Scala analysis: xen18-erlich-beatles-17
10L 7s MOS for Beatles, L=88.84, s=44.10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.840 cents 88.840000 2: 132.940 cents 132.940000 3: 221.780 cents 221.780000 4: 265.880 cents 265.880000 5: 354.720 cents 354.720000 6: 443.560 cents 443.560000 7: 487.660 cents 487.660000 8: 576.500 cents 576.500000 9: 620.600 cents 620.600000 10: 709.440 cents 709.440000 11: 753.540 cents 753.540000 12: 842.380 cents 842.380000 13: 931.220 cents 931.220000 14: 975.320 cents 975.320000 15: 1064.160 cents 1064.160000 16: 1108.260 cents 1108.260000 17: 1197.100 cents 1197.100000
SHOW/INTERVAL
0: 88.8400 cents 88.8400 1: 88.8400 cents 88.8400 2: 44.1000 cents 44.1000 3: 88.8400 cents 88.8400 4: 44.1000 cents 44.1000 5: 88.8400 cents 88.8400 6: 88.8400 cents 88.8400 7: 44.1000 cents 44.1000 8: 88.8400 cents 88.8400 9: 44.1000 cents 44.1000 10: 88.8400 cents 88.8400 11: 44.1000 cents 44.1000 12: 88.8400 cents 88.8400 13: 88.8400 cents 88.8400 14: 44.1000 cents 44.1000 15: 88.8400 cents 88.8400 16: 44.1000 cents 44.1000 17: 88.8400 cents 88.8400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 44.10000 cents 1: 10 88.84000 cents 2: 14 132.94000 cents 2: 3 177.68000 cents 3: 4 177.04000 cents 3: 13 221.78000 cents 4: 11 265.88000 cents 4: 6 310.62000 cents 5: 1 309.98000 cents 5: 16 354.72000 cents 6: 8 398.82000 cents 6: 9 443.56000 cents 7: 15 487.66000 cents 7: 2 532.40000 cents 8: 5 531.76000 cents 8: 12 576.50000 cents 9: 12 620.60000 cents 9: 5 665.34000 cents 10: 2 664.70000 cents 10: 15 709.44000 cents 11: 9 753.54000 cents 11: 8 798.28000 cents 12: 16 842.38000 cents 12: 1 887.12000 cents 13: 6 886.48000 cents 13: 11 931.22000 cents 14: 13 975.32000 cents 14: 4 1020.06000 cents 15: 3 1019.42000 cents 15: 14 1064.16000 cents 16: 10 1108.26000 cents 16: 7 1153.00000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 88.8 132.9 221.8 265.9 354.7 443.6 487.7 576.5 620.6 709.4 753.5 842.4 931.2 975.3 1064.2 1108.3 1197.1 88.8 : 44.1 132.9 177.0 265.9 354.7 398.8 487.7 531.8 620.6 664.7 753.5 842.4 886.5 975.3 1019.4 1108.3 1197.1 132.9 : 88.8 132.9 221.8 310.6 354.7 443.6 487.7 576.5 620.6 709.4 798.3 842.4 931.2 975.3 1064.2 1153.0 1197.1 221.8 : 44.1 132.9 221.8 265.9 354.7 398.8 487.7 531.8 620.6 709.4 753.5 842.4 886.5 975.3 1064.2 1108.3 1197.1 265.9 : 88.8 177.7 221.8 310.6 354.7 443.6 487.7 576.5 665.3 709.4 798.3 842.4 931.2 1020.1 1064.2 1153.0 1197.1 354.7 : 88.8 132.9 221.8 265.9 354.7 398.8 487.7 576.5 620.6 709.4 753.5 842.4 931.2 975.3 1064.2 1108.3 1197.1 443.6 : 44.1 132.9 177.0 265.9 310.0 398.8 487.7 531.8 620.6 664.7 753.5 842.4 886.5 975.3 1019.4 1108.3 1197.1 487.7 : 88.8 132.9 221.8 265.9 354.7 443.6 487.7 576.5 620.6 709.4 798.3 842.4 931.2 975.3 1064.2 1153.0 1197.1 576.5 : 44.1 132.9 177.0 265.9 354.7 398.8 487.7 531.8 620.6 709.4 753.5 842.4 886.5 975.3 1064.2 1108.3 1197.1 620.6 : 88.8 132.9 221.8 310.6 354.7 443.6 487.7 576.5 665.3 709.4 798.3 842.4 931.2 1020.1 1064.2 1153.0 1197.1 709.4 : 44.1 132.9 221.8 265.9 354.7 398.8 487.7 576.5 620.6 709.4 753.5 842.4 931.2 975.3 1064.2 1108.3 1197.1 753.5 : 88.8 177.7 221.8 310.6 354.7 443.6 532.4 576.5 665.3 709.4 798.3 887.1 931.2 1020.1 1064.2 1153.0 1197.1 842.4 : 88.8 132.9 221.8 265.9 354.7 443.6 487.7 576.5 620.6 709.4 798.3 842.4 931.2 975.3 1064.2 1108.3 1197.1 931.2 : 44.1 132.9 177.0 265.9 354.7 398.8 487.7 531.8 620.6 709.4 753.5 842.4 886.5 975.3 1019.4 1108.3 1197.1 975.3 : 88.8 132.9 221.8 310.6 354.7 443.6 487.7 576.5 665.3 709.4 798.3 842.4 931.2 975.3 1064.2 1153.0 1197.1 1064.2: 44.1 132.9 221.8 265.9 354.7 398.8 487.7 576.5 620.6 709.4 753.5 842.4 886.5 975.3 1064.2 1108.3 1197.1 1108.3: 88.8 177.7 221.8 310.6 354.7 443.6 532.4 576.5 665.3 709.4 798.3 842.4 931.2 1020.1 1064.2 1153.0 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.1000 .. 88.8400 cents 44.74000 cents 44.10000 cents 2: 132.9400 .. 177.6800 cents 44.74000 cents 44.10000 cents 3: 177.0400 .. 221.7800 cents 44.74000 cents -0.64000 cents 4: 265.8800 .. 310.6200 cents 44.74000 cents 44.10000 cents 5: 309.9800 .. 354.7200 cents 44.74000 cents -0.64000 cents 6: 398.8200 .. 443.5600 cents 44.74000 cents 44.10000 cents 7: 487.6600 .. 532.4000 cents 44.74000 cents 44.10000 cents 8: 531.7600 .. 576.5000 cents 44.74000 cents -0.64000 cents 9: 620.6000 .. 665.3400 cents 44.74000 cents 44.10000 cents 10: 664.7000 .. 709.4400 cents 44.74000 cents -0.64000 cents 11: 753.5400 .. 798.2800 cents 44.74000 cents 44.10000 cents 12: 842.3800 .. 887.1200 cents 44.74000 cents 44.10000 cents 13: 886.4800 .. 931.2200 cents 44.74000 cents -0.64000 cents 14: 975.3200 .. 1020.0600 cents 44.74000 cents 44.10000 cents 15: 1019.4200 .. 1064.1600 cents 44.74000 cents -0.64000 cents 16: 1108.2600 .. 1153.0000 cents 44.74000 cents 44.10000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 44.10000 cents, class 1 Average step (divided formal octave): 70.4176 cents Largest one step interval : 88.84000 cents Average / Smallest step : 1.596772 Largest / Average step : 1.261616 Largest / Smallest step : 2.014512 Median interval of one step : 88.84000 cents, amount: 10 Most common interval of one step : 88.84000 cents, amount: 10 Least squares average step : 70.26726 cents, oct.: 1194.54343 cents Scale is not proper Scale has Myhill's property chromas: 44.74000 cents and 0.64000 cents, ratio: 69.906250 generators: 5 of 354.72000 cents and 12 of 842.38000 cents ET pair of linear temperament : 10&27 Scale is distributional even Scale is a mode of a 1819-tone equal temperament with octave 1197.100 cents degrees: 135 202 337 404 539 674 741 876 943 1078 1145 1280 1415 1482 1617 1684 1819 generators: 539 and 1280 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABAABABA Step pattern size order : LSLSLLSLSLSLLSLSL Scale is a Constant Structure, by a margin of 0.64000 cents Scale diversity : 1.167184 Lumma stability : 0.405229 Lumma impropriety factor : 0.003208 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 0.64000 cents Most common intervals : 354.72000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 443.560 842.380 cents Most common triad is 0.0 354.720 842.380 cents, amount: 15 Number of recognisable fifths : 15, average 709.4400 cents Number of recognisable fourths : 15, average 487.6600 cents Scale contains two identical conjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.8930 c. M: 21.0541 c. 27: 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 P M ME I SD: 0.1161 c. M:-0.1896 c. 955: 71 35 71 35 71 71 35 71 35 71 35 71 71 35 71 35 71 N M DE I SD: 0.1113 c. M:-0.1818 c. 982: 73 36 73 36 73 73 36 73 36 73 36 73 73 36 73 36 73 N M DE I SD: 0.1051 c. M:-0.1716 c. 1009: 75 37 75 37 75 75 37 75 37 75 37 75 75 37 75 37 75 N M DE I SD: 0.0991 c. M:-0.1619 c. 1036: 77 38 77 38 77 77 38 77 38 77 38 77 77 38 77 38 77 N M DE I SD: 0.0935 c. M:-0.1527 c. 1063: 79 39 79 39 79 79 39 79 39 79 39 79 79 39 79 39 79 N M DE I SD: 0.0882 c. M:-0.1440 c. 1090: 81 40 81 40 81 81 40 81 40 81 40 81 81 40 81 40 81 N M DE I SD: 0.0831 c. M:-0.1358 c. 1117: 83 41 83 41 83 83 41 83 41 83 41 83 83 41 83 41 83 N M DE I SD: 0.0783 c. M:-0.1279 c. 1144: 85 42 85 42 85 85 42 85 42 85 42 85 85 42 85 42 85 N M DE I SD: 0.0737 c. M:-0.1204 c. 1171: 87 43 87 43 87 87 43 87 43 87 43 87 87 43 87 43 87 N M DE I SD: 0.0694 c. M:-0.1133 c. 1198: 89 44 89 44 89 89 44 89 44 89 44 89 89 44 89 44 89 N M DE I SD: 0.0652 c. M:-0.1064 c. 1225: 91 45 91 45 91 91 45 91 45 91 45 91 91 45 91 45 91 N M DE I SD: 0.0612 c. M:-0.0999 c. 1252: 93 46 93 46 93 93 46 93 46 93 46 93 93 46 93 46 93 N M DE I SD: 0.0574 c. M:-0.0937 c. 1279: 95 47 95 47 95 95 47 95 47 95 47 95 95 47 95 47 95 N M DE I SD: 0.0537 c. M:-0.0877 c. 1306: 97 48 97 48 97 97 48 97 48 97 48 97 97 48 97 48 97 N M DE I SD: 0.0502 c. M:-0.0820 c. 1333: 99 49 99 49 99 99 49 99 49 99 49 99 99 49 99 49 99 N M DE I SD: 0.0468 c. M:-0.0765 c. 1360: 101 50 101 50 101 101 50 101 50 101 50 101 101 50 101 50 101 N M DE I SD: 0.0436 c. M:-0.0712 c. 1387: 103 51 103 51 103 103 51 103 51 103 51 103 103 51 103 51 103 N M DE I SD: 0.0405 c. M:-0.0661 c. 1414: 105 52 105 52 105 105 52 105 52 105 52 105 105 52 105 52 105 N M DE I SD: 0.0375 c. M:-0.0612 c. 1441: 107 53 107 53 107 107 53 107 53 107 53 107 107 53 107 53 107 N M DE I SD: 0.0346 c. M:-0.0565 c. 1468: 109 54 109 54 109 109 54 109 54 109 54 109 109 54 109 54 109 N M DE I SD: 0.0318 c. M:-0.0520 c. 1495: 111 55 111 55 111 111 55 111 55 111 55 111 111 55 111 55 111 N M DE I SD: 0.0292 c. M:-0.0476 c. 1522: 113 56 113 56 113 113 56 113 56 113 56 113 113 56 113 56 113 N M DE I SD: 0.0266 c. M:-0.0434 c. 1549: 115 57 115 57 115 115 57 115 57 115 57 115 115 57 115 57 115 N M DE I SD: 0.0241 c. M:-0.0394 c. 1576: 117 58 117 58 117 117 58 117 58 117 58 117 117 58 117 58 117 N M DE I SD: 0.0217 c. M:-0.0354 c. 1603: 119 59 119 59 119 119 59 119 59 119 59 119 119 59 119 59 119 N M DE I SD: 0.0194 c. M:-0.0316 c. 1630: 121 60 121 60 121 121 60 121 60 121 60 121 121 60 121 60 121 N M DE I SD: 0.0171 c. M:-0.0280 c. 1657: 123 61 123 61 123 123 61 123 61 123 61 123 123 61 123 61 123 N M DE I SD: 0.0150 c. M: 0.0244 c. 1684: 125 62 125 62 125 125 62 125 62 125 62 125 125 62 125 62 125 N M DE I SD: 0.0129 c. M:-0.0210 c. 1711: 127 63 127 63 127 127 63 127 63 127 63 127 127 63 127 63 127 N M DE I SD: 0.0108 c. M:-0.0177 c. 1738: 129 64 129 64 129 129 64 129 64 129 64 129 129 64 129 64 129 N M DE I SD: 0.0089 c. M:-0.0145 c. 1765: 131 65 131 65 131 131 65 131 65 131 65 131 131 65 131 65 131 N M DE I SD: 0.0069 c. M:-0.0113 c. 1792: 133 66 133 66 133 133 66 133 66 133 66 133 133 66 133 66 133 N M DE I SD: 0.0051 c. M:-0.0083 c. 1819: 135 67 135 67 135 135 67 135 67 135 67 135 135 67 135 67 135 N M DE I SD: 0.0033 c. M:-0.0054 c. 1846: 137 68 137 68 137 137 68 137 68 137 68 137 137 68 137 68 137 N M DE I SD: 0.0015 c. M:-0.0025 c. 1873: 139 69 139 69 139 139 69 139 69 139 69 139 139 69 139 69 139 N M DE I SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 2.9000 cents 2 .. 4 match: 2 H SD: 4.0136 cents 3 .. 6 match: 3 H SD: 14.4471 cents 4 .. 8 match: 4 H SD: 8.3095 cents 5 .. 10 match: 5 H SD: 12.9342 cents 6 .. 12 match: 6 H SD: 7.7360 cents 7 .. 14 match: 7 H SD: 4.6881 cents 8 .. 16 match: 8 H SD: 6.2015 cents 9 .. 18 match: 9 H SD: 7.3298 cents 10 .. 20 match: 10 H SD: 7.4477 cents 11 .. 22 match: 11 H SD: 6.5568 cents 12 .. 24 match: 12 H SD: 6.2516 cents 13 .. 26 match: 13 H SD: 4.6586 cents 14 .. 28 match: 14 H SD: 5.1877 cents 15 .. 30 match: 11 SD: 6.4609 cents 16 .. 32 match: 14 S SD: 5.0873 cents 17 .. 34 match: 14 S SD: 4.8832 cents 18 .. 36 match: 16 SD: 3.7990 cents 19 .. 38 match: 12 SD: 4.9850 cents 20 .. 40 match: 16 SD: 4.4363 cents 21 .. 42 match: 15 SD: 3.0525 cents 22 .. 44 match: 16 SD: 3.4327 cents 23 .. 46 match: 16 SD: 3.6683 cents 24 .. 48 match: 17 SD: 3.3055 cents 25 .. 50 match: 17 SD: 3.2417 cents 26 .. 52 match: 15 SD: 3.3517 cents 27 .. 54 match: 16 SD: 3.0974 cents 28 .. 56 match: 17 SD: 2.9144 cents 29 .. 58 match: 16 SD: 3.4268 cents 30 .. 60 match: 16 SD: 2.4936 cents 31 .. 62 match: 16 SD: 2.4979 cents 33 .. 66 match: 16 SD: 3.0316 cents 34 .. 68 match: 17 SD: 2.6224 cents 35 .. 70 match: 17 SD: 1.9284 cents 37 .. 74 match: 17 SD: 1.7383 cents 48 .. 96 match: 17 SD: 1.6917 cents 49 .. 98 match: 17 SD: 1.5172 cents 53 .. 106 match: 17 SD: 1.3196 cents 58 .. 116 match: 17 SD: 1.2379 cents 59 .. 118 match: 17 SD: 1.2294 cents 61 .. 122 match: 17 SD: 1.0962 cents 73 .. 146 match: 17 SD: 0.9991 cents 79 .. 158 match: 17 SD: 0.8015 cents 96 .. 192 match: 17 SD: 0.7952 cents 97 .. 194 match: 17 SD: 0.7560 cents 102 .. 204 match: 17 SD: 0.7488 cents 110 .. 220 match: 17 SD: 0.7050 cents 114 .. 228 match: 17 SD: 0.5909 cents 126 .. 252 match: 17 SD: 0.5675 cents 132 .. 264 match: 17 SD: 0.5273 cents 154 .. 307 match: 17 SD: 0.5090 cents 167 .. 333 match: 17 SD: 0.4505 cents 174 .. 347 match: 17 SD: 0.3979 cents 185 .. 369 match: 17 SD: 0.3437 cents 211 .. 421 match: 17 SD: 0.3180 cents 212 .. 423 match: 17 SD: 0.3050 cents 225 .. 449 match: 17 SD: 0.2756 cents 251 .. 501 match: 17 SD: 0.2678 cents 264 .. 527 match: 17 SD: 0.2074 cents 338 .. 675 match: 17 SD: 0.1903 cents 378 .. 755 match: 17 SD: 0.1864 cents 387 .. 773 match: 17 SD: 0.1674 cents 415 .. 829 match: 17 SD: 0.1573 cents 418 .. 835 match: 17 SD: 0.1540 cents 452 .. 902 match: 17 SD: 0.1499 cents 476 .. 950 match: 17 SD: 0.1088 cents