Scala analysis: 494_M2
Miscellaneous tetrachord 25/19 * 931/925 * 148/147
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/19 475.114412 2: 49/37 486.307774 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 148/147 11.7372 1: 25/19 475.1144 2: 931/925 11.1934 3: 148/147 11.7372
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 931/925 11.193 cents 1: 1 148/147 11.737 cents 1: 1 25/19 475.114 cents 2: 1 76/75 22.931 cents 2: 1 49/37 486.308 cents 2: 1 3700/2793 486.852 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 : 475.1 486.3 498.0 475.1: 11.2 22.9 498.0 486.3: 11.7 486.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 11.1934 .. 475.1144 cents 23125/17689, 463.9210 cents 931/925, 11.1934 cents 2: 22.9306 .. 486.8516 cents 23125/17689, 463.9210 cents 1444/1875,-452.1838 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 931/925, 11.1934 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/19, 475.1144 cents Average / Smallest step : 14.831557 Largest / Average step : 2.861876 Largest / Smallest step : 42.446084 Median interval of one step : 148/147, 11.7372 cents, amount: 1 Least squares average step : 210.13321 cents, oct.: 630.39963 cents Scale is not proper Scale has trivalence property Scale is a mode of a 934-tone equal temperament with octave 4/3 degrees: 891 912 934 Least number of segments generator : 469 of 250.089 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 543 of 289.549 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 11.19336 cents Scale diversity :-0.121042 Lumma stability : 0.044949 Lumma impropriety factor : 0.907918 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 : 136900/136857, 0.5439 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 486.5797 cents 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 463.9210 cents: 1 -- Rational properties -- Prime limit : 37 Odd number limit : 2793 (O: 931 U: 2793) Highest odd numerator or denominator: 49 Scale harmonicity : 0.013861 Fundamental : 1/2109, -11.0423 octaves, 0.1241 Hz. Guide tone : 4900, 12.2586 octaves, 1281965.270 Hz. Exponens Consonantiae : 1.033410E+07, 23.30091 octaves Euler's gradus suavitatis : 79 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 13244 Sum of van Prooijen's expressibility: 3.56526, average 1.18842 Sum of Tenney's harmonic distance : 7.01427, average 2.33809 Vogel's harmonic complexity : 48.00000 Wille's k value : 1396 Wilson's harmonic complexity : 83 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 15.63441, average 2.60574 Lattice compactness (without 2's) : 12.92163, average 2.15360 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 0 -0.33333 1 1 5: 0 .. 2 0.66667 2 7: 0 .. 2 0.66667 2 19: -1 .. 0 -0.33333 1 1 37: -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: <7 11 16 19 30 37| Scale is weakly epimorphic with val: <7 11 16 19 30 40| Scale is JI-epimorphic with val: <7 11 16 19 31 36| Scale is weakly epimorphic with val: <7 11 16 19 31 39| Scale is weakly epimorphic with val: <7 11 16 20 30 36| Scale is weakly epimorphic with val: <7 11 16 20 30 39| Scale is JI-epimorphic with val: <7 11 16 20 31 38| Scale is weakly epimorphic with val: <7 11 16 21 30 38| Scale is weakly epimorphic with val: <7 11 16 21 31 37| Scale is JI-epimorphic with val: <7 11 16 21 31 40| Scale is weakly epimorphic with val: <7 11 17 19 30 36| Scale is weakly epimorphic with val: <7 11 17 19 30 39| Scale is weakly epimorphic with val: <7 11 17 19 32 37| Scale is weakly epimorphic with val: <7 11 17 19 32 40| Scale is weakly epimorphic with val: <7 11 17 20 30 38| Scale is weakly epimorphic with val: <7 11 17 20 32 36| Scale is weakly epimorphic with val: <7 11 17 20 32 39| Scale is weakly epimorphic with val: <7 11 17 21 30 37| Scale is weakly epimorphic with val: <7 11 17 21 30 40| Scale is weakly epimorphic with val: <7 11 17 21 32 38| Scale is weakly epimorphic with val: <7 11 18 19 31 37| Scale is weakly epimorphic with val: <7 11 18 19 31 40| Scale is weakly epimorphic with val: <7 11 18 19 32 36| Scale is weakly epimorphic with val: <7 11 18 19 32 39| Scale is weakly epimorphic with val: <7 11 18 20 31 36| Scale is weakly epimorphic with val: <7 11 18 20 31 39| Scale is weakly epimorphic with val: <7 11 18 20 32 38| Scale is weakly epimorphic with val: <7 11 18 21 31 38| Scale is weakly epimorphic with val: <7 11 18 21 32 37| Scale is weakly epimorphic with val: <7 11 18 21 32 40| Scale is weakly epimorphic with val: <7 12 16 20 31 37| Scale is weakly epimorphic with val: <7 12 16 21 31 39| Scale is weakly epimorphic with val: <7 12 17 19 31 37| Scale is weakly epimorphic with val: <7 12 17 19 31 40| Scale is weakly epimorphic with val: <7 12 17 20 30 37| Scale is weakly epimorphic with val: <7 12 17 20 31 36| Scale is weakly epimorphic with val: <7 12 17 20 31 39| Scale is weakly epimorphic with val: <7 12 17 21 30 39| Scale is weakly epimorphic with val: <7 12 17 21 31 38| Scale is weakly epimorphic with val: <7 12 18 20 32 37| Scale is weakly epimorphic with val: <7 12 18 21 32 39|
FIT/MODE
3: 3 0 0 N M DE S SD: 14.8725 c. M:-22.9306 c. 4: 4 0 0 N M DE S SD: 14.8725 c. M:-22.9306 c. 5: 5 0 0 N M DE S SD: 14.8725 c. M:-22.9306 c. 12: 11 1 0 N G T3 SD: 12.6850 c. M: 18.5732 c. 13: 12 1 0 N G T3 SD: 11.1703 c. M: 15.3806 c. 14: 13 1 0 N G T3 SD: 9.9605 c. M: 12.6441 c. 17: 16 0 1 N G T3 SD: 10.7837 c. M: 17.5595 c. 18: 17 0 1 N G T3 SD: 9.5965 c. M: 15.9319 c. 19: 18 0 1 N G T3 SD: 8.5697 c. M: 14.4757 c. 20: 19 0 1 N G T3 SD: 7.6856 c. M: 13.1650 c. 21: 20 0 1 N G T3 SD: 6.9311 c. M: 11.9792 c. 22: 21 0 1 N G T3 SD: 6.2961 c. M: 10.9012 c. 23: 22 0 1 N G T3 SD: 5.7728 c. M: 9.9169 c. 24: 23 0 1 N G T3 SD: 5.3545 c. M: 9.0147 c. 25: 24 0 1 N G T3 SD: 5.0345 c. M: 8.1846 c. 26: 25 0 1 N G T3 SD: 4.8056 c. M: 7.4184 c. 27: 26 0 1 N G T3 SD: 4.6590 c. M: 6.7089 c. 28: 27 0 1 N G T3 SD: 4.5846 c. M: 6.0501 c. 29: 28 0 1 N G T3 SD: 4.5715 c. M:-5.7566 c. 32: 30 1 1 N M DE S SD: 5.2230 c. M: 8.1972 c. 33: 31 1 1 N M DE S SD: 4.6143 c. M: 7.2540 c. 34: 32 1 1 N M DE S SD: 4.0416 c. M: 6.3662 c. 35: 33 1 1 N M DE S SD: 3.5016 c. M: 5.5291 c. 36: 34 1 1 N M DE S SD: 2.9918 c. M: 4.7386 c. 37: 35 1 1 N M DE S SD: 2.5097 c. M: 3.9908 c. 38: 36 1 1 N M DE S SD: 2.0533 c. M: 3.2823 c. 39: 37 1 1 N M DE S SD: 1.6207 c. M: 2.6102 c. 40: 38 1 1 N M DE S SD: 1.2107 c. M: 1.9717 c. 41: 39 1 1 N M DE S SD: 0.8225 c. M: 1.3643 c. 42: 40 1 1 N M DE S SD: 0.4591 c. M: 0.7858 c. 43: 41 1 1 N M DE S SD: 0.1621 c. M: 0.2343 c. 87: 83 2 2 N M DE S SD: 0.1672 c. M:-0.2879 c. 130: 124 3 3 N M DE S SD: 0.1445 c. M:-0.2439 c. 173: 165 4 4 N M DE S SD: 0.1405 c. M:-0.2217 c. 216: 206 5 5 N M DE S SD: 0.1409 c. M:-0.2084 c. 217: 207 5 5 N M DE S SD: 0.1515 c. M:-0.2615 c. 259: 247 6 6 N M DE S SD: 0.1423 c. M:-0.1995 c. 302: 288 7 7 N M DE S SD: 0.1439 c. M:-0.1931 c. 303: 289 7 7 N M DE S SD: 0.1415 c. M:-0.2312 c. 304: 290 7 7 N M DE S SD: 0.1554 c. M:-0.2691 c. 345: 329 8 8 N M DE S SD: 0.1454 c. M:-0.1884 c. 388: 370 9 9 N M DE S SD: 0.1467 c. M:-0.1846 c. 389: 371 9 9 N M DE S SD: 0.1405 c. M:-0.2143 c. 391: 373 9 9 N M DE S SD: 0.1578 c. M:-0.2733 c. 431: 411 10 10 N M DE S SD: 0.1479 c. M:-0.1817 c. 433: 413 10 10 N M DE S SD: 0.1422 c. M:-0.2350 c. 458: 437 10 11 N T3 SD: 0.1407 c. M: 0.2246 c. 498: 475 11 12 N T3 SD: 0.1578 c. M: 0.2639 c. 499: 476 11 12 N T3 SD: 0.1392 c. M: 0.2398 c. 500: 477 11 12 N T3 SD: 0.1252 c. M: 0.2159 c. 501: 478 11 12 N T3 SD: 0.1173 c. M: 0.1920 c. 502: 479 11 12 N T3 SD: 0.1166 c. M: 0.1682 c. 503: 480 11 12 N T3 SD: 0.1233 c. M:-0.1572 c. 541: 516 12 13 N T3 SD: 0.1418 c. M: 0.2306 c. 542: 517 12 13 N T3 SD: 0.1228 c. M: 0.2085 c. 543: 518 12 13 N T3 SD: 0.1077 c. M: 0.1865 c. 544: 519 12 13 N T3 SD: 0.0981 c. M: 0.1646 c. 545: 520 12 13 N T3 SD: 0.0958 c. M: 0.1427 c. 546: 521 12 13 N T3 SD: 0.1010 c. M:-0.1263 c. 585: 558 13 14 N T3 SD: 0.1098 c. M: 0.1818 c. 586: 559 13 14 N T3 SD: 0.0937 c. M: 0.1615 c. 587: 560 13 14 N T3 SD: 0.0825 c. M: 0.1412 c. 588: 561 13 14 N T3 SD: 0.0783 c. M: 0.1210 c. 589: 562 13 14 N T3 SD: 0.0820 c. M: 0.1009 c. 629: 600 14 15 N T3 SD: 0.0828 c. M: 0.1398 c. 630: 601 14 15 N T3 SD: 0.0699 c. M: 0.1210 c. 631: 602 14 15 N T3 SD: 0.0636 c. M: 0.1022 c. 632: 603 14 15 N T3 SD: 0.0657 c. M: 0.0835 c. 672: 641 15 16 N T3 SD: 0.0745 c. M: 0.1210 c. 673: 642 15 16 N T3 SD: 0.0600 c. M: 0.1034 c. 674: 643 15 16 N T3 SD: 0.0514 c. M: 0.0858 c. 675: 644 15 16 N T3 SD: 0.0515 c. M: 0.0683 c. 716: 683 16 17 N T3 SD: 0.0526 c. M: 0.0879 c. 717: 684 16 17 N T3 SD: 0.0415 c. M: 0.0714 c. 718: 685 16 17 N T3 SD: 0.0392 c. M: 0.0549 c. 760: 725 17 18 N T3 SD: 0.0340 c. M: 0.0586 c. 761: 726 17 18 N T3 SD: 0.0286 c. M: 0.0431 c. 803: 766 18 19 N T3 SD: 0.0291 c. M: 0.0472 c. 804: 767 18 19 N T3 SD: 0.0197 c. M: 0.0325 c. 847: 808 19 20 N T3 SD: 0.0133 c. M: 0.0230 c. 890: 849 20 21 N T3 SD: 0.0112 c. M: 0.0144 c. 891: 850 20 21 N T3 SD: 0.0074 c. M:-0.0127 c. 934: 891 21 22 N T3 SD: 0.0035 c. M:-0.0060 c. 1824: 1740 41 43 N T3 SD: 0.0040 c. M: 0.0057 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: 88.8007 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 40.0303 cents 8 x x 11 SD: 53.2729 cents 9 x x 12 S SD: 0.0000 cents 10:13 x x SD: 20.9005 cents 11:14 x 15 SD: 34.7569 cents 12 x x 16 S SD: 0.0000 cents 13:17 x x SD: 10.6867 cents 14:18 x 19 SD: 25.2060 cents 15 x x 20 S SD: 0.0000 cents 16:21 x x SD: 4.3335 cents 17:22 x 23 SD: 19.1405 cents 18 x x 24 S SD: 0.0000 cents 19:25 x x SD: 0.0000 cents 20:26 x 27 SD: 14.9946 cents 21 x x 28 S SD: 0.0000 cents 22:29 x x SD: 3.1448 cents 23:30 x 31 SD: 12.0303 cents 24 x x 32 S SD: 0.0000 cents 25:33 x x SD: 5.5311 cents 26:34 x 35 SD: 9.8573 cents 27 x x 36 S SD: 0.0000 cents 28 x 37 x SD: 3.7896 cents 29:38 x 39 SD: 8.2518 cents 30:39 x 40 SD: 10.4502 cents 31 x 41 x SD: 2.2809 cents 32:42 x 43 SD: 7.0762 cents 33:43 x 44 SD: 8.4348 cents 34 x 45 x SD: 1.0395 cents 35:46 x 47 SD: 6.2400 cents 36:47 x 48 SD: 6.7589 cents 37 x 49 x SD: 0.0000 cents 38:50 x 51 SD: 5.6762 cents 39:51 x 52 SD: 5.3433 cents 40 x 53 x SD: 0.8831 cents 41:54 x 55 SD: 5.3294 cents 42:55 x 56 SD: 4.1318 cents 43 x 57 x SD: 1.6425 cents 44:58 x 59 SD: 5.1503 cents 45:59 x 60 SD: 3.0832 cents 46 x 61 x SD: 2.3027 cents 47:62 x 63 SD: 5.0951 cents 48:63 x 64 SD: 2.1668 cents 49:64:65 x SD: 6.5437 cents 50:66 x 67 SD: 5.1271 cents 51:67 x 68 SD: 1.3589 cents 52:68:69 x SD: 5.6063 cents 53 x 70:71 SD: 4.6959 cents 54:71 x 72 SD: 0.6414 cents 55:72:73 x SD: 4.8192 cents 56 x 74:75 SD: 4.2962 cents 57:75 x 76 SD: 0.0000 cents 58:76:77 x SD: 4.1734 cents 59 x 78:79 SD: 3.9550 cents 60:79 x 80 SD: 0.5769 cents 61:80:81 x SD: 3.6653 cents 62 x 82:83 SD: 3.6653 cents 63:83 x 84 SD: 1.0985 cents 64:84:85 x SD: 3.2937 cents 65 x 86:87 SD: 3.4216 cents 66:87 x 88 SD: 1.5724 cents 67:88:89 x SD: 3.0559 cents 69:91 x 92 SD: 2.0049 cents 70:92:93 x SD: 2.9430 cents 72:95 x 96 SD: 2.4012 cents 73:96:97 x SD: 2.9376 cents 74:97:98:99 SD: 2.9281 cents 75:99 x 100 SD: 2.7656 cents 76:100 x 101 SD: 2.8521 cents 77:101:102:103 SD: 2.6015 cents 78 x 103:104 SD: 2.4949 cents 79:104 x 105 SD: 2.7784 cents 80:105:106:107 SD: 2.3271 cents 81 x 107:108 SD: 2.1837 cents 82:108 x 109 SD: 2.7746 cents 83:109:110:111 SD: 2.1055 cents 84 x 111:112 SD: 1.8948 cents 85:112 x 113 SD: 2.8270 cents 86:113:114:115 SD: 1.9378 cents 88:116 x 117 SD: 2.9218 cents 89:117:118:119 SD: 1.8240 cents 91:120 x 121 SD: 3.0467 cents 92:121:122:123 SD: 1.7620 cents 94:124 x 125 SD: 3.1916 cents 95:125:126:127 SD: 1.7470 cents 96:126:127:128 SD: 1.5695 cents 97:128 x 129 SD: 3.3490 cents 98:129:130:131 SD: 1.7720 cents 99:130:131:132 SD: 1.2604 cents 100:132 x 133 SD: 3.5133 cents 101:133:134:135 SD: 1.8285 cents 102:134:135:136 SD: 0.9699 cents 103 x 136:137 SD: 3.3262 cents 104:137:138:139 SD: 1.9085 cents 105:138:139:140 SD: 0.6970 cents 108:142:143:144 SD: 0.4413 cents 111:146:147:148 SD: 0.2080 cents 114:150:151:152 SD: 0.1033 cents 339:446:449:452 SD: 0.0973 cents 453:596:600:604 SD: 0.0932 cents 567:746:751:756 SD: 0.0925 cents