Scala analysis: Malawi_Asena_05
Asena 5 (Bangwe), Malawi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65.000 cents 65.000000 2: 302.000 cents 302.000000 3: 477.000 cents 477.000000 4: 636.000 cents 636.000000 5: 809.000 cents 809.000000 6: 966.000 cents 966.000000 7: 1135.000 cents 1135.000000 8: 1308.000 cents 1308.000000 9: 1521.000 cents 1521.000000 10: 1711.000 cents 1711.000000 11: 1867.000 cents 1867.000000
SHOW/INTERVAL
0: 156.0000 cents 156.0000 1: 65.0000 cents 65.0000 2: 237.0000 cents 237.0000 3: 175.0000 cents 175.0000 4: 159.0000 cents 159.0000 5: 173.0000 cents 173.0000 6: 157.0000 cents 157.0000 7: 169.0000 cents 169.0000 8: 173.0000 cents 173.0000 9: 213.0000 cents 213.0000 10: 190.0000 cents 190.0000 11: 156.0000 cents 156.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65.00000 cents 1: 1 156.00000 cents 1: 1 157.00000 cents 1: 1 159.00000 cents 1: 1 169.00000 cents 1: 2 173.00000 cents 1: 1 175.00000 cents 1: 1 190.00000 cents 1: 1 213.00000 cents 1: 1 237.00000 cents 2: 1 221.00000 cents 2: 1 302.00000 cents 2: 1 326.00000 cents 2: 1 330.00000 cents 2: 1 332.00000 cents 2: 1 334.00000 cents 2: 1 342.00000 cents 2: 1 346.00000 cents 2: 1 386.00000 cents 2: 1 403.00000 cents 2: 1 412.00000 cents 3: 1 411.00000 cents 3: 1 458.00000 cents 3: 1 477.00000 cents 3: 1 489.00000 cents 3: 2 499.00000 cents 3: 1 507.00000 cents 3: 1 555.00000 cents 3: 1 559.00000 cents 3: 1 571.00000 cents 3: 1 576.00000 cents 4: 1 624.00000 cents 4: 1 633.00000 cents 4: 1 636.00000 cents 4: 1 648.00000 cents 4: 1 658.00000 cents 4: 1 664.00000 cents 4: 1 672.00000 cents 4: 1 712.00000 cents 4: 1 732.00000 cents 4: 1 744.00000 cents 4: 1 745.00000 cents 5: 1 792.00000 cents 5: 1 797.00000 cents 5: 1 809.00000 cents 5: 1 823.00000 cents 5: 1 831.00000 cents 5: 1 833.00000 cents 5: 1 861.00000 cents 5: 1 885.00000 cents 5: 2 901.00000 cents 5: 1 902.00000 cents 6: 1 965.00000 cents 6: 2 966.00000 cents 6: 1 982.00000 cents 6: 1 1006.00000 cents 6: 1 1034.00000 cents 6: 1 1036.00000 cents 6: 1 1044.00000 cents 6: 1 1058.00000 cents 6: 1 1070.00000 cents 6: 1 1075.00000 cents 7: 1 1122.00000 cents 7: 1 1123.00000 cents 7: 1 1135.00000 cents 7: 1 1155.00000 cents 7: 1 1195.00000 cents 7: 1 1203.00000 cents 7: 1 1209.00000 cents 7: 1 1219.00000 cents 7: 1 1231.00000 cents 7: 1 1234.00000 cents 7: 1 1243.00000 cents 8: 1 1291.00000 cents 8: 1 1296.00000 cents 8: 1 1308.00000 cents 8: 1 1312.00000 cents 8: 1 1360.00000 cents 8: 2 1368.00000 cents 8: 1 1378.00000 cents 8: 1 1390.00000 cents 8: 1 1409.00000 cents 8: 1 1456.00000 cents 9: 1 1455.00000 cents 9: 1 1464.00000 cents 9: 1 1481.00000 cents 9: 1 1521.00000 cents 9: 1 1525.00000 cents 9: 1 1533.00000 cents 9: 1 1535.00000 cents 9: 1 1537.00000 cents 9: 1 1541.00000 cents 9: 1 1565.00000 cents 9: 1 1646.00000 cents 10: 1 1630.00000 cents 10: 1 1654.00000 cents 10: 1 1677.00000 cents 10: 1 1692.00000 cents 10: 2 1694.00000 cents 10: 1 1698.00000 cents 10: 1 1708.00000 cents 10: 1 1710.00000 cents 10: 1 1711.00000 cents 10: 1 1802.00000 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 10.40000 = 52/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 65.0 302.0 477.0 636.0 809.0 966.0 1135.0 1308.0 1521.0 1711.0 1867.0 65.0 : 237.0 412.0 571.0 744.0 901.0 1070.0 1243.0 1456.0 1646.0 1802.0 1867.0 302.0 : 175.0 334.0 507.0 664.0 833.0 1006.0 1219.0 1409.0 1565.0 1630.0 1867.0 477.0 : 159.0 332.0 489.0 658.0 831.0 1044.0 1234.0 1390.0 1455.0 1692.0 1867.0 636.0 : 173.0 330.0 499.0 672.0 885.0 1075.0 1231.0 1296.0 1533.0 1708.0 1867.0 809.0 : 157.0 326.0 499.0 712.0 902.0 1058.0 1123.0 1360.0 1535.0 1694.0 1867.0 966.0 : 169.0 342.0 555.0 745.0 901.0 966.0 1203.0 1378.0 1537.0 1710.0 1867.0 1135.0: 173.0 386.0 576.0 732.0 797.0 1034.0 1209.0 1368.0 1541.0 1698.0 1867.0 1308.0: 213.0 403.0 559.0 624.0 861.0 1036.0 1195.0 1368.0 1525.0 1694.0 1867.0 1521.0: 190.0 346.0 411.0 648.0 823.0 982.0 1155.0 1312.0 1481.0 1654.0 1867.0 1711.0: 156.0 221.0 458.0 633.0 792.0 965.0 1122.0 1291.0 1464.0 1677.0 1867.0 1867.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.0000 .. 237.0000 cents 172.00000 cents 65.00000 cents 2: 221.0000 .. 412.0000 cents 191.00000 cents -16.00000 cents 3: 411.0000 .. 576.0000 cents 165.00000 cents -1.00000 cents 4: 624.0000 .. 745.0000 cents 121.00000 cents 48.00000 cents 5: 792.0000 .. 902.0000 cents 110.00000 cents 47.00000 cents 6: 965.0000 .. 1075.0000 cents 110.00000 cents 63.00000 cents 7: 1122.0000 .. 1243.0000 cents 121.00000 cents 47.00000 cents 8: 1291.0000 .. 1456.0000 cents 165.00000 cents 48.00000 cents 9: 1455.0000 .. 1646.0000 cents 191.00000 cents -1.00000 cents 10: 1630.0000 .. 1802.0000 cents 172.00000 cents -16.00000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 65.00000 cents, class 1 Average step (divided formal octave): 169.7273 cents Largest one step interval : 237.00000 cents Average / Smallest step : 2.611189 Largest / Average step : 1.396358 Largest / Smallest step : 3.646154 Median interval of one step : 173.00000 cents, amount: 2 Most common interval of one step : 173.00000 cents, amount: 2 Least squares average step : 166.46245 cents, oct.: 1831.08696 cents Scale is not proper Scale is a mode of a 1867-tone equal temperament with octave 1867.000 cents degrees: 65 302 477 636 809 966 1135 1308 1521 1711 1867 Least number of segments generator : 934 of 934.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1380 of 1380.000 cents and inv. generated superset size: 735 = 724 more = 6681.818% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGEHIJ Step pattern size order : AJGDFCEFIHB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.00000 cents Scale diversity : 0.415919 Lumma stability : 0.205142 Lumma impropriety factor : 0.018211 Rothenberg efficiency : 0.191736 redundancy: 0.808264 Efficiency x scale size : 2.109091 Number of different interval sizes : 104 = 10.40000 / class Number of one step interval sizes : 10 Highest interval variety : 11 Mean interval variety : 10.40000 = 52/5 Median interval variety : 10 Lowest interval variety : 10 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 1, average 712.0000 cents Number of recognisable fourths : 4, average 498.5000 cents Best fifths form a closed circle Formal octave complements present : 1 = 9.0909% 2/1 octave complements present : 2 = 18.1818% -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 47.7610 c. M:-104.7273 c. 12: 0 2 1 1 1 1 1 1 2 1 1 N D3 SD: 35.6196 c. M: 65.0000 c. 16: 1 2 1 1 2 1 2 1 2 2 1 N D3 SD: 33.2237 c. M: 52.5625 c. 19: 0 3 2 1 2 2 1 2 2 2 2 N SD: 37.1195 c. M: 65.0000 c. 20: 1 2 2 2 2 1 2 2 2 2 2 P M ME S SD: 22.6338 c. M: 32.5000 c. Score-11, Diatonicized Chromatic 21: 1 2 2 2 2 2 2 2 2 2 2 SP M ME S SD: 21.1756 c. M: 35.2857 c. 23: 1 3 2 2 2 2 2 2 3 2 2 P D3 SD: 12.4717 c. M:-22.6957 c. 33: 1 4 3 3 3 3 3 3 4 3 3 P SD: 12.8353 c. M: 24.3939 c. 36: 1 5 3 3 4 3 3 3 4 4 3 N SD: 12.8351 c. M:-20.7778 c. 38: 1 5 4 3 3 4 3 4 4 4 3 N SD: 12.6641 c. M: 22.8947 c. 39: 1 5 4 3 4 3 4 3 5 4 3 N SD: 11.6886 c. M: 17.1282 c. 44: 2 5 4 4 4 4 4 4 5 4 4 SP SD: 9.6791 c. M:-19.8636 c. 47: 2 6 4 4 4 4 5 4 5 5 4 P SD: 10.7303 c. M:-16.9787 c. 48: 2 6 4 4 5 4 4 5 5 5 4 P SD: 9.1276 c. M:-14.4583 c. 50: 2 6 5 4 5 4 4 5 6 5 4 P SD: 8.0857 c. M: 14.8000 c. 56: 2 7 5 5 5 5 5 5 6 6 5 P SD: 8.5497 c. M: 20.7321 c. 58: 2 7 6 5 5 5 5 6 6 6 5 P SD: 7.1548 c. M: 12.2931 c. 64: 2 8 6 6 6 5 6 6 7 7 5 N SD: 6.8068 c. M: 10.2812 c. 74: 3 9 7 6 7 6 7 7 8 8 6 P SD: 5.1588 c. M:-10.6892 c. 76: 3 9 7 7 7 6 7 7 9 8 6 P SD: 6.3608 c. M: 10.2500 c. 79: 3 10 7 7 7 7 7 7 9 8 7 P SD: 5.6618 c. M: 9.4304 c. 81: 3 10 8 7 7 7 7 8 9 8 7 P SD: 4.8932 c. M:-9.3827 c. 85: 3 11 8 7 8 7 8 8 9 9 7 N SD: 4.9381 c. M:-9.8824 c. 87: 3 11 8 8 8 7 8 8 10 9 7 N SD: 4.0059 c. M:-7.7931 c. 97: 3 13 9 8 9 8 9 9 11 10 8 N SD: 3.3745 c. M: 7.2577 c. 109: 4 14 10 9 10 9 10 10 13 11 9 N SD: 4.2702 c. M: 6.8073 c. 110: 4 14 10 10 10 9 10 10 13 11 9 N SD: 4.2417 c. M:-8.9636 c. 117: 4 15 11 10 11 10 10 11 13 12 10 N SD: 3.4592 c. M:-7.3932 c. 118: 4 15 11 10 11 10 11 11 13 12 10 N SD: 2.6837 c. M:-5.2288 c. 136: 5 17 13 11 13 11 13 12 16 14 11 N SD: 3.5568 c. M: 5.0441 c. 140: 5 18 13 12 13 11 13 13 16 14 12 N SD: 3.3805 c. M: 5.8286 c. 141: 5 18 13 12 13 12 13 13 16 14 12 N SD: 1.9963 c. M:-3.7376 c. 168: 6 21 16 14 16 14 15 16 19 17 14 N SD: 1.7941 c. M:-3.3452 c. 191: 7 24 18 16 18 16 17 18 22 19 16 N SD: 2.0258 c. M:-3.8796 c. 199: 7 25 19 17 18 17 18 18 23 20 17 N SD: 1.9837 c. M: 3.9146 c. 203: 7 26 19 17 19 17 18 19 23 21 17 N SD: 1.8318 c. M: 3.7635 c. 227: 8 29 21 19 21 19 21 21 26 23 19 N SD: 1.8199 c. M: 3.7137 c. 228: 8 29 21 20 21 19 21 21 26 23 19 N SD: 1.7897 c. M:-3.2149 c. 230: 8 29 22 19 22 19 21 21 26 24 19 N SD: 1.8522 c. M: 3.0478 c. 238: 8 30 23 20 22 20 22 22 27 24 20 N SD: 1.8324 c. M: 3.9076 c. 247: 9 31 23 21 23 21 22 23 28 25 21 N SD: 1.5172 c. M:-3.0283 c. 253: 9 32 24 21 24 21 23 23 29 26 21 N SD: 1.5515 c. M:-2.7391 c. 261: 9 33 25 22 24 22 24 24 30 26 22 N SD: 1.4929 c. M:-2.6437 c. 265: 9 34 25 22 25 22 24 25 30 27 22 N SD: 1.3994 c. M:-2.4226 c. 286: 10 36 27 24 27 24 26 26 33 29 24 N SD: 1.2869 c. M: 2.7867 c. 290: 10 37 27 25 27 24 26 27 33 30 24 N SD: 1.2652 c. M:-2.1793 c. 314: 11 40 29 27 29 26 29 29 36 32 26 N SD: 1.1695 c. M: 2.7707 c. 323: 11 41 30 28 30 27 29 30 37 33 27 N SD: 1.4017 c. M: 3.0248 c. 334: 12 42 31 29 31 28 30 31 38 34 28 N SD: 1.1044 c. M:-2.0778 c. 344: 12 44 32 29 32 29 31 32 39 35 29 N SD: 0.9273 c. M:-1.9302 c. 367: 13 46 35 31 34 31 33 34 42 37 31 N SD: 0.9569 c. M: 1.8556 c. 404: 14 51 38 35 37 34 37 37 46 41 34 N SD: 1.0383 c. M:-1.8366 c. 408: 14 52 38 35 38 34 37 38 46 42 34 N SD: 0.8026 c. M: 1.7745 c. 410: 14 52 39 35 38 34 37 38 47 42 34 N SD: 1.1262 c. M:-1.5512 c. 411: 14 52 39 35 38 35 37 38 47 42 34 N SD: 1.0824 c. M: 2.1898 c. 427: 15 54 40 36 40 36 39 39 49 43 36 N SD: 0.9900 c. M: 2.0070 c. 431: 15 55 40 37 40 36 39 40 49 44 36 N SD: 0.5866 c. M:-1.2251 c. 551: 19 70 52 47 51 46 50 51 63 56 46 N SD: 0.5349 c. M:-1.0163 c. 595: 21 75 56 51 55 50 54 55 68 60 50 N SD: 0.6985 c. M:-0.9765 c. 599: 21 76 56 51 56 50 54 56 68 61 50 N SD: 0.5827 c. M:-1.3840 c. 658: 23 83 62 56 61 55 60 61 75 67 55 N SD: 0.5794 c. M: 1.2888 c. 669: 23 85 63 57 62 56 61 62 76 68 56 N SD: 0.5143 c. M:-0.8535 c. 681: 24 86 64 58 63 57 62 63 78 69 57 N SD: 0.4565 c. M: 0.9721 c. 692: 24 88 65 59 64 58 63 64 79 70 58 N SD: 0.4985 c. M:-0.8483 c. 717: 25 91 67 61 67 60 65 66 82 73 60 N SD: 0.4559 c. M: 0.8396 c. 755: 26 96 71 64 70 64 68 70 86 77 63 N SD: 0.4178 c. M:-0.8834 c. 775: 27 98 73 66 72 65 70 72 88 79 65 N SD: 0.4509 c. M: 0.9006 c. 778: 27 99 73 66 72 66 70 72 89 79 65 N SD: 0.4248 c. M:-1.0964 c. 798: 28 101 75 68 74 67 72 74 91 81 67 N SD: 0.3784 c. M: 0.7531 c. 852: 30 108 80 72 79 72 77 79 97 87 71 N SD: 0.4326 c. M:-0.7394 c. 872: 30 111 82 74 81 73 79 81 99 89 73 N SD: 0.4237 c. M: 0.8509 c. 895: 31 114 84 76 83 75 81 83 102 91 75 N SD: 0.3549 c. M:-0.7017 c. 928: 32 118 87 79 86 78 84 86 106 94 78 N SD: 0.3965 c. M: 0.9246 c. 939: 33 119 88 80 87 79 85 87 107 96 78 N SD: 0.3919 c. M:-0.9137 c. 951: 33 121 89 81 88 80 86 88 109 97 79 N SD: 0.3802 c. M:-0.9075 c. 972: 34 123 91 83 90 82 88 90 111 99 81 N SD: 0.3268 c. M: 0.6461 c. 1015: 35 129 95 87 94 85 92 94 116 103 85 N SD: 0.3631 c. M: 0.6207 c. 1053: 37 133 99 90 97 89 95 98 120 107 88 N SD: 0.3927 c. M:-0.6021 c. 1063: 37 135 100 90 99 89 96 99 121 108 89 N SD: 0.3724 c. M:-0.7272 c. 1069: 37 136 100 91 99 90 97 99 122 109 89 N SD: 0.2825 c. M:-0.5622 c. 1150: 40 146 108 98 106 97 104 107 131 117 96 N SD: 0.2842 c. M:-0.5235 c. 1175: 41 149 110 100 109 99 106 109 134 120 98 N SD: 0.2936 c. M: 0.4996 c. 1186: 41 151 111 101 110 100 107 110 135 121 99 N SD: 0.2621 c. M:-0.5582 c. 1198: 42 152 112 102 111 101 108 111 137 122 100 N SD: 0.2872 c. M: 0.4766 c. 1268: 44 161 119 108 117 107 115 117 145 129 106 N SD: 0.2753 c. M: 0.6538 c. 1272: 44 162 119 108 118 107 115 118 145 130 106 N SD: 0.3268 c. M: 0.4568 c. 1280: 45 162 120 109 119 107 116 119 146 130 107 N SD: 0.3207 c. M:-0.6367 c. 1283: 45 163 120 109 119 108 116 119 146 131 107 N SD: 0.3162 c. M:-0.6781 c. 1295: 45 164 122 110 120 109 117 120 148 132 108 N SD: 0.3007 c. M: 0.6849 c. 1316: 46 167 123 112 122 111 119 122 150 134 110 N SD: 0.2240 c. M: 0.4255 c. 1403: 49 178 131 120 130 118 127 130 160 143 117 N SD: 0.2232 c. M: 0.6023 c. 1436: 50 182 135 122 133 121 130 133 164 146 120 N SD: 0.1761 c. M: 0.3677 c. 1699: 59 216 159 145 157 143 154 157 194 173 142 N SD: 0.1774 c. M: 0.3308 c. 1726: 60 219 162 147 160 145 156 160 197 176 144 N SD: 0.1631 c. M: 0.3053 c. 1844: 64 234 173 157 171 155 167 171 210 188 154 N SD: 0.1556 c. M: 0.2831 c. 1867: 65 237 175 159 173 157 169 173 213 190 156 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 x x x 3 S SD: 36.9014 cents 2 x x x 3 x x 4 x 5 x 6 S SD: 29.6467 cents 3 x x 4 x 5 x 6 x 7:8:9 S SD: 20.1842 cents 4 x 5 x 6 x 7:8:9:10:11:12 S SD: 22.3620 cents 5 x 6 x 7:8:9:10:11:12:13:15 SD: 14.7744 cents 6 x 7:8:9:10 x 12:13:14:16:18 S SD: 16.1724 cents 7 x 8:9:10:11:12:13:15:17:19:21 SD: 12.1657 cents 8 x 10:11:12:13:14:15:17:19:21:24 SD: 15.3519 cents 9:10:11:12:13:14:16:17:19:22:24:26 SD: 13.5714 cents 10:11:12:13:14:16:17:19:21:24:27:29 SD: 12.0664 cents 11:12:13:14:16:18:19:21:23:26:30:32 SD: 11.7532 cents 12:13:14:16:17:19:21:23:26:29:32:35 SD: 8.9904 cents 13:14:15:17:19:21:23:25:28:31:35:38 SD: 8.7573 cents 14:15:17:18:20:22:24:27:30:34:38:41 SD: 8.4961 cents 15:16:18:20:22:24:26:29:32:36:40:44 SD: 5.7647 cents 16:17:19:21:23:26:28:31:34:39:43:47 SD: 5.2151 cents 20:21:24:26:29:32:35:39:43:48:54:59 SD: 4.1133 cents 22:23:26:29:32:35:38:42:47:53:59:65 SD: 3.2163 cents 25:26:30:33:36:40:44:48:53:60:67:74 SD: 2.3717 cents 32:33:38:42:46:51:56:62:68:77:86:94 SD: 1.7758 cents 47:49:56:62:68:75:82:91:100:113:126:138 SD: 1.2223 cents 54:56:64:71:78:86:94:104:115:130:145:159 SD: 1.0617 cents 79:82:94:104:114:126:138:152:168:190:212:232 SD: 0.4289 cents 158:164:188:208:228:252:276:304:336:380:424:465 SD: 0.4219 cents 178:185:212:234:257:284:311:343:379:429:478:523 SD: 0.4217 cents 183:190:218:241:264:292:320:353:390:441:492:538 SD: 0.4028 cents 185:192:220:244:267:295:323:356:394:445:497:544 SD: 0.3971 cents 189:196:225:249:273:302:330:364:402:455:508:556 SD: 0.3566 cents 205:213:244:270:296:327:358:395:436:494:551:603 SD: 0.2807 cents 230:239:274:303:332:367:402:443:490:554:618:676 SD: 0.2417 cents 262:272:312:345:378:418:458:505:558:631:704:770 SD: 0.2265 cents 284:295:338:374:410:453:496:547:605:684:763:835 SD: 0.1893 cents 309:321:368:407:446:493:540:595:658:744:830:908 SD: 0.1742 cents 363:377:432:478:524:579:634:699:773:874:975:1067 SD: 0.1648 cents 388:403:462:511:560:619:678:747:826:934:1042:1141 SD: 0.1558 cents 419:435:499:552:605:669:732:807:892:1009:1126:1232 SD: 0.1292 cents 473:491:563:623:683:755:826:911:1007:1139:1271:1391 SD: 0.1258 cents 498:517:593:656:719:795:870:959:1060:1199:1338:1464 SD: 0.0965 cents