Scala analysis: Malawi_Asena_01
Asena 1 (Bangwe), Malawi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 243.000 cents 243.000000 2: 379.000 cents 379.000000 3: 554.000 cents 554.000000 4: 755.000 cents 755.000000 5: 936.000 cents 936.000000 6: 1116.000 cents 1116.000000 7: 1295.000 cents 1295.000000 8: 1443.000 cents 1443.000000 9: 1579.000 cents 1579.000000 10: 1730.000 cents 1730.000000 11: 1912.000 cents 1912.000000
SHOW/INTERVAL
0: 182.0000 cents 182.0000 1: 243.0000 cents 243.0000 2: 136.0000 cents 136.0000 3: 175.0000 cents 175.0000 4: 201.0000 cents 201.0000 5: 181.0000 cents 181.0000 6: 180.0000 cents 180.0000 7: 179.0000 cents 179.0000 8: 148.0000 cents 148.0000 9: 136.0000 cents 136.0000 10: 151.0000 cents 151.0000 11: 182.0000 cents 182.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 136.00000 cents 1: 1 148.00000 cents 1: 1 151.00000 cents 1: 1 175.00000 cents 1: 1 179.00000 cents 1: 1 180.00000 cents 1: 1 181.00000 cents 1: 1 182.00000 cents 1: 1 201.00000 cents 1: 1 243.00000 cents 2: 1 284.00000 cents 2: 1 287.00000 cents 2: 1 311.00000 cents 2: 1 327.00000 cents 2: 1 333.00000 cents 2: 1 359.00000 cents 2: 1 361.00000 cents 2: 1 376.00000 cents 2: 1 379.00000 cents 2: 1 382.00000 cents 2: 1 425.00000 cents 3: 1 435.00000 cents 3: 1 463.00000 cents 3: 1 469.00000 cents 3: 1 507.00000 cents 3: 1 512.00000 cents 3: 1 540.00000 cents 3: 1 554.00000 cents 3: 1 557.00000 cents 3: 1 561.00000 cents 3: 1 562.00000 cents 3: 1 576.00000 cents 4: 1 614.00000 cents 4: 1 617.00000 cents 4: 1 643.00000 cents 4: 1 688.00000 cents 4: 1 693.00000 cents 4: 2 712.00000 cents 4: 1 736.00000 cents 4: 1 737.00000 cents 4: 1 741.00000 cents 4: 1 755.00000 cents 5: 1 794.00000 cents 5: 1 796.00000 cents 5: 1 824.00000 cents 5: 1 848.00000 cents 5: 1 860.00000 cents 5: 1 873.00000 cents 5: 1 887.00000 cents 5: 1 889.00000 cents 5: 1 916.00000 cents 5: 1 936.00000 cents 5: 1 937.00000 cents 6: 1 975.00000 cents 6: 1 976.00000 cents 6: 1 996.00000 cents 6: 1 1023.00000 cents 6: 1 1025.00000 cents 6: 1 1039.00000 cents 6: 1 1052.00000 cents 6: 1 1064.00000 cents 6: 1 1088.00000 cents 6: 1 1116.00000 cents 6: 1 1118.00000 cents 7: 1 1157.00000 cents 7: 1 1171.00000 cents 7: 1 1175.00000 cents 7: 1 1176.00000 cents 7: 2 1200.00000 cents 7: 1 1219.00000 cents 7: 1 1224.00000 cents 7: 1 1269.00000 cents 7: 1 1295.00000 cents 7: 1 1298.00000 cents 8: 1 1336.00000 cents 8: 1 1350.00000 cents 8: 1 1351.00000 cents 8: 1 1355.00000 cents 8: 1 1358.00000 cents 8: 1 1372.00000 cents 8: 1 1400.00000 cents 8: 1 1405.00000 cents 8: 1 1443.00000 cents 8: 1 1449.00000 cents 8: 1 1477.00000 cents 9: 1 1487.00000 cents 9: 1 1530.00000 cents 9: 1 1533.00000 cents 9: 1 1536.00000 cents 9: 1 1551.00000 cents 9: 1 1553.00000 cents 9: 1 1579.00000 cents 9: 1 1585.00000 cents 9: 1 1601.00000 cents 9: 1 1625.00000 cents 9: 1 1628.00000 cents 10: 1 1669.00000 cents 10: 1 1711.00000 cents 10: 1 1730.00000 cents 10: 1 1731.00000 cents 10: 1 1732.00000 cents 10: 1 1733.00000 cents 10: 1 1737.00000 cents 10: 1 1761.00000 cents 10: 1 1764.00000 cents 10: 2 1776.00000 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 10.60000 = 53/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 243.0 379.0 554.0 755.0 936.0 1116.0 1295.0 1443.0 1579.0 1730.0 1912.0 243.0 : 136.0 311.0 512.0 693.0 873.0 1052.0 1200.0 1336.0 1487.0 1669.0 1912.0 379.0 : 175.0 376.0 557.0 737.0 916.0 1064.0 1200.0 1351.0 1533.0 1776.0 1912.0 554.0 : 201.0 382.0 562.0 741.0 889.0 1025.0 1176.0 1358.0 1601.0 1737.0 1912.0 755.0 : 181.0 361.0 540.0 688.0 824.0 975.0 1157.0 1400.0 1536.0 1711.0 1912.0 936.0 : 180.0 359.0 507.0 643.0 794.0 976.0 1219.0 1355.0 1530.0 1731.0 1912.0 1116.0: 179.0 327.0 463.0 614.0 796.0 1039.0 1175.0 1350.0 1551.0 1732.0 1912.0 1295.0: 148.0 284.0 435.0 617.0 860.0 996.0 1171.0 1372.0 1553.0 1733.0 1912.0 1443.0: 136.0 287.0 469.0 712.0 848.0 1023.0 1224.0 1405.0 1585.0 1764.0 1912.0 1579.0: 151.0 333.0 576.0 712.0 887.0 1088.0 1269.0 1449.0 1628.0 1776.0 1912.0 1730.0: 182.0 425.0 561.0 736.0 937.0 1118.0 1298.0 1477.0 1625.0 1761.0 1912.0 1912.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 136.0000 .. 243.0000 cents 107.00000 cents 136.00000 cents 2: 284.0000 .. 425.0000 cents 141.00000 cents 41.00000 cents 3: 435.0000 .. 576.0000 cents 141.00000 cents 10.00000 cents 4: 614.0000 .. 755.0000 cents 141.00000 cents 38.00000 cents 5: 794.0000 .. 937.0000 cents 143.00000 cents 39.00000 cents 6: 975.0000 .. 1118.0000 cents 143.00000 cents 38.00000 cents 7: 1157.0000 .. 1298.0000 cents 141.00000 cents 39.00000 cents 8: 1336.0000 .. 1477.0000 cents 141.00000 cents 38.00000 cents 9: 1487.0000 .. 1628.0000 cents 141.00000 cents 10.00000 cents 10: 1669.0000 .. 1776.0000 cents 107.00000 cents 41.00000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 136.00000 cents, class 1 Average step (divided formal octave): 173.8182 cents Largest one step interval : 243.00000 cents Average / Smallest step : 1.278075 Largest / Average step : 1.398013 Largest / Smallest step : 1.786765 Median interval of one step : 179.00000 cents, amount: 1 Most common interval of one step : 136.00000 cents, amount: 2 Least squares average step : 178.28261 cents, oct.: 1961.10870 cents Scale is strictly proper Scale is a mode of a 1912-tone equal temperament with octave 1912.000 cents degrees: 243 379 554 755 936 1116 1295 1443 1579 1730 1912 Least number of segments generator : 957 of 957.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1641 of 1641.000 cents and inv. generated superset size: 720 = 709 more = 6545.455% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGHBIJ Step pattern size order : JADIGFEBACH Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 10.00000 cents Scale diversity : 0.324917 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.296025 Rothenberg efficiency : 0.188430 redundancy: 0.811570 Efficiency x scale size : 2.072727 Number of different interval sizes : 106 = 10.60000 / class Number of one step interval sizes : 10 Highest interval variety : 11 Mean interval variety : 10.60000 = 53/5 Median interval variety : 10 Lowest interval variety : 10 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 4, average 701.2500 cents Number of appreciable fifths : 3, average 705.6667 cents Number of recognisable fourths : 2, average 509.5000 cents Number of appreciable fourths : 1, average 507.0000 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 9.0909% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 51.6762 c. M: 78.2727 c. 12: 2 0 1 2 1 1 1 1 1 1 1 N D3 SD: 41.0009 c. M: 76.0000 c. 15: 2 1 1 2 1 2 1 1 1 1 2 N D3 SD: 36.8374 c. M: 72.9333 c. 16: 2 1 2 1 2 1 2 1 1 1 2 N D3 SD: 30.4112 c. M: 57.0000 c. 17: 2 1 2 2 1 2 1 2 1 1 2 N D3 SD: 30.3459 c. M: 57.8235 c. 20: 3 1 2 2 2 2 2 1 2 1 2 N T3 SD: 26.9128 c. M:-46.2000 c. 21: 3 1 2 2 2 2 2 2 1 2 2 P D3 SD: 20.6090 c. M: 31.1905 c. 24: 3 2 2 2 3 2 2 2 2 2 2 P D3 S SD: 17.7388 c. M: 38.0000 c. 25: 3 2 2 3 2 3 2 2 2 2 2 P D3 SD: 18.2177 c. M:-31.2000 c. 27: 3 2 3 3 2 3 2 2 2 2 3 N SD: 21.9732 c. M: 30.5556 c. 28: 4 2 2 3 3 2 3 2 2 2 3 N SD: 17.9789 c. M:-30.7143 c. 29: 4 2 2 3 3 3 3 2 2 2 3 N SD: 17.4801 c. M: 29.7586 c. 30: 4 2 3 3 3 3 2 3 2 2 3 P SD: 17.1465 c. M:-31.2000 c. 31: 4 2 3 3 3 3 3 2 2 3 3 P SD: 14.9133 c. M: 37.0645 c. 32: 4 2 3 4 3 3 3 2 2 3 3 P SD: 16.6870 c. M: 25.5000 c. 34: 4 3 3 3 4 3 3 3 2 3 3 P SD: 14.2178 c. M: 23.9412 c. 38: 5 3 3 4 4 3 4 3 2 3 4 N SD: 14.4130 c. M:-23.5263 c. 40: 5 3 4 4 4 3 4 3 3 3 4 P SD: 11.1636 c. M:-20.0000 c. 41: 5 3 4 4 4 4 4 3 3 3 4 P SD: 6.3914 c. M:-10.7561 c. 62: 8 4 6 6 6 6 6 5 4 5 6 P SD: 7.1118 c. M: 14.8710 c. 65: 8 5 6 7 6 6 6 5 5 5 6 SP SD: 5.5936 c. M:-9.8000 c. 84: 11 6 7 9 8 8 8 6 6 7 8 P SD: 5.7059 c. M: 9.0000 c. 86: 11 6 8 9 8 8 8 7 6 7 8 SP SD: 2.7628 c. M: 5.5116 c. 125: 16 9 11 13 12 12 12 9 9 10 12 P SD: 3.4793 c. M: 5.4960 c. 127: 16 9 12 13 12 12 12 10 9 10 12 SP SD: 2.0516 c. M:-3.0394 c. 180: 23 13 16 19 17 17 17 14 13 14 17 SP SD: 1.8564 c. M:-3.7111 c. 211: 27 15 19 22 20 20 20 16 15 17 20 SP SD: 1.7971 c. M: 2.8863 c. 241: 31 17 22 25 23 23 22 19 17 19 23 SP SD: 1.5638 c. M:-2.9419 c. 253: 32 18 23 27 24 24 23 20 18 20 24 SP SD: 1.4783 c. M: 2.6996 c. 266: 34 19 24 28 25 25 25 21 19 21 25 SP SD: 1.5788 c. M:-2.3534 c. 269: 34 19 25 28 26 25 25 21 19 21 26 SP SD: 1.5237 c. M: 2.8030 c. 276: 35 20 25 29 26 26 26 21 20 22 26 SP SD: 1.1172 c. M: 2.0725 c. 314: 40 22 29 33 30 29 30 24 22 25 30 SP SD: 1.2213 c. M:-1.9936 c. 317: 40 23 29 33 30 30 30 24 23 25 30 SP SD: 1.1758 c. M:-1.7823 c. 322: 41 23 29 34 31 30 30 25 23 25 31 SP SD: 1.1645 c. M:-2.1863 c. 339: 43 24 31 36 32 32 32 26 24 27 32 SP SD: 1.0602 c. M:-2.2271 c. 400: 51 28 37 42 38 37 38 31 28 32 38 SP SD: 1.0371 c. M: 2.2600 c. 403: 51 29 37 42 38 38 38 31 29 32 38 SP SD: 0.9629 c. M:-1.7122 c. 408: 52 29 37 43 39 38 38 32 29 32 39 SP SD: 0.8234 c. M: 1.5882 c. 449: 57 32 41 47 43 42 42 35 32 35 43 SP SD: 0.6851 c. M: 1.2717 c. 505: 64 36 46 53 48 48 47 39 36 40 48 SP SD: 0.7634 c. M: 1.5584 c. 535: 68 38 49 56 51 50 50 42 38 42 51 SP SD: 0.6543 c. M: 1.2729 c. 545: 69 39 50 57 52 51 51 42 39 43 52 SP SD: 0.5898 c. M: 1.1064 c. 607: 77 43 56 64 57 57 57 47 43 48 58 SP SD: 0.6718 c. M: 1.0099 c. 620: 79 44 57 65 59 58 58 48 44 49 59 SP SD: 0.6386 c. M:-1.4968 c. 631: 80 45 58 66 60 59 59 49 45 50 60 SP SD: 0.5832 c. M: 1.1426 c. 639: 81 46 58 67 61 60 60 49 46 50 61 SP SD: 0.6651 c. M:-1.0063 c. 651: 83 46 60 68 62 61 61 50 47 51 62 SP SD: 0.6634 c. M:-1.1167 c. 660: 84 47 60 70 62 62 62 51 47 52 63 SP SD: 0.5193 c. M:-1.1091 c. 694: 88 50 63 73 66 65 65 54 49 55 66 SP SD: 0.5179 c. M:-1.1960 c. 701: 89 50 64 74 66 66 66 54 50 55 67 SP SD: 0.4066 c. M: 0.7447 c. 787: 100 56 72 83 74 74 74 61 56 62 75 SP SD: 0.3815 c. M: 0.8691 c. 843: 107 60 77 89 80 79 79 65 60 67 80 SP SD: 0.4072 c. M:-0.7212 c. 884: 112 63 81 93 84 83 83 68 63 70 84 SP SD: 0.4015 c. M: 0.7557 c. 935: 119 66 86 98 89 88 87 73 66 74 89 SP SD: 0.4616 c. M:-0.7134 c. 942: 120 67 86 99 89 89 88 73 67 74 90 SP SD: 0.3503 c. M: 0.6752 c. 970: 123 69 89 102 92 91 91 75 69 77 92 SP SD: 0.3402 c. M:-0.6557 c. 1028: 131 73 94 108 97 97 96 80 73 81 98 SP SD: 0.3453 c. M:-0.6498 c. 1064: 135 76 97 112 101 100 100 82 76 84 101 SP SD: 0.3766 c. M:-0.6316 c. 1069: 136 76 98 112 101 101 100 83 76 84 102 SP SD: 0.3211 c. M: 0.5688 c. 1124: 143 80 103 118 106 106 105 87 80 89 107 SP SD: 0.3547 c. M:-0.5480 c. 1125: 143 80 103 118 107 106 105 87 80 89 107 SP SD: 0.2668 c. M:-0.6080 c. 1187: 151 84 109 125 112 112 111 92 84 94 113 SP SD: 0.2770 c. M: 0.4659 c. 1211: 154 86 111 127 115 114 113 94 86 96 115 SP SD: 0.2354 c. M:-0.4310 c. 1367: 174 97 125 144 129 129 128 106 97 108 130 SP SD: 0.2351 c. M:-0.4411 c. 1463: 186 104 134 154 138 138 137 113 104 116 139 SP SD: 0.2103 c. M:-0.3903 c. 1595: 203 113 146 168 151 150 149 124 113 126 152 SP SD: 0.2337 c. M: 0.3542 c. 1636: 208 116 150 172 155 154 153 127 116 129 156 SP SD: 0.1885 c. M:-0.3496 c. 1785: 227 127 163 188 169 168 167 138 127 141 170 SP SD: 0.1460 c. M: 0.2162 c. 1826: 232 130 167 192 173 172 171 141 130 144 174 SP SD: 0.1301 c. M:-0.2596 c. 1912: 243 136 175 201 181 180 179 148 136 151 182 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x 2 x x x x 3 S SD: 42.2992 cents 2 x x x 3 x 4 x x 5 x 6 S SD: 25.0302 cents 3 x x 4 x 5:6 x 7 x 8:9 S SD: 20.1009 cents 4 x 5 x 6:7:8 x 9:10:11:12 S SD: 14.3275 cents 5 x 6:7:8:9:10:11 x 12:14:15 S SD: 20.4150 cents 6:7 x 8:9:10:11:13:14:15:16:18 SD: 13.1399 cents 7:8:9:10:11:12:13:15:16:17:19:21 SD: 10.2531 cents 8:9:10:11:12:14:15:17:18:20:22:24 SD: 8.3740 cents 10 x 12:14:15:17:19:21:23:25:27:30 SD: 9.1329 cents 11:13:14:15:17:19:21:23:25:27:30:33 SD: 6.7847 cents 13:15:16:18:20:22:25:27:30:32:35:39 SD: 5.0558 cents 18:21:22:25:28:31:34:38:41:45:49:54 SD: 4.6547 cents 19:22:24:26:29:33:36:40:44:47:52:57 SD: 4.4906 cents 20:23:25:28:31:34:38:42:46:50:54:60 SD: 3.6151 cents 21:24:26:29:32:36:40:44:48:52:57:63 SD: 3.4723 cents 24:28:30:33:37:41:46:51:55:60:65:72 SD: 3.1239 cents 29:33:36:40:45:50:55:61:67:72:79:88 SD: 2.5590 cents 32:37:40:44:49:55:61:68:74:80:87:97 SD: 2.4421 cents 33:38:41:45:51:57:63:70:76:82:90:100 SD: 2.1926 cents 40:46:50:55:62:69:76:85:92:100:109:121 SD: 1.7345 cents 45:52:56:62:70:77:86:95:104:112:122:136 SD: 1.5523 cents 53:61:66:73:82:91:101:112:122:132:144:160 SD: 0.1556 cents 339:390:422:467:524:582:646:716:780:844:921:1023 SD: 0.1414 cents 392:451:488:540:606:673:747:828:902:976:1065:1183 SD: 0.1218 cents 445:512:554:613:688:764:848:940:1024:1108:1209:1343 SD: 0.1100 cents 498:573:620:686:770:855:949:1052:1146:1240:1353:1503 SD: 0.1034 cents 551:634:686:759:852:946:1050:1164:1268:1372:1497:1663 SD: 0.1001 cents 584:672:727:804:903:1003:1113:1234:1344:1454:1586:1762 SD: 0.0976 cents