Scala analysis: 507_M15
Miscellaneous tetrachord 78/77 * 77/76 * 152/117
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78/77 22.338814 tridecimal minor third comma 2: 39/38 44.969647 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 152/117 453.0754 1: 78/77 22.3388 tridecimal minor third comma 2: 77/76 22.6308 approximation to 53-tone comma 3: 152/117 453.0754
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78/77 22.339 cents tridecimal minor third comma 1: 1 77/76 22.631 cents approximation to 53-tone comma 1: 1 152/117 453.075 cents 2: 1 39/38 44.970 cents 2: 1 304/231 475.414 cents 2: 1 154/117 475.706 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 : 22.3 45.0 498.0 22.3 : 22.6 475.7 498.0 45.0 : 453.1 475.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.3388 .. 453.0754 cents 5852/4563, 430.7365 cents 78/77, 22.3388 cents 2: 44.9696 .. 475.7062 cents 5852/4563, 430.7365 cents 4563/5776,-408.1057 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 78/77, 22.3388 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 152/117, 453.0754 cents Average / Smallest step : 7.431684 Largest / Average step : 2.729123 Largest / Smallest step : 20.281979 Median interval of one step : 77/76, 22.6308 cents, amount: 1 Least squares average step : 114.74379 cents, oct.: 344.23138 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1650-tone equal temperament with octave 4/3 degrees: 74 149 1650 Least number of segments generator : 827 of 249.626 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1253 of 378.212 cents and inv. generated superset size: 76 = 73 more = 2533.333% 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 22.33881 cents Scale diversity : 0.028480 Lumma stability : 0.089706 Lumma impropriety factor : 0.819415 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 : 5929/5928, 0.2920 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 430.4445 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 19 Odd number limit : 231 (O: 77 U: 231) Highest odd numerator or denominator: 77 Scale harmonicity : 0.010746 Average absolute harmonicity : 0.083131 Specific harmonicity : 0.052458 Fundamental : 1/8778, -13.0997 octaves, 0.0298 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 1.369368E+06, 20.38508 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 119.5, average 39.83333 Mersenne's string divisions : 11935 Sum of van Prooijen's expressibility: 3.95468, average 1.31823 Sum of Tenney's harmonic distance : 8.02861, average 2.67620 Vogel's harmonic complexity : 39.00000 Wille's k value : 4504 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.81930, average 2.63655 Lattice compactness (without 2's) : 11.55934, average 1.92656 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 0.33333 3 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 19 24 26 31| Scale is weakly epimorphic with val: <7 11 19 24 27 30| Scale is weakly epimorphic with val: <7 11 19 25 27 32| Scale is weakly epimorphic with val: <7 11 19 25 28 31| Scale is weakly epimorphic with val: <7 11 19 26 26 32| Scale is JI-epimorphic with val: <7 11 19 26 28 30| Scale is weakly epimorphic with val: <7 11 20 24 27 32| Scale is weakly epimorphic with val: <7 11 20 24 28 31| Scale is weakly epimorphic with val: <7 11 20 25 26 32| Scale is JI-epimorphic with val: <7 11 20 25 28 30| Scale is weakly epimorphic with val: <7 11 20 26 26 31| Scale is weakly epimorphic with val: <7 11 20 26 27 30| Scale is weakly epimorphic with val: <7 11 21 24 26 32| Scale is JI-epimorphic with val: <7 11 21 24 28 30| Scale is weakly epimorphic with val: <7 11 21 25 26 31| Scale is weakly epimorphic with val: <7 11 21 25 27 30| Scale is weakly epimorphic with val: <7 11 21 26 27 32| Scale is weakly epimorphic with val: <7 11 21 26 28 31| Scale is weakly epimorphic with val: <7 12 19 24 27 31| Scale is weakly epimorphic with val: <7 12 19 24 28 30| Scale is weakly epimorphic with val: <7 12 19 25 28 32| Scale is weakly epimorphic with val: <7 12 20 24 28 32| Scale is weakly epimorphic with val: <7 12 20 26 28 30| Scale is weakly epimorphic with val: <7 12 21 25 28 30|
FIT/MODE
3: 0 0 3 N M DE S SD: 28.9902 c. M: 44.9696 c. 8: 0 1 7 N G T3 SD: 16.3077 c. M: 22.3388 c. 9: 0 1 8 N G T3 SD: 14.2189 c. M: 22.3388 c. 10: 0 1 9 N G T3 SD: 13.1959 c. M: 22.3388 c. 11: 0 1 10 N G T3 SD: 12.8985 c. M: 22.3388 c. 12: 0 1 11 N G T3 SD: 13.0516 c. M: 22.3388 c. 13: 0 1 12 N G T3 SD: 13.4581 c. M: 22.3388 c. 14: 0 1 13 N G T3 SD: 13.9915 c. M: 22.3388 c. 15: 1 0 14 N G T3 SD: 9.2463 c. M: 11.7666 c. 17: 1 1 15 N M DE S SD: 8.8322 c. M:-13.6239 c. 18: 1 1 16 N M DE S SD: 6.7311 c. M:-10.3687 c. 19: 1 1 17 N M DE S SD: 4.8512 c. M:-7.4561 c. 20: 1 1 18 N M DE S SD: 3.1595 c. M:-4.8349 c. 21: 1 1 19 N M DE S SD: 1.6294 c. M:-2.4632 c. 22: 1 1 20 N M DE S SD: 0.2477 c. M:-0.3072 c. 67: 3 3 61 N M DE S SD: 0.2140 c. M: 0.3686 c. 89: 4 4 81 N M DE S SD: 0.1193 c. M: 0.2016 c. 111: 5 5 101 N M DE S SD: 0.0802 c. M: 0.1007 c. 133: 6 6 121 N M DE S SD: 0.0771 c. M:-0.1294 c. 155: 7 7 141 N M DE S SD: 0.0891 c. M:-0.1535 c. 244: 11 11 222 N M DE S SD: 0.0755 c. M:-0.1140 c. 288: 13 13 262 N M DE S SD: 0.0823 c. M:-0.1424 c. 355: 16 16 323 N M DE S SD: 0.0762 c. M:-0.1083 c. 377: 17 17 343 N M DE S SD: 0.0755 c. M:-0.1194 c. 443: 20 20 403 N M DE S SD: 0.0845 c. M:-0.1463 c. 466: 21 21 424 N M DE S SD: 0.0769 c. M:-0.1053 c. 510: 23 23 464 N M DE S SD: 0.0757 c. M:-0.1220 c. 621: 28 28 565 N M DE S SD: 0.0754 c. M:-0.1173 c. 851: 38 39 774 N T3 SD: 0.0791 c. M: 0.0994 c. 852: 38 39 775 N T3 SD: 0.0763 c. M: 0.1255 c. 865: 39 39 787 N M DE S SD: 0.0754 c. M:-0.1164 c. 874: 39 40 795 N T3 SD: 0.0719 c. M: 0.1148 c. 875: 39 40 796 N T3 SD: 0.0810 c. M: 0.1402 c. 887: 40 40 807 N M DE S SD: 0.0756 c. M:-0.1209 c. 896: 40 41 815 N T3 SD: 0.0681 c. M: 0.1047 c. 897: 40 41 816 N T3 SD: 0.0748 c. M: 0.1294 c. 918: 41 42 835 N T3 SD: 0.0650 c. M: 0.0950 c. 919: 41 42 836 N T3 SD: 0.0691 c. M: 0.1192 c. 940: 42 43 855 N T3 SD: 0.0626 c. M: 0.0857 c. 941: 42 43 856 N T3 SD: 0.0640 c. M: 0.1094 c. 962: 43 44 875 N T3 SD: 0.0608 c. M: 0.0769 c. 963: 43 44 876 N T3 SD: 0.0595 c. M: 0.1000 c. 985: 44 45 896 N T3 SD: 0.0556 c. M: 0.0911 c. 986: 44 45 897 N T3 SD: 0.0661 c. M: 0.1137 c. 1006: 45 46 915 N T3 SD: 0.0589 c. M:-0.0821 c. 1007: 45 46 916 N T3 SD: 0.0523 c. M: 0.0826 c. 1008: 45 46 917 N T3 SD: 0.0606 c. M: 0.1047 c. 1028: 46 47 935 N T3 SD: 0.0587 c. M:-0.0870 c. 1029: 46 47 936 N T3 SD: 0.0497 c. M: 0.0744 c. 1030: 46 47 937 N T3 SD: 0.0554 c. M: 0.0960 c. 1051: 47 48 956 N T3 SD: 0.0476 c. M: 0.0666 c. 1052: 47 48 957 N T3 SD: 0.0508 c. M: 0.0878 c. 1073: 48 49 976 N T3 SD: 0.0462 c. M: 0.0591 c. 1074: 48 49 977 N T3 SD: 0.0466 c. M: 0.0798 c. 1095: 49 50 996 N T3 SD: 0.0454 c. M:-0.0591 c. 1096: 49 50 997 N T3 SD: 0.0430 c. M: 0.0722 c. 1118: 50 51 1017 N T3 SD: 0.0399 c. M: 0.0649 c. 1140: 51 52 1037 N T3 SD: 0.0374 c. M: 0.0579 c. 1162: 52 53 1057 N T3 SD: 0.0356 c. M: 0.0511 c. 1163: 52 53 1058 N T3 SD: 0.0406 c. M: 0.0702 c. 1184: 53 54 1077 N T3 SD: 0.0344 c. M: 0.0446 c. 1185: 53 54 1078 N T3 SD: 0.0366 c. M: 0.0634 c. 1206: 54 55 1097 N T3 SD: 0.0338 c. M:-0.0444 c. 1207: 54 55 1098 N T3 SD: 0.0330 c. M: 0.0568 c. 1229: 55 56 1118 N T3 SD: 0.0300 c. M: 0.0504 c. 1251: 56 57 1138 N T3 SD: 0.0275 c. M: 0.0442 c. 1273: 57 58 1158 N T3 SD: 0.0257 c. M: 0.0383 c. 1295: 58 59 1178 N T3 SD: 0.0246 c. M: 0.0326 c. 1296: 58 59 1179 N T3 SD: 0.0290 c. M: 0.0498 c. 1317: 59 60 1198 N T3 SD: 0.0242 c. M:-0.0321 c. 1318: 59 60 1199 N T3 SD: 0.0254 c. M: 0.0439 c. 1339: 60 61 1218 N T3 SD: 0.0246 c. M:-0.0367 c. 1340: 60 61 1219 N T3 SD: 0.0222 c. M: 0.0383 c. 1362: 61 62 1239 N T3 SD: 0.0195 c. M: 0.0328 c. 1384: 62 63 1259 N T3 SD: 0.0175 c. M: 0.0275 c. 1406: 63 64 1279 N T3 SD: 0.0164 c. M: 0.0224 c. 1428: 64 65 1299 N T3 SD: 0.0161 c. M:-0.0218 c. 1451: 65 66 1320 N T3 SD: 0.0164 c. M: 0.0280 c. 1473: 66 67 1340 N T3 SD: 0.0134 c. M: 0.0232 c. 1495: 67 68 1360 N T3 SD: 0.0109 c. M: 0.0184 c. 1517: 68 69 1380 N T3 SD: 0.0094 c. M: 0.0138 c. 1539: 69 70 1400 N T3 SD: 0.0092 c. M:-0.0130 c. 1584: 71 72 1441 N T3 SD: 0.0095 c. M: 0.0148 c. 1606: 72 73 1461 N T3 SD: 0.0063 c. M: 0.0105 c. 1628: 73 74 1481 N T3 SD: 0.0037 c. M: 0.0063 c. 1650: 74 75 1501 N T3 SD: 0.0033 c. M:-0.0053 c. 1739: 78 79 1582 N T3 SD: 0.0030 c. M: 0.0053 c. 1761: 79 80 1602 N T3 SD: 0.0024 c. M:-0.0039 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: 110.9506 cents 7 x 8:9 S SD: 98.2804 cents 8 x 9:11 SD: 83.8153 cents 9 x 10:12 S SD: 68.7170 cents 10 x 11:13 SD: 63.8934 cents 11 x 12:15 S SD: 56.3011 cents 12 x 13:16 SD: 46.8015 cents 13 x 14:17 SD: 44.9271 cents 14 x 15:19 SD: 40.2653 cents 15 x 16:20 S SD: 33.3808 cents 16 x 17:21 SD: 32.9455 cents 17 x 18:23 SD: 29.8041 cents 18 x 19:24 SD: 24.3167 cents 19 x 20:25 S SD: 24.7334 cents 20 x 21:27 SD: 22.4865 cents 21 x 22:28 SD: 17.7837 cents 22 x 23:29 SD: 18.8058 cents 23 x 24:31 SD: 17.1364 cents 24 x 25:32 SD: 12.8514 cents 25 x 26:33 SD: 14.3923 cents 26 x 27:35 SD: 13.1273 cents 27 x 28:36 SD: 8.9956 cents 28 x 29:37 SD: 11.0696 cents 29 x 30:39 SD: 10.1134 cents 30 x 31:40 SD: 5.8986 cents 31 x 32:41 SD: 8.6082 cents 32 x 33:43 SD: 7.9129 cents 33 x 34:44 SD: 3.3564 cents 34 x 35:45 SD: 6.8999 cents 35 x 36:47 SD: 6.4474 cents 36 x 37:48 SD: 1.2322 cents 37 x 38:49 SD: 5.8992 cents 38 x 39:51 SD: 5.6762 cents 39 x 40:52 SD: 0.5693 cents 40 x 41:53 SD: 5.5395 cents 41 x 42:55 SD: 5.5075 cents 42 x 43:56 SD: 2.1164 cents 43 x 44:57 SD: 5.6707 cents 44 x 45:59 SD: 5.7659 cents 45 x 46:60 SD: 3.4595 cents 46 x 47:61 SD: 6.1008 cents 47 x 48:63 SD: 6.2642 cents 48 x 49:64 SD: 4.6364 cents 49 x 50:65 SD: 6.6764 cents 50 x 51:67 SD: 6.8695 cents 51:52 x 68 SD: 5.6392 cents 52:53 x 69 SD: 6.7598 cents 53:54 x 71 SD: 6.4577 cents 54:55 x 72 SD: 4.7139 cents 55:56 x 73 SD: 5.9293 cents 56:57 x 75 SD: 5.6660 cents 57:58:59:76 SD: 5.5525 cents 59:60:61:79 SD: 5.3919 cents 60:61:62:80 SD: 4.4544 cents 62:63:64:83 SD: 4.4369 cents 63:64:65:84 SD: 3.4596 cents 66:67:68:88 SD: 2.5542 cents 69:70:71:92 SD: 1.7269 cents 72:73:74:96 SD: 0.9688 cents 75:76:77:100 SD: 0.2790 cents 153:155:157:204 SD: 0.1081 cents 228:231:234:304 SD: 0.0973 cents 381:386:391:508 SD: 0.0868 cents