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