Scala analysis: Uganda_Harp_138
138 (Harp), Uganda
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 236.000 cents 236.000000 2: 488.000 cents 488.000000 3: 745.000 cents 745.000000 4: 941.000 cents 941.000000 5: 1211.000 cents 1211.000000 6: 1444.000 cents 1444.000000 7: 1701.000 cents 1701.000000
SHOW/INTERVAL
0: 257.0000 cents 257.0000 1: 236.0000 cents 236.0000 2: 252.0000 cents 252.0000 3: 257.0000 cents 257.0000 4: 196.0000 cents 196.0000 5: 270.0000 cents 270.0000 6: 233.0000 cents 233.0000 7: 257.0000 cents 257.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 196.00000 cents 1: 1 233.00000 cents 1: 1 236.00000 cents 1: 1 252.00000 cents 1: 2 257.00000 cents 1: 1 270.00000 cents 2: 1 453.00000 cents 2: 1 466.00000 cents 2: 1 488.00000 cents 2: 1 490.00000 cents 2: 1 493.00000 cents 2: 1 503.00000 cents 2: 1 509.00000 cents 3: 1 699.00000 cents 3: 1 705.00000 cents 3: 1 723.00000 cents 3: 1 726.00000 cents 3: 2 745.00000 cents 3: 1 760.00000 cents 4: 1 941.00000 cents 4: 2 956.00000 cents 4: 1 975.00000 cents 4: 1 978.00000 cents 4: 1 996.00000 cents 4: 1 1002.00000 cents 5: 1 1192.00000 cents 5: 1 1198.00000 cents 5: 1 1208.00000 cents 5: 1 1211.00000 cents 5: 1 1213.00000 cents 5: 1 1235.00000 cents 5: 1 1248.00000 cents 6: 1 1431.00000 cents 6: 2 1444.00000 cents 6: 1 1449.00000 cents 6: 1 1465.00000 cents 6: 1 1468.00000 cents 6: 1 1505.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.33333 = 19/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 236.0 488.0 745.0 941.0 1211.0 1444.0 1701.0 236.0 : 252.0 509.0 705.0 975.0 1208.0 1465.0 1701.0 488.0 : 257.0 453.0 723.0 956.0 1213.0 1449.0 1701.0 745.0 : 196.0 466.0 699.0 956.0 1192.0 1444.0 1701.0 941.0 : 270.0 503.0 760.0 996.0 1248.0 1505.0 1701.0 1211.0: 233.0 490.0 726.0 978.0 1235.0 1431.0 1701.0 1444.0: 257.0 493.0 745.0 1002.0 1198.0 1468.0 1701.0 1701.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 196.0000 .. 270.0000 cents 74.00000 cents 196.00000 cents 2: 453.0000 .. 509.0000 cents 56.00000 cents 183.00000 cents 3: 699.0000 .. 760.0000 cents 61.00000 cents 190.00000 cents 4: 941.0000 .. 1002.0000 cents 61.00000 cents 181.00000 cents 5: 1192.0000 .. 1248.0000 cents 56.00000 cents 190.00000 cents 6: 1431.0000 .. 1505.0000 cents 74.00000 cents 183.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 196.00000 cents, class 1 Average step (divided formal octave): 243.0000 cents Largest one step interval : 270.00000 cents Average / Smallest step : 1.239796 Largest / Average step : 1.111111 Largest / Smallest step : 1.377551 Median interval of one step : 252.00000 cents, amount: 1 Most common interval of one step : 257.00000 cents, amount: 2 Least squares average step : 241.69286 cents, oct.: 1691.85000 cents Scale is strictly proper Scale is a mode of a 1701-tone equal temperament with octave 1701.000 cents degrees: 236 488 745 941 1211 1444 1701 Least number of segments generator : 851 of 851.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1313 of 1313.000 cents and inv. generated superset size: 368 = 361 more = 5257.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFC Step pattern size order : CDEAFBE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 181.00000 cents Scale diversity : 0.526487 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.775426 Rothenberg efficiency : 0.312925 redundancy: 0.687075 Efficiency x scale size : 2.190476 Number of different interval sizes : 38 = 6.33333 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.33333 = 19/3 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 2.00000 cents Number of recognisable fifths : 2, average 702.0000 cents Number of recognisable fourths : 5, average 496.6000 cents Best fifths 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 61.0000 cents: 1 2 5 Limited inverse transpositions with margin 61.0000 cents: 2 4 5 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 14.5504 c. M:-31.0000 c. Lebeng 20: 3 3 3 2 3 3 3 SP M ME I SD: 15.7091 c. M:-22.3000 c. 25: 3 4 4 3 4 3 4 SP M ME S SD: 15.6626 c. M: 31.8800 c. Dicot-7 27: 4 4 4 3 4 4 4 SP M ME I SD: 11.1484 c. M:-16.0000 c. 34: 5 5 5 4 5 5 5 SP M ME I SD: 9.4506 c. M:-14.1471 c. 38: 5 6 6 4 6 5 6 SP T3 SD: 8.9736 c. M:-15.9737 c. 41: 6 6 6 5 6 6 6 SP M ME I SD: 9.0157 c. M:-13.2195 c. 45: 6 7 7 5 7 6 7 SP T3 SD: 6.4688 c. M:-11.0000 c. 52: 7 8 8 6 8 7 8 SP T3 SD: 5.2293 c. M:-7.6346 c. 59: 8 9 9 7 9 8 9 SP T3 SD: 4.9093 c. M:-10.4068 c. 73: 10 11 11 8 12 10 11 SP SD: 3.6260 c. M: 8.9452 c. 80: 11 12 12 9 13 11 12 SP SD: 2.3979 c. M: 5.4500 c. 87: 12 13 13 10 14 12 13 SP SD: 1.7912 c. M:-2.8276 c. 139: 19 21 21 16 22 19 21 SP SD: 1.6259 c. M: 3.4892 c. 146: 20 22 22 17 23 20 22 SP SD: 1.6621 c. M: 2.9863 c. 217: 30 32 33 25 34 30 33 SP SD: 1.7922 c. M: 3.8387 c. 219: 30 33 33 25 35 30 33 SP SD: 1.3839 c. M: 2.9863 c. 223: 31 33 34 25 36 30 34 SP SD: 1.8191 c. M: 2.7803 c. 224: 31 33 34 26 35 31 34 SP SD: 1.6788 c. M: 3.5938 c. 226: 31 34 34 26 36 31 34 SP SD: 1.2260 c. M: 2.6770 c. 230: 32 34 35 26 37 31 35 SP SD: 1.4313 c. M:-1.9609 c. 233: 32 35 35 27 37 32 35 SP SD: 1.2323 c. M: 2.3863 c. 237: 33 35 36 27 38 32 36 SP SD: 1.1394 c. M:-1.9494 c. 244: 34 36 37 28 39 33 37 SP SD: 0.9889 c. M:-2.0082 c. 251: 35 37 38 29 40 34 38 SP SD: 1.0100 c. M:-2.0637 c. 304: 42 45 46 35 48 42 46 SP SD: 1.1906 c. M: 2.3947 c. 309: 43 46 46 36 49 42 47 SP SD: 1.2385 c. M:-1.9320 c. 311: 43 46 47 36 49 43 47 SP SD: 1.1093 c. M: 2.2508 c. 317: 44 47 48 36 51 43 48 SP SD: 1.0628 c. M: 1.9621 c. 324: 45 48 49 37 52 44 49 SP SD: 0.8504 c. M:-1.7500 c. 331: 46 49 50 38 53 45 50 SP SD: 0.7343 c. M:-1.7976 c. 338: 47 50 51 39 54 46 51 SP SD: 0.7425 c. M:-1.8432 c. 344: 48 51 52 39 55 47 52 SP SD: 1.1582 c. M:-1.6599 c. 345: 48 51 52 40 55 47 52 SP SD: 0.8581 c. M:-1.8870 c. 351: 49 52 53 40 56 48 53 SP SD: 1.0008 c. M:-1.4615 c. 358: 50 53 54 41 57 49 54 SP SD: 0.9215 c. M:-1.5698 c. 365: 51 54 55 42 58 50 55 SP SD: 0.9291 c. M:-1.6740 c. 376: 52 56 57 43 60 51 57 SP SD: 0.9074 c. M:-1.4495 c. 383: 53 57 58 44 61 52 58 SP SD: 0.8221 c. M:-1.4621 c. 390: 54 58 59 45 62 53 59 SP SD: 0.8214 c. M:-1.5077 c. 409: 57 60 62 47 65 56 62 SP SD: 0.9158 c. M: 1.4059 c. 411: 57 61 62 47 66 56 62 SP SD: 0.8688 c. M:-1.6350 c. 416: 58 61 63 48 66 57 63 SP SD: 0.8552 c. M: 1.4159 c. 418: 58 62 63 48 67 57 63 SP SD: 0.7880 c. M:-1.6746 c. 425: 59 63 64 49 68 58 64 SP SD: 0.7813 c. M:-1.7129 c. 438: 61 65 66 50 70 60 66 SP SD: 0.8695 c. M:-1.3288 c. 445: 62 66 67 51 71 61 67 SP SD: 0.8050 c. M:-1.2764 c. 452: 63 67 68 52 72 62 68 SP SD: 0.8049 c. M:-1.2257 c. 461: 64 68 70 53 73 63 70 SP SD: 0.6814 c. M: 1.2863 c. 468: 65 69 71 54 74 64 71 SP SD: 0.6212 c. M: 1.0577 c. 475: 66 70 72 55 75 65 72 SP SD: 0.6355 c. M: 0.9768 c. 497: 69 74 75 57 79 68 75 SP SD: 0.7323 c. M:-1.4225 c. 503: 70 74 76 58 80 69 76 SP SD: 0.7110 c. M: 1.0338 c. 504: 70 75 76 58 80 69 76 SP SD: 0.7319 c. M:-1.3750 c. 510: 71 75 77 59 81 70 77 SP SD: 0.7145 c. M: 1.2294 c. 511: 71 76 77 59 81 70 77 SP SD: 0.7839 c. M:-1.3288 c. 517: 72 76 78 60 82 71 78 SP SD: 0.7698 c. M: 1.4294 c. 534: 74 79 81 61 85 73 81 SP SD: 0.7249 c. M: 1.3090 c. 541: 75 80 82 62 86 74 82 SP SD: 0.5608 c. M: 0.8909 c. 548: 76 81 83 63 87 75 83 SP SD: 0.4280 c. M: 0.6697 c. 555: 77 82 84 64 88 76 84 SP SD: 0.3545 c. M: 0.6865 c. 635: 88 94 96 73 101 87 96 SP SD: 0.3854 c. M: 0.7622 c. 642: 89 95 97 74 102 88 97 SP SD: 0.3172 c. M: 0.4860 c. 781: 108 116 118 90 124 107 118 SP SD: 0.3062 c. M: 0.7785 c. 788: 109 117 119 91 125 108 119 SP SD: 0.3028 c. M: 0.7094 c. 808: 112 120 122 93 128 111 122 SP SD: 0.2826 c. M: 0.5111 c. 815: 113 121 123 94 129 112 123 SP SD: 0.2856 c. M: 0.4724 c. 886: 123 131 134 102 141 121 134 SP SD: 0.2627 c. M:-0.4345 c. 893: 124 132 135 103 142 122 135 SP SD: 0.2557 c. M:-0.4625 c. 945: 131 140 143 109 150 129 143 SP SD: 0.2928 c. M:-0.4000 c. 980: 136 145 148 113 156 134 148 SP SD: 0.2848 c. M:-0.5286 c. 993: 138 147 150 114 158 136 150 SP SD: 0.2804 c. M: 0.5680 c. 1000: 139 148 151 115 159 137 151 SP SD: 0.2343 c. M:-0.4390 c. 1007: 140 149 152 116 160 138 152 SP SD: 0.2286 c. M:-0.4846 c. 1032: 143 153 156 119 164 141 156 SP SD: 0.2275 c. M:-0.4680 c. 1052: 146 156 159 121 167 144 159 SP SD: 0.1989 c. M:-0.4002 c. 1059: 147 157 160 122 168 145 160 SP SD: 0.1923 c. M:-0.2946 c. 1139: 158 169 172 131 181 156 172 SP SD: 0.1824 c. M:-0.3468 c. 1146: 159 170 173 132 182 157 173 SP SD: 0.1717 c. M:-0.3325 c. 1457: 202 216 220 168 231 200 220 SP SD: 0.1656 c. M: 0.3363 c. 1555: 216 230 235 179 247 213 235 SP SD: 0.1561 c. M:-0.2804 c. 1562: 217 231 236 180 248 214 236 SP SD: 0.1447 c. M:-0.3105 c. 1600: 222 237 242 184 254 219 242 SP SD: 0.1550 c. M: 0.2762 c. 1607: 223 238 243 185 255 220 243 SP SD: 0.1122 c. M: 0.2141 c. 1614: 224 239 244 186 256 221 244 SP SD: 0.0966 c. M: 0.1524 c. 1694: 235 251 256 195 269 232 256 SP SD: 0.0601 c. M: 0.1281 c. 1701: 236 252 257 196 270 233 257 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 x 3 S SD: 100.6279 cents 2 x x 3 x 4 x 5 S SD: 40.9970 cents 3 x 4 x 5:6:7:8 S SD: 12.5888 cents 4 x 5:6:7:8:9:11 SD: 21.8755 cents 6:7:8:9:10:12:14:16 S SD: 11.7524 cents 7:8:9:11:12:14:16:19 SD: 10.4423 cents 12:14:16:18:21:24:28:32 S SD: 9.4046 cents 13:15:17:20:22:26:30:35 SD: 6.2711 cents 15:17:20:23:26:30:35:40 SD: 5.1079 cents 19:22:25:29:33:38:44:51 SD: 4.8569 cents 21:24:28:32:36:42:48:56 S SD: 3.8582 cents 22:25:29:34:38:44:51:59 SD: 3.8190 cents 28:32:37:43:48:56:64:75 SD: 2.9580 cents 33:38:44:51:57:66:76:88 SD: 2.8578 cents 40:46:53:62:69:81:92:107 SD: 2.6859 cents 43:49:57:66:74:87:99:115 SD: 1.9943 cents 54:62:72:83:93:109:124:144 SD: 1.8531 cents 55:63:73:85:95:111:127:147 SD: 1.7655 cents 61:70:81:94:105:123:140:163 SD: 1.2004 cents 76:87:101:117:131:153:175:203 SD: 0.7713 cents 89:102:118:137:153:179:205:238 SD: 0.6031 cents 145:166:192:223:250:292:334:387 SD: 0.5466 cents 151:173:200:232:260:304:348:403 SD: 0.4365 cents 184:211:244:283:317:370:424:492 SD: 0.4348 cents 205:235:272:315:353:413:472:548 SD: 0.4223 cents 206:236:273:317:355:415:474:550 SD: 0.4149 cents 212:243:281:326:365:427:488:566 SD: 0.2453 cents 301:345:399:463:518:606:693:804 SD: 0.2008 cents 307:352:407:472:529:618:707:820 SD: 0.2001 cents 316:362:419:486:544:636:728:844 SD: 0.1928 cents 390:447:517:600:672:785:898:1042 SD: 0.1899 cents 396:454:525:609:682:797:912:1058 SD: 0.1137 cents 562:644:745:864:968:1131:1294:1501 SD: 0.1019 cents