Scala analysis: 499_M7
Miscellaneous tetrachord 98/97 * 97/96 * 64/49
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98/97 17.756402 2: 49/48 35.696812 slendro diesis, septimal 1/6-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/49 462.3482 2 septatones or septatonic major third 1: 98/97 17.7564 2: 97/96 17.9404 3: 64/49 462.3482 2 septatones or septatonic major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 98/97 17.756 cents 1: 1 97/96 17.940 cents 1: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 2: 1 128/97 480.105 cents 2: 1 194/147 480.289 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 : 17.8 35.7 498.0 17.8 : 17.9 480.3 498.0 35.7 : 462.3 480.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.7564 .. 462.3482 cents 3104/2401, 444.5918 cents 98/97, 17.7564 cents 2: 35.6968 .. 480.2886 cents 3104/2401, 444.5918 cents 2401/3072,-426.6514 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 98/97, 17.7564 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/49, 462.3482 cents Average / Smallest step : 9.349585 Largest / Average step : 2.784978 Largest / Smallest step : 26.038393 Median interval of one step : 97/96, 17.9404 cents, amount: 1 Least squares average step : 113.09179 cents, oct.: 339.27536 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 17.75640 cents Scale diversity :-0.035182 Lumma stability : 0.071304 Lumma impropriety factor : 0.856652 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 : 9409/9408, 0.1840 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 480.1966 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 : 97 Odd number limit : 147 (O: 97 U: 147) Highest odd numerator or denominator: 97 Scale harmonicity : 0.034202 Fundamental : 1/4656, -12.1849 octaves, 0.0562 Hz. Guide tone : 196, 7.6147 octaves, 51278.611 Hz. Exponens Consonantiae : 9.125760E+05, 19.79959 octaves Euler's gradus suavitatis : 117 Sum of Mann's harmonic distance : 149.5, average 49.83333 Mersenne's string divisions : 132405 Sum of van Prooijen's expressibility: 4.15409, average 1.38470 Sum of Tenney's harmonic distance : 8.42862, average 2.80954 Vogel's harmonic complexity : 78.66667 Wille's k value : 2376 Wilson's harmonic complexity : 114 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 22.92778, average 3.82130 Lattice compactness (without 2's) : 10.47214, average 1.74536 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.33333 7 3: -1 .. 0 -0.66667 2 1 7: 0 .. 2 1.33333 4 1 97: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 22 47| Scale is weakly epimorphic with val: <6 11 19 48| Scale is weakly epimorphic with val: <7 11 19 47| Scale is weakly epimorphic with val: <7 11 20 48| = patent Scale is weakly epimorphic with val: <7 11 22 47| Scale is weakly epimorphic with val: <7 12 22 48| Scale is weakly epimorphic with val: <8 11 22 49|
FIT/MODE
3: 0 0 3 N M DE S SD: 23.0185 c. M: 35.6968 c. 10: 0 1 9 N G T3 SD: 13.0935 c. M: 17.7564 c. 11: 0 1 10 N G T3 SD: 11.6486 c. M: 17.7564 c. 12: 0 1 11 N G T3 SD: 10.7860 c. M: 17.7564 c. 13: 0 1 12 N G T3 SD: 10.3622 c. M: 17.7564 c. 14: 0 1 13 N G T3 SD: 10.2519 c. M: 17.7564 c. 15: 0 1 14 N G T3 SD: 10.3523 c. M: 17.7564 c. 16: 0 1 15 N G T3 SD: 10.5856 c. M: 17.7564 c. 17: 0 1 16 N G T3 SD: 10.8973 c. M: 17.7564 c. 18: 0 1 17 N G T3 SD: 11.2507 c. M: 17.7564 c. 19: 0 1 18 N G T3 SD: 11.6223 c. M: 17.7564 c. 20: 1 0 19 N G T3 SD: 7.4741 c. M: 10.7946 c. 22: 1 1 20 N M DE S SD: 6.2078 c. M:-9.5800 c. 23: 1 1 21 N M DE S SD: 4.9372 c. M:-7.6114 c. 24: 1 1 22 N M DE S SD: 3.7724 c. M:-5.8069 c. 25: 1 1 23 N M DE S SD: 2.7009 c. M:-4.1468 c. 26: 1 1 24 N M DE S SD: 1.7120 c. M:-2.6143 c. 27: 1 1 25 N M DE S SD: 0.7968 c. M:-1.1954 c. 28: 1 1 26 N M DE S SD: 0.0728 c. M: 0.1222 c. 195: 7 7 181 N M DE S SD: 0.0786 c. M:-0.1221 c. 223: 8 8 207 N M DE S SD: 0.0674 c. M:-0.1107 c. 251: 9 9 233 N M DE S SD: 0.0598 c. M:-0.1018 c. 279: 10 10 259 N M DE S SD: 0.0547 c. M:-0.0947 c. 307: 11 11 285 N M DE S SD: 0.0514 c. M:-0.0889 c. 335: 12 12 311 N M DE S SD: 0.0494 c. M:-0.0840 c. 363: 13 13 337 N M DE S SD: 0.0482 c. M:-0.0799 c. 391: 14 14 363 N M DE S SD: 0.0476 c. M:-0.0764 c. 419: 15 15 389 N M DE S SD: 0.0475 c. M:-0.0734 c. 447: 16 16 415 N M DE S SD: 0.0477 c. M:-0.0707 c. 475: 17 17 441 N M DE S SD: 0.0480 c. M:-0.0684 c. 503: 18 18 467 N M DE S SD: 0.0484 c. M:-0.0663 c. 531: 19 19 493 N M DE S SD: 0.0490 c. M:-0.0644 c. 559: 20 20 519 N M DE S SD: 0.0495 c. M:-0.0627 c. 586: 21 21 544 N M DE S SD: 0.0529 c. M:-0.0916 c. 587: 21 21 545 N M DE S SD: 0.0501 c. M: 0.0616 c. 698: 25 25 648 N M DE S SD: 0.0487 c. M:-0.0819 c. 754: 27 27 700 N M DE S SD: 0.0479 c. M:-0.0781 c. 810: 29 29 752 N M DE S SD: 0.0475 c. M:-0.0748 c. 1229: 44 44 1141 N M DE S SD: 0.0475 c. M:-0.0743 c. 1379: 49 50 1280 N T3 SD: 0.0481 c. M: 0.0594 c. 1380: 49 50 1281 N T3 SD: 0.0457 c. M: 0.0722 c. 1381: 49 50 1282 N T3 SD: 0.0492 c. M: 0.0850 c. 1397: 50 50 1297 N M DE S SD: 0.0479 c. M:-0.0691 c. 1407: 50 51 1306 N T3 SD: 0.0459 c. M: 0.0576 c. 1408: 50 51 1307 N T3 SD: 0.0439 c. M: 0.0701 c. 1409: 50 51 1308 N T3 SD: 0.0478 c. M: 0.0827 c. 1435: 51 52 1332 N T3 SD: 0.0438 c. M: 0.0558 c. 1436: 51 52 1333 N T3 SD: 0.0422 c. M: 0.0682 c. 1437: 51 52 1334 N T3 SD: 0.0465 c. M: 0.0805 c. 1463: 52 53 1358 N T3 SD: 0.0418 c. M: 0.0542 c. 1464: 52 53 1359 N T3 SD: 0.0406 c. M: 0.0663 c. 1465: 52 53 1360 N T3 SD: 0.0452 c. M: 0.0784 c. 1491: 53 54 1384 N T3 SD: 0.0399 c. M: 0.0526 c. 1492: 53 54 1385 N T3 SD: 0.0391 c. M: 0.0645 c. 1493: 53 54 1386 N T3 SD: 0.0441 c. M: 0.0763 c. 1518: 54 55 1409 N T3 SD: 0.0440 c. M:-0.0653 c. 1519: 54 55 1410 N T3 SD: 0.0381 c. M: 0.0511 c. 1520: 54 55 1411 N T3 SD: 0.0377 c. M: 0.0627 c. 1521: 54 55 1412 N T3 SD: 0.0430 c. M: 0.0743 c. 1546: 55 56 1435 N T3 SD: 0.0420 c. M:-0.0619 c. 1547: 55 56 1436 N T3 SD: 0.0363 c. M: 0.0496 c. 1548: 55 56 1437 N T3 SD: 0.0364 c. M: 0.0610 c. 1549: 55 56 1438 N T3 SD: 0.0420 c. M: 0.0724 c. 1574: 56 57 1461 N T3 SD: 0.0400 c. M:-0.0586 c. 1575: 56 57 1462 N T3 SD: 0.0347 c. M: 0.0481 c. 1576: 56 57 1463 N T3 SD: 0.0351 c. M: 0.0594 c. 1577: 56 57 1464 N T3 SD: 0.0411 c. M: 0.0706 c. 1602: 57 58 1487 N T3 SD: 0.0381 c. M:-0.0555 c. 1603: 57 58 1488 N T3 SD: 0.0331 c. M: 0.0468 c. 1604: 57 58 1489 N T3 SD: 0.0340 c. M: 0.0578 c. 1605: 57 58 1490 N T3 SD: 0.0403 c. M: 0.0688 c. 1630: 58 59 1513 N T3 SD: 0.0363 c. M:-0.0524 c. 1631: 58 59 1514 N T3 SD: 0.0316 c. M: 0.0454 c. 1632: 58 59 1515 N T3 SD: 0.0329 c. M: 0.0563 c. 1659: 59 60 1540 N T3 SD: 0.0302 c. M: 0.0441 c. 1660: 59 60 1541 N T3 SD: 0.0319 c. M: 0.0548 c. 1687: 60 61 1566 N T3 SD: 0.0288 c. M: 0.0429 c. 1688: 60 61 1567 N T3 SD: 0.0309 c. M: 0.0534 c. 1715: 61 62 1592 N T3 SD: 0.0275 c. M: 0.0417 c. 1716: 61 62 1593 N T3 SD: 0.0301 c. M: 0.0520 c. 1742: 62 63 1617 N T3 SD: 0.0295 c. M:-0.0412 c. 1743: 62 63 1618 N T3 SD: 0.0263 c. M: 0.0405 c. 1744: 62 63 1619 N T3 SD: 0.0293 c. M: 0.0507 c. 1770: 63 64 1643 N T3 SD: 0.0280 c. M:-0.0386 c. 1771: 63 64 1644 N T3 SD: 0.0251 c. M: 0.0394 c. 1772: 63 64 1645 N T3 SD: 0.0285 c. M: 0.0494 c. 1798: 64 65 1669 N T3 SD: 0.0265 c. M:-0.0361 c. 1799: 64 65 1670 N T3 SD: 0.0240 c. M: 0.0383 c. 1800: 64 65 1671 N T3 SD: 0.0279 c. M: 0.0481 c. 1826: 65 66 1695 N T3 SD: 0.0251 c. M:-0.0337 c. 1827: 65 66 1696 N T3 SD: 0.0230 c. M: 0.0372 c. 1828: 65 66 1697 N T3 SD: 0.0273 c. M: 0.0469 c. 1854: 66 67 1721 N T3 SD: 0.0237 c. M:-0.0313 c. 1855: 66 67 1722 N T3 SD: 0.0220 c. M: 0.0362 c. 1882: 67 68 1747 N T3 SD: 0.0224 c. M:-0.0291 c. 1883: 67 68 1748 N T3 SD: 0.0211 c. M: 0.0352 c. 1910: 68 69 1773 N T3 SD: 0.0212 c. M:-0.0268 c. 1911: 68 69 1774 N T3 SD: 0.0203 c. M: 0.0342 c. 1938: 69 70 1799 N T3 SD: 0.0199 c. M:-0.0247 c. 1939: 69 70 1800 N T3 SD: 0.0196 c. M: 0.0333 c. 1966: 70 71 1825 N T3 SD: 0.0188 c. M: 0.0234 c. 1967: 70 71 1826 N T3 SD: 0.0189 c. M: 0.0324 c. 1994: 71 72 1851 N T3 SD: 0.0176 c. M: 0.0226 c. 1995: 71 72 1852 N T3 SD: 0.0182 c. M: 0.0315 c. 2022: 72 73 1877 N T3 SD: 0.0166 c. M: 0.0219 c. 2023: 72 73 1878 N T3 SD: 0.0177 c. M: 0.0306 c. 2050: 73 74 1903 N T3 SD: 0.0155 c. M: 0.0211 c. 2051: 73 74 1904 N T3 SD: 0.0172 c. M: 0.0298 c. 2078: 74 75 1929 N T3 SD: 0.0146 c. M: 0.0204 c. 2079: 74 75 1930 N T3 SD: 0.0168 c. M: 0.0290 c. 2106: 75 76 1955 N T3 SD: 0.0136 c. M: 0.0198 c. 2134: 76 77 1981 N T3 SD: 0.0128 c. M: 0.0191 c. 2162: 77 78 2007 N T3 SD: 0.0120 c. M: 0.0184 c. 2190: 78 79 2033 N T3 SD: 0.0112 c. M: 0.0178 c. 2218: 79 80 2059 N T3 SD: 0.0105 c. M: 0.0172 c. 2246: 80 81 2085 N T3 SD: 0.0099 c. M: 0.0166 c. 2274: 81 82 2111 N T3 SD: 0.0094 c. M: 0.0160 c. 2302: 82 83 2137 N T3 SD: 0.0090 c. M: 0.0154 c. 2329: 83 84 2162 N T3 SD: 0.0098 c. M:-0.0153 c. 2330: 83 84 2163 N T3 SD: 0.0086 c. M: 0.0149 c. 2357: 84 85 2188 N T3 SD: 0.0088 c. M:-0.0137 c. 2358: 84 85 2189 N T3 SD: 0.0083 c. M: 0.0143 c. 2385: 85 86 2214 N T3 SD: 0.0079 c. M:-0.0121 c. 2386: 85 86 2215 N T3 SD: 0.0081 c. M: 0.0138 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: 102.6833 cents 8 x 9:11 SD: 88.2237 cents 9 x 10:12 S SD: 73.3535 cents 10 x 11:13 SD: 68.2671 cents 11 x 12:15 S SD: 60.6731 cents 12 x 13:16 SD: 51.4379 cents 13 x 14:17 SD: 49.2573 cents 14 x 15:19 SD: 44.5879 cents 15 x 16:20 S SD: 38.0172 cents 16 x 17:21 SD: 37.2159 cents 17 x 18:23 SD: 34.0599 cents 18 x 19:24 SD: 28.9531 cents 19 x 20:25 S SD: 28.9216 cents 20 x 21:27 SD: 26.6508 cents 21 x 22:28 SD: 22.4201 cents 22 x 23:29 SD: 22.8792 cents 23 x 24:31 SD: 21.1723 cents 24 x 25:32 SD: 17.4878 cents 25 x 26:33 SD: 18.3017 cents 26 x 27:35 SD: 16.9781 cents 27 x 28:36 SD: 13.6320 cents 28 x 29:37 SD: 14.7378 cents 29 x 30:39 SD: 13.6893 cents 30 x 31:40 SD: 10.5350 cents 31 x 32:41 SD: 11.9138 cents 32 x 33:43 SD: 11.0729 cents 33 x 34:44 SD: 7.9928 cents 34 x 35:45 SD: 9.6583 cents 35 x 36:47 SD: 8.9826 cents 36 x 37:48 SD: 5.8686 cents 37 x 38:49 SD: 7.8649 cents 38 x 39:51 SD: 7.3291 cents 39 x 40:52 SD: 4.0671 cents 40 x 41:53 SD: 6.4719 cents 41 x 42:55 SD: 6.0626 cents 42 x 43:56 SD: 2.5200 cents 43 x 44:57 SD: 5.4484 cents 44 x 45:59 SD: 5.1601 cents 45 x 46:60 SD: 1.1769 cents 46 x 47:61 SD: 4.7793 cents 47 x 48:63 SD: 4.6075 cents 48 x 49:64 SD: 0.0000 cents 49 x 50:65 SD: 4.4424 cents 50 x 51:67 SD: 4.3748 cents 51 x 52:68 SD: 1.0398 cents 52 x 53:69 SD: 4.3877 cents 53 x 54:71 SD: 4.4018 cents 54 x 55:72 SD: 1.9651 cents 55 x 56:73 SD: 4.5409 cents 56 x 57:75 SD: 4.6102 cents 57 x 58:76 SD: 2.7938 cents 58 x 59:77 SD: 4.8261 cents 59 x 60:79 SD: 4.9280 cents 60 x 61:80 SD: 3.5404 cents 61 x 62:81 SD: 5.1839 cents 62 x 63:83 SD: 5.3028 cents 63 x 64:84 SD: 4.2164 cents 64 x 65:85 SD: 5.5752 cents 65:66 x 87 SD: 5.4641 cents 66:67 x 88 SD: 4.1388 cents 67:68 x 89 SD: 5.1032 cents 68:69 x 91 SD: 4.9213 cents 69:70 x 92 SD: 3.5769 cents 70:71 x 93 SD: 4.5993 cents 71:72 x 95 SD: 4.4363 cents 72:73:74:96 SD: 4.4128 cents 74:75:76:99 SD: 4.3946 cents 75:76:77:100 SD: 3.7131 cents 78:79:80:104 SD: 3.0666 cents 81:82:83:108 SD: 2.4676 cents 84:85:86:112 SD: 1.9109 cents 87:88:89:116 SD: 1.3924 cents 90:91:92:120 SD: 0.9084 cents 93:94:95:124 SD: 0.4565 cents 96:97:98:128 SD: 0.0613 cents