Scala analysis: Zimbabwe_Mbira_01
Mbira 1 (Mbira), Zimbabwe
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 185.000 cents 185.000000 2: 389.000 cents 389.000000 3: 593.000 cents 593.000000 4: 756.000 cents 756.000000 5: 914.000 cents 914.000000 6: 1051.000 cents 1051.000000 7: 1302.000 cents 1302.000000
SHOW/INTERVAL
0: 251.0000 cents 251.0000 1: 185.0000 cents 185.0000 2: 204.0000 cents 204.0000 3: 204.0000 cents 204.0000 4: 163.0000 cents 163.0000 5: 158.0000 cents 158.0000 6: 137.0000 cents 137.0000 7: 251.0000 cents 251.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 137.00000 cents 1: 1 158.00000 cents 1: 1 163.00000 cents 1: 1 185.00000 cents 1: 2 204.00000 cents 1: 1 251.00000 cents 2: 1 295.00000 cents 2: 1 321.00000 cents 2: 1 367.00000 cents 2: 1 388.00000 cents 2: 1 389.00000 cents 2: 1 408.00000 cents 2: 1 436.00000 cents 3: 1 458.00000 cents 3: 1 525.00000 cents 3: 1 546.00000 cents 3: 1 571.00000 cents 3: 1 573.00000 cents 3: 1 593.00000 cents 3: 1 640.00000 cents 4: 1 662.00000 cents 4: 1 709.00000 cents 4: 1 729.00000 cents 4: 1 731.00000 cents 4: 1 756.00000 cents 4: 1 777.00000 cents 4: 1 844.00000 cents 5: 1 866.00000 cents 5: 1 894.00000 cents 5: 1 913.00000 cents 5: 1 914.00000 cents 5: 1 935.00000 cents 5: 1 981.00000 cents 5: 1 1007.00000 cents 6: 1 1051.00000 cents 6: 2 1098.00000 cents 6: 1 1117.00000 cents 6: 1 1139.00000 cents 6: 1 1144.00000 cents 6: 1 1165.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.66667 = 20/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 185.0 389.0 593.0 756.0 914.0 1051.0 1302.0 185.0 : 204.0 408.0 571.0 729.0 866.0 1117.0 1302.0 389.0 : 204.0 367.0 525.0 662.0 913.0 1098.0 1302.0 593.0 : 163.0 321.0 458.0 709.0 894.0 1098.0 1302.0 756.0 : 158.0 295.0 546.0 731.0 935.0 1139.0 1302.0 914.0 : 137.0 388.0 573.0 777.0 981.0 1144.0 1302.0 1051.0: 251.0 436.0 640.0 844.0 1007.0 1165.0 1302.0 1302.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 137.0000 .. 251.0000 cents 114.00000 cents 137.00000 cents 2: 295.0000 .. 436.0000 cents 141.00000 cents 44.00000 cents 3: 458.0000 .. 640.0000 cents 182.00000 cents 22.00000 cents 4: 662.0000 .. 844.0000 cents 182.00000 cents 22.00000 cents 5: 866.0000 .. 1007.0000 cents 141.00000 cents 22.00000 cents 6: 1051.0000 .. 1165.0000 cents 114.00000 cents 44.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 137.00000 cents, class 1 Average step (divided formal octave): 186.0000 cents Largest one step interval : 251.00000 cents Average / Smallest step : 1.357664 Largest / Average step : 1.349462 Largest / Smallest step : 1.832117 Median interval of one step : 185.00000 cents, amount: 1 Most common interval of one step : 204.00000 cents, amount: 2 Least squares average step : 183.97143 cents, oct.: 1287.80000 cents Scale is strictly proper Scale is a mode of a 1302-tone equal temperament with octave 1302.000 cents degrees: 185 389 593 756 914 1051 1302 Least number of segments generator : 653 of 653.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 893 of 893.000 cents and inv. generated superset size: 360 = 353 more = 5142.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCDEF Step pattern size order : DEECBAF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 22.00000 cents Scale diversity : 1.371362 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.328725 Rothenberg efficiency : 0.299320 redundancy: 0.700680 Efficiency x scale size : 2.095238 Number of different interval sizes : 40 = 6.66667 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.66667 = 20/3 Median interval variety : 6.5 Lowest interval variety : 6 Smallest interval difference : 1.00000 cents Most common intervals : 204.00000 cents & inv., amount: 2 Most common triad is 0.0 204.000 1098.000 cents, amount: 1 Number of recognisable fifths : 1, average 709.0000 cents Number of recognisable fourths : 0 Best major thirds form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.6166 c. M:-65.0000 c. Lebeng 10: 1 2 2 1 1 1 2 N D3 SD: 31.8473 c. M:-58.0000 c. 11: 2 1 2 1 2 1 2 P M ME I SD: 32.1002 c. M:-51.7273 c. Superkleismic-7 13: 2 2 2 2 1 2 2 SP M ME S SD: 27.2730 c. M:-50.6923 c. Glacial-7, Lobonian 14: 2 2 2 2 2 1 3 P T3 SD: 19.6360 c. M: 35.0000 c. 16: 2 3 2 2 2 2 3 P D3 S SD: 18.2155 c. M: 23.6250 c. 17: 2 3 3 2 2 2 3 P D3 SD: 16.9535 c. M: 31.8235 c. 20: 3 3 3 3 2 2 4 P SD: 11.2708 c. M:-25.2000 c. 24: 3 4 4 3 3 2 5 P SD: 12.4503 c. M: 22.2500 c. 26: 4 4 4 3 3 3 5 P SD: 9.3734 c. M:-15.3077 c. 31: 4 5 5 4 4 3 6 SP SD: 8.7505 c. M: 17.0000 c. 33: 5 5 5 4 4 4 6 SP SD: 8.1925 c. M:-14.2727 c. 36: 5 6 5 5 4 4 7 P SD: 7.6948 c. M: 14.3333 c. 40: 6 6 6 5 5 4 8 P SD: 6.6354 c. M:-10.3000 c. 41: 6 6 7 5 5 4 8 P SD: 6.5027 c. M:-10.3659 c. 47: 7 7 7 6 6 5 9 SP SD: 6.2686 c. M: 11.2553 c. 48: 7 7 8 6 6 5 9 SP SD: 5.9877 c. M: 9.2500 c. 50: 7 8 8 6 6 5 10 P SD: 4.4854 c. M: 9.4000 c. 57: 8 9 9 7 7 6 11 SP SD: 1.2787 c. M: 2.2632 c. 134: 19 21 21 17 16 14 26 SP SD: 0.9980 c. M:-1.8806 c. 191: 27 30 30 24 23 20 37 SP SD: 0.6898 c. M: 1.2199 c. 198: 28 31 31 25 24 21 38 SP SD: 0.8048 c. M: 1.1818 c. 248: 35 39 39 31 30 26 48 SP SD: 0.6682 c. M: 1.2500 c. 281: 40 44 44 35 34 30 54 SP SD: 0.6344 c. M: 1.2100 c. 332: 47 52 52 42 40 35 64 SP SD: 0.6044 c. M:-0.8855 c. 338: 48 53 53 42 41 36 65 SP SD: 0.6036 c. M: 1.0592 c. 358: 51 56 56 45 43 38 69 SP SD: 0.5103 c. M: 1.1453 c. 389: 55 61 61 49 47 41 75 SP SD: 0.5301 c. M: 0.9126 c. 415: 59 65 65 52 50 44 80 SP SD: 0.3941 c. M: 1.0313 c. 472: 67 74 74 59 57 50 91 SP SD: 0.3716 c. M: 0.9449 c. 499: 71 78 78 63 60 53 96 SP SD: 0.5256 c. M: 0.7735 c. 513: 73 80 81 64 62 54 99 SP SD: 0.4811 c. M:-0.8947 c. 520: 74 81 82 65 63 55 100 SP SD: 0.4600 c. M: 0.9038 c. 529: 75 83 83 66 64 56 102 SP SD: 0.4027 c. M: 0.8771 c. 543: 77 85 85 68 66 57 105 SP SD: 0.5700 c. M: 0.7680 c. 549: 78 86 86 69 66 58 106 SP SD: 0.4368 c. M: 0.9399 c. 556: 79 87 87 70 67 59 107 SP SD: 0.4192 c. M: 0.7266 c. 606: 86 95 95 76 73 64 117 SP SD: 0.3893 c. M: 0.8812 c. 613: 87 96 96 77 74 65 118 SP SD: 0.3665 c. M: 0.6884 c. 647: 92 101 102 81 78 68 125 SP SD: 0.4904 c. M:-0.6491 c. 648: 92 102 101 81 79 68 125 SP SD: 0.3904 c. M:-0.7963 c. 654: 93 102 103 82 79 69 126 SP SD: 0.3869 c. M: 0.7890 c. 655: 93 103 102 82 80 69 126 SP SD: 0.4844 c. M: 0.6412 c. 663: 94 104 104 83 80 70 128 SP SD: 0.3829 c. M: 0.8326 c. 670: 95 105 105 84 81 71 129 SP SD: 0.3571 c. M: 0.6567 c. 689: 98 108 108 86 84 72 133 SP SD: 0.3261 c. M:-0.6125 c. 709: 101 111 111 89 86 74 137 SP SD: 0.4333 c. M:-0.5924 c. 711: 101 111 112 89 86 75 137 SP SD: 0.3509 c. M: 0.7806 c. 725: 103 114 113 91 88 76 140 SP SD: 0.3415 c. M:-0.7021 c. 746: 106 117 117 93 91 78 144 SP SD: 0.3124 c. M:-0.5416 c. 773: 110 121 121 97 94 81 149 SP SD: 0.2756 c. M:-0.6003 c. 779: 111 122 122 97 95 82 150 SP SD: 0.3793 c. M: 0.5392 c. 782: 111 123 122 98 95 82 151 SP SD: 0.3059 c. M:-0.6010 c. 803: 114 126 126 100 98 84 155 SP SD: 0.3266 c. M:-0.4807 c. 810: 115 127 127 101 99 85 156 SP SD: 0.3265 c. M:-0.6148 c. 823: 117 129 129 103 100 86 159 SP SD: 0.2939 c. M: 0.5407 c. 830: 118 130 130 104 101 87 160 SP SD: 0.2113 c. M:-0.5373 c. 887: 126 139 139 111 108 93 171 SP SD: 0.1844 c. M:-0.4825 c. 896: 127 141 140 112 109 94 173 SP SD: 0.3175 c. M: 0.4531 c. 903: 128 142 141 113 110 95 174 SP SD: 0.3145 c. M: 0.4651 c. 907: 129 142 142 114 110 95 175 SP SD: 0.2747 c. M:-0.5094 c. 913: 130 143 143 114 111 96 176 SP SD: 0.2258 c. M:-0.3888 c. 944: 134 148 148 118 115 99 182 SP SD: 0.1935 c. M:-0.4343 c. 964: 137 151 151 121 117 101 186 SP SD: 0.2116 c. M:-0.3714 c. 970: 138 152 152 121 118 102 187 SP SD: 0.2069 c. M: 0.3031 c. 997: 142 156 156 125 121 105 192 SP SD: 0.2202 c. M:-0.4403 c. 1021: 145 160 160 128 124 107 197 SP SD: 0.1746 c. M:-0.3330 c. 1047: 149 164 164 131 127 110 202 SP SD: 0.1748 c. M:-0.2894 c. 1054: 150 165 165 132 128 111 203 SP SD: 0.1572 c. M:-0.2941 c. 1104: 157 173 173 138 134 116 213 SP SD: 0.1443 c. M:-0.2120 c. 1111: 158 174 174 139 135 117 214 SP SD: 0.1186 c. M:-0.2097 c. 1168: 166 183 183 146 142 123 225 SP SD: 0.1145 c. M: 0.2158 c. 1245: 177 195 195 156 151 131 240 SP SD: 0.0585 c. M:-0.1036 c. 1302: 185 204 204 163 158 137 251 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 102.0000 cents 2 x x x 3 x x 4 S SD: 57.7167 cents 3 x x 4 x 5 x 6 S SD: 47.4916 cents 4 x 5 x 6:7 x 8 S SD: 31.9550 cents 5 x 6:7:8 x 9:11 SD: 23.5835 cents 6:7 x 8:9:10:11:13 SD: 24.0711 cents 7:8:9:10:11:12:13:15 SD: 11.6549 cents 12:13:15:17:19:20:22:25 SD: 10.7763 cents 15:17:19:21:23:25:28:32 SD: 8.6031 cents 16:18:20:23:25:27:29:34 SD: 7.0268 cents 17:19:21:24:26:29:31:36 SD: 5.0886 cents 20:22:25:28:31:34:37:42 SD: 4.6296 cents 24:27:30:34:37:41:44:51 SD: 3.7573 cents 27:30:34:38:42:46:50:57 SD: 3.4391 cents 35:39:44:49:54:59:64:74 SD: 2.7311 cents 36:40:45:51:56:61:66:76 SD: 2.3374 cents 44:49:55:62:68:75:81:93 SD: 1.8694 cents 56:62:70:79:87:95:103:119 SD: 1.8202 cents 59:66:74:83:91:100:108:125 SD: 1.7790 cents 68:76:85:96:105:115:125:144 SD: 1.6444 cents 71:79:89:100:110:120:130:151 SD: 1.2133 cents 79:88:99:111:122:134:145:168 SD: 1.0696 cents 91:101:114:128:141:154:167:193 SD: 0.9252 cents 98:109:123:138:152:166:180:208 SD: 0.9108 cents 108:120:135:152:167:183:198:229 SD: 0.6732 cents 115:128:144:162:178:195:211:244 SD: 0.1121 cents 568:632:711:800:879:963:1042:1205 SD: 0.0882 cents