Scala analysis: Malawi_Asena_04
Asena 4 (Bangwe), Malawi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 210.000 cents 210.000000 2: 382.000 cents 382.000000 3: 567.000 cents 567.000000 4: 708.000 cents 708.000000 5: 888.000 cents 888.000000 6: 1072.000 cents 1072.000000 7: 1279.000 cents 1279.000000 8: 1446.000 cents 1446.000000 9: 1614.000 cents 1614.000000 10: 1767.000 cents 1767.000000
SHOW/INTERVAL
0: 153.0000 cents 153.0000 1: 210.0000 cents 210.0000 2: 172.0000 cents 172.0000 3: 185.0000 cents 185.0000 4: 141.0000 cents 141.0000 5: 180.0000 cents 180.0000 6: 184.0000 cents 184.0000 7: 207.0000 cents 207.0000 8: 167.0000 cents 167.0000 9: 168.0000 cents 168.0000 10: 153.0000 cents 153.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 141.00000 cents 1: 1 153.00000 cents 1: 1 167.00000 cents 1: 1 168.00000 cents 1: 1 172.00000 cents 1: 1 180.00000 cents 1: 1 184.00000 cents 1: 1 185.00000 cents 1: 1 207.00000 cents 1: 1 210.00000 cents 2: 2 321.00000 cents 2: 1 326.00000 cents 2: 1 335.00000 cents 2: 1 357.00000 cents 2: 1 363.00000 cents 2: 1 364.00000 cents 2: 1 374.00000 cents 2: 1 382.00000 cents 2: 1 391.00000 cents 3: 1 488.00000 cents 3: 1 498.00000 cents 3: 1 505.00000 cents 3: 1 506.00000 cents 3: 1 531.00000 cents 3: 1 535.00000 cents 3: 1 542.00000 cents 3: 1 558.00000 cents 3: 1 567.00000 cents 3: 1 571.00000 cents 4: 1 678.00000 cents 4: 1 690.00000 cents 4: 1 695.00000 cents 4: 1 698.00000 cents 4: 1 703.00000 cents 4: 1 708.00000 cents 4: 1 712.00000 cents 4: 1 720.00000 cents 4: 1 726.00000 cents 4: 1 738.00000 cents 5: 1 861.00000 cents 5: 1 862.00000 cents 5: 1 870.00000 cents 5: 2 879.00000 cents 5: 2 888.00000 cents 5: 1 897.00000 cents 5: 1 905.00000 cents 5: 1 906.00000 cents 6: 1 1029.00000 cents 6: 1 1041.00000 cents 6: 1 1047.00000 cents 6: 1 1055.00000 cents 6: 1 1059.00000 cents 6: 1 1064.00000 cents 6: 1 1069.00000 cents 6: 1 1072.00000 cents 6: 1 1077.00000 cents 6: 1 1089.00000 cents 7: 1 1196.00000 cents 7: 1 1200.00000 cents 7: 1 1209.00000 cents 7: 1 1225.00000 cents 7: 1 1232.00000 cents 7: 1 1236.00000 cents 7: 1 1261.00000 cents 7: 1 1262.00000 cents 7: 1 1269.00000 cents 7: 1 1279.00000 cents 8: 1 1376.00000 cents 8: 1 1385.00000 cents 8: 1 1393.00000 cents 8: 1 1403.00000 cents 8: 1 1404.00000 cents 8: 1 1410.00000 cents 8: 1 1432.00000 cents 8: 1 1441.00000 cents 8: 2 1446.00000 cents 9: 1 1557.00000 cents 9: 1 1560.00000 cents 9: 1 1582.00000 cents 9: 1 1583.00000 cents 9: 1 1587.00000 cents 9: 1 1595.00000 cents 9: 1 1599.00000 cents 9: 1 1600.00000 cents 9: 1 1614.00000 cents 9: 1 1626.00000 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 9.55556 = 86/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 210.0 382.0 567.0 708.0 888.0 1072.0 1279.0 1446.0 1614.0 1767.0 210.0 : 172.0 357.0 498.0 678.0 862.0 1069.0 1236.0 1404.0 1557.0 1767.0 382.0 : 185.0 326.0 506.0 690.0 897.0 1064.0 1232.0 1385.0 1595.0 1767.0 567.0 : 141.0 321.0 505.0 712.0 879.0 1047.0 1200.0 1410.0 1582.0 1767.0 708.0 : 180.0 364.0 571.0 738.0 906.0 1059.0 1269.0 1441.0 1626.0 1767.0 888.0 : 184.0 391.0 558.0 726.0 879.0 1089.0 1261.0 1446.0 1587.0 1767.0 1072.0: 207.0 374.0 542.0 695.0 905.0 1077.0 1262.0 1403.0 1583.0 1767.0 1279.0: 167.0 335.0 488.0 698.0 870.0 1055.0 1196.0 1376.0 1560.0 1767.0 1446.0: 168.0 321.0 531.0 703.0 888.0 1029.0 1209.0 1393.0 1600.0 1767.0 1614.0: 153.0 363.0 535.0 720.0 861.0 1041.0 1225.0 1432.0 1599.0 1767.0 1767.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 141.0000 .. 210.0000 cents 69.00000 cents 141.00000 cents 2: 321.0000 .. 391.0000 cents 70.00000 cents 111.00000 cents 3: 488.0000 .. 571.0000 cents 83.00000 cents 97.00000 cents 4: 678.0000 .. 738.0000 cents 60.00000 cents 107.00000 cents 5: 861.0000 .. 906.0000 cents 45.00000 cents 123.00000 cents 6: 1029.0000 .. 1089.0000 cents 60.00000 cents 123.00000 cents 7: 1196.0000 .. 1279.0000 cents 83.00000 cents 107.00000 cents 8: 1376.0000 .. 1446.0000 cents 70.00000 cents 97.00000 cents 9: 1557.0000 .. 1626.0000 cents 69.00000 cents 111.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 141.00000 cents, class 1 Average step (divided formal octave): 176.7000 cents Largest one step interval : 210.00000 cents Average / Smallest step : 1.253191 Largest / Average step : 1.188455 Largest / Smallest step : 1.489362 Median interval of one step : 176.00000 cents, amount: 0 Least squares average step : 179.47013 cents, oct.: 1794.70130 cents Scale is strictly proper Scale is a mode of a 1767-tone equal temperament with octave 1767.000 cents degrees: 210 382 567 708 888 1072 1279 1446 1614 1767 Least number of segments generator : 886 of 886.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1237 of 1237.000 cents and inv. generated superset size: 422 = 412 more = 4220.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGHIJ Step pattern size order : JEHAFGICDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 97.00000 cents Scale diversity : 0.462567 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.655348 Rothenberg efficiency : 0.208889 redundancy: 0.791111 Efficiency x scale size : 2.088889 Number of different interval sizes : 86 = 9.55556 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 9.55556 = 86/9 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 7, average 703.7143 cents Number of appreciable fifths : 6, average 701.0000 cents Number of recognisable fourths : 4, average 499.2500 cents Formal octave complements present : 1 = 10.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 83.0000 cents: 5 Limited inverse transpositions with margin 83.0000 cents: 3 7 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 26.1405 c. M: 42.1000 c. 18: 2 2 2 1 2 2 2 2 1 2 SP B ME S SD: 19.7186 c. M: 43.3333 c. Supersharp-10 22: 3 2 2 2 2 2 3 2 2 2 SP D3 SD: 15.7411 c. M:-30.9545 c. 26: 3 3 2 2 3 3 3 2 3 2 SP D3 SD: 17.6159 c. M: 28.3846 c. 28: 3 3 3 2 3 3 3 3 2 3 SP B ME S SD: 15.1163 c. M: 36.3214 c. Supersharp-10 31: 4 3 3 2 4 3 3 3 3 3 SP D3 SD: 18.1246 c. M: 25.0000 c. 32: 4 3 3 3 3 3 4 3 3 3 SP D3 SD: 11.5938 c. M: 22.8438 c. 33: 4 3 4 2 4 3 4 3 3 3 SP D3 SD: 11.3474 c. M:-22.2727 c. 34: 4 3 4 3 3 4 4 3 3 3 SP D3 SD: 12.8093 c. M:-20.2647 c. 40: 5 4 4 3 4 4 5 4 4 3 SP T3 SD: 10.6625 c. M:-20.4750 c. 42: 5 4 4 4 4 4 5 4 4 4 SP D3 SD: 12.8665 c. M: 20.2143 c. 43: 5 4 5 3 4 5 5 4 4 4 SP SD: 10.8709 c. M: 25.0465 c. 44: 5 5 4 4 4 5 5 4 4 4 SP B D3 S SD: 9.8952 c. M:-19.5909 c. 46: 5 5 5 3 5 5 5 5 4 4 SP T3 SD: 10.1754 c. M: 17.9348 c. 48: 6 4 5 4 5 5 6 4 5 4 SP SD: 9.3377 c. M: 14.8125 c. 50: 6 5 5 4 5 5 6 5 5 4 SP T3 SD: 6.3465 c. M: 11.8000 c. 59: 7 6 6 5 6 6 7 5 6 5 SP SD: 6.9399 c. M:-10.7797 c. 60: 7 6 6 5 6 6 7 6 6 5 SP T3 SD: 6.5861 c. M: 12.6500 c. 65: 8 6 7 5 7 6 8 6 6 6 SP SD: 6.5376 c. M: 11.8000 c. 66: 8 6 7 5 7 7 8 6 6 6 SP SD: 5.9211 c. M: 11.9091 c. 68: 8 7 7 5 7 7 8 7 6 6 SP SD: 5.6308 c. M:-9.1765 c. 76: 9 7 8 6 8 8 9 7 7 7 SP SD: 6.5855 c. M: 10.5000 c. 77: 9 8 8 6 8 8 9 7 7 7 SP SD: 5.6696 c. M:-8.1169 c. 78: 9 8 8 6 8 8 9 8 7 7 SP SD: 5.5426 c. M: 10.3846 c. 82: 10 8 8 7 8 9 9 8 8 7 SP SD: 4.8705 c. M: 7.6220 c. 83: 10 8 9 6 9 8 10 8 8 7 SP SD: 4.6529 c. M:-7.8072 c. 84: 10 8 9 7 8 9 10 8 8 7 SP SD: 4.0704 c. M:-7.2143 c. 94: 11 9 10 8 9 10 11 9 9 8 SP SD: 3.5526 c. M:-6.3191 c. 105: 13 10 11 8 11 11 12 10 10 9 SP SD: 4.1865 c. M:-8.7714 c. 109: 13 11 11 9 11 11 13 10 11 9 SP SD: 3.9926 c. M:-7.1009 c. 112: 13 11 12 9 11 12 13 11 10 10 SP SD: 3.3872 c. M:-5.4643 c. 115: 14 11 12 9 12 12 13 11 11 10 SP SD: 2.7214 c. M:-5.1130 c. 127: 15 12 14 10 13 13 15 12 12 11 SP SD: 2.5456 c. M: 6.3386 c. 128: 15 13 13 10 13 14 15 12 12 11 SP SD: 3.5452 c. M:-4.8359 c. 130: 15 13 14 10 13 14 15 12 13 11 SP SD: 3.4703 c. M: 6.1154 c. 134: 16 13 14 11 13 14 16 13 12 12 SP SD: 3.1783 c. M: 5.2388 c. 135: 16 13 14 11 14 14 16 12 13 12 SP SD: 3.1617 c. M: 6.2222 c. 137: 16 14 14 11 14 14 16 13 13 12 SP SD: 2.3543 c. M:-4.9343 c. 149: 18 14 16 12 15 15 18 14 14 13 SP SD: 2.5497 c. M: 4.6846 c. 152: 18 15 16 12 15 16 18 14 15 13 SP SD: 2.4837 c. M: 4.5000 c. 153: 18 15 16 12 16 16 18 14 15 13 SP SD: 2.1708 c. M: 3.5098 c. 175: 21 17 18 14 18 18 21 16 17 15 SP SD: 1.7905 c. M:-3.3371 c. 185: 22 18 19 15 19 19 22 17 18 16 SP SD: 1.8296 c. M: 3.7459 c. 193: 23 19 20 15 20 20 23 18 18 17 SP SD: 1.7863 c. M: 3.0311 c. 199: 24 19 21 16 20 21 23 19 19 17 SP SD: 1.6967 c. M:-3.1055 c. 209: 25 20 22 17 21 22 24 20 20 18 SP SD: 1.3673 c. M: 2.3636 c. 269: 32 26 28 22 27 28 32 25 26 23 SP SD: 1.3667 c. M: 2.0855 c. 277: 33 27 29 22 28 29 32 27 26 24 SP SD: 1.3244 c. M: 3.1877 c. 287: 34 28 30 23 29 30 34 27 27 25 SP SD: 0.8694 c. M:-1.6132 c. 384: 46 37 40 31 39 40 45 36 37 33 SP SD: 0.8287 c. M:-1.6719 c. 392: 47 38 41 31 40 41 46 37 37 34 SP SD: 0.9400 c. M:-1.8597 c. 402: 48 39 42 32 41 42 47 38 38 35 SP SD: 0.4741 c. M:-0.9851 c. 496: 59 48 52 40 50 52 58 47 47 43 SP SD: 0.5520 c. M:-0.9375 c. 579: 69 56 61 46 59 60 68 55 55 50 SP SD: 0.4737 c. M: 0.8135 c. 589: 70 57 62 47 60 61 69 56 56 51 SP SD: 0.5477 c. M: 1.0000 c. 623: 74 61 65 50 63 65 73 59 59 54 SP SD: 0.4900 c. M:-1.0690 c. 666: 79 65 70 53 68 69 78 63 63 58 SP SD: 0.4895 c. M: 0.8829 c. 689: 82 67 72 55 70 72 81 65 65 60 SP SD: 0.4572 c. M: 0.8752 c. 699: 83 68 73 56 71 73 82 66 66 61 SP SD: 0.5203 c. M: 1.2017 c. 704: 84 68 74 56 72 73 83 66 67 61 SP SD: 0.5103 c. M:-1.0710 c. 714: 85 69 75 57 73 74 84 67 68 62 SP SD: 0.4828 c. M: 0.8824 c. 716: 85 70 75 57 73 74 84 68 68 62 SP SD: 0.4789 c. M: 0.9413 c. 717: 85 70 75 57 73 75 84 68 68 62 SP SD: 0.4341 c. M: 0.8033 c. 776: 92 76 81 62 79 81 91 73 74 67 SP SD: 0.3916 c. M:-0.7088 c. 786: 93 77 82 63 80 82 92 74 75 68 SP SD: 0.3913 c. M: 0.9275 c. 808: 96 79 84 65 82 84 95 76 77 70 SP SD: 0.4115 c. M:-0.7042 c. 832: 99 81 87 66 85 87 97 79 79 72 SP SD: 0.3752 c. M: 0.7752 c. 869: 103 85 91 69 89 90 102 82 83 75 SP SD: 0.3835 c. M:-0.5834 c. 876: 104 85 92 70 89 91 103 83 83 76 SP SD: 0.4354 c. M: 0.9075 c. 891: 106 87 93 71 91 93 104 84 85 77 SP SD: 0.4281 c. M:-0.8923 c. 898: 107 87 94 72 91 94 105 85 85 78 SP SD: 0.3711 c. M: 0.5646 c. 925: 110 90 97 74 94 96 109 87 88 80 SP SD: 0.4063 c. M:-0.8811 c. 926: 110 90 97 74 94 97 108 88 88 80 SP SD: 0.3733 c. M: 0.6836 c. 935: 111 91 98 75 95 97 110 88 89 81 SP SD: 0.3339 c. M:-0.6898 c. 981: 117 95 103 78 100 102 115 93 93 85 SP SD: 0.3135 c. M:-0.7431 c. 991: 118 96 104 79 101 103 116 94 94 86 SP SD: 0.3066 c. M: 0.5550 c. 1050: 125 102 110 84 107 109 123 99 100 91 SP SD: 0.2965 c. M:-0.5486 c. 1068: 127 104 112 85 109 111 125 101 102 92 SP SD: 0.3405 c. M:-0.7865 c. 1078: 128 105 113 86 110 112 126 102 103 93 SP SD: 0.2922 c. M:-0.5594 c. 1096: 130 107 115 87 112 114 128 104 104 95 SP SD: 0.3041 c. M: 0.5046 c. 1101: 131 107 115 88 112 115 129 104 105 95 SP SD: 0.2961 c. M:-0.5341 c. 1118: 133 109 117 89 114 116 131 106 106 97 SP SD: 0.3056 c. M:-0.4812 c. 1119: 133 109 117 89 114 117 131 106 106 97 SP SD: 0.3051 c. M: 0.5684 c. 1129: 134 110 118 90 115 118 132 107 107 98 SP SD: 0.3501 c. M: 0.5872 c. 1134: 135 110 119 90 116 118 133 107 108 98 SP SD: 0.2744 c. M: 0.5767 c. 1144: 136 111 120 91 117 119 134 108 109 99 SP SD: 0.2669 c. M: 0.5822 c. 1178: 140 115 123 94 120 123 138 111 112 102 SP SD: 0.2739 c. M:-0.5000 c. 1188: 141 116 124 95 121 124 139 112 113 103 SP SD: 0.2309 c. M:-0.3965 c. 1271: 151 124 133 101 130 132 149 120 121 110 SP SD: 0.2154 c. M: 0.3659 c. 1337: 159 130 140 107 136 139 157 126 127 116 SP SD: 0.2094 c. M:-0.3859 c. 1355: 161 132 142 108 138 141 159 128 129 117 SP SD: 0.2001 c. M:-0.4251 c. 1365: 162 133 143 109 139 142 160 129 130 118 SP SD: 0.1396 c. M: 0.2901 c. 1757: 209 171 184 140 179 183 206 166 167 152 SP SD: 0.1488 c. M:-0.2396 c. 1767: 210 172 185 141 180 184 207 167 168 153 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 x x 3 S SD: 78.1886 cents 2 x x x 3 x x 4 x 5:6 S SD: 39.7311 cents 3 x x 4 x 5 x 6:7 x 8 S SD: 25.4554 cents 4 x 5 x 6:7 x 8:9:10:11 S SD: 17.8503 cents 5 x 6:7 x 8:9:10:12:13:14 S SD: 20.1847 cents 6:7 x 8:9:10:11:13:14:15:17 SD: 13.4249 cents 7:8:9:10:11:12:13:15:16:18:19 SD: 13.1030 cents 8:9:10:11:12:13:15:17:18:20:22 SD: 7.9462 cents 13:15:16:18:20:22:24:27:30:33:36 SD: 6.4871 cents 15:17:19:21:23:25:28:31:35:38:42 SD: 5.7720 cents 16:18:20:22:24:27:30:33:37:41:44 SD: 4.5664 cents 21:24:26:29:32:35:39:44:48:53:58 SD: 3.9319 cents 23:26:29:32:35:38:43:48:53:58:64 SD: 3.8036 cents 24:27:30:33:36:40:45:50:55:61:67 SD: 3.0001 cents 30:34:37:42:45:50:56:63:69:76:83 SD: 2.9370 cents 31:35:39:43:47:52:58:65:71:79:86 SD: 2.7836 cents 33:37:41:46:50:55:61:69:76:84:92 SD: 2.3260 cents 36:41:45:50:54:60:67:75:83:91:100 SD: 2.1401 cents 44:50:55:61:66:73:82:92:101:112:122 SD: 2.0622 cents 45:51:56:62:68:75:84:94:104:114:125 SD: 1.9862 cents 46:52:57:64:69:77:85:96:106:117:128 SD: 1.8240 cents 48:54:60:67:72:80:89:100:111:122:133 SD: 1.8103 cents 49:55:61:68:74:82:91:103:113:124:136 SD: 1.5734 cents 52:59:65:72:78:87:97:109:120:132:144 SD: 1.5140 cents 54:61:67:75:81:90:100:113:124:137:150 SD: 1.4472 cents 57:64:71:79:86:95:106:119:131:145:158 SD: 1.3806 cents 61:69:76:85:92:102:113:128:141:155:169 SD: 1.2292 cents 69:78:86:96:104:115:128:144:159:175:191 SD: 1.0327 cents 77:87:96:107:116:129:143:161:178:196:214 SD: 0.9226 cents 85:96:106:118:128:142:158:178:196:216:236 SD: 0.2314 cents 279:315:348:387:420:466:518:584:643:709:774 SD: 0.1491 cents 364:411:454:505:548:608:676:762:839:925:1010 SD: 0.1031 cents 449:507:560:623:676:750:834:940:1035:1141:1246 SD: 0.0960 cents