:26 x 27 SD: 13.5737 cents 21 x x 28 S SD: 0.0000 cents 22 x 29 x SD: 5.7676 cents 23:30 x 31 SD: 10.8010 cents 24 x x 32 S SD: 0.0000 cents 25 x 33 x SD: 3.3813 cents 26:34 x 35 SD: 8.8717 cents 27:35 x 36 SD: 10.7531 cents 28 x 37 x SD: 1.5087 cents 29:38 x 39 SD: 7.5652 cents 30:39 x 40 SD: 8.2835 cents 31 x 41 x SD: 0.0000 cents 32:42 x 43 SD: 6.7364 cents 33:43 x 44 SD: 6.2681 cents 34 x 45 x SD: 1.2415 cents 35:46 x 47 SD: 6.2724 cents 36:47 x 48 SD: 4.5921 cents 37 x 49 x SD: 2.2809 cents 38:50 x 51 SD: 6.0757 cents 39:51 x 52 SD: 3.1766 cents 40 x 53 x SD: 3.1640 cents 41:54 x 55 SD: 6.0626 cents 42:55 x 56 SD: 1.9651 cents 43:56:57 x SD: 7.0162 cents 44 x 58:59 SD: 5.6894 cents 45:59 x 60 SD: 0.9165 cents 46:60:61 x SD: 5.8600 cents 47 x 62:63 SD: 5.1133 cents 48:63 x 64 SD: 0.0000 cents 49:64:65 x SD: 4.9438 cents 50 x 66:67 SD: 4.6365 cents 51:67 x 68 SD: 0.8079 cents 52:68:69 x SD: 4.2593 cents 53 x 70:71 SD: 4.2454 cents 54:71 x 72 SD: 1.5253 cents 55:72:73 x SD: 3.8034 cents 56 x 74:75 SD: 3.9289 cents 57:75 x 76 SD: 2.1668 cents 58:76:77 x SD: 3.5659 cents 60:79 x 80 SD: 2.7436 cents 61:80:81 x SD: 3.5197 cents 63:83 x 84 SD: 3.2653 cents 64:84 x 85 SD: 3.3879 cents 65:85:86:87 SD: 3.0723 cents 66 x 87:88 SD: 2.8838 cents 67:88 x 89 SD: 3.2939 cents 68:89:90:91 SD: 2.6975 cents 69 x 91:92 SD: 2.4513 cents 70:92 x 93 SD: 3.3131 cents 71:93:94:95 SD: 2.4122 cents 72 x 95:96 SD: 2.0551 cents 73:96 x 97 SD: 3.4179 cents 74:97:98:99 SD: 2.2178 cents 76:100 x 101 SD: 3.5818 cents 77:101:102:103 SD: 2.1120 cents 79:104 x 105 SD: 3.7833 cents 80:105:106:107 SD: 2.0867 cents 81:106:107:108 SD: 1.8356 cents 82:108 x 109 SD: 4.0064 cents 83:109:110:111 SD: 2.1279 cents 84:110:111:112 SD: 1.4033 cents 85 x 112:113 SD: 4.1190 cents 86:113:114:115 SD: 2.2191 cents 87:114:115:116 SD: 1.0021 cents 88 x 116:117 SD: 3.7922 cents 89:117:118:119 SD: 2.3447 cents 90:118:119:120 SD: 0.6307 cents 93:122:123:124 SD: 0.2956 cents 96:126:127:128 SD: 0.1466 cents 285:374:377:380 SD: 0.1380 cents 381:500:504:508 SD: 0.1322 cents 477:626:631:636 SD: 0.1313 cents