Scala analysis: 505_M13
Miscellaneous tetrachord 82/81 * 81/80 * 160/123
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 82/81 21.242402 2: 41/40 42.748692 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 160/123 455.2963 1: 82/81 21.2424 2: 81/80 21.5063 syntonic comma, Didymus comma 3: 160/123 455.2963
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 82/81 21.242 cents 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 160/123 455.296 cents 2: 1 41/40 42.749 cents 2: 1 320/243 476.539 cents grave fourth 2: 1 54/41 476.803 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 : 21.2 42.7 498.0 21.2 : 21.5 476.8 498.0 42.7 : 455.3 476.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.2424 .. 455.2963 cents 2160/1681, 434.0539 cents 82/81, 21.2424 cents 2: 42.7487 .. 476.8026 cents 2160/1681, 434.0539 cents 5043/6400,-412.5476 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 82/81, 21.2424 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 160/123, 455.2963 cents Average / Smallest step : 7.815265 Largest / Average step : 2.742501 Largest / Smallest step : 21.433372 Median interval of one step : 81/80, 21.5063 cents, amount: 1 Least squares average step : 114.34820 cents, oct.: 343.04460 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1829-tone equal temperament with octave 4/3 degrees: 78 157 1829 Least number of segments generator : 915 of 249.159 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1019 of 277.478 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 21.24240 cents Scale diversity : 0.013114 Lumma stability : 0.085303 Lumma impropriety factor : 0.828334 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 : 6561/6560, 0.2639 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 433.7900 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 41 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.045317 Fundamental : 1/3240, -11.6618 octaves, 0.0807 Hz. Guide tone : 164, 7.3576 octaves, 42906.593 Hz. Exponens Consonantiae : 5.313600E+05, 19.01933 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 125.5, average 41.83333 Mersenne's string divisions : 92421 Sum of van Prooijen's expressibility: 3.99839, average 1.33280 Sum of Tenney's harmonic distance : 8.11632, average 2.70544 Vogel's harmonic complexity : 40.66667 Wille's k value : 1660 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 23.62444, average 3.93741 Lattice compactness (without 2's) : 14.53732, average 2.42289 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 6 3: -4 .. 0 -1.66667 5 1 5: -1 .. 0 -0.33333 1 41: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 37| Scale is weakly epimorphic with val: <6 10 17 38| Scale is weakly epimorphic with val: <6 10 18 37| Scale is weakly epimorphic with val: <6 11 15 41| Scale is weakly epimorphic with val: <6 11 16 37| Scale is weakly epimorphic with val: <6 11 18 41| Scale is weakly epimorphic with val: <6 11 19 40| Scale is weakly epimorphic with val: <7 10 16 36| Scale is weakly epimorphic with val: <7 10 17 41| Scale is weakly epimorphic with val: <7 10 19 36| Scale is JI-epimorphic with val: <7 11 15 38| Scale is weakly epimorphic with val: <7 11 15 41| Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 17 39| = patent Scale is weakly epimorphic with val: <7 11 17 42| Scale is weakly epimorphic with val: <7 11 18 38| Scale is weakly epimorphic with val: <7 11 18 41| Scale is weakly epimorphic with val: <7 12 15 39| Scale is weakly epimorphic with val: <7 12 18 42| Scale is weakly epimorphic with val: <8 11 17 39| Scale is weakly epimorphic with val: <8 12 15 42|
FIT/MODE
3: 0 0 3 N M DE S SD: 27.5602 c. M: 42.7487 c. 8: 0 1 7 N G T3 SD: 16.6509 c. M: 21.2424 c. 9: 0 1 8 N G T3 SD: 14.2564 c. M: 21.2424 c. 10: 0 1 9 N G T3 SD: 12.9232 c. M: 21.2424 c. 11: 0 1 10 N G T3 SD: 12.3509 c. M: 21.2424 c. 12: 0 1 11 N G T3 SD: 12.2854 c. M: 21.2424 c. 13: 0 1 12 N G T3 SD: 12.5291 c. M: 21.2424 c. 14: 0 1 13 N G T3 SD: 12.9448 c. M: 21.2424 c. 15: 0 1 14 N G T3 SD: 13.4457 c. M: 21.2424 c. 16: 0 1 15 N G T3 SD: 13.9796 c. M: 21.2424 c. 17: 1 0 16 N G T3 SD: 9.0522 c. M: 13.4519 c. 18: 1 1 16 N M DE S SD: 8.1609 c. M:-12.5896 c. 19: 1 1 17 N M DE S SD: 6.2810 c. M:-9.6771 c. 20: 1 1 18 N M DE S SD: 4.5891 c. M:-7.0558 c. 21: 1 1 19 N M DE S SD: 3.0584 c. M:-4.6842 c. 22: 1 1 20 N M DE S SD: 1.6674 c. M:-2.5281 c. 23: 1 1 21 N M DE S SD: 0.4011 c. M:-0.5596 c. 47: 2 2 43 N M DE S SD: 0.2108 c. M: 0.3619 c. 70: 3 3 64 N M DE S SD: 0.0683 c. M:-0.1024 c. 233: 10 10 213 N M DE S SD: 0.0767 c. M:-0.1329 c. 303: 13 13 277 N M DE S SD: 0.0730 c. M:-0.1259 c. 373: 16 16 341 N M DE S SD: 0.0712 c. M:-0.1215 c. 397: 17 17 363 N M DE S SD: 0.0734 c. M: 0.0950 c. 443: 19 19 405 N M DE S SD: 0.0701 c. M:-0.1184 c. 467: 20 20 427 N M DE S SD: 0.0722 c. M: 0.0896 c. 513: 22 22 469 N M DE S SD: 0.0695 c. M:-0.1163 c. 537: 23 23 491 N M DE S SD: 0.0714 c. M:-0.0891 c. 583: 25 25 533 N M DE S SD: 0.0691 c. M:-0.1146 c. 653: 28 28 597 N M DE S SD: 0.0689 c. M:-0.1133 c. 723: 31 31 661 N M DE S SD: 0.0687 c. M:-0.1122 c. 793: 34 34 725 N M DE S SD: 0.0685 c. M:-0.1114 c. 863: 37 37 789 N M DE S SD: 0.0684 c. M:-0.1106 c. 933: 40 40 853 N M DE S SD: 0.0684 c. M:-0.1100 c. 965: 41 42 882 N T3 SD: 0.0696 c. M:-0.0883 c. 966: 41 42 883 N T3 SD: 0.0651 c. M: 0.1038 c. 967: 41 42 884 N T3 SD: 0.0726 c. M: 0.1257 c. 979: 42 42 895 N M DE S SD: 0.0723 c. M:-0.1242 c. 988: 42 43 903 N T3 SD: 0.0703 c. M:-0.0993 c. 989: 42 43 904 N T3 SD: 0.0621 c. M: 0.0919 c. 990: 42 43 905 N T3 SD: 0.0658 c. M: 0.1132 c. 1004: 43 43 918 N M DE S SD: 0.0717 c. M:-0.0882 c. 1012: 43 44 925 N T3 SD: 0.0606 c. M: 0.0804 c. 1013: 43 44 926 N T3 SD: 0.0603 c. M: 0.1013 c. 1014: 43 44 927 N T3 SD: 0.0712 c. M: 0.1222 c. 1027: 44 44 939 N M DE S SD: 0.0694 c. M:-0.0955 c. 1035: 44 45 946 N T3 SD: 0.0605 c. M:-0.0784 c. 1036: 44 45 947 N T3 SD: 0.0561 c. M: 0.0899 c. 1037: 44 45 948 N T3 SD: 0.0637 c. M: 0.1103 c. 1058: 45 46 967 N T3 SD: 0.0616 c. M:-0.0888 c. 1059: 45 46 968 N T3 SD: 0.0535 c. M: 0.0790 c. 1060: 45 46 969 N T3 SD: 0.0573 c. M: 0.0990 c. 1082: 46 47 989 N T3 SD: 0.0523 c. M: 0.0686 c. 1083: 46 47 990 N T3 SD: 0.0521 c. M: 0.0881 c. 1106: 47 48 1011 N T3 SD: 0.0483 c. M: 0.0777 c. 1107: 47 48 1012 N T3 SD: 0.0561 c. M: 0.0969 c. 1128: 48 49 1031 N T3 SD: 0.0540 c. M:-0.0796 c. 1129: 48 49 1032 N T3 SD: 0.0459 c. M: 0.0678 c. 1130: 48 49 1033 N T3 SD: 0.0500 c. M: 0.0865 c. 1152: 49 50 1053 N T3 SD: 0.0451 c. M: 0.0582 c. 1153: 49 50 1054 N T3 SD: 0.0450 c. M: 0.0766 c. 1176: 50 51 1075 N T3 SD: 0.0414 c. M: 0.0670 c. 1177: 50 51 1076 N T3 SD: 0.0495 c. M: 0.0850 c. 1198: 51 52 1095 N T3 SD: 0.0474 c. M:-0.0715 c. 1199: 51 52 1096 N T3 SD: 0.0393 c. M: 0.0578 c. 1200: 51 52 1097 N T3 SD: 0.0436 c. M: 0.0755 c. 1222: 52 53 1117 N T3 SD: 0.0387 c. M: 0.0490 c. 1223: 52 53 1118 N T3 SD: 0.0388 c. M: 0.0663 c. 1246: 53 54 1139 N T3 SD: 0.0353 c. M: 0.0575 c. 1269: 54 55 1160 N T3 SD: 0.0333 c. M: 0.0490 c. 1270: 54 55 1161 N T3 SD: 0.0380 c. M: 0.0657 c. 1292: 55 56 1181 N T3 SD: 0.0330 c. M: 0.0408 c. 1293: 55 56 1182 N T3 SD: 0.0333 c. M: 0.0572 c. 1316: 56 57 1203 N T3 SD: 0.0299 c. M: 0.0490 c. 1339: 57 58 1224 N T3 SD: 0.0280 c. M: 0.0411 c. 1340: 57 58 1225 N T3 SD: 0.0330 c. M: 0.0569 c. 1362: 58 59 1245 N T3 SD: 0.0279 c. M:-0.0349 c. 1363: 58 59 1246 N T3 SD: 0.0284 c. M: 0.0490 c. 1386: 59 60 1267 N T3 SD: 0.0250 c. M: 0.0414 c. 1409: 60 61 1288 N T3 SD: 0.0233 c. M: 0.0340 c. 1432: 61 62 1309 N T3 SD: 0.0234 c. M:-0.0303 c. 1433: 61 62 1310 N T3 SD: 0.0240 c. M: 0.0416 c. 1456: 62 63 1331 N T3 SD: 0.0206 c. M: 0.0344 c. 1479: 63 64 1352 N T3 SD: 0.0189 c. M: 0.0275 c. 1502: 64 65 1373 N T3 SD: 0.0193 c. M:-0.0261 c. 1503: 64 65 1374 N T3 SD: 0.0202 c. M: 0.0349 c. 1526: 65 66 1395 N T3 SD: 0.0166 c. M: 0.0282 c. 1549: 66 67 1416 N T3 SD: 0.0150 c. M: 0.0216 c. 1573: 67 68 1438 N T3 SD: 0.0169 c. M: 0.0288 c. 1596: 68 69 1459 N T3 SD: 0.0131 c. M: 0.0224 c. 1619: 69 70 1480 N T3 SD: 0.0114 c. M: 0.0163 c. 1666: 71 72 1523 N T3 SD: 0.0099 c. M: 0.0172 c. 1689: 72 73 1544 N T3 SD: 0.0081 c. M: 0.0114 c. 1736: 74 75 1587 N T3 SD: 0.0072 c. M: 0.0124 c. 1759: 75 76 1608 N T3 SD: 0.0051 c. M: 0.0068 c. 1806: 77 78 1651 N T3 SD: 0.0051 c. M: 0.0079 c. 1829: 78 79 1672 N T3 SD: 0.0024 c. M:-0.0031 c. 1899: 81 82 1736 N T3 SD: 0.0009 c. M:-0.0012 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: 112.0611 cents 7 x 8:9 S SD: 99.3330 cents 8 x 9:11 SD: 84.8690 cents 9 x 10:12 S SD: 69.8275 cents 10 x 11:13 SD: 64.9376 cents 11 x 12:15 S SD: 57.3445 cents 12 x 13:16 SD: 47.9120 cents 13 x 14:17 SD: 45.9588 cents 14 x 15:19 SD: 41.2945 cents 15 x 16:20 S SD: 34.4913 cents 16 x 17:21 SD: 33.9596 cents 17 x 18:23 SD: 30.8135 cents 18 x 19:24 SD: 25.4272 cents 19 x 20:25 S SD: 25.7226 cents 20 x 21:27 SD: 23.4678 cents 21 x 22:28 SD: 18.8942 cents 22 x 23:29 SD: 19.7588 cents 23 x 24:31 SD: 18.0768 cents 24 x 25:32 SD: 13.9619 cents 25 x 26:33 SD: 15.2917 cents 26 x 27:35 SD: 14.0063 cents 27 x 28:36 SD: 10.1061 cents 28 x 29:37 SD: 11.8867 cents 29 x 30:39 SD: 10.8973 cents 30 x 31:40 SD: 7.0091 cents 31 x 32:41 SD: 9.2970 cents 32 x 33:43 SD: 8.5480 cents 33 x 34:44 SD: 4.4669 cents 34 x 35:45 SD: 7.3914 cents 35 x 36:47 SD: 6.8573 cents 36 x 37:48 SD: 2.3427 cents 37 x 38:49 SD: 6.1127 cents 38 x 39:51 SD: 5.7838 cents 39 x 40:52 SD: 0.5412 cents 40 x 41:53 SD: 5.4271 cents 41 x 42:55 SD: 5.2873 cents 42 x 43:56 SD: 1.0059 cents 43 x 44:57 SD: 5.2582 cents 44 x 45:59 SD: 5.2673 cents 45 x 46:60 SD: 2.3490 cents 46 x 47:61 SD: 5.4645 cents 47 x 48:63 SD: 5.5688 cents 48 x 49:64 SD: 3.5259 cents 49 x 50:65 SD: 5.8915 cents 50 x 51:67 SD: 6.0462 cents 51 x 52:68 SD: 4.5657 cents 52 x 53:69 SD: 6.4245 cents 53 x 54:71 SD: 6.6009 cents 54:55 x 72 SD: 5.2621 cents 55:56 x 73 SD: 6.3492 cents 56:57 x 75 SD: 6.0791 cents 57:58 x 76 SD: 4.4334 cents 58:59 x 77 SD: 5.6054 cents 59:60 x 79 SD: 5.3685 cents 60:61:62:80 SD: 5.2797 cents 62:63:64:83 SD: 5.1582 cents 63:64:65:84 SD: 4.2848 cents 66:67:68:88 SD: 3.3792 cents 69:70:71:92 SD: 2.5515 cents 72:73:74:96 SD: 1.7922 cents 75:76:77:100 SD: 1.0935 cents 78:79:80:104 SD: 0.4510 cents 81:82:83:108 SD: 0.1738 cents 159:161:163:212 SD: 0.1596 cents 240:243:246:320 SD: 0.0880 cents 321:325:329:428 SD: 0.0790 cents