Scala analysis: fortheloveofa5th

for the love of a 5th

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        137.322 cents     137.321990
  2:        274.169 cents     274.168630
  3:        411.015 cents     411.015270
  4:        547.862 cents     547.861910
  5:        651.126 cents     651.125700
  6:        788.448 cents     788.447690
  7:        925.294 cents     925.294330
  8:       1062.141 cents    1062.140970
  9:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        137.8590 cents    137.8590
  1:        137.3220 cents    137.3220
  2:        136.8466 cents    136.8466
  3:        136.8466 cents    136.8466
  4:        136.8466 cents    136.8466
  5:        103.2638 cents    103.2638
  6:        137.3220 cents    137.3220
  7:        136.8466 cents    136.8466
  8:        136.8466 cents    136.8466
  9:        137.8590 cents    137.8590
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 103.26379 cents
  1:   5 136.84664 cents
  1:   2 137.32199 cents
  1:   1 137.85903 cents
  2:   1 240.11043 cents
  2:   1 240.58578 cents
  2:   3 273.69328 cents
  2:   2 274.16863 cents
  2:   1 274.70567 cents
  2:   1 275.18102 cents
  3:   1 376.95707 cents
  3:   2 377.43242 cents
  3:   1 410.53992 cents
  3:   2 411.01527 cents
  3:   1 411.55231 cents
  3:   2 412.02766 cents
  4:   1 513.80371 cents
  4:   3 514.27906 cents
  4:   1 547.86191 cents
  4:   4 548.87430 cents
  5:   4 651.12570 cents
  5:   1 652.13809 cents
  5:   3 685.72094 cents
  5:   1 686.19629 cents
  6:   2 787.97234 cents
  6:   1 788.44769 cents
  6:   2 788.98473 cents
  6:   1 789.46008 cents
  6:   2 822.56758 cents
  6:   1 823.04293 cents
  7:   1 924.81898 cents
  7:   1 925.29433 cents
  7:   2 925.83137 cents
  7:   3 926.30672 cents
  7:   1 959.41422 cents
  7:   1 959.88957 cents
  8:   1 1062.14097 cents
  8:   2 1062.67801 cents
  8:   5 1063.15336 cents
  8:   1 1096.73621 cents
Highest number of different intervals for one interval class: 6
Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6     7     8      9     
 0.0   : 137.3 274.2 411.0 547.9 651.1 788.4 925.3 1062.1 1200.0
 137.3 : 136.8 273.7 410.5 513.8 651.1 788.0 924.8 1062.7 1200.0
 274.2 : 136.8 273.7 377.0 514.3 651.1 788.0 925.8 1063.2 1200.0
 411.0 : 136.8 240.1 377.4 514.3 651.1 789.0 926.3 1063.2 1200.0
 547.9 : 103.3 240.6 377.4 514.3 652.1 789.5 926.3 1063.2 1200.0
 651.1 : 137.3 274.2 411.0 548.9 686.2 823.0 959.9 1096.7 1200.0
 788.4 : 136.8 273.7 411.6 548.9 685.7 822.6 959.4 1062.7 1200.0
 925.3 : 136.8 274.7 412.0 548.9 685.7 822.6 925.8 1063.2 1200.0
 1062.1: 137.9 275.2 412.0 548.9 685.7 789.0 926.3 1063.2 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  103.2638  .. 137.8590 cents      34.59524 cents                     103.26379 cents
  2:  240.1104  .. 275.1810 cents      35.07059 cents                     102.25140 cents
  3:  376.9571  .. 412.0277 cents      35.07059 cents                     101.77605 cents
  4:  513.8037  .. 548.8743 cents      35.07059 cents                     101.77605 cents
  5:  651.1257  .. 686.1963 cents      35.07059 cents                     102.25140 cents
  6:  787.9723  .. 823.0429 cents      35.07059 cents                     101.77605 cents
  7:  924.8190  .. 959.8896 cents      35.07059 cents                     101.77605 cents
  8:  1062.1410 .. 1096.7362 cents     34.59524 cents                     102.25140 cents
SHOW DATA
Number of notes                     : 9
-- Interval properties --
Smallest interval                   : 103.26379 cents, class 1
Average step (divided formal octave): 133.3333 cents
Largest one step interval           : 137.85903 cents
Average / Smallest step             : 1.291192
Largest / Average step              : 1.033943
Largest / Smallest step             : 1.335018
Median interval of one step         : 136.84664 cents, amount: 5
Most common interval of one step    : 136.84664 cents, amount: 5
Least squares average step          : 132.87949 cents, oct.:  1195.91543 cents
Scale is strictly proper
Step pattern alph. order: ABBBCABBD
Step pattern size order : CBBBACBBD
Scale is a Constant Structure, by a margin of 101.77605 cents
Scale diversity                     : 1.200325
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.766988
Rothenberg efficiency               : 0.346120   redundancy: 0.653880
Efficiency x scale size             : 3.115079
Number of different interval sizes  : 40 = 5.00000 / class
Number of one step interval sizes   : 4
Highest interval variety            : 6
Mean interval variety               : 5.00000 = 5
Median interval variety             : 4
Lowest interval variety             : 4
Smallest interval difference        : 0.47535 cents
Most common intervals               : 136.84664 cents & inv., amount: 5
Most common triad is 0.0 136.847 1063.153 cents, amount: 3
Number of recognisable fifths       : 4, average 685.8398 cents
Number of appreciable fifths        : 0
Best fifths form a closed circle
Formal octave complements present   : 1 = 11.1111%
-- Rational properties --
FIT/MODE
  9:  1 1 1 1 1 1 1 1 1  SP B ME I SD: 9.8019 c. M:-15.5410 c.  Pelog Nawanada: Sunda
 26:  3 3 3 3 2 3 3 3 3  SP M ME I SD: 3.4717 c. M:-5.9842 c. 
 35:  4 4 4 4 3 4 4 4 4  SP M ME I SD: 0.4105 c. M:-0.7162 c. 
 671: 77 76 77 76 58 77 76 77 77  SP        SD: 0.4111 c. M: 0.7042 c. 
 682: 78 78 78 77 59 78 78 78 78  SP        SD: 0.4092 c. M:-0.7149 c. 
 687: 79 78 78 79 59 78 79 78 79  SP        SD: 0.4674 c. M: 0.6748 c. 
 688: 79 78 79 78 59 79 79 78 79  SP        SD: 0.4473 c. M:-0.8685 c. 
 691: 79 79 79 79 59 79 79 79 79  SP M DE I SD: 0.4426 c. M:-0.9080 c. 
 695: 80 79 79 79 60 80 79 79 80  SP        SD: 0.4197 c. M:-0.8075 c. 
 696: 80 79 79 80 60 79 80 79 80  SP        SD: 0.4649 c. M: 0.6704 c. 
 697: 80 79 80 79 60 80 79 80 80  SP        SD: 0.3965 c. M: 0.7606 c. 
 706: 81 80 81 80 61 81 80 81 81  SP        SD: 0.3825 c. M: 0.6484 c. 
 722: 83 82 82 83 62 82 83 82 83  SP        SD: 0.4479 c. M: 0.6361 c. 
 723: 83 82 83 82 62 83 82 83 83  SP        SD: 0.4217 c. M: 0.8130 c. 
 728: 83 83 83 83 63 83 83 83 84  SP   T3   SD: 0.4978 c. M: 0.6092 c. 
 729: 83 84 83 83 63 83 83 83 84  SP        SD: 0.4819 c. M:-0.7285 c. 
 730: 84 83 83 83 63 84 83 83 84  SP        SD: 0.3923 c. M:-0.7602 c. 
 732: 84 83 84 83 63 84 83 84 84  SP        SD: 0.3710 c. M: 0.7042 c. 
 741: 85 84 85 84 64 85 84 85 85  SP        SD: 0.3575 c. M: 0.5980 c. 
 763: 87 87 87 87 66 87 87 87 88  SP   T3   SD: 0.4609 c. M: 0.5487 c. 
 765: 88 87 87 87 66 88 87 87 88  SP        SD: 0.3682 c. M:-0.7172 c. 
 767: 88 87 88 87 66 88 87 88 88  SP        SD: 0.3488 c. M: 0.6529 c. 
 776: 89 88 89 88 67 89 88 89 89  SP        SD: 0.3356 c. M: 0.5521 c. 
 798: 91 91 91 91 69 91 91 91 92  SP   T3   SD: 0.4276 c. M: 0.4935 c. 
 800: 92 91 91 91 69 92 91 91 92  SP        SD: 0.3470 c. M:-0.6780 c. 
 802: 92 91 92 91 69 92 91 92 92  SP        SD: 0.3294 c. M: 0.6061 c. 
 811: 93 92 93 92 70 93 92 93 93  SP        SD: 0.3165 c. M: 0.5101 c. 
 833: 95 95 95 95 72 95 95 95 96  SP   T3   SD: 0.3974 c. M: 0.4672 c. 
 835: 96 95 95 95 72 96 95 95 96  SP        SD: 0.3285 c. M:-0.6421 c. 
 837: 96 95 96 95 72 96 95 96 96  SP        SD: 0.3125 c. M: 0.5631 c. 
 846: 97 96 97 96 73 97 96 97 97  SP        SD: 0.2998 c. M: 0.4716 c. 
 868: 99 99 99 99 75 99 99 99 100  SP   T3   SD: 0.3701 c. M: 0.4556 c. 
 870: 100 99 99 99 75 100 99 99 100  SP        SD: 0.3122 c. M:-0.6090 c. 
 872: 100 99 100 99 75 100 99 100 100  SP        SD: 0.2979 c. M: 0.5237 c. 
 881: 101 100 101 100 76 101 100 101 101  SP        SD: 0.2854 c. M: 0.4362 c. 
 907: 104 103 104 103 78 104 103 104 104  SP        SD: 0.2852 c. M: 0.4873 c. 
 916: 105 104 105 104 79 105 104 105 105  SP        SD: 0.2730 c. M: 0.4035 c. 
 929: 106 106 106 106 80 106 106 106 107  SP   T3   SD: 0.3222 c. M: 0.5037 c. 
 931: 107 106 106 106 80 107 106 106 107  SP        SD: 0.2872 c. M:-0.5942 c. 
 940: 108 107 107 107 81 108 107 107 108  SP        SD: 0.2858 c. M:-0.5504 c. 
 942: 108 107 108 107 81 108 107 108 108  SP        SD: 0.2744 c. M: 0.4536 c. 
 951: 109 108 109 108 82 109 108 109 109  SP        SD: 0.2624 c. M: 0.3732 c. 
 964: 110 110 110 110 83 110 110 110 111  SP   T3   SD: 0.3017 c. M: 0.4809 c. 
 966: 111 110 110 110 83 111 110 110 111  SP        SD: 0.2767 c. M:-0.5662 c. 
 975: 112 111 111 111 84 112 111 111 112  SP        SD: 0.2751 c. M:-0.5242 c. 
 977: 112 111 112 111 84 112 111 112 112  SP        SD: 0.2651 c. M:-0.4484 c. 
 986: 113 112 113 112 85 113 112 113 113  SP        SD: 0.2533 c. M: 0.3450 c. 
 999: 114 114 114 114 86 114 114 114 115  SP   T3   SD: 0.2831 c. M: 0.4597 c. 
 1001: 115 114 114 114 86 115 114 114 115  SP        SD: 0.2677 c. M:-0.5401 c. 
 1010: 116 115 115 115 87 116 115 115 116  SP        SD: 0.2660 c. M:-0.4998 c. 
 1012: 116 115 116 115 87 116 115 116 116  SP        SD: 0.2573 c. M:-0.4472 c. 
 1021: 117 116 117 116 88 117 116 117 117  SP        SD: 0.2457 c. M:-0.3468 c. 
 1034: 118 118 118 118 89 118 118 118 119  SP   T3   SD: 0.2662 c. M: 0.4400 c. 
 1036: 119 118 118 118 89 119 118 118 119  SP        SD: 0.2601 c. M:-0.5158 c. 
 1045: 120 119 119 119 90 120 119 119 120  SP        SD: 0.2582 c. M:-0.4771 c. 
 1047: 120 119 120 119 90 120 119 120 120  SP        SD: 0.2507 c. M:-0.4460 c. 
 1056: 121 120 121 120 91 121 120 121 121  SP        SD: 0.2393 c. M:-0.3590 c. 
 1069: 122 122 122 122 92 122 122 122 123  SP   T3   SD: 0.2510 c. M: 0.4215 c. 
 1082: 124 123 124 123 93 124 123 124 124  SP        SD: 0.2453 c. M:-0.4450 c. 
 1091: 125 124 125 124 94 125 124 125 125  SP        SD: 0.2341 c. M:-0.3705 c. 
 1104: 126 126 126 126 95 126 126 126 127  SP   T3   SD: 0.2373 c. M: 0.4042 c. 
 1126: 129 128 129 128 97 129 128 129 129  SP        SD: 0.2299 c. M:-0.3812 c. 
 1139: 130 130 130 130 98 130 130 130 131  SP   T3   SD: 0.2250 c. M: 0.3880 c. 
 1174: 134 134 134 134 101 134 134 134 135  SP   T3   SD: 0.2141 c. M: 0.3727 c. 
 1183: 135 135 135 135 102 135 135 135 136  SP   T3   SD: 0.2140 c. M: 0.3820 c. 
 1209: 138 138 138 138 104 138 138 138 139  SP   T3   SD: 0.2044 c. M: 0.3584 c. 
 1218: 139 139 139 139 105 139 139 139 140  SP   T3   SD: 0.2041 c. M: 0.3762 c. 
 1233: 141 141 140 141 106 141 141 140 142  SP        SD: 0.2075 c. M: 0.3405 c. 
 1244: 142 142 142 142 107 142 142 142 143  SP   T3   SD: 0.1958 c. M: 0.3448 c. 
 1253: 143 143 143 143 108 143 143 143 144  SP   T3   SD: 0.1954 c. M: 0.3707 c. 
 1268: 145 145 144 145 109 145 145 144 146  SP        SD: 0.1993 c. M: 0.3113 c. 
 1279: 146 146 146 146 110 146 146 146 147  SP   T3   SD: 0.1883 c. M: 0.3400 c. 
 1288: 147 147 147 147 111 147 147 147 148  SP   T3   SD: 0.1877 c. M: 0.3655 c. 
 1303: 149 149 148 149 112 149 149 148 150  SP        SD: 0.1921 c. M: 0.2837 c. 
 1314: 150 150 150 150 113 150 150 150 151  SP   T3   SD: 0.1819 c. M: 0.3357 c. 
 1323: 151 151 151 151 114 151 151 151 152  SP   T3   SD: 0.1811 c. M: 0.3605 c. 
 1338: 153 153 152 153 115 153 153 152 154  SP        SD: 0.1859 c. M:-0.2708 c. 
 1349: 154 154 154 154 116 154 154 154 155  SP   T3   SD: 0.1765 c. M: 0.3316 c. 
 1358: 155 155 155 155 117 155 155 155 156  SP   T3   SD: 0.1755 c. M: 0.3559 c. 
 1373: 157 157 156 157 118 157 157 156 158  SP        SD: 0.1806 c. M:-0.2701 c. 
 1384: 158 158 158 158 119 158 158 158 159  SP   T3   SD: 0.1719 c. M: 0.3278 c. 
 1393: 159 159 159 159 120 159 159 159 160  SP   T3   SD: 0.1707 c. M: 0.3514 c. 
 1419: 162 162 162 162 122 162 162 162 163  SP   T3   SD: 0.1682 c. M: 0.3241 c. 
 1428: 163 163 163 163 123 163 163 163 164  SP   T3   SD: 0.1668 c. M: 0.3472 c. 
 1454: 166 166 166 166 125 166 166 166 167  SP   T3   SD: 0.1652 c. M: 0.3206 c. 
 1463: 167 167 167 167 126 167 167 167 168  SP   T3   SD: 0.1637 c. M: 0.3432 c. 
 1489: 170 170 170 170 128 170 170 170 171  SP   T3   SD: 0.1630 c. M: 0.3173 c. 
 1498: 171 171 171 171 129 171 171 171 172  SP   T3   SD: 0.1613 c. M: 0.3393 c. 
 1533: 175 175 175 175 132 175 175 175 176  SP   T3   SD: 0.1595 c. M: 0.3357 c. 
 1568: 179 179 179 179 135 179 179 179 180  SP   T3   SD: 0.1584 c. M: 0.3322 c. 
 1603: 183 183 183 183 138 183 183 183 184  SP   T3   SD: 0.1577 c. M: 0.3289 c. 
 1638: 187 187 187 187 141 187 187 187 188  SP   T3   SD: 0.1575 c. M: 0.3257 c. 
 1712: 196 195 195 196 147 196 195 195 197  SP        SD: 0.1582 c. M:-0.2689 c. 
 1720: 197 196 196 196 148 197 196 196 198  SP        SD: 0.1532 c. M: 0.2805 c. 
 1729: 198 197 197 197 149 198 197 197 199  SP        SD: 0.1475 c. M: 0.2621 c. 
 1755: 201 200 200 200 151 201 200 200 202  SP        SD: 0.1425 c. M: 0.2606 c. 
 1764: 202 201 201 201 152 202 201 201 203  SP        SD: 0.1365 c. M: 0.2429 c. 
 1790: 205 204 204 204 154 205 204 204 206  SP        SD: 0.1323 c. M: 0.2415 c. 
 1799: 206 205 205 205 155 206 205 205 207  SP        SD: 0.1259 c. M: 0.2243 c. 
 1825: 209 208 208 208 157 209 208 208 210  SP        SD: 0.1225 c. M: 0.2232 c. 
 1834: 210 209 209 209 158 210 209 209 211  SP        SD: 0.1157 c. M: 0.2065 c. 
 1860: 213 212 212 212 160 213 212 212 214  SP        SD: 0.1132 c. M: 0.2055 c. 
 1869: 214 213 213 213 161 214 213 213 215  SP        SD: 0.1060 c. M: 0.1894 c. 
 1895: 217 216 216 216 163 217 216 216 218  SP        SD: 0.1043 c. M: 0.1885 c. 
 1904: 218 217 217 217 164 218 217 217 219  SP        SD: 0.0966 c. M: 0.1728 c. 
 1930: 221 220 220 220 166 221 220 220 222  SP        SD: 0.0958 c. M: 0.1721 c. 
 1939: 222 221 221 221 167 222 221 221 223  SP        SD: 0.0875 c. M: 0.1569 c. 
 1965: 225 224 224 224 169 225 224 224 226  SP        SD: 0.0878 c. M: 0.1562 c. 
 1974: 226 225 225 225 170 226 225 225 227  SP        SD: 0.0788 c. M: 0.1415 c. 
 2000: 229 228 228 228 172 229 228 228 230  SP        SD: 0.0803 c. M: 0.1410 c. 
 2009: 230 229 229 229 173 230 229 229 231  SP        SD: 0.0705 c. M: 0.1267 c. 
 2035: 233 232 232 232 175 233 232 232 234  SP        SD: 0.0732 c. M: 0.1262 c. 
 2044: 234 233 233 233 176 234 233 233 235  SP        SD: 0.0624 c. M: 0.1124 c. 
 2070: 237 236 236 236 178 237 236 236 238  SP        SD: 0.0665 c. M: 0.1120 c. 
 2079: 238 237 237 237 179 238 237 237 239  SP        SD: 0.0547 c. M: 0.0986 c. 
 2114: 242 241 241 241 182 242 241 241 243  SP        SD: 0.0472 c. M: 0.0852 c. 
 2149: 246 245 245 245 185 246 245 245 247  SP        SD: 0.0402 c. M: 0.0722 c. 
 2184: 250 249 249 249 188 250 249 249 251  SP        SD: 0.0334 c. M: 0.0597 c. 
 2219: 254 253 253 253 191 254 253 253 255  SP        SD: 0.0272 c. M: 0.0476 c. 
 2254: 258 257 257 257 194 258 257 257 259  SP        SD: 0.0215 c. M: 0.0358 c. 
 2289: 262 261 261 261 197 262 261 261 263  SP        SD: 0.0168 c. M:-0.0306 c. 
 2324: 266 265 265 265 200 266 265 265 267  SP        SD: 0.0137 c. M:-0.0274 c. 
 2359: 270 269 269 269 203 270 269 269 271  SP        SD: 0.0131 c. M:-0.0243 c. 
 2394: 274 273 273 273 206 274 273 273 275  SP        SD: 0.0152 c. M:-0.0235 c. 
FIT/HARMONIC
 1 x x x x x x x x 2  S SD: 0.0000 cents
 2 x x x x 3 x x x 4  S SD: 25.4147 cents
 3 x x x 4 x x 5 x 6  S SD: 21.4928 cents
 4 x x 5 x 6 x 7 x 8  S SD: 17.8339 cents
 5 x 6 x 7 x 8 x 9:10  S SD: 14.8887 cents
 6 x 7 x 8:9 x 10:11:12  S SD: 13.9020 cents
 7 x 8:9 x 10:11:12:13:14  S SD: 8.7454 cents
 8:9 x 10:11:12:13:14:15:16  S SD: 14.2136 cents
 9:10 x 11:12:13:14:15:17:18    SD: 13.9830 cents
 10:11:12:13:14:15:16:17:18:20  S SD: 11.5482 cents
 11:12:13:14:15:16:17:19:20:22    SD: 6.0412 cents
 19:21:22:24:26:28:30:32:35:38    SD: 5.8022 cents
 21:23:25:27:29:31:33:36:39:42    SD: 5.6602 cents
 22:24:26:28:30:32:35:38:41:44    SD: 4.2852 cents
 24:26:28:30:33:35:38:41:44:48    SD: 3.3302 cents
 33:36:39:42:45:48:52:56:61:66    SD: 2.8743 cents
 35:38:41:44:48:51:55:60:65:70    SD: 2.3187 cents
 40:43:47:51:55:58:63:68:74:80    SD: 2.2065 cents
 48:52:56:61:66:70:76:82:89:96    SD: 1.5162 cents
 59:64:69:75:81:86:93:101:109:118    SD: 0.9499 cents
 86:93:101:109:118:125:136:147:159:172    SD: 0.9362 cents
 97:105:114:123:133:141:153:166:179:194    SD: 0.9290 cents
 99:107:116:126:136:144:156:169:183:198    SD: 0.8840 cents
 105:114:123:133:144:153:166:179:194:210    SD: 0.8182 cents
 112:121:131:142:154:163:177:191:207:224    SD: 0.8058 cents
 116:126:136:147:159:169:183:198:214:232    SD: 0.7468 cents
 123:133:144:156:169:179:194:210:227:246    SD: 0.4375 cents
 156:169:183:198:214:227:246:266:288:312    SD: 0.4351 cents
 180:195:211:228:247:262:284:307:332:360    SD: 0.4236 cents
 191:207:224:242:262:278:301:326:353:382    SD: 0.4030 cents
 204:221:239:259:280:297:322:348:377:408    SD: 0.3859 cents
 215:233:252:273:295:313:339:367:397:430    SD: 0.3745 cents
 217:235:254:275:298:316:342:370:401:434    SD: 0.3447 cents
 228:247:267:289:313:332:360:389:421:456    SD: 0.3327 cents
 239:259:280:303:328:348:377:408:441:478    SD: 0.2960 cents
 269:291:315:341:369:392:424:459:497:538    SD: 0.2326 cents
 314:340:368:398:431:457:495:536:580:628    SD: 0.2079 cents
 385:417:451:488:528:561:607:657:711:770    SD: 0.1866 cents
 425:460:498:539:583:619:670:725:785:850    SD: 0.1291 cents
 484:524:567:614:664:705:763:826:894:968    SD: 0.1228 cents
 508:550:595:644:697:740:801:867:938:1016    SD: 0.0927 cents