Scala analysis: 497_M5
Miscellaneous tetrachord 104/103 * 103/102 * 17/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 104/103 16.727029 2: 52/51 33.617251 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/13 464.4277 1: 104/103 16.7270 2: 103/102 16.8902 3: 17/13 464.4277
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104/103 16.727 cents 1: 1 103/102 16.890 cents 1: 1 17/13 464.428 cents 2: 1 52/51 33.617 cents 2: 1 136/103 481.155 cents 2: 1 103/78 481.318 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 : 16.7 33.6 498.0 16.7 : 16.9 481.3 498.0 33.6 : 464.4 481.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.7270 .. 464.4277 cents 1751/1352, 447.7007 cents 104/103, 16.7270 cents 2: 33.6173 .. 481.3180 cents 1751/1352, 447.7007 cents 676/867,-430.8105 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/103, 16.7270 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/13, 464.4277 cents Average / Smallest step : 9.924954 Largest / Average step : 2.797505 Largest / Smallest step : 27.765107 Median interval of one step : 103/102, 16.8902 cents, amount: 1 Least squares average step : 112.72118 cents, oct.: 338.16354 cents Scale is not proper Scale has trivalence property 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 16.72703 cents Scale diversity :-0.049279 Lumma stability : 0.067171 Lumma impropriety factor : 0.865003 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 : 10609/10608, 0.1632 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 481.2364 cents Number of appreciable 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 : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 103 Odd number limit : 103 (O: 103 U: 103) Highest odd numerator or denominator: 103 Scale harmonicity : 0.017260 Fundamental : 1/5253, -12.3589 octaves, 0.0498 Hz. Guide tone : 104, 6.7004 octaves, 27209.059 Hz. Exponens Consonantiae : 5.463120E+05, 19.05937 octaves Euler's gradus suavitatis : 136 Sum of Mann's harmonic distance : 158.5, average 52.83333 Mersenne's string divisions : 149247 Sum of van Prooijen's expressibility: 4.19753, average 1.39918 Sum of Tenney's harmonic distance : 8.53263, average 2.84421 Vogel's harmonic complexity : 92.00000 Wille's k value : 875 Wilson's harmonic complexity : 136 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.92241, average 2.15374 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.66667 2 1 13: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 103: -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: <7 10 26 27 48| Scale is weakly epimorphic with val: <7 10 27 28 49| Scale is weakly epimorphic with val: <7 10 28 29 47| Scale is weakly epimorphic with val: <7 10 29 30 48| Scale is weakly epimorphic with val: <7 10 29 31 47| Scale is weakly epimorphic with val: <7 10 30 31 49| Scale is weakly epimorphic with val: <7 10 30 32 48| Scale is weakly epimorphic with val: <7 11 25 27 47| Scale is weakly epimorphic with val: <7 11 25 29 48| Scale is weakly epimorphic with val: <7 11 25 30 47| Scale is weakly epimorphic with val: <7 11 25 32 48| Scale is weakly epimorphic with val: <7 11 25 33 47| Scale is weakly epimorphic with val: <7 11 26 27 49| Scale is weakly epimorphic with val: <7 11 26 28 48| Scale is weakly epimorphic with val: <7 11 26 30 49| Scale is weakly epimorphic with val: <7 11 26 31 48| Scale is weakly epimorphic with val: <7 11 26 33 49| Scale is JI-epimorphic with val: <7 11 27 28 47| Scale is weakly epimorphic with val: <7 11 27 29 49| Scale is weakly epimorphic with val: <7 11 27 31 47| Scale is weakly epimorphic with val: <7 11 27 32 49| Scale is JI-epimorphic with val: <7 11 28 29 48| Scale is weakly epimorphic with val: <7 11 28 30 47| Scale is weakly epimorphic with val: <7 11 28 32 48| Scale is weakly epimorphic with val: <7 11 28 33 47| Scale is JI-epimorphic with val: <7 11 29 30 49| Scale is weakly epimorphic with val: <7 11 29 31 48| Scale is weakly epimorphic with val: <7 11 29 33 49| Scale is weakly epimorphic with val: <7 11 30 31 47| Scale is weakly epimorphic with val: <7 11 30 32 49| Scale is weakly epimorphic with val: <7 12 29 30 47| Scale is weakly epimorphic with val: <7 12 29 33 47| Scale is weakly epimorphic with val: <7 12 30 31 48| Scale is weakly epimorphic with val: <8 11 25 27 48| Scale is weakly epimorphic with val: <8 11 26 27 47| Scale is weakly epimorphic with val: <8 11 26 28 49| Scale is weakly epimorphic with val: <8 11 26 30 47| Scale is weakly epimorphic with val: <8 11 26 33 47| Scale is weakly epimorphic with val: <8 11 27 28 48| Scale is weakly epimorphic with val: <8 11 27 29 47| Scale is weakly epimorphic with val: <8 11 27 31 48| Scale is weakly epimorphic with val: <8 11 28 29 49| Scale is weakly epimorphic with val: <8 11 28 30 48| Scale is weakly epimorphic with val: <8 11 28 32 49| Scale is weakly epimorphic with val: <8 11 29 31 49| Scale is weakly epimorphic with val: <8 11 30 32 47| Scale is weakly epimorphic with val: <8 12 26 27 48| Scale is weakly epimorphic with val: <8 12 26 28 47| Scale is weakly epimorphic with val: <8 12 26 31 47| Scale is weakly epimorphic with val: <8 12 27 28 49| Scale is weakly epimorphic with val: <8 12 27 29 48| Scale is weakly epimorphic with val: <8 12 27 32 48| Scale is weakly epimorphic with val: <8 12 28 29 47| Scale is weakly epimorphic with val: <8 12 28 30 49| Scale is weakly epimorphic with val: <8 12 28 33 49| Scale is weakly epimorphic with val: <8 12 29 30 48| Scale is weakly epimorphic with val: <8 12 30 31 49|
FIT/MODE
3: 0 0 3 N M DE S SD: 21.6788 c. M: 33.6173 c. 10: 0 1 9 N G T3 SD: 13.4390 c. M: 16.7270 c. 11: 0 1 10 N G T3 SD: 11.7720 c. M: 16.7270 c. 12: 0 1 11 N G T3 SD: 10.6769 c. M: 16.7270 c. 13: 0 1 12 N G T3 SD: 10.0304 c. M: 16.7270 c. 14: 0 1 13 N G T3 SD: 9.7233 c. M: 16.7270 c. 15: 0 1 14 N G T3 SD: 9.6603 c. M: 16.7270 c. 16: 0 1 15 N G T3 SD: 9.7637 c. M: 16.7270 c. 17: 0 1 16 N G T3 SD: 9.9743 c. M: 16.7270 c. 18: 0 1 17 N G T3 SD: 10.2498 c. M: 16.7270 c. 19: 0 1 18 N G T3 SD: 10.5612 c. M: 16.7270 c. 20: 1 0 19 N G T3 SD: 6.8989 c. M: 8.7150 c. 22: 1 1 20 N M DE S SD: 7.5474 c. M:-11.6596 c. 23: 1 1 21 N M DE S SD: 6.2767 c. M:-9.6910 c. 24: 1 1 22 N M DE S SD: 5.1120 c. M:-7.8865 c. 25: 1 1 23 N M DE S SD: 4.0404 c. M:-6.2263 c. 26: 1 1 24 N M DE S SD: 3.0513 c. M:-4.6939 c. 27: 1 1 25 N M DE S SD: 2.1355 c. M:-3.2750 c. 28: 1 1 26 N M DE S SD: 1.2852 c. M:-1.9574 c. 29: 1 1 27 N M DE S SD: 0.4945 c. M:-0.7307 c. 30: 1 1 28 N M DE S SD: 0.2499 c. M: 0.4143 c. 59: 2 2 55 N M DE S SD: 0.1243 c. M:-0.1559 c. 89: 3 3 83 N M DE S SD: 0.0425 c. M:-0.0610 c. 237: 8 8 221 N M DE S SD: 0.0490 c. M:-0.0846 c. 326: 11 11 304 N M DE S SD: 0.0453 c. M:-0.0782 c. 415: 14 14 387 N M DE S SD: 0.0438 c. M:-0.0745 c. 504: 17 17 470 N M DE S SD: 0.0430 c. M:-0.0721 c. 563: 19 19 525 N M DE S SD: 0.0467 c. M:-0.0809 c. 564: 19 19 526 N M DE S SD: 0.0459 c. M: 0.0610 c. 593: 20 20 553 N M DE S SD: 0.0427 c. M:-0.0704 c. 653: 22 22 609 N M DE S SD: 0.0453 c. M: 0.0583 c. 682: 23 23 636 N M DE S SD: 0.0424 c. M:-0.0692 c. 742: 25 25 692 N M DE S SD: 0.0448 c. M: 0.0563 c. 771: 26 26 719 N M DE S SD: 0.0423 c. M:-0.0683 c. 800: 27 27 746 N M DE S SD: 0.0473 c. M:-0.0820 c. 831: 28 28 775 N M DE S SD: 0.0445 c. M: 0.0547 c. 860: 29 29 802 N M DE S SD: 0.0422 c. M:-0.0675 c. 949: 32 32 885 N M DE S SD: 0.0422 c. M:-0.0669 c. 1038: 35 35 968 N M DE S SD: 0.0422 c. M:-0.0664 c. 1127: 38 38 1051 N M DE S SD: 0.0421 c. M:-0.0660 c. 1216: 41 41 1134 N M DE S SD: 0.0421 c. M:-0.0656 c. 1305: 44 44 1217 N M DE S SD: 0.0421 c. M:-0.0653 c. 1363: 46 46 1271 N M DE S SD: 0.0471 c. M:-0.0815 c. 1365: 46 46 1273 N M DE S SD: 0.0435 c. M:-0.0569 c. 1394: 47 47 1300 N M DE S SD: 0.0421 c. M:-0.0650 c. 1526: 51 52 1423 N T3 SD: 0.0474 c. M: 0.0820 c. 1541: 52 52 1437 N M DE S SD: 0.0458 c. M:-0.0792 c. 1543: 52 52 1439 N M DE S SD: 0.0434 c. M:-0.0574 c. 1554: 52 53 1449 N T3 SD: 0.0407 c. M: 0.0614 c. 1555: 52 53 1450 N T3 SD: 0.0423 c. M: 0.0721 c. 1556: 52 53 1451 N T3 SD: 0.0481 c. M: 0.0829 c. 1571: 53 53 1465 N M DE S SD: 0.0441 c. M:-0.0753 c. 1572: 53 53 1466 N M DE S SD: 0.0421 c. M:-0.0646 c. 1583: 53 54 1476 N T3 SD: 0.0406 c. M: 0.0521 c. 1584: 53 54 1477 N T3 SD: 0.0391 c. M: 0.0626 c. 1585: 53 54 1478 N T3 SD: 0.0423 c. M: 0.0732 c. 1613: 54 55 1504 N T3 SD: 0.0381 c. M: 0.0535 c. 1614: 54 55 1505 N T3 SD: 0.0382 c. M: 0.0638 c. 1615: 54 55 1506 N T3 SD: 0.0428 c. M: 0.0741 c. 1631: 55 55 1521 N M DE S SD: 0.0423 c. M:-0.0679 c. 1642: 55 56 1531 N T3 SD: 0.0391 c. M:-0.0508 c. 1643: 55 56 1532 N T3 SD: 0.0362 c. M: 0.0548 c. 1644: 55 56 1533 N T3 SD: 0.0379 c. M: 0.0649 c. 1645: 55 56 1534 N T3 SD: 0.0438 c. M: 0.0751 c. 1661: 56 56 1549 N M DE S SD: 0.0422 c. M:-0.0644 c. 1671: 56 57 1558 N T3 SD: 0.0417 c. M:-0.0626 c. 1672: 56 57 1559 N T3 SD: 0.0362 c. M: 0.0461 c. 1673: 56 57 1560 N T3 SD: 0.0349 c. M: 0.0561 c. 1674: 56 57 1561 N T3 SD: 0.0381 c. M: 0.0660 c. 1701: 57 58 1586 N T3 SD: 0.0381 c. M:-0.0542 c. 1702: 57 58 1587 N T3 SD: 0.0339 c. M: 0.0475 c. 1703: 57 58 1588 N T3 SD: 0.0341 c. M: 0.0573 c. 1704: 57 58 1589 N T3 SD: 0.0388 c. M: 0.0671 c. 1731: 58 59 1614 N T3 SD: 0.0349 c. M:-0.0461 c. 1732: 58 59 1615 N T3 SD: 0.0321 c. M: 0.0488 c. 1733: 58 59 1616 N T3 SD: 0.0340 c. M: 0.0585 c. 1761: 59 60 1642 N T3 SD: 0.0322 c. M: 0.0407 c. 1762: 59 60 1643 N T3 SD: 0.0310 c. M: 0.0502 c. 1763: 59 60 1644 N T3 SD: 0.0344 c. M: 0.0596 c. 1790: 60 61 1669 N T3 SD: 0.0343 c. M:-0.0495 c. 1791: 60 61 1670 N T3 SD: 0.0301 c. M: 0.0421 c. 1792: 60 61 1671 N T3 SD: 0.0305 c. M: 0.0514 c. 1793: 60 61 1672 N T3 SD: 0.0353 c. M: 0.0607 c. 1820: 61 62 1697 N T3 SD: 0.0312 c. M:-0.0418 c. 1821: 61 62 1698 N T3 SD: 0.0285 c. M: 0.0435 c. 1822: 61 62 1699 N T3 SD: 0.0305 c. M: 0.0526 c. 1850: 62 63 1725 N T3 SD: 0.0287 c. M: 0.0358 c. 1851: 62 63 1726 N T3 SD: 0.0275 c. M: 0.0448 c. 1852: 62 63 1727 N T3 SD: 0.0311 c. M: 0.0538 c. 1879: 63 64 1752 N T3 SD: 0.0308 c. M:-0.0452 c. 1880: 63 64 1753 N T3 SD: 0.0266 c. M: 0.0372 c. 1881: 63 64 1754 N T3 SD: 0.0272 c. M: 0.0461 c. 1882: 63 64 1755 N T3 SD: 0.0321 c. M: 0.0550 c. 1909: 64 65 1780 N T3 SD: 0.0279 c. M:-0.0380 c. 1910: 64 65 1781 N T3 SD: 0.0252 c. M: 0.0386 c. 1911: 64 65 1782 N T3 SD: 0.0274 c. M: 0.0473 c. 1939: 65 66 1808 N T3 SD: 0.0254 c. M: 0.0313 c. 1940: 65 66 1809 N T3 SD: 0.0244 c. M: 0.0400 c. 1941: 65 66 1810 N T3 SD: 0.0281 c. M: 0.0486 c. 1968: 66 67 1835 N T3 SD: 0.0277 c. M:-0.0413 c. 1969: 66 67 1836 N T3 SD: 0.0235 c. M: 0.0328 c. 1970: 66 67 1837 N T3 SD: 0.0242 c. M: 0.0413 c. 1999: 67 68 1864 N T3 SD: 0.0222 c. M: 0.0342 c. 2000: 67 68 1865 N T3 SD: 0.0246 c. M: 0.0425 c. 2028: 68 69 1891 N T3 SD: 0.0225 c. M:-0.0278 c. 2029: 68 69 1892 N T3 SD: 0.0215 c. M: 0.0355 c. 2030: 68 69 1893 N T3 SD: 0.0254 c. M: 0.0437 c. 2057: 69 70 1918 N T3 SD: 0.0248 c. M:-0.0377 c. 2058: 69 70 1919 N T3 SD: 0.0207 c. M: 0.0287 c. 2059: 69 70 1920 N T3 SD: 0.0215 c. M: 0.0368 c. 2088: 70 71 1947 N T3 SD: 0.0195 c. M: 0.0301 c. 2089: 70 71 1948 N T3 SD: 0.0220 c. M: 0.0381 c. 2117: 71 72 1974 N T3 SD: 0.0198 c. M:-0.0249 c. 2118: 71 72 1975 N T3 SD: 0.0189 c. M: 0.0315 c. 2147: 72 73 2002 N T3 SD: 0.0181 c. M: 0.0250 c. 2148: 72 73 2003 N T3 SD: 0.0190 c. M: 0.0328 c. 2177: 73 74 2030 N T3 SD: 0.0169 c. M: 0.0264 c. 2178: 73 74 2031 N T3 SD: 0.0197 c. M: 0.0341 c. 2206: 74 75 2057 N T3 SD: 0.0173 c. M:-0.0222 c. 2207: 74 75 2058 N T3 SD: 0.0165 c. M: 0.0277 c. 2236: 75 76 2085 N T3 SD: 0.0156 c. M: 0.0216 c. 2237: 75 76 2086 N T3 SD: 0.0168 c. M: 0.0291 c. 2266: 76 77 2113 N T3 SD: 0.0146 c. M: 0.0230 c. 2295: 77 78 2140 N T3 SD: 0.0151 c. M:-0.0198 c. 2296: 77 78 2141 N T3 SD: 0.0143 c. M: 0.0243 c. 2325: 78 79 2168 N T3 SD: 0.0134 c. M: 0.0184 c. 2326: 78 79 2169 N T3 SD: 0.0148 c. M: 0.0256 c. 2355: 79 80 2196 N T3 SD: 0.0125 c. M: 0.0198 c. 2384: 80 81 2223 N T3 SD: 0.0130 c. M:-0.0175 c. 2385: 80 81 2224 N T3 SD: 0.0123 c. M: 0.0211 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 x 8 S SD: 0.0000 cents 7 x 8:9 S SD: 103.6735 cents 8 x 9:11 SD: 89.2155 cents 9 x 10:12 S SD: 74.3932 cents 10 x 11:13 SD: 69.2526 cents 11 x 12:15 S SD: 61.6589 cents 12 x 13:16 SD: 52.4777 cents 13 x 14:17 SD: 50.2360 cents 14 x 15:19 SD: 45.5658 cents 15 x 16:20 S SD: 39.0570 cents 16 x 17:21 SD: 38.1853 cents 17 x 18:23 SD: 35.0276 cents 18 x 19:24 SD: 29.9929 cents 19 x 20:25 S SD: 29.8790 cents 20 x 21:27 SD: 27.6054 cents 21 x 22:28 SD: 23.4599 cents 22 x 23:29 SD: 23.8210 cents 23 x 24:31 SD: 22.1098 cents 24 x 25:32 SD: 18.5276 cents 25 x 26:33 SD: 19.2228 cents 26 x 27:35 SD: 17.8929 cents 27 x 28:36 SD: 14.6718 cents 28 x 29:37 SD: 15.6312 cents 29 x 30:39 SD: 14.5735 cents 30 x 31:40 SD: 11.5748 cents 31 x 32:41 SD: 12.7692 cents 32 x 33:43 SD: 11.9149 cents 33 x 34:44 SD: 9.0326 cents 34 x 35:45 SD: 10.4607 cents 35 x 36:47 SD: 9.7654 cents 36 x 37:48 SD: 6.9084 cents 37 x 38:49 SD: 8.5923 cents 38 x 39:51 SD: 8.0274 cents 39 x 40:52 SD: 5.1069 cents 40 x 41:53 SD: 7.0922 cents 41 x 42:55 SD: 6.6406 cents 42 x 43:56 SD: 3.5598 cents 43 x 44:57 SD: 5.9189 cents 44 x 45:59 SD: 5.5718 cents 45 x 46:60 SD: 2.2167 cents 46 x 47:61 SD: 5.0517 cents 47 x 48:63 SD: 4.8054 cents 48 x 49:64 SD: 1.0398 cents 49 x 50:65 SD: 4.4795 cents 50 x 51:67 SD: 4.3301 cents 51 x 52:68 SD: 0.0000 cents 52 x 53:69 SD: 4.1839 cents 53 x 54:71 SD: 4.1217 cents 54 x 55:72 SD: 0.9253 cents 55 x 56:73 SD: 4.1255 cents 56 x 57:75 SD: 4.1328 cents 57 x 58:76 SD: 1.7540 cents 58 x 59:77 SD: 4.2458 cents 59 x 60:79 SD: 4.3017 cents 60 x 61:80 SD: 2.5006 cents 61 x 62:81 SD: 4.4842 cents 62 x 63:83 SD: 4.5702 cents 63 x 64:84 SD: 3.1766 cents 64 x 65:85 SD: 4.7913 cents 65 x 66:87 SD: 4.8939 cents 66 x 67:88 SD: 3.7916 cents 67 x 68:89 SD: 5.1329 cents 68 x 69:91 SD: 5.2434 cents 69:70 x 92 SD: 4.0916 cents 70:71 x 93 SD: 4.9918 cents 71:72 x 95 SD: 4.8238 cents 72:73 x 96 SD: 3.5762 cents 73:74 x 97 SD: 4.5246 cents 74:75 x 99 SD: 4.3729 cents 75:76 x 100 SD: 3.1018 cents 76:77 x 101 SD: 4.1047 cents 78:79:80:104 SD: 3.8399 cents 81:82:83:108 SD: 3.2407 cents 84:85:86:112 SD: 2.6840 cents 87:88:89:116 SD: 2.1653 cents 90:91:92:120 SD: 1.6809 cents 93:94:95:124 SD: 1.2276 cents 96:97:98:128 SD: 0.8026 cents 99:100:101:132 SD: 0.4041 cents 102:103:104:136 SD: 0.0544 cents