Scala analysis: Uganda_Harp_126
126 (Harp), Uganda
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 229.000 cents 229.000000 2: 469.000 cents 469.000000 3: 705.000 cents 705.000000 4: 955.000 cents 955.000000 5: 1193.000 cents 1193.000000 6: 1447.000 cents 1447.000000 7: 1686.000 cents 1686.000000
SHOW/INTERVAL
0: 239.0000 cents 239.0000 1: 229.0000 cents 229.0000 2: 240.0000 cents 240.0000 3: 236.0000 cents 236.0000 4: 250.0000 cents 250.0000 5: 238.0000 cents 238.0000 6: 254.0000 cents 254.0000 7: 239.0000 cents 239.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 229.00000 cents 1: 1 236.00000 cents 1: 1 238.00000 cents 1: 1 239.00000 cents 1: 1 240.00000 cents 1: 1 250.00000 cents 1: 1 254.00000 cents 2: 1 468.00000 cents 2: 1 469.00000 cents 2: 1 476.00000 cents 2: 1 486.00000 cents 2: 1 488.00000 cents 2: 1 492.00000 cents 2: 1 493.00000 cents 3: 1 705.00000 cents 3: 1 708.00000 cents 3: 1 722.00000 cents 3: 1 724.00000 cents 3: 1 726.00000 cents 3: 1 731.00000 cents 3: 1 742.00000 cents 4: 1 944.00000 cents 4: 1 955.00000 cents 4: 1 960.00000 cents 4: 1 962.00000 cents 4: 1 964.00000 cents 4: 1 978.00000 cents 4: 1 981.00000 cents 5: 1 1193.00000 cents 5: 1 1194.00000 cents 5: 1 1198.00000 cents 5: 1 1200.00000 cents 5: 1 1210.00000 cents 5: 1 1217.00000 cents 5: 1 1218.00000 cents 6: 1 1432.00000 cents 6: 1 1436.00000 cents 6: 1 1446.00000 cents 6: 1 1447.00000 cents 6: 1 1448.00000 cents 6: 1 1450.00000 cents 6: 1 1457.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 229.0 469.0 705.0 955.0 1193.0 1447.0 1686.0 229.0 : 240.0 476.0 726.0 964.0 1218.0 1457.0 1686.0 469.0 : 236.0 486.0 724.0 978.0 1217.0 1446.0 1686.0 705.0 : 250.0 488.0 742.0 981.0 1210.0 1450.0 1686.0 955.0 : 238.0 492.0 731.0 960.0 1200.0 1436.0 1686.0 1193.0: 254.0 493.0 722.0 962.0 1198.0 1448.0 1686.0 1447.0: 239.0 468.0 708.0 944.0 1194.0 1432.0 1686.0 1686.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 229.0000 .. 254.0000 cents 25.00000 cents 229.00000 cents 2: 468.0000 .. 493.0000 cents 25.00000 cents 214.00000 cents 3: 705.0000 .. 742.0000 cents 37.00000 cents 212.00000 cents 4: 944.0000 .. 981.0000 cents 37.00000 cents 202.00000 cents 5: 1193.0000 .. 1218.0000 cents 25.00000 cents 212.00000 cents 6: 1432.0000 .. 1457.0000 cents 25.00000 cents 214.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 229.00000 cents, class 1 Average step (divided formal octave): 240.8571 cents Largest one step interval : 254.00000 cents Average / Smallest step : 1.051778 Largest / Average step : 1.054567 Largest / Smallest step : 1.109170 Median interval of one step : 239.00000 cents, amount: 1 Least squares average step : 239.65000 cents, oct.: 1677.55000 cents Scale is strictly proper Scale is a mode of a 1686-tone equal temperament with octave 1686.000 cents degrees: 229 469 705 955 1193 1447 1686 Least number of segments generator : 845 of 845.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1445 of 1445.000 cents and inv. generated superset size: 137 = 130 more = 1957.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : AEBFCGD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 202.00000 cents Scale diversity : 0.484379 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.896797 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 2, average 706.5000 cents Number of recognisable fourths : 4, average 489.7500 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 37.0000 cents: 1 2 3 4 5 6 Limited inverse transpositions with margin 37.0000 cents: 1 2 3 4 5 6 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 10.7760 c. M:-17.5714 c. Lebeng 43: 6 6 6 6 6 7 6 SP M ME S SD: 8.7093 c. M: 16.7209 c. 44: 6 6 6 7 6 7 6 SP D3 S SD: 7.8934 c. M: 15.2727 c. 48: 6 7 7 7 7 7 7 SP M ME S SD: 9.1431 c. M: 18.2500 c. 50: 7 7 7 7 7 8 7 SP M ME S SD: 7.1603 c. M: 12.8000 c. 51: 7 7 7 8 7 8 7 SP D3 S SD: 5.8489 c. M: 10.7647 c. 57: 8 8 8 8 8 9 8 SP M ME S SD: 6.2639 c. M: 9.8421 c. 58: 8 8 8 9 8 9 8 SP D3 S SD: 4.5195 c. M: 7.3448 c. 65: 9 9 9 10 9 10 9 SP D3 S SD: 3.7630 c. M:-5.5538 c. 72: 10 10 10 11 10 11 10 SP D3 S SD: 3.4673 c. M:-5.1667 c. 79: 11 11 11 12 11 12 11 SP D3 S SD: 3.4941 c. M:-5.7595 c. 86: 12 12 12 13 12 13 12 SP D3 S SD: 3.7036 c. M:-6.2558 c. 93: 13 13 13 14 13 14 13 SP D3 S SD: 3.9956 c. M:-6.6774 c. 103: 14 15 14 15 15 15 15 SP D3 S SD: 3.9929 c. M: 6.5340 c. 108: 15 15 15 16 15 17 15 SP SD: 3.9122 c. M: 6.5556 c. 110: 15 16 15 16 16 16 16 SP D3 S SD: 3.8923 c. M: 6.2364 c. 112: 15 16 16 16 16 17 16 SP T3 SD: 3.4551 c. M: 6.6250 c. 113: 15 16 16 17 16 17 16 SP SD: 3.4502 c. M: 6.4690 c. 119: 16 17 17 17 17 18 17 SP T3 SD: 3.0175 c. M: 5.7395 c. 120: 16 17 17 18 17 18 17 SP SD: 2.7841 c. M: 5.3500 c. 126: 17 18 18 18 18 19 18 SP T3 SD: 2.7436 c. M: 4.9524 c. 127: 17 18 18 19 18 19 18 SP SD: 2.2632 c. M: 4.3543 c. 134: 18 19 19 20 19 20 19 SP SD: 1.9025 c. M: 3.4627 c. 141: 19 20 20 21 20 21 20 SP SD: 1.7190 c. M:-2.7447 c. 148: 20 21 21 22 21 22 21 SP SD: 1.7078 c. M:-3.1486 c. 155: 21 22 22 23 22 23 22 SP SD: 1.8294 c. M:-3.5161 c. 168: 23 24 23 25 24 25 24 SP SD: 1.8646 c. M:-2.6786 c. 170: 23 24 24 25 24 26 24 SP SD: 1.9807 c. M: 2.9059 c. 175: 24 25 24 26 25 26 25 SP SD: 1.8875 c. M:-3.0800 c. 177: 24 25 25 26 25 27 25 SP SD: 1.5778 c. M: 2.4576 c. 184: 25 26 26 27 26 28 26 SP SD: 1.2628 c. M: 2.0435 c. 191: 26 27 27 28 27 29 27 SP SD: 1.0647 c. M: 1.6597 c. 198: 27 28 28 29 28 30 28 SP SD: 1.0115 c. M:-1.7576 c. 270: 37 38 38 40 38 41 38 SP SD: 1.0821 c. M:-2.0444 c. 277: 38 39 39 41 39 42 39 SP SD: 1.1624 c. M:-2.2924 c. 284: 39 40 40 42 40 43 40 SP SD: 1.2859 c. M:-2.5282 c. 287: 39 41 40 43 40 43 41 SP SD: 1.2611 c. M:-2.5540 c. 288: 39 41 40 43 41 43 41 SP SD: 1.2169 c. M: 2.5000 c. 295: 40 42 41 44 42 44 42 SP SD: 1.0672 c. M: 2.0237 c. 302: 41 43 42 45 43 45 43 SP SD: 0.9754 c. M:-1.7152 c. 309: 42 44 43 46 44 46 44 SP SD: 0.9481 c. M:-1.9320 c. 325: 44 46 46 48 46 49 46 SP SD: 0.8982 c. M: 2.1077 c. 332: 45 47 47 49 47 50 47 SP SD: 0.8084 c. M: 1.7952 c. 339: 46 48 48 50 48 51 48 SP SD: 0.7818 c. M: 1.4956 c. 366: 50 52 51 54 52 55 52 SP SD: 0.8401 c. M: 1.4426 c. 404: 55 57 57 60 57 61 57 SP SD: 0.8393 c. M: 1.5941 c. 411: 56 58 58 61 58 62 58 SP SD: 0.8476 c. M: 1.3504 c. 418: 57 59 59 62 59 63 59 SP SD: 0.8924 c. M: 1.1148 c. 424: 58 60 59 63 60 64 60 SP SD: 0.8198 c. M:-1.6321 c. 431: 59 61 60 64 61 65 61 SP SD: 0.8093 c. M:-1.7981 c. 443: 60 63 62 66 62 67 63 SP SD: 0.9104 c. M: 1.7630 c. 445: 60 64 62 66 63 67 63 SP SD: 0.7463 c. M: 1.6742 c. 450: 61 64 63 67 63 68 64 SP SD: 0.7797 c. M: 1.5600 c. 452: 61 65 63 67 64 68 64 SP SD: 0.7178 c. M: 1.4646 c. 457: 62 65 64 68 64 69 65 SP SD: 0.6741 c. M: 1.3632 c. 464: 63 66 65 69 65 70 66 SP SD: 0.6023 c. M: 1.1724 c. 471: 64 67 66 70 66 71 67 SP SD: 0.5724 c. M: 0.9873 c. 478: 65 68 67 71 67 72 68 SP SD: 0.5867 c. M:-0.8703 c. 479: 65 68 67 71 68 72 68 SP SD: 0.6859 c. M: 1.1253 c. 485: 66 69 68 72 68 73 69 SP SD: 0.6388 c. M:-0.9794 c. 486: 66 69 68 72 69 73 69 SP SD: 0.5721 c. M: 0.9877 c. 493: 67 70 69 73 70 74 70 SP SD: 0.4886 c. M: 0.8540 c. 500: 68 71 70 74 71 75 71 SP SD: 0.4478 c. M: 0.7240 c. 657: 89 94 92 97 93 99 93 SP SD: 0.4761 c. M:-0.7078 c. 684: 93 97 96 101 97 103 97 SP SD: 0.4892 c. M: 1.0789 c. 691: 94 98 97 102 98 104 98 SP SD: 0.4511 c. M: 0.9826 c. 698: 95 99 98 103 99 105 99 SP SD: 0.4386 c. M: 0.8883 c. 701: 95 100 98 104 99 106 99 SP SD: 0.4094 c. M:-0.8916 c. 708: 96 101 99 105 100 107 100 SP SD: 0.3662 c. M:-0.8644 c. 712: 97 101 100 105 101 107 101 SP SD: 0.4884 c. M: 0.7051 c. 715: 97 102 100 106 101 108 101 SP SD: 0.3523 c. M:-0.8378 c. 722: 98 103 101 107 102 109 102 SP SD: 0.3693 c. M:-0.8116 c. 729: 99 104 102 108 103 110 103 SP SD: 0.4118 c. M:-0.7860 c. 736: 100 105 103 109 104 111 104 SP SD: 0.4716 c. M:-0.7609 c. 756: 103 107 106 112 107 114 107 SP SD: 0.4497 c. M:-0.7063 c. 763: 104 108 107 113 108 115 108 SP SD: 0.4326 c. M:-0.8087 c. 773: 105 110 108 115 109 116 110 SP SD: 0.4170 c. M: 0.9224 c. 780: 106 111 109 116 110 117 111 SP SD: 0.4119 c. M: 0.9308 c. 810: 110 115 114 120 114 122 115 SP SD: 0.4187 c. M: 0.6667 c. 856: 116 122 120 127 121 129 121 SP SD: 0.4179 c. M:-0.6752 c. 869: 118 124 121 129 123 131 123 SP SD: 0.4066 c. M: 0.7215 c. 876: 119 125 122 130 124 132 124 SP SD: 0.3871 c. M:-0.6164 c. 883: 120 126 123 131 125 133 125 SP SD: 0.3866 c. M:-0.7123 c. 899: 122 128 126 133 127 136 127 SP SD: 0.3754 c. M:-0.8220 c. 906: 123 129 127 134 128 137 128 SP SD: 0.3546 c. M:-0.8013 c. 913: 124 130 128 135 129 138 129 SP SD: 0.3531 c. M:-0.7809 c. 930: 126 133 130 138 131 140 132 SP SD: 0.3656 c. M: 0.5742 c. 943: 128 134 132 140 133 142 134 SP SD: 0.4272 c. M: 0.5801 c. 945: 128 135 132 140 134 142 134 SP SD: 0.3978 c. M: 0.6317 c. 950: 129 135 133 141 134 143 135 SP SD: 0.3654 c. M: 0.5895 c. 957: 130 136 134 142 135 144 136 SP SD: 0.3137 c. M: 0.5987 c. 964: 131 137 135 143 136 145 137 SP SD: 0.2766 c. M: 0.6079 c. 971: 132 138 136 144 137 146 138 SP SD: 0.2595 c. M: 0.6169 c. 974: 132 139 136 145 137 147 138 SP SD: 0.3570 c. M:-0.5154 c. 978: 133 139 137 145 138 147 139 SP SD: 0.2651 c. M: 0.6258 c. 1029: 140 146 144 153 145 155 146 SP SD: 0.3040 c. M: 0.4519 c. 1036: 141 147 145 154 146 156 147 SP SD: 0.2847 c. M:-0.4653 c. 1043: 142 148 146 155 147 157 148 SP SD: 0.2837 c. M:-0.5417 c. 1114: 151 159 156 165 157 168 158 SP SD: 0.2650 c. M: 0.4668 c. 1121: 152 160 157 166 158 169 159 SP SD: 0.2629 c. M: 0.3898 c. 1172: 159 167 164 174 165 177 166 SP SD: 0.2233 c. M: 0.4283 c. 1179: 160 168 165 175 166 178 167 SP SD: 0.1964 c. M: 0.3588 c. 1186: 161 169 166 176 167 179 168 SP SD: 0.1888 c. M:-0.3052 c. 1193: 162 170 167 177 168 180 169 SP SD: 0.2019 c. M:-0.3529 c. 1347: 183 192 188 200 190 203 191 SP SD: 0.1968 c. M:-0.3764 c. 1409: 191 201 197 209 199 212 200 SP SD: 0.2285 c. M: 0.4507 c. 1416: 192 202 198 210 200 213 201 SP SD: 0.2063 c. M: 0.3898 c. 1423: 193 203 199 211 201 214 202 SP SD: 0.1968 c. M: 0.3338 c. 1474: 200 210 206 219 208 222 209 SP SD: 0.1817 c. M: 0.4030 c. 1481: 201 211 207 220 209 223 210 SP SD: 0.1513 c. M: 0.3180 c. 1488: 202 212 208 221 210 224 211 SP SD: 0.1346 c. M: 0.2339 c. 1495: 203 213 209 222 211 225 212 SP SD: 0.1360 c. M:-0.2120 c. 1665: 226 237 233 247 235 251 236 SP SD: 0.1359 c. M: 0.2216 c. 1672: 227 238 234 248 236 252 237 SP SD: 0.0902 c. M: 0.1471 c. 1679: 228 239 235 249 237 253 238 SP SD: 0.0449 c. M: 0.0733 c. 1686: 229 240 236 250 238 254 239 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 x 3 S SD: 108.0342 cents 2 x x 3 x 4 x 5 S SD: 33.3260 cents 3 x 4 x 5:6:7:8 S SD: 16.0284 cents 4 x 5:6:7:8:9:11 SD: 19.1555 cents 6:7:8:9:10:12:14:16 S SD: 12.6702 cents 10:11:13:15:17:20:23:26 SD: 11.7195 cents 12:14:16:18:21:24:28:32 S SD: 7.9117 cents 14:16:18:21:24:28:32:37 SD: 6.3152 cents 16:18:21:24:28:32:37:42 SD: 4.8077 cents 20:23:26:30:35:40:46:53 SD: 3.6780 cents 22:25:29:33:38:44:51:58 SD: 2.9082 cents 35:40:46:53:61:70:81:93 SD: 2.7159 cents 36:41:47:54:63:72:83:95 SD: 2.6984 cents 42:48:55:63:73:84:97:111 SD: 1.3420 cents 71:81:93:107:123:141:164:188 SD: 1.2445 cents 77:88:101:116:134:153:178:204 SD: 1.2378 cents 84:96:110:126:146:167:194:222 SD: 1.0139 cents 91:104:119:137:158:181:210:241 SD: 0.9418 cents 99:113:130:149:172:197:228:262 SD: 0.7584 cents 106:121:139:159:184:211:245:281 SD: 0.7290 cents 113:129:148:170:196:225:261:299 SD: 0.6035 cents 141:161:185:212:245:281:325:373 SD: 0.4726 cents 163:186:214:245:283:325:376:432 SD: 0.4625 cents 177:202:232:266:307:353:408:469 SD: 0.4503 cents 205:234:269:308:356:408:473:543 SD: 0.3106 cents 219:250:287:329:380:436:505:580 SD: 0.2470 cents 247:282:324:371:429:492:570:654 SD: 0.2252 cents 360:411:472:541:625:717:830:953 SD: 0.1661 cents 382:436:501:574:663:761:881:1012 SD: 0.1476 cents 424:484:556:637:736:845:978:1123 SD: 0.1464 cents 466:532:611:700:809:928:1075:1234 SD: 0.1147 cents