Scala analysis: 503_M11
Miscellaneous tetrachord 86/85 * 85/84 * 56/43
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86/85 20.248582 2: 43/42 40.736798 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/43 457.3082 1: 86/85 20.2486 2: 85/84 20.4882 3: 56/43 457.3082
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 86/85 20.249 cents 1: 1 85/84 20.488 cents 1: 1 56/43 457.308 cents 2: 1 43/42 40.737 cents 2: 1 112/85 477.557 cents 2: 1 170/129 477.796 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 : 20.2 40.7 498.0 20.2 : 20.5 477.8 498.0 40.7 : 457.3 477.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.2486 .. 457.3082 cents 2380/1849, 437.0596 cents 86/85, 20.2486 cents 2: 40.7368 .. 477.7964 cents 2380/1849, 437.0596 cents 1849/2352,-416.5714 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 86/85, 20.2486 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/43, 457.3082 cents Average / Smallest step : 8.198846 Largest / Average step : 2.754620 Largest / Smallest step : 22.584702 Median interval of one step : 85/84, 20.4882 cents, amount: 1 Least squares average step : 113.98980 cents, oct.: 341.96939 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2017-tone equal temperament with octave 4/3 degrees: 82 165 2017 Least number of segments generator : 1009 of 249.146 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1770 of 437.055 cents and inv. generated superset size: 34 = 31 more = 1133.333% Number of contiguous 1-step segments: 0 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 20.24858 cents Scale diversity :-0.000742 Lumma stability : 0.081312 Lumma impropriety factor : 0.836413 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 : 7225/7224, 0.2396 cents Number of recognisable fifths : 0 Number of recognisable 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 with margin 436.8200 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 43 Odd number limit : 129 (O: 85 U: 129) Highest odd numerator or denominator: 85 Scale harmonicity : 0.019058 Fundamental : 1/3570, -11.8017 octaves, 0.0733 Hz. Guide tone : 172, 7.4263 octaves, 44999.597 Hz. Exponens Consonantiae : 6.140400E+05, 19.22797 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 131.5, average 43.83333 Mersenne's string divisions : 101745 Sum of van Prooijen's expressibility: 4.04001, average 1.34667 Sum of Tenney's harmonic distance : 8.19982, average 2.73327 Vogel's harmonic complexity : 50.66667 Wille's k value : 1827 Wilson's harmonic complexity : 75 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.69087, average 2.28181 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 43: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 16 19 29 39| Scale is weakly epimorphic with val: <7 11 16 19 30 38| Scale is weakly epimorphic with val: <7 11 16 19 30 41| Scale is weakly epimorphic with val: <7 11 16 20 30 37| Scale is JI-epimorphic with val: <7 11 16 20 30 40| Scale is weakly epimorphic with val: <7 11 16 20 31 39| Scale is weakly epimorphic with val: <7 11 16 21 29 37| Scale is weakly epimorphic with val: <7 11 16 21 29 40| Scale is weakly epimorphic with val: <7 11 16 21 31 38| Scale is JI-epimorphic with val: <7 11 16 21 31 41| Scale is weakly epimorphic with val: <7 11 17 19 29 38| Scale is weakly epimorphic with val: <7 11 17 19 29 41| Scale is weakly epimorphic with val: <7 11 17 19 31 39| Scale is weakly epimorphic with val: <7 11 17 20 29 37| Scale is JI-epimorphic with val: <7 11 17 20 29 40| Scale is weakly epimorphic with val: <7 11 17 20 30 39| = patent Scale is weakly epimorphic with val: <7 11 17 21 30 38| Scale is JI-epimorphic with val: <7 11 17 21 30 41| Scale is weakly epimorphic with val: <7 11 17 21 31 37| Scale is weakly epimorphic with val: <7 11 17 21 31 40| Scale is weakly epimorphic with val: <7 11 18 19 30 39| Scale is weakly epimorphic with val: <7 11 18 19 31 38| Scale is weakly epimorphic with val: <7 11 18 19 31 41| Scale is weakly epimorphic with val: <7 11 18 20 29 39| Scale is weakly epimorphic with val: <7 11 18 20 31 37| Scale is weakly epimorphic with val: <7 11 18 20 31 40| Scale is weakly epimorphic with val: <7 11 18 21 29 38| Scale is JI-epimorphic with val: <7 11 18 21 29 41| Scale is weakly epimorphic with val: <7 11 18 21 30 37| Scale is weakly epimorphic with val: <7 11 18 21 30 40| Scale is weakly epimorphic with val: <7 12 16 19 31 41| Scale is weakly epimorphic with val: <7 12 16 21 29 41| Scale is weakly epimorphic with val: <7 12 17 19 30 41| Scale is weakly epimorphic with val: <7 12 18 19 29 41|
FIT/MODE
3: 0 0 3 N M DE S SD: 26.2646 c. M: 40.7368 c. 9: 0 1 8 N G T3 SD: 14.4131 c. M: 20.2486 c. 10: 0 1 9 N G T3 SD: 12.8092 c. M: 20.2486 c. 11: 0 1 10 N G T3 SD: 11.9808 c. M: 20.2486 c. 12: 0 1 11 N G T3 SD: 11.6989 c. M: 20.2486 c. 13: 0 1 12 N G T3 SD: 11.7741 c. M: 20.2486 c. 14: 0 1 13 N G T3 SD: 12.0645 c. M: 20.2486 c. 15: 0 1 14 N G T3 SD: 12.4735 c. M: 20.2486 c. 16: 0 1 15 N G T3 SD: 12.9401 c. M: 20.2486 c. 17: 1 0 16 N G T3 SD: 8.4211 c. M: 11.4400 c. 18: 1 1 16 N M DE S SD: 9.4564 c. M:-14.6015 c. 19: 1 1 17 N M DE S SD: 7.5764 c. M:-11.6890 c. 20: 1 1 18 N M DE S SD: 5.8844 c. M:-9.0677 c. 21: 1 1 19 N M DE S SD: 4.3537 c. M:-6.6961 c. 22: 1 1 20 N M DE S SD: 2.9622 c. M:-4.5400 c. 23: 1 1 21 N M DE S SD: 1.6919 c. M:-2.5715 c. 24: 1 1 22 N M DE S SD: 0.5296 c. M:-0.7670 c. 49: 2 2 45 N M DE S SD: 0.0653 c. M: 0.0801 c. 220: 9 9 202 N M DE S SD: 0.0731 c. M:-0.1260 c. 269: 11 11 247 N M DE S SD: 0.0679 c. M:-0.1176 c. 318: 13 13 292 N M DE S SD: 0.0652 c. M:-0.1117 c. 367: 15 15 337 N M DE S SD: 0.0637 c. M:-0.1075 c. 416: 17 17 382 N M DE S SD: 0.0628 c. M:-0.1042 c. 465: 19 19 427 N M DE S SD: 0.0623 c. M:-0.1016 c. 489: 20 20 449 N M DE S SD: 0.0701 c. M:-0.1214 c. 514: 21 21 472 N M DE S SD: 0.0621 c. M:-0.0996 c. 563: 23 23 517 N M DE S SD: 0.0619 c. M:-0.0978 c. 612: 25 25 562 N M DE S SD: 0.0619 c. M:-0.0964 c. 758: 31 31 696 N M DE S SD: 0.0693 c. M:-0.1200 c. 759: 31 31 697 N M DE S SD: 0.0620 c. M:-0.0932 c. 1062: 43 44 975 N T3 SD: 0.0603 c. M: 0.0829 c. 1063: 43 44 976 N T3 SD: 0.0606 c. M: 0.1019 c. 1064: 43 44 977 N T3 SD: 0.0702 c. M: 0.1208 c. 1077: 44 44 989 N M DE S SD: 0.0620 c. M:-0.0987 c. 1086: 44 45 997 N T3 SD: 0.0609 c. M:-0.0790 c. 1087: 44 45 998 N T3 SD: 0.0564 c. M: 0.0885 c. 1088: 44 45 999 N T3 SD: 0.0619 c. M: 0.1071 c. 1111: 45 46 1020 N T3 SD: 0.0548 c. M: 0.0757 c. 1112: 45 46 1021 N T3 SD: 0.0555 c. M: 0.0939 c. 1113: 45 46 1022 N T3 SD: 0.0653 c. M: 0.1120 c. 1135: 46 47 1042 N T3 SD: 0.0555 c. M:-0.0722 c. 1136: 46 47 1043 N T3 SD: 0.0514 c. M: 0.0813 c. 1137: 46 47 1044 N T3 SD: 0.0572 c. M: 0.0990 c. 1160: 47 48 1065 N T3 SD: 0.0497 c. M: 0.0692 c. 1161: 47 48 1066 N T3 SD: 0.0508 c. M: 0.0866 c. 1184: 48 49 1087 N T3 SD: 0.0505 c. M:-0.0659 c. 1185: 48 49 1088 N T3 SD: 0.0467 c. M: 0.0746 c. 1186: 48 49 1089 N T3 SD: 0.0529 c. M: 0.0916 c. 1209: 49 50 1110 N T3 SD: 0.0451 c. M: 0.0631 c. 1210: 49 50 1111 N T3 SD: 0.0466 c. M: 0.0798 c. 1233: 50 51 1132 N T3 SD: 0.0459 c. M:-0.0601 c. 1234: 50 51 1133 N T3 SD: 0.0425 c. M: 0.0685 c. 1235: 50 51 1134 N T3 SD: 0.0491 c. M: 0.0848 c. 1257: 51 52 1154 N T3 SD: 0.0488 c. M:-0.0736 c. 1258: 51 52 1155 N T3 SD: 0.0408 c. M: 0.0576 c. 1259: 51 52 1156 N T3 SD: 0.0428 c. M: 0.0736 c. 1282: 52 53 1177 N T3 SD: 0.0417 c. M:-0.0547 c. 1283: 52 53 1178 N T3 SD: 0.0386 c. M: 0.0628 c. 1284: 52 53 1179 N T3 SD: 0.0456 c. M: 0.0785 c. 1306: 53 54 1199 N T3 SD: 0.0446 c. M:-0.0678 c. 1307: 53 54 1200 N T3 SD: 0.0369 c. M: 0.0524 c. 1308: 53 54 1201 N T3 SD: 0.0393 c. M: 0.0679 c. 1331: 54 55 1222 N T3 SD: 0.0377 c. M:-0.0498 c. 1332: 54 55 1223 N T3 SD: 0.0350 c. M: 0.0576 c. 1356: 55 56 1245 N T3 SD: 0.0333 c. M: 0.0476 c. 1357: 55 56 1246 N T3 SD: 0.0361 c. M: 0.0625 c. 1380: 56 57 1267 N T3 SD: 0.0341 c. M:-0.0451 c. 1381: 56 57 1268 N T3 SD: 0.0317 c. M: 0.0527 c. 1405: 57 58 1290 N T3 SD: 0.0299 c. M: 0.0432 c. 1406: 57 58 1291 N T3 SD: 0.0332 c. M: 0.0576 c. 1429: 58 59 1312 N T3 SD: 0.0307 c. M:-0.0409 c. 1430: 58 59 1313 N T3 SD: 0.0287 c. M: 0.0482 c. 1454: 59 60 1335 N T3 SD: 0.0267 c. M: 0.0391 c. 1455: 59 60 1336 N T3 SD: 0.0306 c. M: 0.0529 c. 1478: 60 61 1357 N T3 SD: 0.0275 c. M:-0.0368 c. 1479: 60 61 1358 N T3 SD: 0.0259 c. M: 0.0439 c. 1503: 61 62 1380 N T3 SD: 0.0238 c. M: 0.0352 c. 1504: 61 62 1381 N T3 SD: 0.0283 c. M: 0.0486 c. 1527: 62 63 1402 N T3 SD: 0.0246 c. M:-0.0331 c. 1528: 62 63 1403 N T3 SD: 0.0234 c. M: 0.0400 c. 1552: 63 64 1425 N T3 SD: 0.0210 c. M: 0.0315 c. 1576: 64 65 1447 N T3 SD: 0.0218 c. M:-0.0296 c. 1577: 64 65 1448 N T3 SD: 0.0210 c. M: 0.0362 c. 1601: 65 66 1470 N T3 SD: 0.0185 c. M: 0.0281 c. 1625: 66 67 1492 N T3 SD: 0.0192 c. M:-0.0263 c. 1626: 66 67 1493 N T3 SD: 0.0189 c. M: 0.0327 c. 1650: 67 68 1515 N T3 SD: 0.0161 c. M: 0.0249 c. 1674: 68 69 1537 N T3 SD: 0.0167 c. M:-0.0232 c. 1675: 68 69 1538 N T3 SD: 0.0170 c. M: 0.0294 c. 1699: 69 70 1560 N T3 SD: 0.0138 c. M: 0.0219 c. 1723: 70 71 1582 N T3 SD: 0.0144 c. M:-0.0202 c. 1724: 70 71 1583 N T3 SD: 0.0153 c. M: 0.0263 c. 1748: 71 72 1605 N T3 SD: 0.0118 c. M: 0.0191 c. 1772: 72 73 1627 N T3 SD: 0.0122 c. M:-0.0174 c. 1773: 72 73 1628 N T3 SD: 0.0139 c. M: 0.0234 c. 1797: 73 74 1650 N T3 SD: 0.0098 c. M: 0.0164 c. 1821: 74 75 1672 N T3 SD: 0.0102 c. M:-0.0148 c. 1846: 75 76 1695 N T3 SD: 0.0081 c. M: 0.0138 c. 1870: 76 77 1717 N T3 SD: 0.0082 c. M:-0.0123 c. 1895: 77 78 1740 N T3 SD: 0.0066 c. M: 0.0114 c. 1919: 78 79 1762 N T3 SD: 0.0064 c. M:-0.0100 c. 1944: 79 80 1785 N T3 SD: 0.0053 c. M: 0.0091 c. 1968: 80 81 1807 N T3 SD: 0.0048 c. M:-0.0077 c. 1993: 81 82 1830 N T3 SD: 0.0045 c. M: 0.0069 c. 2017: 82 83 1852 N T3 SD: 0.0033 c. M:-0.0056 c. 2042: 83 84 1875 N T3 SD: 0.0042 c. M: 0.0054 c. 2066: 84 85 1897 N T3 SD: 0.0022 c. M:-0.0036 c. 2115: 86 87 1942 N T3 SD: 0.0019 c. M:-0.0029 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 7:8 S SD: 113.0671 cents 7 x 8:9 S SD: 100.2876 cents 8 x 9:11 SD: 85.8247 cents 9 x 10:12 S SD: 70.8335 cents 10 x 11:13 SD: 65.8854 cents 11 x 12:15 S SD: 58.2918 cents 12 x 13:16 SD: 48.9179 cents 13 x 14:17 SD: 46.8965 cents 14 x 15:19 SD: 42.2302 cents 15 x 16:20 S SD: 35.4972 cents 16 x 17:21 SD: 34.8832 cents 17 x 18:23 SD: 31.7336 cents 18 x 19:24 SD: 26.4331 cents 19 x 20:25 S SD: 26.6268 cents 20 x 21:27 SD: 24.3663 cents 21 x 22:28 SD: 19.9001 cents 22 x 23:29 SD: 20.6357 cents 23 x 24:31 SD: 18.9446 cents 24 x 25:32 SD: 14.9678 cents 25 x 26:33 SD: 16.1291 cents 26 x 27:35 SD: 14.8295 cents 27 x 28:36 SD: 11.1121 cents 28 x 29:37 SD: 12.6655 cents 29 x 30:39 SD: 11.6534 cents 30 x 31:40 SD: 8.0150 cents 31 x 32:41 SD: 9.9867 cents 32 x 33:43 SD: 9.2015 cents 33 x 34:44 SD: 5.4728 cents 34 x 35:45 SD: 7.9451 cents 35 x 36:47 SD: 7.3548 cents 36 x 37:48 SD: 3.3486 cents 37 x 38:49 SD: 6.4667 cents 38 x 39:51 SD: 6.0579 cents 39 x 40:52 SD: 1.5471 cents 40 x 41:53 SD: 5.5195 cents 41 x 42:55 SD: 5.2850 cents 42 x 43:56 SD: 0.0000 cents 43 x 44:57 SD: 5.0690 cents 44 x 45:59 SD: 4.9891 cents 45 x 46:60 SD: 1.3431 cents 46 x 47:61 SD: 5.0322 cents 47 x 48:63 SD: 5.0681 cents 48 x 49:64 SD: 2.5200 cents 49 x 50:65 SD: 5.2823 cents 50 x 51:67 SD: 5.3900 cents 51 x 52:68 SD: 3.5598 cents 52 x 53:69 SD: 5.6971 cents 53 x 54:71 SD: 5.8424 cents 54 x 55:72 SD: 4.4851 cents 55 x 56:73 SD: 6.1901 cents 56 x 57:75 SD: 6.3516 cents 57:58 x 76 SD: 4.9303 cents 58:59 x 77 SD: 5.9848 cents 59:60 x 79 SD: 5.7420 cents 60:61 x 80 SD: 4.1838 cents 61:62 x 81 SD: 5.3149 cents 62:63 x 83 SD: 5.1006 cents 63:64:65:84 SD: 5.0325 cents 65:66:67:87 SD: 4.9437 cents 66:67:68:88 SD: 4.1269 cents 69:70:71:92 SD: 3.2990 cents 72:73:74:96 SD: 2.5394 cents 75:76:77:100 SD: 1.8400 cents 78:79:80:104 SD: 1.1942 cents 81:82:83:108 SD: 0.5972 cents 84:85:86:112 SD: 0.0799 cents