Scala analysis: Malawi_Asena_21
Asena 21 (Valimba), Malawi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184.000 cents 184.000000 2: 398.000 cents 398.000000 3: 575.000 cents 575.000000 4: 734.000 cents 734.000000 5: 904.000 cents 904.000000 6: 1079.000 cents 1079.000000 7: 1200.000 cents 1200.000000 8: 1384.000 cents 1384.000000 9: 1567.000 cents 1567.000000 10: 1717.000 cents 1717.000000 11: 1934.000 cents 1934.000000 12: 2104.000 cents 2104.000000
SHOW/INTERVAL
0: 170.0000 cents 170.0000 1: 184.0000 cents 184.0000 2: 214.0000 cents 214.0000 3: 177.0000 cents 177.0000 4: 159.0000 cents 159.0000 5: 170.0000 cents 170.0000 6: 175.0000 cents 175.0000 7: 121.0000 cents 121.0000 8: 184.0000 cents 184.0000 9: 183.0000 cents 183.0000 10: 150.0000 cents 150.0000 11: 217.0000 cents 217.0000 12: 170.0000 cents 170.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 121.00000 cents 1: 1 150.00000 cents 1: 1 159.00000 cents 1: 2 170.00000 cents 1: 1 175.00000 cents 1: 1 177.00000 cents 1: 1 183.00000 cents 1: 2 184.00000 cents 1: 1 214.00000 cents 1: 1 217.00000 cents 2: 1 296.00000 cents 2: 1 305.00000 cents 2: 1 329.00000 cents 2: 1 333.00000 cents 2: 1 336.00000 cents 2: 1 345.00000 cents 2: 1 354.00000 cents 2: 2 367.00000 cents 2: 1 387.00000 cents 2: 1 391.00000 cents 2: 1 398.00000 cents 3: 1 466.00000 cents 3: 1 480.00000 cents 3: 1 488.00000 cents 3: 1 504.00000 cents 3: 1 506.00000 cents 3: 1 517.00000 cents 3: 1 537.00000 cents 3: 2 550.00000 cents 3: 1 568.00000 cents 3: 1 571.00000 cents 3: 1 575.00000 cents 4: 1 625.00000 cents 4: 1 638.00000 cents 4: 1 650.00000 cents 4: 1 663.00000 cents 4: 1 681.00000 cents 4: 2 720.00000 cents 4: 1 721.00000 cents 4: 2 734.00000 cents 4: 1 745.00000 cents 4: 1 785.00000 cents 5: 1 802.00000 cents 5: 1 809.00000 cents 5: 1 813.00000 cents 5: 1 833.00000 cents 5: 1 855.00000 cents 5: 1 895.00000 cents 5: 4 904.00000 cents 5: 1 935.00000 cents 5: 1 962.00000 cents 6: 1 983.00000 cents 6: 1 986.00000 cents 6: 1 992.00000 cents 6: 1 1016.00000 cents 6: 1 1025.00000 cents 6: 1 1030.00000 cents 6: 1 1074.00000 cents 6: 1 1079.00000 cents 6: 1 1088.00000 cents 6: 1 1112.00000 cents 6: 1 1118.00000 cents 6: 1 1121.00000 cents 7: 1 1142.00000 cents 7: 1 1169.00000 cents 7: 4 1200.00000 cents 7: 1 1209.00000 cents 7: 1 1249.00000 cents 7: 1 1271.00000 cents 7: 1 1291.00000 cents 7: 1 1295.00000 cents 7: 1 1302.00000 cents 8: 1 1319.00000 cents 8: 1 1359.00000 cents 8: 2 1370.00000 cents 8: 1 1383.00000 cents 8: 2 1384.00000 cents 8: 1 1423.00000 cents 8: 1 1441.00000 cents 8: 1 1454.00000 cents 8: 1 1466.00000 cents 8: 1 1479.00000 cents 9: 1 1529.00000 cents 9: 1 1533.00000 cents 9: 1 1536.00000 cents 9: 2 1554.00000 cents 9: 1 1567.00000 cents 9: 1 1587.00000 cents 9: 1 1598.00000 cents 9: 1 1600.00000 cents 9: 1 1616.00000 cents 9: 1 1624.00000 cents 9: 1 1638.00000 cents 10: 1 1706.00000 cents 10: 1 1713.00000 cents 10: 1 1717.00000 cents 10: 2 1737.00000 cents 10: 1 1750.00000 cents 10: 1 1759.00000 cents 10: 1 1768.00000 cents 10: 1 1771.00000 cents 10: 1 1775.00000 cents 10: 1 1799.00000 cents 10: 1 1808.00000 cents 11: 1 1887.00000 cents 11: 1 1890.00000 cents 11: 2 1920.00000 cents 11: 1 1921.00000 cents 11: 1 1927.00000 cents 11: 1 1929.00000 cents 11: 2 1934.00000 cents 11: 1 1945.00000 cents 11: 1 1954.00000 cents 11: 1 1983.00000 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 10.36364 = 114/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 184.0 398.0 575.0 734.0 904.0 1079.0 1200.0 1384.0 1567.0 1717.0 1934.0 2104.0 184.0 : 214.0 391.0 550.0 720.0 895.0 1016.0 1200.0 1383.0 1533.0 1750.0 1920.0 2104.0 398.0 : 177.0 336.0 506.0 681.0 802.0 986.0 1169.0 1319.0 1536.0 1706.0 1890.0 2104.0 575.0 : 159.0 329.0 504.0 625.0 809.0 992.0 1142.0 1359.0 1529.0 1713.0 1927.0 2104.0 734.0 : 170.0 345.0 466.0 650.0 833.0 983.0 1200.0 1370.0 1554.0 1768.0 1945.0 2104.0 904.0 : 175.0 296.0 480.0 663.0 813.0 1030.0 1200.0 1384.0 1598.0 1775.0 1934.0 2104.0 1079.0: 121.0 305.0 488.0 638.0 855.0 1025.0 1209.0 1423.0 1600.0 1759.0 1929.0 2104.0 1200.0: 184.0 367.0 517.0 734.0 904.0 1088.0 1302.0 1479.0 1638.0 1808.0 1983.0 2104.0 1384.0: 183.0 333.0 550.0 720.0 904.0 1118.0 1295.0 1454.0 1624.0 1799.0 1920.0 2104.0 1567.0: 150.0 367.0 537.0 721.0 935.0 1112.0 1271.0 1441.0 1616.0 1737.0 1921.0 2104.0 1717.0: 217.0 387.0 571.0 785.0 962.0 1121.0 1291.0 1466.0 1587.0 1771.0 1954.0 2104.0 1934.0: 170.0 354.0 568.0 745.0 904.0 1074.0 1249.0 1370.0 1554.0 1737.0 1887.0 2104.0 2104.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 121.0000 .. 217.0000 cents 96.00000 cents 121.00000 cents 2: 296.0000 .. 398.0000 cents 102.00000 cents 79.00000 cents 3: 466.0000 .. 575.0000 cents 109.00000 cents 68.00000 cents 4: 625.0000 .. 785.0000 cents 160.00000 cents 50.00000 cents 5: 802.0000 .. 962.0000 cents 160.00000 cents 17.00000 cents 6: 983.0000 .. 1121.0000 cents 138.00000 cents 21.00000 cents 7: 1142.0000 .. 1302.0000 cents 160.00000 cents 21.00000 cents 8: 1319.0000 .. 1479.0000 cents 160.00000 cents 17.00000 cents 9: 1529.0000 .. 1638.0000 cents 109.00000 cents 50.00000 cents 10: 1706.0000 .. 1808.0000 cents 102.00000 cents 68.00000 cents 11: 1887.0000 .. 1983.0000 cents 96.00000 cents 79.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 121.00000 cents, class 1 Average step (divided formal octave): 175.3333 cents Largest one step interval : 217.00000 cents Average / Smallest step : 1.449036 Largest / Average step : 1.237643 Largest / Smallest step : 1.793388 Median interval of one step : 176.00000 cents, amount: 0 Least squares average step : 175.23385 cents, oct.: 2102.80615 cents Scale is strictly proper Scale is a mode of a 2104-tone equal temperament with octave 2104.000 cents degrees: 184 398 575 734 904 1079 1200 1384 1567 1717 1934 2104 Least number of segments generator : 1053 of 1053.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1649 of 1649.000 cents and inv. generated superset size: 839 = 827 more = 6991.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGAHIJE Step pattern size order : HIFCDEAHGBJD Scale is a Constant Structure, by a margin of 17.00000 cents Scale diversity : 0.158740 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.338403 Rothenberg efficiency : 0.190236 redundancy: 0.809764 Efficiency x scale size : 2.282828 Number of different interval sizes : 114 = 10.36364 / class Number of one step interval sizes : 10 Highest interval variety : 12 Mean interval variety : 10.36364 = 114/11 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 1.00000 cents Most common intervals : 904.00000 cents & inv., amount: 4 Number of recognisable fifths : 2, average 720.0000 cents Number of appreciable fifths : 0 Number of recognisable fourths : 4, average 494.5000 cents Number of appreciable fourths : 3, average 499.3333 cents Formal octave complements present : 3 = 25.0000% 2/1 octave complements present : 1 = 8.3333% -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.6136 c. M: 49.0000 c. Twelve-tone Chromatic (1/11-comma) 21: 2 2 2 1 2 2 1 2 2 1 2 2 P D3 SD: 21.0765 c. M:-36.0476 c. 23: 2 2 2 2 2 2 1 2 2 2 2 2 SP M ME SD: 16.3175 c. M: 32.0870 c. 26: 2 3 2 2 2 2 2 2 2 2 3 2 P D3 I SD: 15.9846 c. M: 29.4615 c. 32: 3 3 3 2 3 2 2 3 3 2 3 3 P SD: 15.2420 c. M: 27.2500 c. 35: 3 4 3 2 3 3 2 3 3 3 3 3 P SD: 13.5814 c. M:-26.3143 c. 37: 3 4 3 3 3 3 2 3 3 3 4 3 P SD: 12.2890 c. M: 31.6486 c. 39: 3 4 4 3 3 3 2 4 3 3 4 3 P SD: 14.5817 c. M: 22.1538 c. 43: 4 4 4 3 4 3 3 3 4 3 5 3 P SD: 13.8124 c. M:-25.6744 c. 44: 4 4 4 3 4 4 2 4 4 3 4 4 SP SD: 11.7206 c. M: 21.2727 c. 47: 4 5 4 3 4 4 3 4 4 3 5 4 P SD: 8.8150 c. M: 17.7447 c. 49: 4 5 4 4 4 4 3 4 4 4 5 4 SP SD: 9.8953 c. M: 21.2041 c. 55: 5 5 5 4 5 4 3 5 5 4 6 4 SP SD: 9.8386 c. M:-16.9818 c. 58: 5 6 5 4 5 5 3 5 5 4 6 5 P SD: 6.8783 c. M: 12.0345 c. 70: 6 7 6 5 6 6 4 6 6 5 7 6 SP SD: 5.7716 c. M: 12.6286 c. 72: 6 8 6 5 6 6 4 6 7 5 7 6 P SD: 7.2061 c. M:-11.1111 c. 74: 6 8 6 6 6 6 4 7 6 5 8 6 P SD: 6.6776 c. M: 13.4054 c. 86: 8 8 8 6 7 7 5 8 7 6 9 7 P SD: 6.2650 c. M:-12.1628 c. 88: 8 9 7 7 7 7 5 8 8 6 9 7 P SD: 5.6528 c. M:-11.0000 c. 89: 8 9 7 7 7 8 5 8 7 7 9 7 SP SD: 6.4243 c. M:-10.7865 c. 90: 8 9 8 6 8 7 5 8 8 6 10 7 P SD: 6.3859 c. M: 10.4222 c. 91: 8 9 8 7 7 8 5 8 8 6 10 7 P SD: 4.8251 c. M:-8.1538 c. 102: 9 10 9 8 8 8 6 9 9 7 11 8 P SD: 4.4721 c. M:-8.5882 c. 109: 10 11 9 8 9 9 6 10 9 8 11 9 P SD: 4.4506 c. M:-9.0275 c. 110: 10 11 9 8 9 9 7 9 10 8 11 9 SP SD: 5.0389 c. M: 7.8727 c. 111: 10 11 9 9 9 9 6 10 10 8 11 9 SP SD: 4.7514 c. M:-7.9009 c. 114: 10 12 9 9 9 9 7 10 10 8 12 9 P SD: 3.9053 c. M: 8.5439 c. 115: 10 12 9 9 9 10 7 10 10 8 12 9 SP SD: 5.1642 c. M: 7.8348 c. 117: 10 12 10 9 9 10 7 10 10 8 12 10 P SD: 4.6449 c. M: 9.8291 c. 121: 11 12 10 9 10 10 7 11 10 9 12 10 SP SD: 3.6706 c. M:-7.2727 c. 123: 11 12 11 9 10 10 7 11 11 8 13 10 P SD: 3.9741 c. M:-6.7236 c. 125: 11 13 10 10 10 10 7 11 11 9 13 10 P SD: 3.6440 c. M:-6.6080 c. 126: 11 13 10 10 10 11 7 11 11 9 13 10 SP SD: 3.4262 c. M: 7.2540 c. 137: 12 14 11 11 11 11 8 12 12 10 14 11 SP SD: 2.8310 c. M: 6.7664 c. 138: 12 14 12 10 11 12 8 12 12 10 14 11 SP SD: 3.4387 c. M:-5.8406 c. 146: 13 15 12 11 12 12 8 13 13 10 15 12 P SD: 2.9687 c. M:-5.5068 c. 149: 13 15 13 11 12 12 9 13 13 11 15 12 SP SD: 2.7412 c. M: 5.8188 c. 158: 14 16 13 12 13 13 9 14 14 11 16 13 SP SD: 2.0658 c. M:-4.3418 c. 173: 15 18 14 13 14 15 10 15 15 12 18 14 SP SD: 2.9135 c. M: 4.2890 c. 175: 15 18 15 13 14 15 10 15 15 13 18 14 SP SD: 2.3375 c. M: 4.0286 c. 184: 16 19 15 14 15 15 11 16 16 13 19 15 SP SD: 1.9389 c. M: 4.1304 c. 195: 17 20 16 15 16 16 11 17 17 14 20 16 SP SD: 1.9662 c. M: 3.1436 c. 238: 21 24 20 18 19 20 14 21 20 17 25 19 SP SD: 1.8763 c. M:-3.9328 c. 249: 22 25 21 19 20 21 14 22 21 18 26 20 SP SD: 1.6777 c. M: 3.7871 c. 252: 22 26 21 19 20 21 15 22 22 18 26 20 SP SD: 2.0885 c. M:-3.0159 c. 259: 23 26 22 19 21 22 15 22 23 18 27 21 SP SD: 2.0544 c. M: 2.9961 c. 260: 23 26 22 20 21 21 15 23 23 18 27 21 SP SD: 1.8608 c. M:-2.9077 c. 261: 23 26 22 20 21 22 15 23 22 19 27 21 SP SD: 1.7990 c. M: 3.1073 c. 263: 23 27 22 20 21 22 15 23 23 19 27 21 SP SD: 1.4142 c. M:-3.0000 c. 275: 24 28 23 21 22 23 16 24 24 19 29 22 SP SD: 1.3058 c. M: 3.1964 c. 286: 25 29 24 22 23 24 16 25 25 20 30 23 SP SD: 1.3564 c. M: 2.9021 c. 289: 25 30 24 22 23 24 17 25 25 21 30 23 SP SD: 1.5375 c. M:-2.5536 c. 298: 26 30 25 23 24 25 17 26 26 21 31 24 SP SD: 1.3134 c. M: 3.1074 c. 301: 26 31 25 23 24 25 18 26 26 22 31 24 SP SD: 1.7911 c. M:-2.5482 c. 307: 27 31 26 23 25 25 18 27 27 22 31 25 SP SD: 1.5905 c. M:-3.2085 c. 310: 27 32 26 23 25 26 18 27 27 22 32 25 SP SD: 1.1445 c. M:-2.4387 c. 321: 28 33 27 24 26 27 18 28 28 23 33 26 SP SD: 1.1196 c. M:-2.4953 c. 322: 28 33 27 24 26 27 19 28 28 23 33 26 SP SD: 1.3707 c. M: 2.2857 c. 333: 29 34 28 25 27 28 19 29 29 24 34 27 SP SD: 0.7751 c. M:-1.5826 c. 435: 38 44 37 33 35 36 25 38 38 31 45 35 SP SD: 0.6652 c. M: 1.3839 c. 482: 42 49 41 36 39 40 28 42 42 34 50 39 SP SD: 0.7231 c. M: 1.4979 c. 493: 43 50 42 37 40 41 28 43 43 35 51 40 SP SD: 0.8633 c. M: 1.3651 c. 505: 44 51 43 38 41 42 29 44 44 36 52 41 SP SD: 0.7933 c. M: 2.1980 c. 517: 45 53 43 39 42 43 30 45 45 37 53 42 SP SD: 0.7642 c. M: 1.4662 c. 528: 46 54 44 40 43 44 30 46 46 38 54 43 SP SD: 0.8514 c. M: 1.3485 c. 538: 47 55 45 41 43 45 31 47 47 38 56 43 SP SD: 0.8326 c. M:-1.8364 c. 544: 48 55 46 41 44 45 31 48 47 39 56 44 SP SD: 0.8251 c. M:-1.6471 c. 556: 49 56 47 42 45 46 32 49 48 40 57 45 SP SD: 0.6697 c. M:-1.4245 c. 559: 49 57 47 42 45 47 32 49 48 40 58 45 SP SD: 0.8107 c. M: 1.2326 c. 561: 49 57 47 43 45 47 32 49 49 40 58 45 SP SD: 0.7437 c. M:-1.2299 c. 582: 51 59 49 44 47 48 34 51 50 42 60 47 SP SD: 0.7301 c. M: 1.6942 c. 593: 52 60 50 45 48 49 34 52 52 42 61 48 SP SD: 0.5732 c. M:-1.2428 c. 607: 53 62 51 46 49 50 35 53 53 43 63 49 SP SD: 0.6951 c. M: 1.2175 c. 608: 53 62 51 46 49 51 35 53 53 43 63 49 SP SD: 0.5401 c. M:-0.8026 c. 619: 54 63 52 47 50 51 36 54 54 44 64 50 SP SD: 0.5452 c. M: 1.5073 c. 745: 65 76 63 56 60 62 43 65 65 53 77 60 SP SD: 0.4338 c. M:-1.1289 c. 757: 66 77 64 57 61 63 44 66 66 54 78 61 SP SD: 0.5093 c. M:-0.6975 c. 768: 67 78 65 58 62 64 44 67 67 55 79 62 SP SD: 0.3963 c. M: 0.7604 c. 903: 79 92 76 68 73 75 52 79 79 64 93 73 SP SD: 0.3833 c. M:-1.0975 c. 914: 80 93 77 69 74 76 52 80 80 65 94 74 SP SD: 0.4655 c. M: 0.6740 c. 915: 80 93 77 69 74 76 53 80 79 66 94 74 SP SD: 0.4581 c. M: 1.0721 c. 926: 81 94 78 70 75 77 53 81 81 66 95 75 SP SD: 0.3898 c. M:-0.7754 c. 940: 82 96 79 71 76 78 54 82 82 67 97 76 SP SD: 0.3258 c. M: 0.7319 c. 952: 83 97 80 72 77 79 55 83 83 68 98 77 SP SD: 0.3062 c. M: 0.5630 c. 1152: 101 117 97 87 93 96 66 101 100 82 119 93 SP SD: 0.2531 c. M:-0.4653 c. 1336: 117 136 112 101 108 111 77 117 116 95 138 108 SP SD: 0.2278 c. M:-0.4371 c. 1347: 118 137 113 102 109 112 77 118 117 96 139 109 SP SD: 0.2862 c. M: 0.3920 c. 1359: 119 138 114 103 110 113 78 119 118 97 140 110 SP SD: 0.2378 c. M: 0.6188 c. 1485: 130 151 125 112 120 124 85 130 129 106 153 120 SP SD: 0.2273 c. M:-0.6283 c. 1496: 131 152 126 113 121 124 86 131 130 107 154 121 SP SD: 0.2195 c. M: 0.3262 c. 1622: 142 165 136 123 131 135 93 142 141 116 167 131 SP SD: 0.2149 c. M:-0.4451 c. 1669: 146 170 140 126 135 139 96 146 145 119 172 135 SP SD: 0.1734 c. M:-0.3607 c. 1771: 155 180 149 134 143 147 102 155 154 126 183 143 SP SD: 0.1457 c. M: 0.2976 c. 2092: 183 213 176 158 169 174 120 183 182 149 216 169 SP SD: 0.1641 c. M:-0.2811 c. 2104: 184 214 177 159 170 175 121 184 183 150 217 170 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 x x x 3 x S SD: 16.0225 cents 2 x x x 3 x x 4 x 5 x 6:7 S SD: 16.2840 cents 3 x x 4 x 5 x 6:7 x 8:9:10 S SD: 17.4656 cents 4 x 5 x 6:7 x 8:9:10:11:12:13 S SD: 12.3571 cents 5 x 6:7:8 x 9:10:11:12:13:15:17 SD: 15.8561 cents 6:7 x 8:9:10:11:12:13:15:16:18:20 SD: 12.6260 cents 7:8:9:10:11:12:13:14:16:17:19:21:24 SD: 9.8070 cents 8:9:10:11:12:13:15:16:18:20:22:24:27 SD: 7.9986 cents 10:11:13:14:15:17:19:20:22:25:27:31:34 SD: 7.1789 cents 12:13:15:17:18:20:22:24:27:30:32:37:40 SD: 6.9854 cents 13:14:16:18:20:22:24:26:29:32:35:40:44 SD: 6.1738 cents 15:17:19:21:23:25:28:30:33:37:40:46:51 SD: 4.2992 cents 17:19:21:24:26:29:32:34:38:42:46:52:57 SD: 4.1538 cents 19:21:24:26:29:32:35:38:42:47:51:58:64 SD: 3.5577 cents 23:26:29:32:35:39:43:46:51:57:62:70:78 SD: 2.8802 cents 26:29:33:36:40:44:48:52:58:64:70:79:88 SD: 2.7708 cents 27:30:34:38:41:46:50:54:60:67:73:83:91 SD: 2.7112 cents 28:31:35:39:43:47:52:56:62:69:75:86:94 SD: 2.2500 cents 34:38:43:47:52:57:63:68:76:84:92:104:115 SD: 2.2398 cents 35:39:44:49:53:59:65:70:78:87:94:107:118 SD: 1.8864 cents 36:40:45:50:55:61:67:72:80:89:97:110:121 SD: 1.4522 cents 46:51:58:64:70:78:86:92:102:114:124:141:155 SD: 1.4378 cents 51:57:64:71:78:86:95:102:113:126:137:156:172 SD: 1.1721 cents 53:59:67:74:81:89:99:106:118:131:143:162:179 SD: 0.9768 cents 70:78:88:98:107:118:131:140:156:173:189:214:236 SD: 0.9330 cents 74:82:93:103:113:125:138:148:165:183:200:226:249 SD: 0.8926 cents 81:90:102:113:124:137:151:162:180:200:218:248:273 SD: 0.7330 cents 89:99:112:124:136:150:166:178:198:220:240:272:300 SD: 0.0982 cents 464:516:584:647:709:782:865:928:1032:1147:1251:1418:1564 SD: 0.0905 cents 553:615:696:771:845:932:1031:1106:1230:1367:1491:1690:1864 SD: 0.0725 cents