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