Scala analysis: 504_M12
Miscellaneous tetrachord 84/83 * 83/82 * 82/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 84/83 20.733590 2: 42/41 41.718502 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 82/63 456.3265 1: 84/83 20.7336 2: 83/82 20.9849 3: 82/63 456.3265
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 84/83 20.734 cents 1: 1 83/82 20.985 cents 1: 1 82/63 456.326 cents 2: 1 42/41 41.719 cents 2: 1 328/249 477.060 cents 2: 1 83/63 477.311 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 : 20.7 41.7 498.0 20.7 : 21.0 477.3 498.0 41.7 : 456.3 477.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.7336 .. 456.3265 cents 3403/2646, 435.5929 cents 84/83, 20.7336 cents 2: 41.7185 .. 477.3114 cents 3403/2646, 435.5929 cents 1323/1681,-414.6080 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 84/83, 20.7336 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 82/63, 456.3265 cents Average / Smallest step : 8.007055 Largest / Average step : 2.748706 Largest / Smallest step : 22.009044 Median interval of one step : 83/82, 20.9849 cents, amount: 1 Least squares average step : 114.16469 cents, oct.: 342.49406 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1898-tone equal temperament with octave 4/3 degrees: 79 159 1898 Least number of segments generator : 951 of 249.547 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 959 of 251.647 cents and inv. generated superset size: 88 = 85 more = 2933.333% 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 20.73359 cents Scale diversity : 0.006011 Lumma stability : 0.083260 Lumma impropriety factor : 0.832471 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 : 6889/6888, 0.2513 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 435.3416 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 83 Odd number limit : 249 (O: 83 U: 249) Highest odd numerator or denominator: 83 Scale harmonicity : 0.056757 Fundamental : 1/10209, -13.3176 octaves, 0.0256 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 8.575560E+05, 19.70987 octaves Euler's gradus suavitatis : 135 Sum of Mann's harmonic distance : 128.5, average 42.83333 Mersenne's string divisions : 97027 Sum of van Prooijen's expressibility: 4.00898, average 1.33633 Sum of Tenney's harmonic distance : 8.15857, average 2.71952 Vogel's harmonic complexity : 93.00000 Wille's k value : 2614 Wilson's harmonic complexity : 137 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.10317, average 2.01719 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.33333 3 1 7: 0 .. 1 0.66667 2 41: -1 .. 0 -0.33333 1 1 83: -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 11 22 36 46| Scale is weakly epimorphic with val: <7 10 22 36 47| Scale is weakly epimorphic with val: <7 11 18 37 45| Scale is weakly epimorphic with val: <7 11 18 38 47| Scale is weakly epimorphic with val: <7 11 18 40 45| Scale is weakly epimorphic with val: <7 11 18 41 47| Scale is weakly epimorphic with val: <7 11 19 36 45| Scale is weakly epimorphic with val: <7 11 19 38 46| Scale is weakly epimorphic with val: <7 11 19 39 45| Scale is weakly epimorphic with val: <7 11 19 41 46| Scale is weakly epimorphic with val: <7 11 19 42 45| Scale is weakly epimorphic with val: <7 11 20 36 47| Scale is weakly epimorphic with val: <7 11 20 37 46| Scale is weakly epimorphic with val: <7 11 20 39 47| Scale is weakly epimorphic with val: <7 11 20 40 46| Scale is weakly epimorphic with val: <7 11 20 42 47| Scale is JI-epimorphic with val: <7 11 21 37 45| Scale is weakly epimorphic with val: <7 11 21 38 47| Scale is weakly epimorphic with val: <7 11 21 40 45| Scale is weakly epimorphic with val: <7 11 21 41 47| Scale is weakly epimorphic with val: <7 11 22 36 45| Scale is JI-epimorphic with val: <7 11 22 38 46| Scale is weakly epimorphic with val: <7 11 22 39 45| Scale is weakly epimorphic with val: <7 11 22 41 46| Scale is weakly epimorphic with val: <7 11 22 42 45| Scale is weakly epimorphic with val: <7 12 20 36 45| Scale is weakly epimorphic with val: <7 12 21 37 46| Scale is weakly epimorphic with val: <7 12 22 37 45| Scale is weakly epimorphic with val: <7 12 22 38 47| Scale is weakly epimorphic with val: <7 12 22 40 45| Scale is weakly epimorphic with val: <8 11 20 36 46| Scale is weakly epimorphic with val: <8 11 21 36 45| Scale is weakly epimorphic with val: <8 11 21 37 47| Scale is weakly epimorphic with val: <8 11 21 39 45| Scale is weakly epimorphic with val: <8 11 21 42 45| Scale is weakly epimorphic with val: <8 11 22 37 46| Scale is weakly epimorphic with val: <8 11 22 38 45| Scale is weakly epimorphic with val: <8 11 22 40 46| Scale is weakly epimorphic with val: <8 12 19 36 45| Scale is weakly epimorphic with val: <8 12 20 37 46| Scale is weakly epimorphic with val: <8 12 20 38 45| Scale is weakly epimorphic with val: <8 12 20 41 45| Scale is weakly epimorphic with val: <8 12 21 36 46| Scale is weakly epimorphic with val: <8 12 21 38 47| Scale is weakly epimorphic with val: <8 12 21 39 46| Scale is weakly epimorphic with val: <8 12 21 42 46| Scale is weakly epimorphic with val: <8 12 22 37 47| Scale is weakly epimorphic with val: <8 12 22 39 45| Scale is weakly epimorphic with val: <8 12 22 40 47|
FIT/MODE
3: 0 0 3 N M DE S SD: 26.8968 c. M: 41.7185 c. 8: 0 1 7 N G T3 SD: 16.8489 c. M: 20.7336 c. 9: 0 1 8 N G T3 SD: 14.3223 c. M: 20.7336 c. 10: 0 1 9 N G T3 SD: 12.8487 c. M: 20.7336 c. 11: 0 1 10 N G T3 SD: 12.1456 c. M: 20.7336 c. 12: 0 1 11 N G T3 SD: 11.9712 c. M: 20.7336 c. 13: 0 1 12 N G T3 SD: 12.1311 c. M: 20.7336 c. 14: 0 1 13 N G T3 SD: 12.4850 c. M: 20.7336 c. 15: 0 1 14 N G T3 SD: 12.9408 c. M: 20.7336 c. 16: 1 0 15 N G T3 SD: 8.5674 c. M: 10.5907 c. 19: 1 1 17 N M DE S SD: 6.9443 c. M:-10.7073 c. 20: 1 1 18 N M DE S SD: 5.2523 c. M:-8.0860 c. 21: 1 1 19 N M DE S SD: 3.7216 c. M:-5.7144 c. 22: 1 1 20 N M DE S SD: 2.3302 c. M:-3.5583 c. 23: 1 1 21 N M DE S SD: 1.0606 c. M:-1.5898 c. 24: 1 1 22 N M DE S SD: 0.1244 c. M: 0.2148 c. 119: 5 5 109 N M DE S SD: 0.1355 c. M:-0.1927 c. 143: 6 6 131 N M DE S SD: 0.1039 c. M:-0.1634 c. 167: 7 7 153 N M DE S SD: 0.0846 c. M:-0.1425 c. 191: 8 8 175 N M DE S SD: 0.0733 c. M:-0.1269 c. 215: 9 9 197 N M DE S SD: 0.0675 c. M:-0.1148 c. 239: 10 10 219 N M DE S SD: 0.0652 c. M:-0.1051 c. 263: 11 11 241 N M DE S SD: 0.0650 c. M:-0.0972 c. 287: 12 12 263 N M DE S SD: 0.0661 c. M:-0.0906 c. 311: 13 13 285 N M DE S SD: 0.0679 c. M:-0.0850 c. 454: 19 19 416 N M DE S SD: 0.0660 c. M:-0.1097 c. 502: 21 21 460 N M DE S SD: 0.0649 c. M:-0.1010 c. 957: 40 40 877 N M DE S SD: 0.0686 c. M: 0.0846 c. 966: 40 41 885 N T3 SD: 0.0685 c. M: 0.1106 c. 980: 41 41 898 N M DE S SD: 0.0650 c. M:-0.1030 c. 1013: 42 43 928 N T3 SD: 0.0640 c. M: 0.0841 c. 1014: 42 43 929 N T3 SD: 0.0629 c. M: 0.1045 c. 1015: 42 43 930 N T3 SD: 0.0723 c. M: 0.1248 c. 1027: 43 43 941 N M DE S SD: 0.0693 c. M:-0.1193 c. 1028: 43 43 942 N M DE S SD: 0.0649 c. M:-0.0990 c. 1037: 43 44 950 N T3 SD: 0.0605 c. M: 0.0818 c. 1038: 43 44 951 N T3 SD: 0.0605 c. M: 0.1017 c. 1039: 43 44 952 N T3 SD: 0.0707 c. M: 0.1215 c. 1051: 44 44 963 N M DE S SD: 0.0683 c. M:-0.1170 c. 1060: 44 45 971 N T3 SD: 0.0666 c. M:-0.0985 c. 1061: 44 45 972 N T3 SD: 0.0572 c. M: 0.0795 c. 1062: 44 45 973 N T3 SD: 0.0583 c. M: 0.0990 c. 1063: 44 45 974 N T3 SD: 0.0693 c. M: 0.1184 c. 1076: 45 45 986 N M DE S SD: 0.0652 c. M:-0.0954 c. 1084: 45 46 993 N T3 SD: 0.0627 c. M:-0.0915 c. 1085: 45 46 994 N T3 SD: 0.0541 c. M: 0.0773 c. 1086: 45 46 995 N T3 SD: 0.0563 c. M: 0.0964 c. 1109: 46 47 1016 N T3 SD: 0.0513 c. M: 0.0753 c. 1110: 46 47 1017 N T3 SD: 0.0545 c. M: 0.0939 c. 1133: 47 48 1038 N T3 SD: 0.0487 c. M: 0.0733 c. 1134: 47 48 1039 N T3 SD: 0.0529 c. M: 0.0915 c. 1156: 48 49 1059 N T3 SD: 0.0520 c. M:-0.0725 c. 1157: 48 49 1060 N T3 SD: 0.0463 c. M: 0.0714 c. 1158: 48 49 1061 N T3 SD: 0.0515 c. M: 0.0892 c. 1180: 49 50 1081 N T3 SD: 0.0488 c. M:-0.0666 c. 1181: 49 50 1082 N T3 SD: 0.0440 c. M: 0.0696 c. 1182: 49 50 1083 N T3 SD: 0.0503 c. M: 0.0871 c. 1204: 50 51 1103 N T3 SD: 0.0458 c. M:-0.0610 c. 1205: 50 51 1104 N T3 SD: 0.0420 c. M: 0.0678 c. 1206: 50 51 1105 N T3 SD: 0.0493 c. M: 0.0850 c. 1228: 51 52 1125 N T3 SD: 0.0429 c. M:-0.0556 c. 1229: 51 52 1126 N T3 SD: 0.0402 c. M: 0.0661 c. 1252: 52 53 1147 N T3 SD: 0.0402 c. M:-0.0504 c. 1253: 52 53 1148 N T3 SD: 0.0385 c. M: 0.0645 c. 1276: 53 54 1169 N T3 SD: 0.0377 c. M: 0.0468 c. 1277: 53 54 1170 N T3 SD: 0.0371 c. M: 0.0630 c. 1300: 54 55 1191 N T3 SD: 0.0353 c. M: 0.0456 c. 1301: 54 55 1192 N T3 SD: 0.0358 c. M: 0.0615 c. 1324: 55 56 1213 N T3 SD: 0.0330 c. M: 0.0444 c. 1325: 55 56 1214 N T3 SD: 0.0348 c. M: 0.0600 c. 1348: 56 57 1235 N T3 SD: 0.0309 c. M: 0.0433 c. 1349: 56 57 1236 N T3 SD: 0.0339 c. M: 0.0586 c. 1372: 57 58 1257 N T3 SD: 0.0290 c. M: 0.0422 c. 1373: 57 58 1258 N T3 SD: 0.0331 c. M: 0.0573 c. 1396: 58 59 1279 N T3 SD: 0.0273 c. M: 0.0412 c. 1397: 58 59 1280 N T3 SD: 0.0326 c. M: 0.0560 c. 1419: 59 60 1300 N T3 SD: 0.0317 c. M:-0.0485 c. 1420: 59 60 1301 N T3 SD: 0.0257 c. M: 0.0402 c. 1444: 60 61 1323 N T3 SD: 0.0243 c. M: 0.0392 c. 1468: 61 62 1345 N T3 SD: 0.0231 c. M: 0.0383 c. 1491: 62 63 1366 N T3 SD: 0.0247 c. M:-0.0358 c. 1492: 62 63 1367 N T3 SD: 0.0220 c. M: 0.0373 c. 1515: 63 64 1388 N T3 SD: 0.0226 c. M:-0.0318 c. 1516: 63 64 1389 N T3 SD: 0.0212 c. M: 0.0365 c. 1539: 64 65 1410 N T3 SD: 0.0206 c. M:-0.0280 c. 1540: 64 65 1411 N T3 SD: 0.0206 c. M: 0.0356 c. 1563: 65 66 1432 N T3 SD: 0.0187 c. M:-0.0242 c. 1564: 65 66 1433 N T3 SD: 0.0201 c. M: 0.0348 c. 1587: 66 67 1454 N T3 SD: 0.0170 c. M: 0.0209 c. 1588: 66 67 1455 N T3 SD: 0.0199 c. M: 0.0340 c. 1611: 67 68 1476 N T3 SD: 0.0154 c. M: 0.0204 c. 1635: 68 69 1498 N T3 SD: 0.0139 c. M: 0.0198 c. 1659: 69 70 1520 N T3 SD: 0.0126 c. M: 0.0192 c. 1683: 70 71 1542 N T3 SD: 0.0116 c. M: 0.0187 c. 1707: 71 72 1564 N T3 SD: 0.0108 c. M: 0.0182 c. 1731: 72 73 1586 N T3 SD: 0.0102 c. M: 0.0177 c. 1755: 73 74 1608 N T3 SD: 0.0100 c. M: 0.0172 c. 1779: 74 75 1630 N T3 SD: 0.0100 c. M: 0.0167 c. 1802: 75 76 1651 N T3 SD: 0.0094 c. M:-0.0156 c. 1803: 75 76 1652 N T3 SD: 0.0103 c. M: 0.0162 c. 1826: 76 77 1673 N T3 SD: 0.0077 c. M:-0.0125 c. 1850: 77 78 1695 N T3 SD: 0.0060 c. M:-0.0096 c. 1874: 78 79 1717 N T3 SD: 0.0045 c. M:-0.0067 c. 1898: 79 80 1739 N T3 SD: 0.0031 c. M:-0.0039 c. 1922: 80 81 1761 N T3 SD: 0.0020 c. M: 0.0033 c. 1946: 81 82 1783 N T3 SD: 0.0020 c. M: 0.0030 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: 112.5762 cents 7 x 8:9 S SD: 99.8217 cents 8 x 9:11 SD: 85.3582 cents 9 x 10:12 S SD: 70.3426 cents 10 x 11:13 SD: 65.4227 cents 11 x 12:15 S SD: 57.8293 cents 12 x 13:16 SD: 48.4271 cents 13 x 14:17 SD: 46.4386 cents 14 x 15:19 SD: 41.7732 cents 15 x 16:20 S SD: 35.0064 cents 16 x 17:21 SD: 34.4320 cents 17 x 18:23 SD: 31.2839 cents 18 x 19:24 SD: 25.9423 cents 19 x 20:25 S SD: 26.1847 cents 20 x 21:27 SD: 23.9268 cents 21 x 22:28 SD: 19.4093 cents 22 x 23:29 SD: 20.2063 cents 23 x 24:31 SD: 18.5194 cents 24 x 25:32 SD: 14.4770 cents 25 x 26:33 SD: 15.7180 cents 26 x 27:35 SD: 14.4249 cents 27 x 28:36 SD: 10.6212 cents 28 x 29:37 SD: 12.2814 cents 29 x 30:39 SD: 11.2796 cents 30 x 31:40 SD: 7.5242 cents 31 x 32:41 SD: 9.6432 cents 32 x 33:43 SD: 8.8744 cents 33 x 34:44 SD: 4.9820 cents 34 x 35:45 SD: 7.6634 cents 35 x 36:47 SD: 7.0986 cents 36 x 37:48 SD: 2.8578 cents 37 x 38:49 SD: 6.2763 cents 38 x 39:51 SD: 5.9044 cents 39 x 40:52 SD: 1.0563 cents 40 x 41:53 SD: 5.4515 cents 41 x 42:55 SD: 5.2621 cents 42 x 43:56 SD: 0.4909 cents 43 x 44:57 SD: 5.1377 cents 44 x 45:59 SD: 5.1020 cents 45 x 46:60 SD: 1.8339 cents 46 x 47:61 SD: 5.2234 cents 47 x 48:63 SD: 5.2945 cents 48 x 49:64 SD: 3.0108 cents 49 x 50:65 SD: 5.5652 cents 50 x 51:67 SD: 5.6974 cents 51 x 52:68 SD: 4.0506 cents 52 x 53:69 SD: 6.0421 cents 53 x 54:71 SD: 6.2038 cents 54 x 55:72 SD: 4.9759 cents 55:56 x 73 SD: 6.5504 cents 56:57 x 75 SD: 6.2779 cents 57:58 x 76 SD: 4.6878 cents 58:59 x 77 SD: 5.7974 cents 59:60 x 79 SD: 5.5573 cents 60:61 x 80 SD: 3.9413 cents 61:62 x 81 SD: 5.1372 cents 63:64:65:84 SD: 4.6677 cents 65:66:67:87 SD: 4.6204 cents 66:67:68:88 SD: 3.7620 cents 69:70:71:92 SD: 2.9342 cents 72:73:74:96 SD: 2.1747 cents 75:76:77:100 SD: 1.4755 cents 78:79:80:104 SD: 0.8305 cents 81:82:83:108 SD: 0.2399 cents 165:167:169:220 SD: 0.0931 cents 246:249:252:328 SD: 0.0838 cents 411:416:421:548 SD: 0.0747 cents