Scala analysis: 508_M16
Miscellaneous tetrachord 76/75 * 75/74 * 74/57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76/75 22.930588 2: 38/37 46.168977 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 74/57 451.8760 1: 76/75 22.9306 2: 75/74 23.2384 3: 74/57 451.8760
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76/75 22.931 cents 1: 1 75/74 23.238 cents 1: 1 74/57 451.876 cents 2: 1 38/37 46.169 cents 2: 1 296/225 474.807 cents 2: 1 25/19 475.114 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 : 22.9 46.2 498.0 22.9 : 23.2 475.1 498.0 46.2 : 451.9 474.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9306 .. 451.8760 cents 925/722, 428.9454 cents 76/75, 22.9306 cents 2: 46.1690 .. 475.1144 cents 925/722, 428.9454 cents 1083/1369,-405.7070 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 76/75, 22.9306 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 74/57, 451.8760 cents Average / Smallest step : 7.239893 Largest / Average step : 2.721899 Largest / Smallest step : 19.706256 Median interval of one step : 75/74, 23.2384 cents, amount: 1 Least squares average step : 114.95740 cents, oct.: 344.87219 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1564-tone equal temperament with octave 4/3 degrees: 72 145 1564 Least number of segments generator : 783 of 249.341 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1273 of 405.378 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 22.93059 cents Scale diversity : 0.036809 Lumma stability : 0.092082 Lumma impropriety factor : 0.814599 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 : 5625/5624, 0.3078 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 428.6376 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 37 Odd number limit : 225 (O: 75 U: 225) Highest odd numerator or denominator: 75 Scale harmonicity : 0.019390 Fundamental : 1/2775, -11.4383 octaves, 0.0943 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 2.109000E+05, 17.68620 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 116.5, average 38.83333 Mersenne's string divisions : 79275 Sum of van Prooijen's expressibility: 3.92038, average 1.30679 Sum of Tenney's harmonic distance : 7.98304, average 2.66101 Vogel's harmonic complexity : 46.66667 Wille's k value : 712 Wilson's harmonic complexity : 69 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.23017, average 2.20503 Lattice compactness (without 2's) : 10.33584, average 1.72264 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -0.66667 2 19: 0 .. 1 0.66667 2 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 31 36| Scale is weakly epimorphic with val: <6 10 15 31 39| Scale is weakly epimorphic with val: <6 10 15 32 35| Scale is weakly epimorphic with val: <6 10 16 33 35| Scale is weakly epimorphic with val: <6 10 16 33 38| Scale is weakly epimorphic with val: <6 10 16 33 41| Scale is weakly epimorphic with val: <6 10 16 34 37| Scale is weakly epimorphic with val: <6 10 17 33 36| Scale is weakly epimorphic with val: <6 10 18 32 35| Scale is weakly epimorphic with val: <6 10 19 34 37| Scale is weakly epimorphic with val: <6 11 15 32 36| Scale is weakly epimorphic with val: <6 11 15 32 39| Scale is weakly epimorphic with val: <6 11 15 34 37| Scale is weakly epimorphic with val: <6 11 16 33 36| Scale is weakly epimorphic with val: <6 11 16 34 35| Scale is weakly epimorphic with val: <6 11 16 34 38| Scale is weakly epimorphic with val: <6 11 16 34 41| Scale is weakly epimorphic with val: <6 11 17 32 35| Scale is weakly epimorphic with val: <6 11 18 34 37| Scale is weakly epimorphic with val: <6 11 19 33 36| Scale is weakly epimorphic with val: <7 10 15 29 37| Scale is weakly epimorphic with val: <7 10 15 29 40| Scale is weakly epimorphic with val: <7 10 15 31 35| Scale is weakly epimorphic with val: <7 10 15 34 38| Scale is weakly epimorphic with val: <7 10 16 31 36| Scale is weakly epimorphic with val: <7 10 16 31 39| Scale is weakly epimorphic with val: <7 10 16 33 37| Scale is weakly epimorphic with val: <7 10 17 32 36| Scale is weakly epimorphic with val: <7 10 17 33 35| Scale is weakly epimorphic with val: <7 10 17 33 38| Scale is weakly epimorphic with val: <7 10 17 33 41| Scale is weakly epimorphic with val: <7 10 18 31 35| Scale is weakly epimorphic with val: <7 10 18 34 38| Scale is weakly epimorphic with val: <7 10 19 33 37| Scale is weakly epimorphic with val: <7 11 15 28 36| Scale is weakly epimorphic with val: <7 11 15 28 39| Scale is weakly epimorphic with val: <7 11 15 29 35| Scale is weakly epimorphic with val: <7 11 15 29 38| Scale is weakly epimorphic with val: <7 11 15 29 41| Scale is weakly epimorphic with val: <7 11 15 31 36| Scale is weakly epimorphic with val: <7 11 15 31 39| Scale is weakly epimorphic with val: <7 11 15 32 35| Scale is weakly epimorphic with val: <7 11 15 32 38| Scale is weakly epimorphic with val: <7 11 15 32 41| Scale is weakly epimorphic with val: <7 11 15 34 36| Scale is weakly epimorphic with val: <7 11 15 34 39| Scale is weakly epimorphic with val: <7 11 16 28 37| Scale is weakly epimorphic with val: <7 11 16 28 40| Scale is JI-epimorphic with val: <7 11 16 30 35| Scale is weakly epimorphic with val: <7 11 16 30 38| Scale is weakly epimorphic with val: <7 11 16 30 41| Scale is weakly epimorphic with val: <7 11 16 31 37| Scale is weakly epimorphic with val: <7 11 16 31 40| Scale is weakly epimorphic with val: <7 11 16 33 35| Scale is weakly epimorphic with val: <7 11 16 33 38| Scale is weakly epimorphic with val: <7 11 16 33 41| Scale is weakly epimorphic with val: <7 11 16 34 37| Scale is weakly epimorphic with val: <7 11 16 34 40| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 29 40| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 30 39| Scale is JI-epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 32 40| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 17 33 39| Scale is weakly epimorphic with val: <7 11 18 28 36| Scale is weakly epimorphic with val: <7 11 18 28 39| Scale is weakly epimorphic with val: <7 11 18 29 35| Scale is weakly epimorphic with val: <7 11 18 29 38| Scale is weakly epimorphic with val: <7 11 18 29 41| Scale is weakly epimorphic with val: <7 11 18 31 36| Scale is weakly epimorphic with val: <7 11 18 31 39| Scale is weakly epimorphic with val: <7 11 18 32 35| Scale is weakly epimorphic with val: <7 11 18 32 38| Scale is weakly epimorphic with val: <7 11 18 32 41| Scale is weakly epimorphic with val: <7 11 18 34 36| Scale is JI-epimorphic with val: <7 11 18 34 39| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is weakly epimorphic with val: <7 11 19 28 40| Scale is weakly epimorphic with val: <7 11 19 30 35| Scale is weakly epimorphic with val: <7 11 19 30 38| Scale is weakly epimorphic with val: <7 11 19 30 41| Scale is weakly epimorphic with val: <7 11 19 31 37| Scale is weakly epimorphic with val: <7 11 19 31 40| Scale is weakly epimorphic with val: <7 11 19 33 35| Scale is weakly epimorphic with val: <7 11 19 33 38| Scale is weakly epimorphic with val: <7 11 19 33 41| Scale is weakly epimorphic with val: <7 11 19 34 37| Scale is weakly epimorphic with val: <7 11 19 34 40| Scale is weakly epimorphic with val: <7 12 15 31 37| Scale is weakly epimorphic with val: <7 12 15 31 40| Scale is weakly epimorphic with val: <7 12 15 32 36| Scale is weakly epimorphic with val: <7 12 16 31 35| Scale is weakly epimorphic with val: <7 12 16 33 36| Scale is weakly epimorphic with val: <7 12 16 33 39| Scale is weakly epimorphic with val: <7 12 16 34 38| Scale is weakly epimorphic with val: <7 12 17 33 37| Scale is weakly epimorphic with val: <7 12 18 32 36| Scale is weakly epimorphic with val: <7 12 19 31 35| Scale is weakly epimorphic with val: <7 12 19 34 38| Scale is weakly epimorphic with val: <8 11 15 28 35| Scale is weakly epimorphic with val: <8 11 15 28 38| Scale is weakly epimorphic with val: <8 11 15 28 41| Scale is weakly epimorphic with val: <8 11 15 32 37| Scale is weakly epimorphic with val: <8 11 16 30 37| Scale is weakly epimorphic with val: <8 11 16 30 40| Scale is weakly epimorphic with val: <8 11 16 31 36| Scale is weakly epimorphic with val: <8 11 16 34 39| Scale is weakly epimorphic with val: <8 11 17 30 35| Scale is weakly epimorphic with val: <8 11 17 32 36| Scale is weakly epimorphic with val: <8 11 17 32 39| Scale is weakly epimorphic with val: <8 11 17 33 38| Scale is weakly epimorphic with val: <8 11 18 32 37| Scale is weakly epimorphic with val: <8 11 18 34 35| Scale is weakly epimorphic with val: <8 11 18 34 38| Scale is weakly epimorphic with val: <8 11 18 34 41| Scale is weakly epimorphic with val: <8 11 19 31 36| Scale is weakly epimorphic with val: <8 11 19 34 39| Scale is weakly epimorphic with val: <8 12 15 29 35| Scale is weakly epimorphic with val: <8 12 15 29 38| Scale is weakly epimorphic with val: <8 12 15 29 41| Scale is weakly epimorphic with val: <8 12 15 31 36| Scale is weakly epimorphic with val: <8 12 15 34 39| Scale is weakly epimorphic with val: <8 12 16 30 35| Scale is weakly epimorphic with val: <8 12 16 31 37| Scale is weakly epimorphic with val: <8 12 16 31 40| Scale is weakly epimorphic with val: <8 12 16 33 38| Scale is weakly epimorphic with val: <8 12 17 32 37| Scale is weakly epimorphic with val: <8 12 17 33 36| Scale is weakly epimorphic with val: <8 12 17 33 39| Scale is weakly epimorphic with val: <8 12 18 31 36| Scale is weakly epimorphic with val: <8 12 18 34 39| Scale is weakly epimorphic with val: <8 12 19 30 35| Scale is weakly epimorphic with val: <8 12 19 33 38|
FIT/MODE
3: 0 0 3 N M DE S SD: 29.7623 c. M: 46.1690 c. 8: 0 1 7 N G T3 SD: 16.1719 c. M: 22.9306 c. 9: 0 1 8 N G T3 SD: 14.2582 c. M: 22.9306 c. 10: 0 1 9 N G T3 SD: 13.4043 c. M: 22.9306 c. 11: 0 1 10 N G T3 SD: 13.2490 c. M: 22.9306 c. 12: 0 1 11 N G T3 SD: 13.5102 c. M: 22.9306 c. 13: 0 1 12 N G T3 SD: 13.9947 c. M: 22.9306 c. 14: 0 1 13 N G T3 SD: 14.5837 c. M: 22.9306 c. 15: 1 0 14 N G T3 SD: 9.5506 c. M: 12.9660 c. 16: 1 1 14 N M DE S SD: 10.4239 c. M:-16.0866 c. 17: 1 1 15 N M DE S SD: 8.0601 c. M:-12.4246 c. 18: 1 1 16 N M DE S SD: 5.9591 c. M:-9.1694 c. 19: 1 1 17 N M DE S SD: 4.0793 c. M:-6.2568 c. 20: 1 1 18 N M DE S SD: 2.3878 c. M:-3.6355 c. 21: 1 1 19 N M DE S SD: 0.8593 c. M:-1.2639 c. 22: 1 1 20 N M DE S SD: 0.5420 c. M: 0.8922 c. 43: 2 2 39 N M DE S SD: 0.1641 c. M:-0.2343 c. 65: 3 3 59 N M DE S SD: 0.1175 c. M: 0.1956 c. 108: 5 5 98 N M DE S SD: 0.0796 c. M:-0.1271 c. 151: 7 7 137 N M DE S SD: 0.0911 c. M:-0.1576 c. 173: 8 8 157 N M DE S SD: 0.0847 c. M: 0.1070 c. 259: 12 12 235 N M DE S SD: 0.0843 c. M:-0.1449 c. 281: 13 13 255 N M DE S SD: 0.0811 c. M:-0.1106 c. 389: 18 18 353 N M DE S SD: 0.0801 c. M:-0.1152 c. 454: 21 21 412 N M DE S SD: 0.0822 c. M:-0.1067 c. 475: 22 22 431 N M DE S SD: 0.0814 c. M:-0.1368 c. 497: 23 23 451 N M DE S SD: 0.0798 c. M:-0.1178 c. 561: 26 26 509 N M DE S SD: 0.0876 c. M:-0.1517 c. 583: 27 27 529 N M DE S SD: 0.0809 c. M:-0.1350 c. 605: 28 28 549 N M DE S SD: 0.0796 c. M:-0.1194 c. 627: 29 29 569 N M DE S SD: 0.0829 c. M:-0.1050 c. 670: 31 31 608 N M DE S SD: 0.0805 c. M:-0.1133 c. 712: 33 33 646 N M DE S SD: 0.0883 c. M:-0.1530 c. 713: 33 33 647 N M DE S SD: 0.0795 c. M:-0.1206 c. 800: 37 37 726 N M DE S SD: 0.0832 c. M:-0.1040 c. 808: 37 38 733 N T3 SD: 0.0797 c. M: 0.1241 c. 821: 38 38 745 N M DE S SD: 0.0795 c. M:-0.1214 c. 829: 38 39 752 N T3 SD: 0.0785 c. M: 0.1010 c. 830: 38 39 753 N T3 SD: 0.0769 c. M: 0.1285 c. 831: 38 39 754 N T3 SD: 0.0908 c. M: 0.1560 c. 842: 39 39 764 N M DE S SD: 0.0818 c. M:-0.1380 c. 851: 39 40 772 N T3 SD: 0.0719 c. M: 0.1060 c. 852: 39 40 773 N T3 SD: 0.0769 c. M: 0.1328 c. 872: 40 41 791 N T3 SD: 0.0731 c. M:-0.0944 c. 873: 40 41 792 N T3 SD: 0.0682 c. M: 0.1107 c. 874: 40 41 793 N T3 SD: 0.0792 c. M: 0.1368 c. 894: 41 42 811 N T3 SD: 0.0657 c. M: 0.0896 c. 895: 41 42 812 N T3 SD: 0.0673 c. M: 0.1151 c. 916: 42 43 831 N T3 SD: 0.0609 c. M: 0.0945 c. 917: 42 43 832 N T3 SD: 0.0689 c. M: 0.1194 c. 937: 43 44 850 N T3 SD: 0.0608 c. M: 0.0747 c. 938: 43 44 851 N T3 SD: 0.0590 c. M: 0.0991 c. 959: 44 45 870 N T3 SD: 0.0550 c. M: 0.0797 c. 960: 44 45 871 N T3 SD: 0.0598 c. M: 0.1035 c. 980: 45 46 889 N T3 SD: 0.0573 c. M:-0.0781 c. 981: 45 46 890 N T3 SD: 0.0519 c. M: 0.0845 c. 1002: 46 47 909 N T3 SD: 0.0504 c. M: 0.0662 c. 1003: 46 47 910 N T3 SD: 0.0518 c. M: 0.0890 c. 1024: 47 48 929 N T3 SD: 0.0461 c. M: 0.0711 c. 1025: 47 48 930 N T3 SD: 0.0542 c. M: 0.0934 c. 1045: 48 49 948 N T3 SD: 0.0470 c. M:-0.0610 c. 1046: 48 49 949 N T3 SD: 0.0448 c. M: 0.0758 c. 1067: 49 50 968 N T3 SD: 0.0415 c. M: 0.0588 c. 1068: 49 50 969 N T3 SD: 0.0463 c. M: 0.0802 c. 1088: 50 51 987 N T3 SD: 0.0448 c. M:-0.0650 c. 1089: 50 51 988 N T3 SD: 0.0389 c. M: 0.0635 c. 1110: 51 52 1007 N T3 SD: 0.0382 c. M: 0.0474 c. 1111: 51 52 1008 N T3 SD: 0.0394 c. M: 0.0680 c. 1132: 52 53 1027 N T3 SD: 0.0341 c. M: 0.0522 c. 1154: 53 54 1047 N T3 SD: 0.0333 c. M: 0.0568 c. 1175: 54 55 1066 N T3 SD: 0.0306 c. M: 0.0417 c. 1176: 54 55 1067 N T3 SD: 0.0355 c. M: 0.0612 c. 1196: 55 56 1085 N T3 SD: 0.0350 c. M:-0.0543 c. 1197: 55 56 1086 N T3 SD: 0.0282 c. M: 0.0463 c. 1218: 56 57 1105 N T3 SD: 0.0283 c. M:-0.0372 c. 1219: 56 57 1106 N T3 SD: 0.0293 c. M: 0.0508 c. 1240: 57 58 1125 N T3 SD: 0.0243 c. M: 0.0366 c. 1262: 58 59 1145 N T3 SD: 0.0239 c. M: 0.0410 c. 1283: 59 60 1164 N T3 SD: 0.0216 c. M: 0.0275 c. 1305: 60 61 1184 N T3 SD: 0.0193 c. M: 0.0320 c. 1327: 61 62 1204 N T3 SD: 0.0211 c. M: 0.0363 c. 1348: 62 63 1223 N T3 SD: 0.0160 c. M: 0.0235 c. 1370: 63 64 1243 N T3 SD: 0.0160 c. M: 0.0278 c. 1391: 64 65 1262 N T3 SD: 0.0143 c. M:-0.0192 c. 1413: 65 66 1282 N T3 SD: 0.0118 c. M: 0.0198 c. 1456: 67 68 1321 N T3 SD: 0.0090 c. M: 0.0123 c. 1478: 68 69 1341 N T3 SD: 0.0098 c. M: 0.0165 c. 1499: 69 70 1360 N T3 SD: 0.0086 c. M:-0.0140 c. 1521: 70 71 1380 N T3 SD: 0.0054 c. M: 0.0094 c. 1564: 72 73 1419 N T3 SD: 0.0034 c. M:-0.0053 c. 1629: 75 76 1478 N T3 SD: 0.0016 c. M: 0.0027 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: 110.3510 cents 7 x 8:9 S SD: 97.7125 cents 8 x 9:11 SD: 83.2470 cents 9 x 10:12 S SD: 68.1174 cents 10 x 11:13 SD: 63.3304 cents 11 x 12:15 S SD: 55.7388 cents 12 x 13:16 SD: 46.2018 cents 13 x 14:17 SD: 44.3715 cents 14 x 15:19 SD: 39.7114 cents 15 x 16:20 S SD: 32.7812 cents 16 x 17:21 SD: 32.4005 cents 17 x 18:23 SD: 29.2621 cents 18 x 19:24 SD: 23.7170 cents 19 x 20:25 S SD: 24.2037 cents 20 x 21:27 SD: 21.9617 cents 21 x 22:28 SD: 17.1840 cents 22 x 23:29 SD: 18.2985 cents 23 x 24:31 SD: 16.6372 cents 24 x 25:32 SD: 12.2517 cents 25 x 26:33 SD: 13.9193 cents 26 x 27:35 SD: 12.6678 cents 27 x 28:36 SD: 8.3960 cents 28 x 29:37 SD: 10.6504 cents 29 x 30:39 SD: 9.7166 cents 30 x 31:40 SD: 5.2989 cents 31 x 32:41 SD: 8.2745 cents 32 x 33:43 SD: 7.6154 cents 33 x 34:44 SD: 2.7567 cents 34 x 35:45 SD: 6.6964 cents 35 x 36:47 SD: 6.2968 cents 36 x 37:48 SD: 0.6325 cents 37 x 38:49 SD: 5.8686 cents 38 x 39:51 SD: 5.7078 cents 39 x 40:52 SD: 1.1690 cents 40 x 41:53 SD: 5.6902 cents 41 x 42:55 SD: 5.7133 cents 42 x 43:56 SD: 2.7161 cents 43 x 44:57 SD: 5.9679 cents 44 x 45:59 SD: 6.1026 cents 45 x 46:60 SD: 4.0592 cents 46 x 47:61 SD: 6.4976 cents 47 x 48:63 SD: 6.6866 cents 48 x 49:64 SD: 5.2361 cents 49 x 50:65 SD: 7.1364 cents 50:51 x 67 SD: 7.1315 cents 51:52 x 68 SD: 5.3433 cents 52:53 x 69 SD: 6.5295 cents 53:54 x 71 SD: 6.2309 cents 54:55 x 72 SD: 4.4180 cents 55:56 x 73 SD: 5.7117 cents 57:58:59:76 SD: 5.1069 cents 59:60:61:79 SD: 4.9987 cents 60:61:62:80 SD: 4.0089 cents 63:64:65:84 SD: 3.0142 cents 66:67:68:88 SD: 2.1090 cents 69:70:71:92 SD: 1.2822 cents 72:73:74:96 SD: 0.5271 cents 75:76:77:100 SD: 0.2025 cents 147:149:151:196 SD: 0.1862 cents 222:225:228:296 SD: 0.1026 cents 297:301:305:396 SD: 0.0922 cents