Scala analysis: 510_M18
Miscellaneous tetrachord 70/69 * 69/68 * 136/105
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70/69 24.910272 2: 35/34 50.184211 septendecimal 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 136/105 447.8608 1: 70/69 24.9103 2: 69/68 25.2739 3: 136/105 447.8608
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 70/69 24.910 cents 1: 1 69/68 25.274 cents 1: 1 136/105 447.861 cents 2: 1 35/34 50.184 cents septendecimal 1/4-tone 2: 1 272/207 472.771 cents 2: 1 46/35 473.135 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 : 24.9 50.2 498.0 24.9 : 25.3 473.1 498.0 50.2 : 447.9 472.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.9103 .. 447.8608 cents 1564/1225, 422.9505 cents 70/69, 24.9103 cents 2: 50.1842 .. 473.1347 cents 1564/1225, 422.9505 cents 3675/4624,-397.6766 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 70/69, 24.9103 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 136/105, 447.8608 cents Average / Smallest step : 6.664520 Largest / Average step : 2.697713 Largest / Smallest step : 17.978960 Median interval of one step : 69/68, 25.2739 cents, amount: 1 Least squares average step : 115.67241 cents, oct.: 347.01722 cents Scale is not proper Scale has trivalence property 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 24.91027 cents Scale diversity : 0.064848 Lumma stability : 0.100032 Lumma impropriety factor : 0.798475 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 : 4761/4760, 0.3637 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 422.5868 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 23 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 69 Scale harmonicity : 0.010576 Average absolute harmonicity : 0.083740 Specific harmonicity : 0.052627 Fundamental : 1/2346, -11.1960 octaves, 0.1115 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 3.284400E+05, 18.32527 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 107.5, average 35.83333 Mersenne's string divisions : 67137 Sum of van Prooijen's expressibility: 3.86004, average 1.28668 Sum of Tenney's harmonic distance : 7.83868, average 2.61289 Vogel's harmonic complexity : 37.33333 Wille's k value : 1207 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.72344, average 2.45391 Lattice compactness (without 2's) : 10.19615, average 1.69936 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: 0 .. 1 0.66667 2 7: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 23: -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 16 19 29 33| Scale is weakly epimorphic with val: <7 11 16 19 30 32| Scale is weakly epimorphic with val: <7 11 16 19 30 35| Scale is weakly epimorphic with val: <7 11 16 20 30 34| Scale is weakly epimorphic with val: <7 11 16 20 31 33| Scale is weakly epimorphic with val: <7 11 16 21 29 34| Scale is weakly epimorphic with val: <7 11 16 21 31 32| Scale is weakly epimorphic with val: <7 11 16 21 31 35| Scale is weakly epimorphic with val: <7 11 17 19 30 34| Scale is weakly epimorphic with val: <7 11 17 19 31 33| Scale is weakly epimorphic with val: <7 11 17 20 29 34| Scale is weakly epimorphic with val: <7 11 17 20 31 32| Scale is weakly epimorphic with val: <7 11 17 20 31 35| Scale is JI-epimorphic with val: <7 11 17 21 29 33| Scale is weakly epimorphic with val: <7 11 17 21 30 32| Scale is weakly epimorphic with val: <7 11 17 21 30 35| Scale is weakly epimorphic with val: <7 11 18 19 29 34| Scale is weakly epimorphic with val: <7 11 18 19 31 32| Scale is weakly epimorphic with val: <7 11 18 19 31 35| Scale is JI-epimorphic with val: <7 11 18 20 29 33| Scale is weakly epimorphic with val: <7 11 18 20 30 32| Scale is weakly epimorphic with val: <7 11 18 20 30 35| Scale is JI-epimorphic with val: <7 11 18 21 30 34| Scale is weakly epimorphic with val: <7 11 18 21 31 33| Scale is weakly epimorphic with val: <7 12 18 21 29 33|
FIT/MODE
3: 0 0 3 N M DE S SD: 32.3470 c. M: 50.1842 c. 7: 0 1 6 N G T3 SD: 18.7977 c. M: 24.9103 c. 8: 0 1 7 N G T3 SD: 15.9817 c. M: 24.9103 c. 9: 0 1 8 N G T3 SD: 14.6866 c. M: 24.9103 c. 10: 0 1 9 N G T3 SD: 14.3836 c. M: 24.9103 c. 11: 0 1 10 N G T3 SD: 14.6584 c. M: 24.9103 c. 12: 0 1 11 N G T3 SD: 15.2301 c. M: 24.9103 c. 13: 0 1 12 N G T3 SD: 15.9321 c. M: 24.9103 c. 14: 1 0 13 N G T3 SD: 10.4430 c. M: 14.6096 c. 16: 1 1 14 N M DE S SD: 7.8396 c. M:-12.0714 c. 17: 1 1 15 N M DE S SD: 5.4759 c. M:-8.4093 c. 18: 1 1 16 N M DE S SD: 3.3752 c. M:-5.1541 c. 19: 1 1 17 N M DE S SD: 1.4968 c. M:-2.2416 c. 20: 1 1 18 N M DE S SD: 0.2193 c. M: 0.3797 c. 79: 4 4 71 N M DE S SD: 0.2289 c. M:-0.3072 c. 99: 5 5 89 N M DE S SD: 0.1576 c. M:-0.2435 c. 119: 6 6 107 N M DE S SD: 0.1183 c. M:-0.2012 c. 139: 7 7 125 N M DE S SD: 0.0996 c. M:-0.1711 c. 159: 8 8 143 N M DE S SD: 0.0940 c. M:-0.1486 c. 179: 9 9 161 N M DE S SD: 0.0957 c. M:-0.1311 c. 199: 10 10 179 N M DE S SD: 0.1008 c. M: 0.1294 c. 258: 13 13 232 N M DE S SD: 0.1069 c. M:-0.1850 c. 298: 15 15 268 N M DE S SD: 0.0955 c. M:-0.1591 c. 338: 17 17 304 N M DE S SD: 0.0942 c. M:-0.1393 c. 378: 19 19 340 N M DE S SD: 0.0980 c. M:-0.1237 c. 397: 20 20 357 N M DE S SD: 0.1040 c. M:-0.1802 c. 418: 21 21 376 N M DE S SD: 0.1038 c. M: 0.1414 c. 437: 22 22 393 N M DE S SD: 0.0966 c. M:-0.1629 c. 457: 23 23 411 N M DE S SD: 0.0948 c. M:-0.1554 c. 497: 25 25 447 N M DE S SD: 0.0940 c. M:-0.1423 c. 577: 29 29 519 N M DE S SD: 0.0989 c. M:-0.1215 c. 616: 31 31 554 N M DE S SD: 0.0945 c. M:-0.1537 c. 655: 33 33 589 N M DE S SD: 0.1051 c. M:-0.1821 c. 656: 33 33 590 N M DE S SD: 0.0939 c. M:-0.1438 c. 703: 35 36 632 N T3 SD: 0.0941 c. M:-0.1162 c. 704: 35 36 633 N T3 SD: 0.0901 c. M: 0.1495 c. 705: 35 36 634 N T3 SD: 0.1077 c. M: 0.1846 c. 715: 36 36 643 N M DE S SD: 0.0976 c. M:-0.1661 c. 723: 36 37 650 N T3 SD: 0.0874 c. M: 0.1114 c. 724: 36 37 651 N T3 SD: 0.0862 c. M: 0.1456 c. 743: 37 38 668 N T3 SD: 0.0812 c. M: 0.1086 c. 744: 37 38 669 N T3 SD: 0.0829 c. M: 0.1419 c. 763: 38 39 686 N T3 SD: 0.0757 c. M: 0.1059 c. 764: 38 39 687 N T3 SD: 0.0802 c. M: 0.1384 c. 783: 39 40 704 N T3 SD: 0.0707 c. M: 0.1034 c. 784: 39 40 705 N T3 SD: 0.0780 c. M: 0.1351 c. 803: 40 41 722 N T3 SD: 0.0663 c. M: 0.1011 c. 804: 40 41 723 N T3 SD: 0.0763 c. M: 0.1319 c. 822: 41 42 739 N T3 SD: 0.0724 c. M:-0.1050 c. 823: 41 42 740 N T3 SD: 0.0624 c. M: 0.0988 c. 842: 42 43 757 N T3 SD: 0.0665 c. M:-0.0935 c. 843: 42 43 758 N T3 SD: 0.0591 c. M: 0.0966 c. 862: 43 44 775 N T3 SD: 0.0609 c. M:-0.0825 c. 863: 43 44 776 N T3 SD: 0.0564 c. M: 0.0946 c. 882: 44 45 793 N T3 SD: 0.0558 c. M:-0.0720 c. 883: 44 45 794 N T3 SD: 0.0542 c. M: 0.0926 c. 902: 45 46 811 N T3 SD: 0.0511 c. M: 0.0632 c. 903: 45 46 812 N T3 SD: 0.0525 c. M: 0.0908 c. 922: 46 47 829 N T3 SD: 0.0469 c. M: 0.0620 c. 923: 46 47 830 N T3 SD: 0.0514 c. M: 0.0890 c. 942: 47 48 847 N T3 SD: 0.0431 c. M: 0.0609 c. 943: 47 48 848 N T3 SD: 0.0507 c. M: 0.0872 c. 962: 48 49 865 N T3 SD: 0.0398 c. M: 0.0598 c. 982: 49 50 883 N T3 SD: 0.0371 c. M: 0.0587 c. 1002: 50 51 901 N T3 SD: 0.0349 c. M: 0.0577 c. 1022: 51 52 919 N T3 SD: 0.0333 c. M: 0.0568 c. 1041: 52 53 936 N T3 SD: 0.0347 c. M:-0.0509 c. 1042: 52 53 937 N T3 SD: 0.0323 c. M: 0.0558 c. 1061: 53 54 954 N T3 SD: 0.0307 c. M:-0.0428 c. 1062: 53 54 955 N T3 SD: 0.0318 c. M: 0.0549 c. 1081: 54 55 972 N T3 SD: 0.0270 c. M:-0.0349 c. 1082: 54 55 973 N T3 SD: 0.0319 c. M: 0.0541 c. 1101: 55 56 990 N T3 SD: 0.0237 c. M: 0.0306 c. 1121: 56 57 1008 N T3 SD: 0.0210 c. M: 0.0302 c. 1141: 57 58 1026 N T3 SD: 0.0188 c. M: 0.0298 c. 1161: 58 59 1044 N T3 SD: 0.0174 c. M: 0.0295 c. 1181: 59 60 1062 N T3 SD: 0.0168 c. M: 0.0291 c. 1201: 60 61 1080 N T3 SD: 0.0170 c. M: 0.0288 c. 1220: 61 62 1097 N T3 SD: 0.0171 c. M:-0.0285 c. 1221: 61 62 1098 N T3 SD: 0.0179 c. M: 0.0284 c. 1240: 62 63 1115 N T3 SD: 0.0135 c. M:-0.0219 c. 1260: 63 64 1133 N T3 SD: 0.0101 c. M:-0.0156 c. 1280: 64 65 1151 N T3 SD: 0.0071 c. M:-0.0094 c. 1300: 65 66 1169 N T3 SD: 0.0050 c. M: 0.0080 c. 1320: 66 67 1187 N T3 SD: 0.0048 c. M: 0.0080 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: 108.3433 cents 7 x 8:9 S SD: 95.8142 cents 8 x 9:11 SD: 81.3474 cents 9 x 10:12 S SD: 66.1098 cents 10 x 11:13 SD: 61.4508 cents 11 x 12:15 S SD: 53.8619 cents 12 x 13:16 SD: 44.1942 cents 13 x 14:17 SD: 42.5204 cents 14 x 15:19 SD: 37.8672 cents 15 x 16:20 S SD: 30.7735 cents 16 x 17:21 SD: 30.5909 cents 17 x 18:23 SD: 27.4651 cents 18 x 19:24 SD: 21.7094 cents 19 x 20:25 S SD: 22.4558 cents 20 x 21:27 SD: 20.2351 cents 21 x 22:28 SD: 15.1764 cents 22 x 23:29 SD: 16.6450 cents 23 x 24:31 SD: 15.0198 cents 24 x 25:32 SD: 10.2441 cents 25 x 26:33 SD: 12.4157 cents 26 x 27:35 SD: 11.2259 cents 27 x 28:36 SD: 6.3883 cents 28 x 29:37 SD: 9.3908 cents 29 x 30:39 SD: 8.5617 cents 30 x 31:40 SD: 3.2913 cents 31 x 32:41 SD: 7.4054 cents 32 x 33:43 SD: 6.9111 cents 33 x 34:44 SD: 0.7491 cents 34 x 35:45 SD: 6.3883 cents 35 x 36:47 SD: 6.2014 cents 36 x 37:48 SD: 1.3751 cents 37 x 38:49 SD: 6.2025 cents 38 x 39:51 SD: 6.2464 cents 39 x 40:52 SD: 3.1766 cents 40 x 41:53 SD: 6.5784 cents 41 x 42:55 SD: 6.7533 cents 42 x 43:56 SD: 4.7237 cents 43 x 44:57 SD: 7.2410 cents 44 x 45:59 SD: 7.4735 cents 45 x 46:60 SD: 6.0668 cents 46:47 x 61 SD: 7.7595 cents 47:48 x 63 SD: 7.3736 cents 48:49 x 64 SD: 5.3933 cents 49:50 x 65 SD: 6.7032 cents 50:51 x 67 SD: 6.3719 cents 51:52:53:68 SD: 6.1923 cents 53:54:55:71 SD: 5.9281 cents 54:55:56:72 SD: 4.8334 cents 56:57:58:75 SD: 4.7608 cents 57:58:59:76 SD: 3.6155 cents 60:61:62:80 SD: 2.5180 cents 63:64:65:84 SD: 1.5245 cents 66:67:68:88 SD: 0.6243 cents 69:70:71:92 SD: 0.2390 cents 135:137:139:180 SD: 0.2201 cents 204:207:210:272 SD: 0.1212 cents 273:277:281:364 SD: 0.1089 cents