Scala analysis: Malawi_Asena_08

Asena 8 (Bangwe), Malawi

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        173.000 cents     173.000000
  2:        390.000 cents     390.000000
  3:        547.000 cents     547.000000
  4:        707.000 cents     707.000000
  5:        875.000 cents     875.000000
  6:       1081.000 cents    1081.000000
  7:       1249.000 cents    1249.000000
  8:       1402.000 cents    1402.000000
SHOW/INTERVAL
  0:        153.0000 cents    153.0000
  1:        173.0000 cents    173.0000
  2:        217.0000 cents    217.0000
  3:        157.0000 cents    157.0000
  4:        160.0000 cents    160.0000
  5:        168.0000 cents    168.0000
  6:        206.0000 cents    206.0000
  7:        168.0000 cents    168.0000
  8:        153.0000 cents    153.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 153.00000 cents
  1:   1 157.00000 cents
  1:   1 160.00000 cents
  1:   2 168.00000 cents
  1:   1 173.00000 cents
  1:   1 206.00000 cents
  1:   1 217.00000 cents
  2:   1 317.00000 cents
  2:   1 321.00000 cents
  2:   1 326.00000 cents
  2:   1 328.00000 cents
  2:   3 374.00000 cents
  2:   1 390.00000 cents
  3:   1 485.00000 cents
  3:   1 494.00000 cents
  3:   1 527.00000 cents
  3:   2 534.00000 cents
  3:   1 542.00000 cents
  3:   1 543.00000 cents
  3:   1 547.00000 cents
  4:   1 691.00000 cents
  4:   1 695.00000 cents
  4:   2 700.00000 cents
  4:   2 702.00000 cents
  4:   1 707.00000 cents
  4:   1 711.00000 cents
  5:   1 855.00000 cents
  5:   1 859.00000 cents
  5:   1 860.00000 cents
  5:   2 868.00000 cents
  5:   1 875.00000 cents
  5:   1 908.00000 cents
  5:   1 917.00000 cents
  6:   1 1012.00000 cents
  6:   3 1028.00000 cents
  6:   1 1074.00000 cents
  6:   1 1076.00000 cents
  6:   1 1081.00000 cents
  6:   1 1085.00000 cents
  7:   1 1185.00000 cents
  7:   1 1196.00000 cents
  7:   1 1229.00000 cents
  7:   2 1234.00000 cents
  7:   1 1242.00000 cents
  7:   1 1245.00000 cents
  7:   1 1249.00000 cents
Highest number of different intervals for one interval class: 7
Average number of different intervals per interval class: 6.57143 = 46/7
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6      7      8     
 0.0   : 173.0 390.0 547.0 707.0 875.0 1081.0 1249.0 1402.0
 173.0 : 217.0 374.0 534.0 702.0 908.0 1076.0 1229.0 1402.0
 390.0 : 157.0 317.0 485.0 691.0 859.0 1012.0 1185.0 1402.0
 547.0 : 160.0 328.0 534.0 702.0 855.0 1028.0 1245.0 1402.0
 707.0 : 168.0 374.0 542.0 695.0 868.0 1085.0 1242.0 1402.0
 875.0 : 206.0 374.0 527.0 700.0 917.0 1074.0 1234.0 1402.0
 1081.0: 168.0 321.0 494.0 711.0 868.0 1028.0 1196.0 1402.0
 1249.0: 153.0 326.0 543.0 700.0 860.0 1028.0 1234.0 1402.0
 1402.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  153.0000  .. 217.0000 cents      64.00000 cents                     153.00000 cents
  2:  317.0000  .. 390.0000 cents      73.00000 cents                     100.00000 cents
  3:  485.0000  .. 547.0000 cents      62.00000 cents                     95.00000 cents
  4:  691.0000  .. 711.0000 cents      20.00000 cents                     144.00000 cents
  5:  855.0000  .. 917.0000 cents      62.00000 cents                     144.00000 cents
  6:  1012.0000 .. 1085.0000 cents     73.00000 cents                     95.00000 cents
  7:  1185.0000 .. 1249.0000 cents     64.00000 cents                     100.00000 cents
SHOW DATA
Number of notes                     : 8
-- Interval properties --
Smallest interval                   : 153.00000 cents, class 1
Average step (divided formal octave): 175.2500 cents
Largest one step interval           : 217.00000 cents
Average / Smallest step             : 1.145425
Largest / Average step              : 1.238231
Largest / Smallest step             : 1.418301
Median interval of one step         : 168.00000 cents, amount: 2
Most common interval of one step    : 168.00000 cents, amount: 2
Least squares average step          : 177.65686 cents, oct.:  1421.25490 cents
Scale is strictly proper
Scale is a mode of a 1402-tone equal temperament with octave  1402.000 cents
  degrees: 173 390 547 707 875 1081 1249 1402
Least number of segments generator  : 705 of 705.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 835 of 835.000 cents and inv.
  generated superset size: 405 = 397 more = 5062.500%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABCDEFEG
Step pattern size order : EGBCDFDA
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 95.00000 cents
Scale diversity                     : 0.964685
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.701854
Rothenberg efficiency               : 0.294643   redundancy: 0.705357
Efficiency x scale size             : 2.357143
Number of different interval sizes  : 46 = 6.57143 / class
Number of one step interval sizes   : 7
Highest interval variety            : 7
Mean interval variety               : 6.57143 = 46/7
Median interval variety             : 6
Lowest interval variety             : 6
Smallest interval difference        : 1.00000 cents
Most common intervals               : 374.00000 cents & inv., amount: 3
Number of recognisable fifths       : 8, average 701.0000 cents
Number of recognisable fourths      : 2, average 489.5000 cents
Number of appreciable fourths       : 1, average 494.0000 cents
Formal octave complements present   : 1 = 12.5000%
2/1 octave complements present      : 0 = 0.0000%
Limited transpositions with margin 73.0000 cents:
 4
Limited inverse transpositions with margin 73.0000 cents:
 3 7
-- Rational properties --
FIT/MODE
  8:  1 1 1 1 1 1 1 1  SP B ME I SD: 20.6753 c. M: 39.5000 c. 
 17:  2 3 2 2 2 2 2 2  SP M ME   SD: 22.3066 c. M:-35.2353 c. 
 18:  2 3 2 2 2 3 2 2  SP B ME   SD: 9.7790 c. M: 18.2222 c. 
 26:  3 4 3 3 3 4 3 3  SP B ME   SD: 8.7510 c. M: 12.5385 c. 
 39:  5 6 4 5 4 6 5 4  SP   D3   SD: 8.0587 c. M: 12.2308 c. 
 40:  5 6 5 4 5 6 5 4  SP B D3   SD: 7.4792 c. M:-13.8000 c. 
 43:  5 7 5 5 5 6 5 5  SP   D3   SD: 7.1984 c. M:-10.3023 c. 
 47:  6 7 5 6 5 7 6 5  SP   D3   SD: 6.9441 c. M: 10.0638 c. 
 48:  6 7 6 5 6 7 6 5  SP B D3   SD: 5.7051 c. M: 10.2917 c. 
 54:  7 8 6 6 7 8 6 6  SP B      SD: 5.8385 c. M:-9.4444 c. 
 56:  7 9 6 6 7 8 7 6  SP        SD: 4.9548 c. M:-10.5714 c. 
 58:  7 9 7 6 7 9 7 6  SP B D3   SD: 5.8457 c. M:-8.9655 c. 
 61:  8 9 7 7 7 9 7 7  SP        SD: 5.4249 c. M:-10.8689 c. 
 62:  8 9 7 7 8 9 7 7  SP B      SD: 5.5134 c. M:-7.9032 c. 
 64:  8 10 7 7 8 9 8 7  SP        SD: 3.8639 c. M: 7.5938 c. 
 67:  8 11 7 8 8 10 8 7  SP        SD: 5.3097 c. M:-7.5821 c. 
 71:  9 11 8 8 8 11 8 8  SP        SD: 4.8031 c. M: 6.1549 c. 
 72:  9 11 8 8 9 11 8 8  SP B      SD: 4.2280 c. M:-9.4444 c. 
 74:  9 12 8 8 9 11 9 8  SP        SD: 3.9581 c. M:-7.8649 c. 
 75:  9 12 8 9 9 11 9 8  SP        SD: 3.5262 c. M: 4.8933 c. 
 82:  10 13 9 9 10 12 10 9  SP        SD: 3.0701 c. M: 6.0000 c. 
 90:  11 14 10 10 11 13 11 10  SP        SD: 3.4369 c. M: 6.1333 c. 
 101: 12 16 11 12 12 15 12 11  SP        SD: 3.1426 c. M: 6.4257 c. 
 108: 13 17 12 12 13 16 13 12  SP        SD: 3.6253 c. M: 6.0000 c. 
 109: 13 17 12 13 13 16 13 12  SP        SD: 3.5172 c. M: 6.7798 c. 
 111: 14 17 12 13 13 17 13 12  SP        SD: 3.0381 c. M:-5.2342 c. 
 115: 14 18 13 13 14 17 13 13  SP        SD: 2.7842 c. M: 5.4870 c. 
 119: 15 18 13 14 14 18 14 13  SP        SD: 2.7228 c. M: 5.0504 c. 
 123: 15 19 14 14 15 18 15 13  SP        SD: 2.3462 c. M:-4.8211 c. 
 125: 15 20 14 14 15 18 15 14  SP        SD: 2.9673 c. M: 4.7600 c. 
 127: 16 19 15 14 15 19 15 14  SP        SD: 2.7997 c. M:-4.9685 c. 
 128: 16 20 14 15 15 19 15 14  SP        SD: 2.7747 c. M:-4.9531 c. 
 130: 16 20 15 15 15 19 16 14  SP        SD: 2.4458 c. M:-4.7846 c. 
 131: 16 20 15 15 16 19 16 14  SP        SD: 2.3432 c. M: 4.7176 c. 
 136: 17 21 15 16 16 20 16 15  SP        SD: 2.0403 c. M:-4.3088 c. 
 139: 17 22 15 16 17 20 17 15  SP        SD: 2.0120 c. M:-3.3669 c. 
 144: 18 22 16 17 17 21 17 16  SP        SD: 1.9954 c. M:-3.7361 c. 
 154: 19 24 17 18 18 23 18 17  SP        SD: 1.6634 c. M:-3.1039 c. 
 162: 20 25 18 19 19 24 19 18  SP        SD: 1.5691 c. M: 2.7778 c. 
 165: 20 26 18 19 20 24 20 18  SP        SD: 1.8360 c. M: 3.1939 c. 
 176: 22 27 20 20 21 26 21 19  SP        SD: 1.7997 c. M:-2.6477 c. 
 184: 23 28 21 21 22 27 22 20  SP        SD: 1.3752 c. M:-2.2500 c. 
 202: 25 31 23 23 24 30 24 22  SP        SD: 0.9969 c. M:-1.7327 c. 
 244: 30 38 27 28 29 36 29 27  SP        SD: 1.1222 c. M: 2.1393 c. 
 258: 32 40 29 29 31 38 31 28  SP        SD: 0.9335 c. M:-1.8450 c. 
 266: 33 41 30 30 32 39 32 29  SP        SD: 0.6138 c. M:-1.1504 c. 
 341: 42 53 38 39 41 50 41 37  SP        SD: 0.4888 c. M:-0.8768 c. 
 349: 43 54 39 40 42 51 42 38  SP        SD: 0.4239 c. M:-0.7479 c. 
 367: 45 57 41 42 44 54 44 40  SP        SD: 0.4975 c. M: 1.0926 c. 
 420: 52 65 47 48 50 62 50 46  SP        SD: 0.5100 c. M:-0.6762 c. 
 428: 53 66 48 49 51 63 51 47  SP        SD: 0.4725 c. M: 0.9579 c. 
 543: 67 84 61 62 65 80 65 59  SP        SD: 0.4452 c. M:-0.8379 c. 
 551: 68 85 62 63 66 81 66 60  SP        SD: 0.3493 c. M: 0.6969 c. 
 585: 72 91 65 67 70 86 70 64  SP        SD: 0.3832 c. M:-0.6427 c. 
 607: 75 94 68 69 73 89 73 66  SP        SD: 0.3251 c. M:-0.5585 c. 
 615: 76 95 69 70 74 90 74 67  SP        SD: 0.2772 c. M: 0.4341 c. 
 633: 78 98 71 72 76 93 76 69  SP        SD: 0.2192 c. M: 0.4629 c. 
 769: 95 119 86 88 92 113 92 84  SP        SD: 0.1804 c. M:-0.3810 c. 
 777: 96 120 87 89 93 114 93 85  SP        SD: 0.2432 c. M: 0.3719 c. 
 787: 97 122 88 90 94 116 94 86  SP        SD: 0.2166 c. M:-0.3393 c. 
 974: 120 151 109 111 117 143 117 106  SP        SD: 0.2076 c. M:-0.4209 c. 
 982: 121 152 110 112 118 144 118 107  SP        SD: 0.2181 c. M: 0.2892 c. 
 1035: 128 160 116 118 124 152 124 113  SP        SD: 0.1764 c. M:-0.3874 c. 
 1053: 130 163 118 120 126 155 126 115  SP        SD: 0.1405 c. M: 0.2479 c. 
 1061: 131 164 119 121 127 156 127 116  SP        SD: 0.1571 c. M: 0.2818 c. 
 1136: 140 176 127 130 136 167 136 124  SP        SD: 0.1437 c. M: 0.2694 c. 
 1376: 170 213 154 157 165 202 165 150  SP        SD: 0.1654 c. M:-0.2369 c. 
 1384: 171 214 155 158 166 203 166 151  SP        SD: 0.1272 c. M:-0.2370 c. 
 1394: 172 216 156 159 167 205 167 152  SP        SD: 0.1187 c. M:-0.2267 c. 
 1402: 173 217 157 160 168 206 168 153  SP        SD: 0.0000 c. M: 0.0000 c. 
FIT/HARMONIC
 1 x x x x x x 2 x  S SD: 49.0000 cents
 2 x x x 3 x x 4 x  S SD: 24.6295 cents
 3 x x 4 x 5 x 6:7  S SD: 23.8398 cents
 4 x 5 x 6:7 x 8:9  S SD: 21.2104 cents
 5 x 6:7 x 8:9:10:11  S SD: 22.5705 cents
 6:7 x 8:9:10:11:12:13  S SD: 19.5596 cents
 7:8:9:10:11:12:13:14:16  S SD: 18.8754 cents
 8:9:10:11:12:13:15:16:18    SD: 8.5321 cents
 16:18:20:22:24:27:30:33:36  S SD: 5.6465 cents
 20:22:25:27:30:33:37:41:45    SD: 4.3639 cents
 27:30:34:37:41:45:50:56:61    SD: 3.9574 cents
 28:31:35:38:42:46:52:58:63    SD: 3.6545 cents
 29:32:36:40:44:48:54:60:65    SD: 3.3299 cents
 32:35:40:44:48:53:60:66:72    SD: 2.6624 cents
 36:40:45:49:54:60:67:74:81    SD: 2.5870 cents
 38:42:48:52:57:63:71:78:85    SD: 2.2900 cents
 40:44:50:55:60:66:75:82:90    SD: 2.0985 cents
 48:53:60:66:72:80:90:99:108    SD: 1.8629 cents
 56:62:70:77:84:93:105:115:126    SD: 1.5050 cents
 59:65:74:81:89:98:110:121:133    SD: 1.4466 cents
 67:74:84:92:101:111:125:138:151    SD: 0.8747 cents
 103:114:129:141:155:171:192:212:231    SD: 0.8646 cents
 105:116:132:144:158:174:196:216:236    SD: 0.7830 cents
 123:136:154:169:185:204:230:253:276    SD: 0.6418 cents
 135:149:169:185:203:224:252:278:303    SD: 0.5568 cents
 143:158:179:196:215:237:267:294:321    SD: 0.4022 cents
 190:210:238:261:286:315:355:391:427    SD: 0.3916 cents
 202:223:253:277:304:335:377:416:454    SD: 0.3476 cents
 210:232:263:288:316:348:392:432:472    SD: 0.1382 cents
 436:482:546:598:656:723:814:897:980    SD: 0.1341 cents
 541:598:678:742:814:897:1010:1113:1216    SD: 0.1306 cents
 573:633:718:786:862:950:1070:1179:1288    SD: 0.1168 cents
 581:642:728:797:874:963:1085:1195:1306    SD: 0.1112 cents