Scala analysis: Malawi_Asena_09
Asena 9 (Bangwe), Malawi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 132.000 cents 132.000000 2: 356.000 cents 356.000000 3: 540.000 cents 540.000000 4: 708.000 cents 708.000000 5: 902.000 cents 902.000000 6: 1057.000 cents 1057.000000 7: 1217.000 cents 1217.000000
SHOW/INTERVAL
0: 160.0000 cents 160.0000 1: 132.0000 cents 132.0000 2: 224.0000 cents 224.0000 3: 184.0000 cents 184.0000 4: 168.0000 cents 168.0000 5: 194.0000 cents 194.0000 6: 155.0000 cents 155.0000 7: 160.0000 cents 160.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 132.00000 cents 1: 1 155.00000 cents 1: 1 160.00000 cents 1: 1 168.00000 cents 1: 1 184.00000 cents 1: 1 194.00000 cents 1: 1 224.00000 cents 2: 1 292.00000 cents 2: 1 315.00000 cents 2: 1 349.00000 cents 2: 1 352.00000 cents 2: 1 356.00000 cents 2: 1 362.00000 cents 2: 1 408.00000 cents 3: 1 447.00000 cents 3: 1 509.00000 cents 3: 1 516.00000 cents 3: 1 517.00000 cents 3: 1 540.00000 cents 3: 1 546.00000 cents 3: 1 576.00000 cents 4: 1 641.00000 cents 4: 1 671.00000 cents 4: 1 677.00000 cents 4: 1 700.00000 cents 4: 1 701.00000 cents 4: 1 708.00000 cents 4: 1 770.00000 cents 5: 1 809.00000 cents 5: 1 855.00000 cents 5: 1 861.00000 cents 5: 1 865.00000 cents 5: 1 868.00000 cents 5: 1 902.00000 cents 5: 1 925.00000 cents 6: 1 993.00000 cents 6: 1 1023.00000 cents 6: 1 1033.00000 cents 6: 1 1049.00000 cents 6: 1 1057.00000 cents 6: 1 1062.00000 cents 6: 1 1085.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 132.0 356.0 540.0 708.0 902.0 1057.0 1217.0 132.0 : 224.0 408.0 576.0 770.0 925.0 1085.0 1217.0 356.0 : 184.0 352.0 546.0 701.0 861.0 993.0 1217.0 540.0 : 168.0 362.0 517.0 677.0 809.0 1033.0 1217.0 708.0 : 194.0 349.0 509.0 641.0 865.0 1049.0 1217.0 902.0 : 155.0 315.0 447.0 671.0 855.0 1023.0 1217.0 1057.0: 160.0 292.0 516.0 700.0 868.0 1062.0 1217.0 1217.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.0000 .. 224.0000 cents 92.00000 cents 132.00000 cents 2: 292.0000 .. 408.0000 cents 116.00000 cents 68.00000 cents 3: 447.0000 .. 576.0000 cents 129.00000 cents 39.00000 cents 4: 641.0000 .. 770.0000 cents 129.00000 cents 65.00000 cents 5: 809.0000 .. 925.0000 cents 116.00000 cents 39.00000 cents 6: 993.0000 .. 1085.0000 cents 92.00000 cents 68.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 132.00000 cents, class 1 Average step (divided formal octave): 173.8571 cents Largest one step interval : 224.00000 cents Average / Smallest step : 1.317100 Largest / Average step : 1.288414 Largest / Smallest step : 1.696970 Median interval of one step : 168.00000 cents, amount: 1 Least squares average step : 176.19286 cents, oct.: 1233.35000 cents Scale is strictly proper Scale is a mode of a 1217-tone equal temperament with octave 1217.000 cents degrees: 132 356 540 708 902 1057 1217 Least number of segments generator : 609 of 609.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1185 of 1185.000 cents and inv. generated superset size: 370 = 363 more = 5285.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : AGEDFBC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 39.00000 cents Scale diversity : 1.510186 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.446179 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 3, average 703.0000 cents Number of recognisable fourths : 1, average 509.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 93.0000 cents: 6 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.6166 c. M:-41.8571 c. Lebeng 14: 1 3 2 2 2 2 2 P T3 SD: 23.4825 c. M: 45.0714 c. 15: 2 2 3 2 2 2 2 SP M ME S SD: 21.6312 c. M: 31.4667 c. 16: 2 3 2 2 3 2 2 SP M ME S SD: 15.9472 c. M:-24.3125 c. Mavila-7, Antiaeolian 17: 2 3 3 2 3 2 2 P D3 SD: 18.3777 c. M:-32.7059 c. 20: 2 4 3 3 3 2 3 P SD: 13.9608 c. M: 22.5500 c. 24: 3 4 4 3 4 3 3 SP D3 SD: 11.3634 c. M:-20.1250 c. 27: 3 5 4 4 4 3 4 SP SD: 9.3985 c. M: 20.2963 c. 28: 3 5 4 4 5 3 4 SP T3 S SD: 11.1897 c. M: 18.4286 c. 30: 3 6 4 4 5 4 4 SP SD: 10.5685 c. M: 18.3667 c. 31: 3 6 5 4 5 4 4 P SD: 6.6919 c. M: 14.2258 c. 38: 4 7 6 5 6 5 5 SP SD: 3.5484 c. M: 5.2632 c. 74: 8 14 11 10 12 9 10 SP SD: 3.1232 c. M:-5.8108 c. 81: 9 15 12 11 13 10 11 SP SD: 3.0168 c. M: 5.2716 c. 86: 9 16 13 12 14 11 11 SP SD: 3.0250 c. M: 4.6395 c. 92: 10 17 14 13 14 12 12 SP SD: 2.7966 c. M:-6.3261 c. 93: 10 17 14 13 15 12 12 SP SD: 2.1397 c. M: 3.4731 c. 108: 12 20 16 15 17 14 14 SP SD: 2.4269 c. M:-4.5926 c. 112: 12 21 17 15 18 14 15 SP SD: 2.1389 c. M:-3.3036 c. 113: 12 21 17 16 18 14 15 SP SD: 1.9892 c. M:-2.8142 c. 120: 13 22 18 17 19 15 16 SP SD: 1.5353 c. M: 2.4917 c. 146: 16 27 22 20 23 19 19 SP SD: 1.5616 c. M:-2.4315 c. 151: 16 28 23 21 24 19 20 SP SD: 1.4445 c. M: 3.0464 c. 158: 17 29 24 22 25 20 21 SP SD: 1.1180 c. M: 1.7532 c. 167: 18 31 25 23 27 21 22 SP SD: 0.9593 c. M:-1.6407 c. 174: 19 32 26 24 28 22 23 SP SD: 0.9778 c. M: 1.5805 c. 205: 22 38 31 28 33 26 27 SP SD: 0.8143 c. M: 1.5463 c. 212: 23 39 32 29 34 27 28 SP SD: 0.8352 c. M: 1.9104 c. 259: 28 48 39 36 41 33 34 SP SD: 0.7534 c. M:-1.5251 c. 266: 29 49 40 37 42 34 35 SP SD: 0.6600 c. M:-1.1541 c. 297: 32 55 45 41 47 38 39 SP SD: 0.6440 c. M:-0.8923 c. 304: 33 56 46 42 48 39 40 SP SD: 0.5655 c. M: 1.2599 c. 325: 35 60 49 45 52 41 43 SP SD: 0.6396 c. M: 1.0185 c. 332: 36 61 50 46 53 42 44 SP SD: 0.7076 c. M: 1.2892 c. 349: 38 64 53 48 56 44 46 SP SD: 0.5525 c. M:-1.1605 c. 359: 39 66 54 50 57 46 47 SP SD: 0.5087 c. M: 0.9944 c. 387: 42 71 59 53 62 49 51 SP SD: 0.5123 c. M:-0.8889 c. 394: 43 72 60 54 63 50 52 SP SD: 0.5861 c. M:-0.8198 c. 397: 43 73 60 55 63 51 52 SP SD: 0.4385 c. M: 0.7456 c. 433: 47 80 65 60 69 55 57 SP SD: 0.4147 c. M:-0.9492 c. 471: 51 87 71 65 75 60 62 SP SD: 0.2599 c. M:-0.5732 c. 564: 61 104 85 78 90 72 74 SP SD: 0.2945 c. M: 0.5496 c. 629: 68 116 95 87 100 80 83 SP SD: 0.3231 c. M: 0.5898 c. 653: 71 120 99 90 104 83 86 SP SD: 0.2544 c. M:-0.4747 c. 708: 77 130 107 98 113 90 93 SP SD: 0.2608 c. M:-0.4364 c. 739: 80 136 112 102 118 94 97 SP SD: 0.2578 c. M:-0.4574 c. 746: 81 137 113 103 119 95 98 SP SD: 0.1641 c. M: 0.3619 c. 820: 89 151 124 113 131 104 108 SP SD: 0.2123 c. M:-0.3610 c. 913: 99 168 138 126 146 116 120 SP SD: 0.1883 c. M:-0.4195 c. 920: 100 169 139 127 147 117 121 SP SD: 0.2079 c. M: 0.2880 c. 951: 103 175 144 131 152 121 125 SP SD: 0.1846 c. M: 0.3228 c. 1005: 109 185 152 139 160 128 132 SP SD: 0.1762 c. M:-0.4030 c. 1012: 110 186 153 140 161 129 133 SP SD: 0.1649 c. M:-0.3132 c. 1043: 113 192 158 144 166 133 137 SP SD: 0.1631 c. M:-0.2637 c. 1050: 114 193 159 145 167 134 138 SP SD: 0.1526 c. M: 0.2610 c. 1059: 115 195 160 146 169 135 139 SP SD: 0.1668 c. M:-0.2616 c. 1179: 128 217 178 163 188 150 155 SP SD: 0.1144 c. M:-0.1696 c. 1217: 132 224 184 168 194 155 160 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 17.0000 cents 2 x x x 3 x x 4 S SD: 9.0214 cents 3 x x 4 x 5 x 6 S SD: 16.1948 cents 4 x 5 x 6:7 x 8 S SD: 18.8914 cents 5 x 6:7 x 8:9:10 S SD: 22.8710 cents 6 x 7:8:9:10:11:12 S SD: 16.9962 cents 8:9:10:11:12:13:15:16 SD: 15.1860 cents 9:10:11:12:14:15:17:18 SD: 14.3954 cents 10:11:12:14:15:17:18:20 SD: 11.6764 cents 12:13:15:16:18:20:22:24 SD: 8.3512 cents 13:14:16:18:20:22:24:26 S SD: 6.9783 cents 14:15:17:19:21:24:26:28 SD: 6.6872 cents 22:24:27:30:33:37:41:44 SD: 4.7778 cents 25:27:31:34:38:42:46:50 SD: 4.3339 cents 34:37:42:46:51:57:63:69 SD: 4.1872 cents 35:38:43:48:53:59:64:71 SD: 3.0979 cents 36:39:44:49:54:61:66:73 SD: 2.9236 cents 38:41:47:52:57:64:70:77 SD: 2.1286 cents 49:53:60:67:74:83:90:99 SD: 2.0552 cents 51:55:63:70:77:86:94:103 SD: 2.0336 cents 52:56:64:71:78:88:96:105 SD: 1.8073 cents 61:66:75:83:92:103:112:123 SD: 1.6804 cents 63:68:77:86:95:106:116:127 SD: 1.4101 cents 79:85:97:108:119:133:145:160 SD: 1.3264 cents 87:94:107:119:131:146:160:176 SD: 1.1058 cents 88:95:108:120:132:148:162:178 SD: 1.0966 cents 101:109:124:138:152:170:186:204 SD: 0.1623 cents 503:543:618:687:757:847:926:1016 SD: 0.1335 cents