Scala analysis: Uganda_Harp_125
125 (Harp), Uganda
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 239.000 cents 239.000000 2: 475.000 cents 475.000000 3: 713.000 cents 713.000000 4: 948.000 cents 948.000000 5: 1192.000 cents 1192.000000 6: 1437.000 cents 1437.000000 7: 1687.000 cents 1687.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 239.0000 cents 239.0000 2: 236.0000 cents 236.0000 3: 238.0000 cents 238.0000 4: 235.0000 cents 235.0000 5: 244.0000 cents 244.0000 6: 245.0000 cents 245.0000 7: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 235.00000 cents 1: 1 236.00000 cents 1: 1 238.00000 cents 1: 1 239.00000 cents 1: 1 244.00000 cents 1: 1 245.00000 cents 1: 1 250.00000 cents 2: 1 473.00000 cents 2: 1 474.00000 cents 2: 1 475.00000 cents 2: 1 479.00000 cents 2: 2 489.00000 cents 2: 1 495.00000 cents 3: 1 709.00000 cents 3: 1 713.00000 cents 3: 1 717.00000 cents 3: 1 724.00000 cents 3: 1 725.00000 cents 3: 1 734.00000 cents 3: 1 739.00000 cents 4: 1 948.00000 cents 4: 1 953.00000 cents 4: 1 962.00000 cents 4: 1 963.00000 cents 4: 1 970.00000 cents 4: 1 974.00000 cents 4: 1 978.00000 cents 5: 1 1192.00000 cents 5: 2 1198.00000 cents 5: 1 1208.00000 cents 5: 1 1212.00000 cents 5: 1 1213.00000 cents 5: 1 1214.00000 cents 6: 1 1437.00000 cents 6: 1 1442.00000 cents 6: 1 1443.00000 cents 6: 1 1448.00000 cents 6: 1 1449.00000 cents 6: 1 1451.00000 cents 6: 1 1452.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.66667 = 20/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 239.0 475.0 713.0 948.0 1192.0 1437.0 1687.0 239.0 : 236.0 474.0 709.0 953.0 1198.0 1448.0 1687.0 475.0 : 238.0 473.0 717.0 962.0 1212.0 1451.0 1687.0 713.0 : 235.0 479.0 724.0 974.0 1213.0 1449.0 1687.0 948.0 : 244.0 489.0 739.0 978.0 1214.0 1452.0 1687.0 1192.0: 245.0 495.0 734.0 970.0 1208.0 1443.0 1687.0 1437.0: 250.0 489.0 725.0 963.0 1198.0 1442.0 1687.0 1687.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 235.0000 .. 250.0000 cents 15.00000 cents 235.00000 cents 2: 473.0000 .. 495.0000 cents 22.00000 cents 223.00000 cents 3: 709.0000 .. 739.0000 cents 30.00000 cents 214.00000 cents 4: 948.0000 .. 978.0000 cents 30.00000 cents 209.00000 cents 5: 1192.0000 .. 1214.0000 cents 22.00000 cents 214.00000 cents 6: 1437.0000 .. 1452.0000 cents 15.00000 cents 223.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 235.00000 cents, class 1 Average step (divided formal octave): 241.0000 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.025532 Largest / Average step : 1.037344 Largest / Smallest step : 1.063830 Median interval of one step : 239.00000 cents, amount: 1 Least squares average step : 239.36429 cents, oct.: 1675.55000 cents Scale is strictly proper Scale is a mode of a 1687-tone equal temperament with octave 1687.000 cents degrees: 239 475 713 948 1192 1437 1687 Least number of segments generator : 844 of 844.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1206 of 1206.000 cents and inv. generated superset size: 497 = 490 more = 7100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : DBCAEFG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 209.00000 cents Scale diversity : 0.471736 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.920569 Rothenberg efficiency : 0.299320 redundancy: 0.700680 Efficiency x scale size : 2.095238 Number of different interval sizes : 40 = 6.66667 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.66667 = 20/3 Median interval variety : 6.5 Lowest interval variety : 6 Smallest interval difference : 1.00000 cents Most common intervals : 489.00000 cents & inv., amount: 2 Number of recognisable fifths : 3, average 713.0000 cents Number of appreciable fifths : 2, average 711.0000 cents Number of recognisable fourths : 3, average 491.0000 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 30.0000 cents: 1 2 3 4 5 6 Limited inverse transpositions with margin 30.0000 cents: 1 2 3 4 5 6 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 9.7027 c. M:-16.0000 c. Lebeng 41: 6 6 5 6 6 6 6 SP M ME S SD: 9.3381 c. M:-18.7561 c. 45: 6 7 6 6 7 6 7 SP M ME S SD: 9.8557 c. M: 14.0667 c. 47: 7 6 7 6 7 7 7 SP D3 S SD: 8.6208 c. M: 14.7660 c. 48: 7 7 6 7 7 7 7 SP M ME S SD: 8.1666 c. M:-17.0417 c. 52: 7 8 7 7 8 7 8 SP M ME S SD: 8.3667 c. M: 11.9038 c. 54: 8 7 8 7 8 8 8 SP D3 S SD: 6.8719 c. M:-10.9259 c. 61: 9 8 9 8 9 9 9 SP D3 S SD: 5.6897 c. M:-9.9016 c. 64: 9 9 9 9 9 10 9 SP M ME S SD: 5.3837 c. M:-12.7656 c. 68: 10 9 10 9 10 10 10 SP D3 S SD: 4.9313 c. M:-9.0882 c. 71: 10 10 10 10 10 10 11 SP M ME S SD: 4.6730 c. M: 11.3662 c. 75: 11 10 11 10 11 11 11 SP D3 S SD: 4.4951 c. M:-8.4267 c. 78: 11 11 11 11 11 11 12 SP M ME S SD: 4.0112 c. M: 9.5385 c. 79: 11 11 11 11 12 11 12 SP D3 S SD: 5.8235 c. M: 8.4051 c. 82: 12 11 12 11 12 12 12 SP D3 S SD: 4.2960 c. M:-7.8780 c. 83: 12 11 12 12 12 12 12 SP M ME S SD: 5.6721 c. M: 7.5181 c. 85: 12 12 12 12 12 12 13 SP M ME S SD: 3.6248 c. M: 8.0118 c. 86: 12 12 12 12 13 12 13 SP D3 S SD: 4.8485 c. M: 6.8140 c. 89: 13 12 13 12 13 13 13 SP D3 S SD: 4.2601 c. M:-7.4157 c. 92: 13 13 13 13 13 13 14 SP M ME S SD: 3.4577 c. M: 6.7174 c. 93: 13 13 13 13 14 13 14 SP D3 S SD: 4.0987 c. M: 5.5484 c. 96: 14 13 14 13 14 14 14 SP D3 S SD: 4.3282 c. M:-7.4896 c. 99: 14 14 14 14 14 14 15 SP M ME S SD: 3.4505 c. M:-6.2626 c. 114: 16 16 16 16 16 17 17 SP D3 S SD: 3.4611 c. M: 8.1404 c. 116: 16 17 16 16 17 17 17 SP D3 SD: 3.3684 c. M: 6.3103 c. 121: 17 17 17 17 17 18 18 SP D3 S SD: 2.8647 c. M: 6.9174 c. 127: 18 18 18 17 19 18 19 SP SD: 3.1761 c. M: 4.8740 c. 128: 18 18 18 18 18 19 19 SP D3 S SD: 2.3934 c. M: 5.8281 c. 134: 19 19 19 18 20 19 20 SP SD: 3.0800 c. M:-4.6045 c. 135: 19 19 19 19 19 20 20 SP D3 S SD: 2.0526 c. M: 4.8519 c. 142: 20 20 20 20 20 21 21 SP D3 S SD: 1.8490 c. M: 3.9718 c. 149: 21 21 21 21 21 22 22 SP D3 S SD: 1.7796 c. M: 3.1745 c. 156: 22 22 22 22 22 23 23 SP D3 S SD: 1.8235 c. M:-3.6410 c. 191: 27 27 27 26 28 28 28 SP SD: 1.9251 c. M: 2.9267 c. 198: 28 28 28 27 29 29 29 SP SD: 1.9376 c. M:-2.9141 c. 203: 29 28 29 28 29 30 30 SP S SD: 1.7945 c. M: 3.6207 c. 210: 30 29 30 29 30 31 31 SP S SD: 1.6596 c. M: 3.0667 c. 217: 31 30 31 30 31 32 32 SP S SD: 1.5926 c. M: 2.5484 c. 221: 31 31 31 31 32 32 33 SP SD: 1.8968 c. M: 3.0860 c. 224: 32 31 32 31 32 33 33 SP S SD: 1.5887 c. M:-2.4688 c. 228: 32 32 32 32 33 33 34 SP SD: 1.6096 c. M: 2.6842 c. 235: 33 33 33 33 34 34 35 SP SD: 1.3649 c. M: 2.3064 c. 242: 34 34 34 34 35 35 36 SP SD: 1.1711 c. M: 1.9835 c. 249: 35 35 35 35 36 36 37 SP SD: 1.0393 c. M: 1.8715 c. 256: 36 36 36 36 37 37 38 SP SD: 0.9792 c. M: 1.7656 c. 262: 37 37 37 36 38 38 39 SP SD: 1.1833 c. M:-1.7214 c. 263: 37 37 37 37 38 38 39 SP SD: 0.9911 c. M: 1.6654 c. 296: 42 41 42 41 43 43 44 SP SD: 1.1504 c. M: 1.9561 c. 303: 43 42 43 42 44 44 45 SP SD: 0.9378 c. M: 1.7492 c. 310: 44 43 44 43 45 45 46 SP SD: 0.7549 c. M: 1.5516 c. 317: 45 44 45 44 46 46 47 SP SD: 0.6150 c. M: 1.3628 c. 324: 46 45 46 45 47 47 48 SP SD: 0.5389 c. M: 1.1821 c. 331: 47 46 47 46 48 48 49 SP SD: 0.5420 c. M: 1.0091 c. 338: 48 47 48 47 49 49 50 SP SD: 0.6143 c. M:-0.8787 c. 452: 64 63 64 63 65 66 67 SP SD: 0.6528 c. M: 1.3960 c. 459: 65 64 65 64 66 67 68 SP SD: 0.5643 c. M: 1.1765 c. 466: 66 65 66 65 67 68 69 SP SD: 0.5093 c. M: 0.9635 c. 473: 67 66 67 66 68 69 70 SP SD: 0.4949 c. M: 0.7569 c. 580: 82 81 82 81 84 84 86 SP SD: 0.4697 c. M: 0.8948 c. 715: 101 100 101 100 103 104 106 SP SD: 0.4987 c. M: 0.7524 c. 722: 102 101 102 101 104 105 107 SP SD: 0.4735 c. M: 0.6773 c. 729: 103 102 103 102 105 106 108 SP SD: 0.4669 c. M:-0.7929 c. 735: 104 103 104 102 106 107 109 SP SD: 0.4477 c. M:-0.8190 c. 742: 105 104 105 103 107 108 110 SP SD: 0.4399 c. M:-0.9057 c. 764: 108 107 108 106 111 111 113 SP SD: 0.4283 c. M: 0.7186 c. 767: 109 107 108 107 111 111 114 SP SD: 0.4241 c. M:-0.7432 c. 771: 109 108 109 107 112 112 114 SP SD: 0.4250 c. M: 0.5668 c. 774: 110 108 109 108 112 112 115 SP SD: 0.4075 c. M:-0.7545 c. 788: 112 110 111 110 114 114 117 SP SD: 0.4294 c. M:-0.7766 c. 790: 112 110 112 110 114 115 117 SP SD: 0.4096 c. M: 0.9316 c. 795: 113 111 112 111 115 115 118 SP SD: 0.4636 c. M:-0.7874 c. 797: 113 111 113 111 115 116 118 SP SD: 0.3973 c. M: 0.8620 c. 817: 116 114 115 114 118 119 121 SP SD: 0.3896 c. M: 0.6193 c. 824: 117 115 116 115 119 120 122 SP SD: 0.3451 c. M:-0.5376 c. 828: 117 116 117 115 120 120 123 SP SD: 0.4133 c. M: 0.6196 c. 831: 118 116 117 116 120 121 123 SP SD: 0.3176 c. M:-0.5499 c. 835: 118 117 118 116 121 121 124 SP SD: 0.3621 c. M: 0.5976 c. 838: 119 117 118 117 121 122 124 SP SD: 0.3105 c. M:-0.5621 c. 849: 120 119 120 118 123 123 126 SP SD: 0.3064 c. M: 0.5548 c. 852: 121 119 120 119 123 124 126 SP SD: 0.3548 c. M:-0.5857 c. 856: 121 120 121 119 124 124 127 SP SD: 0.3083 c. M: 0.5339 c. 863: 122 121 122 120 125 125 128 SP SD: 0.3295 c. M: 0.5133 c. 916: 130 128 129 128 132 133 136 SP SD: 0.3578 c. M:-0.4771 c. 920: 130 129 130 128 133 134 136 SP SD: 0.3535 c. M: 0.6196 c. 945: 134 132 133 132 137 137 140 SP SD: 0.3454 c. M: 0.7111 c. 991: 140 139 140 138 143 144 147 SP SD: 0.3314 c. M: 0.6751 c. 998: 141 140 141 139 144 145 148 SP SD: 0.3272 c. M: 0.6563 c. 1073: 152 150 151 150 155 156 159 SP SD: 0.3189 c. M: 0.7810 c. 1080: 153 151 152 151 156 157 160 SP SD: 0.2886 c. M: 0.7111 c. 1087: 154 152 153 152 157 158 161 SP SD: 0.2705 c. M: 0.6421 c. 1093: 155 153 154 152 158 159 162 SP SD: 0.2711 c. M: 0.4501 c. 1094: 155 153 154 153 158 159 162 SP SD: 0.2664 c. M: 0.5740 c. 1100: 156 154 155 153 159 160 163 SP SD: 0.2513 c. M:-0.4273 c. 1107: 157 155 156 154 160 161 164 SP SD: 0.2461 c. M:-0.4688 c. 1114: 158 156 157 155 161 162 165 SP SD: 0.2559 c. M:-0.5099 c. 1121: 159 157 158 156 162 163 166 SP SD: 0.2786 c. M:-0.5504 c. 1128: 160 158 159 157 163 164 167 SP SD: 0.3109 c. M:-0.5904 c. 1148: 163 160 162 160 166 167 170 SP SD: 0.2917 c. M:-0.5305 c. 1155: 164 161 163 161 167 168 171 SP SD: 0.2711 c. M:-0.5394 c. 1162: 165 162 164 162 168 169 172 SP SD: 0.2627 c. M:-0.5482 c. 1173: 166 164 166 163 170 170 174 SP SD: 0.2738 c. M: 0.3964 c. 1180: 167 165 167 164 171 171 175 SP SD: 0.2710 c. M:-0.4008 c. 1200: 170 168 169 167 174 174 178 SP SD: 0.2348 c. M: 0.4683 c. 1207: 171 169 170 168 175 175 179 SP SD: 0.2071 c. M: 0.3728 c. 1214: 172 170 171 169 176 176 180 SP SD: 0.1928 c. M:-0.2949 c. 1221: 173 171 172 170 177 177 181 SP SD: 0.1944 c. M:-0.3677 c. 1228: 174 172 173 171 178 178 182 SP SD: 0.2109 c. M:-0.4397 c. 1335: 189 187 188 186 193 194 198 SP SD: 0.2280 c. M: 0.3588 c. 1342: 190 188 189 187 194 195 199 SP SD: 0.1874 c. M: 0.2891 c. 1349: 191 189 190 188 195 196 200 SP SD: 0.1539 c. M: 0.2202 c. 1356: 192 190 191 189 196 197 201 SP SD: 0.1323 c. M:-0.2463 c. 1363: 193 191 192 190 197 198 202 SP SD: 0.1281 c. M:-0.2810 c. 1666: 236 233 235 232 241 242 247 SP SD: 0.1223 c. M: 0.2017 c. 1673: 237 234 236 233 242 243 248 SP SD: 0.0812 c. M: 0.1339 c. 1680: 238 235 237 234 243 244 249 SP SD: 0.0404 c. M: 0.0667 c. 1687: 239 236 238 235 244 245 250 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 x 3 S SD: 107.5519 cents 2 x x 3 x 4 x 5 S SD: 33.8686 cents 3 x 4 x 5:6:7:8 S SD: 15.0460 cents 4 x 5:6:7:8:9:11 SD: 19.5197 cents 6:7:8:9:10:12:14:16 S SD: 11.5691 cents 12:14:16:18:21:24:28:32 S SD: 7.7484 cents 14:16:18:21:24:28:32:37 SD: 6.5709 cents 18:21:24:27:31:36:41:48 SD: 6.0667 cents 19:22:25:29:33:38:44:50 SD: 4.8033 cents 20:23:26:30:35:40:46:53 SD: 4.7060 cents 22:25:29:33:38:44:50:58 SD: 4.1291 cents 25:29:33:38:43:50:57:66 SD: 4.0049 cents 26:30:34:39:45:52:60:69 SD: 3.1935 cents 34:39:45:51:59:68:78:90 SD: 2.6167 cents 41:47:54:62:71:82:94:109 SD: 1.5846 cents 67:77:88:101:116:133:154:178 SD: 1.3077 cents 80:92:105:121:138:159:183:212 SD: 1.2974 cents 82:94:108:124:142:163:188:217 SD: 0.8738 cents 88:101:116:133:152:175:202:233 SD: 0.7241 cents 102:117:134:154:176:203:234:270 SD: 0.7206 cents 108:124:142:163:187:215:248:286 SD: 0.5170 cents 177:203:233:267:306:352:406:469 SD: 0.4252 cents 196:225:258:296:339:390:450:519 SD: 0.3787 cents 202:232:266:305:349:402:463:535 SD: 0.3687 cents 218:250:287:329:377:434:500:578 SD: 0.3556 cents 222:255:292:335:384:442:509:588 SD: 0.2366 cents 310:356:408:468:536:617:711:821 SD: 0.1761 cents 351:403:462:530:607:699:805:930 SD: 0.1521 cents 406:466:534:613:702:808:931:1076 SD: 0.1452 cents 440:505:579:664:761:876:1009:1166 SD: 0.1381 cents 453:520:596:684:783:902:1039:1200 SD: 0.1347 cents 520:597:684:785:899:1035:1193:1378 SD: 0.1246 cents