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