Scala analysis: Malawi_Asena_03
Asena 3 (Bangwe), Malawi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 161.000 cents 161.000000 2: 403.000 cents 403.000000 3: 540.000 cents 540.000000 4: 771.000 cents 771.000000 5: 901.000 cents 901.000000 6: 1135.000 cents 1135.000000 7: 1263.000 cents 1263.000000 8: 1442.000 cents 1442.000000 9: 1596.000 cents 1596.000000 10: 1772.000 cents 1772.000000
SHOW/INTERVAL
0: 176.0000 cents 176.0000 1: 161.0000 cents 161.0000 2: 242.0000 cents 242.0000 3: 137.0000 cents 137.0000 4: 231.0000 cents 231.0000 5: 130.0000 cents 130.0000 6: 234.0000 cents 234.0000 7: 128.0000 cents 128.0000 8: 179.0000 cents 179.0000 9: 154.0000 cents 154.0000 10: 176.0000 cents 176.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128.00000 cents 1: 1 130.00000 cents 1: 1 137.00000 cents 1: 1 154.00000 cents 1: 1 161.00000 cents 1: 1 176.00000 cents 1: 1 179.00000 cents 1: 1 231.00000 cents 1: 1 234.00000 cents 1: 1 242.00000 cents 2: 1 307.00000 cents 2: 1 330.00000 cents 2: 1 333.00000 cents 2: 1 337.00000 cents 2: 1 361.00000 cents 2: 1 362.00000 cents 2: 1 364.00000 cents 2: 1 368.00000 cents 2: 1 379.00000 cents 2: 1 403.00000 cents 3: 1 461.00000 cents 3: 1 491.00000 cents 3: 1 492.00000 cents 3: 1 498.00000 cents 3: 1 509.00000 cents 3: 1 540.00000 cents 3: 1 541.00000 cents 3: 1 579.00000 cents 3: 1 595.00000 cents 3: 1 610.00000 cents 4: 1 637.00000 cents 4: 1 670.00000 cents 4: 1 671.00000 cents 4: 1 695.00000 cents 4: 1 716.00000 cents 4: 1 723.00000 cents 4: 1 732.00000 cents 4: 1 733.00000 cents 4: 1 740.00000 cents 4: 1 771.00000 cents 5: 1 798.00000 cents 5: 1 825.00000 cents 5: 1 860.00000 cents 5: 1 870.00000 cents 5: 1 871.00000 cents 5: 1 901.00000 cents 5: 1 902.00000 cents 5: 1 912.00000 cents 5: 1 947.00000 cents 5: 1 974.00000 cents 6: 1 1001.00000 cents 6: 1 1032.00000 cents 6: 1 1039.00000 cents 6: 1 1040.00000 cents 6: 1 1049.00000 cents 6: 1 1056.00000 cents 6: 1 1077.00000 cents 6: 1 1101.00000 cents 6: 1 1102.00000 cents 6: 1 1135.00000 cents 7: 1 1162.00000 cents 7: 1 1177.00000 cents 7: 1 1193.00000 cents 7: 1 1231.00000 cents 7: 1 1232.00000 cents 7: 1 1263.00000 cents 7: 1 1274.00000 cents 7: 1 1280.00000 cents 7: 1 1281.00000 cents 7: 1 1311.00000 cents 8: 1 1369.00000 cents 8: 1 1393.00000 cents 8: 1 1404.00000 cents 8: 1 1408.00000 cents 8: 1 1410.00000 cents 8: 1 1411.00000 cents 8: 1 1435.00000 cents 8: 1 1439.00000 cents 8: 1 1442.00000 cents 8: 1 1465.00000 cents 9: 1 1530.00000 cents 9: 1 1538.00000 cents 9: 1 1541.00000 cents 9: 1 1593.00000 cents 9: 1 1596.00000 cents 9: 1 1611.00000 cents 9: 1 1618.00000 cents 9: 1 1635.00000 cents 9: 1 1642.00000 cents 9: 1 1644.00000 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 10.00000 = 10
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 161.0 403.0 540.0 771.0 901.0 1135.0 1263.0 1442.0 1596.0 1772.0 161.0 : 242.0 379.0 610.0 740.0 974.0 1102.0 1281.0 1435.0 1611.0 1772.0 403.0 : 137.0 368.0 498.0 732.0 860.0 1039.0 1193.0 1369.0 1530.0 1772.0 540.0 : 231.0 361.0 595.0 723.0 902.0 1056.0 1232.0 1393.0 1635.0 1772.0 771.0 : 130.0 364.0 492.0 671.0 825.0 1001.0 1162.0 1404.0 1541.0 1772.0 901.0 : 234.0 362.0 541.0 695.0 871.0 1032.0 1274.0 1411.0 1642.0 1772.0 1135.0: 128.0 307.0 461.0 637.0 798.0 1040.0 1177.0 1408.0 1538.0 1772.0 1263.0: 179.0 333.0 509.0 670.0 912.0 1049.0 1280.0 1410.0 1644.0 1772.0 1442.0: 154.0 330.0 491.0 733.0 870.0 1101.0 1231.0 1465.0 1593.0 1772.0 1596.0: 176.0 337.0 579.0 716.0 947.0 1077.0 1311.0 1439.0 1618.0 1772.0 1772.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.0000 .. 242.0000 cents 114.00000 cents 128.00000 cents 2: 307.0000 .. 403.0000 cents 96.00000 cents 65.00000 cents 3: 461.0000 .. 610.0000 cents 149.00000 cents 58.00000 cents 4: 637.0000 .. 771.0000 cents 134.00000 cents 27.00000 cents 5: 798.0000 .. 974.0000 cents 176.00000 cents 27.00000 cents 6: 1001.0000 .. 1135.0000 cents 134.00000 cents 27.00000 cents 7: 1162.0000 .. 1311.0000 cents 149.00000 cents 27.00000 cents 8: 1369.0000 .. 1465.0000 cents 96.00000 cents 58.00000 cents 9: 1530.0000 .. 1644.0000 cents 114.00000 cents 65.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 128.00000 cents, class 1 Average step (divided formal octave): 177.2000 cents Largest one step interval : 242.00000 cents Average / Smallest step : 1.384375 Largest / Average step : 1.365688 Largest / Smallest step : 1.890625 Median interval of one step : 168.50000 cents, amount: 0 Least squares average step : 180.38182 cents, oct.: 1803.81818 cents Scale is strictly proper Scale is a mode of a 1772-tone equal temperament with octave 1772.000 cents degrees: 161 403 540 771 901 1135 1263 1442 1596 1772 Least number of segments generator : 887 of 887.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1249 of 1249.000 cents and inv. generated superset size: 591 = 581 more = 5910.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGHIJ Step pattern size order : EJCHBIAGDF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.00000 cents Scale diversity : 0.492422 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.344244 Rothenberg efficiency : 0.200000 redundancy: 0.800000 Efficiency x scale size : 2.000000 Number of different interval sizes : 90 = 10.00000 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 10.00000 = 10 Median interval variety : 10 Lowest interval variety : 10 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 2, average 705.5000 cents Number of appreciable fifths : 1, average 695.0000 cents Number of recognisable fourths : 4, average 497.5000 cents Formal octave complements present : 1 = 10.0000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 36.1270 c. M: 71.8000 c. 12: 1 2 1 1 1 2 1 1 1 1 P D3 SD: 37.6090 c. M:-66.0000 c. 13: 1 2 1 2 1 1 1 2 1 1 P D3 SD: 37.2248 c. M:-57.3846 c. 14: 1 2 1 2 1 2 1 1 1 2 P D3 SD: 34.1616 c. M: 77.1429 c. 17: 2 2 1 2 2 2 1 2 1 2 P D3 SD: 27.4334 c. M:-47.4706 c. 19: 2 2 2 2 2 2 2 1 2 2 SP M ME SD: 27.5487 c. M: 43.0526 c. 20: 2 3 1 3 1 3 1 2 2 2 P T3 SD: 20.6028 c. M:-40.0000 c. 21: 2 3 1 3 2 2 2 2 2 2 SP D3 SD: 19.9787 c. M: 38.0476 c. 22: 2 3 2 3 1 3 2 2 2 2 P D3 SD: 17.2599 c. M:-34.4545 c. 23: 2 3 2 3 2 3 1 3 2 2 P SD: 17.9430 c. M: 30.3043 c. 27: 2 4 2 4 2 3 2 3 2 3 P SD: 16.8944 c. M: 29.7407 c. 28: 3 3 3 3 2 4 2 3 2 3 SP D3 SD: 17.3466 c. M:-29.5714 c. 30: 3 4 2 4 2 4 2 3 3 3 SP T3 SD: 13.9537 c. M: 24.4000 c. 32: 3 4 3 4 2 4 3 3 3 3 SP D3 SD: 12.9093 c. M: 27.5000 c. 34: 3 5 2 5 2 5 2 4 3 3 P SD: 13.7069 c. M:-19.6471 c. 37: 3 5 3 5 3 4 3 4 3 4 SP SD: 16.3692 c. M: 33.4865 c. 38: 3 5 3 5 3 5 3 4 3 4 SP SD: 18.1908 c. M: 29.9474 c. 39: 4 5 3 5 3 5 3 4 3 4 SP SD: 9.0310 c. M:-20.7436 c. 42: 4 6 3 5 3 6 3 4 4 4 SP SD: 9.9091 c. M:-18.9048 c. 43: 4 6 3 6 3 6 3 4 4 4 P SD: 9.9041 c. M:-18.8605 c. 45: 4 6 4 6 3 6 3 5 4 4 P SD: 10.6947 c. M:-18.4889 c. 46: 4 6 4 6 3 6 4 4 4 5 SP SD: 12.3744 c. M: 17.8696 c. 48: 4 7 4 6 3 7 3 5 4 5 P SD: 9.2097 c. M: 15.0000 c. 49: 4 7 4 6 4 6 4 5 4 5 SP SD: 8.3011 c. M: 16.3469 c. 53: 5 7 4 7 4 7 4 5 5 5 SP SD: 4.7944 c. M:-8.8302 c. 69: 6 10 5 9 5 9 5 7 6 7 SP SD: 4.3746 c. M:-7.8986 c. 88: 8 12 7 11 7 11 7 9 7 9 SP SD: 4.9780 c. M:-7.8182 c. 89: 8 12 7 12 6 12 6 9 8 9 SP SD: 4.9449 c. M: 8.6629 c. 91: 8 13 7 12 6 12 7 9 8 9 SP SD: 4.6915 c. M:-7.9011 c. 92: 8 13 7 12 7 12 7 9 8 9 SP SD: 3.8988 c. M:-8.2174 c. 98: 9 13 8 13 7 13 7 10 8 10 SP SD: 3.9525 c. M:-6.5102 c. 101: 9 14 8 13 7 14 7 10 9 10 SP SD: 3.2453 c. M: 6.2277 c. 108: 10 15 8 14 8 14 8 11 9 11 SP SD: 3.1171 c. M:-7.1852 c. 111: 10 15 9 14 8 15 8 11 10 11 SP SD: 3.6039 c. M: 7.0180 c. 112: 10 15 9 15 8 15 8 11 10 11 SP SD: 3.4635 c. M: 7.4643 c. 114: 10 16 9 15 8 15 8 12 10 11 SP SD: 3.7525 c. M:-6.1930 c. 118: 11 16 9 15 9 16 8 12 10 12 SP SD: 3.3188 c. M:-6.2881 c. 122: 11 17 9 16 9 16 9 12 11 12 SP SD: 2.1832 c. M: 4.0656 c. 161: 15 22 12 21 12 21 12 16 14 16 SP SD: 2.1677 c. M:-4.2298 c. 167: 15 23 13 22 12 22 12 17 14 17 SP SD: 1.9755 c. M: 4.3832 c. 173: 16 23 14 22 13 23 12 18 15 17 SP SD: 2.4305 c. M: 3.5318 c. 175: 16 24 13 23 13 23 13 17 16 17 SP SD: 2.4238 c. M: 4.1486 c. 177: 16 24 14 23 13 23 13 18 15 18 SP SD: 2.0422 c. M: 4.2034 c. 181: 16 25 14 24 13 24 13 18 16 18 SP SD: 1.9640 c. M: 4.3591 c. 189: 17 26 15 24 14 25 14 19 16 19 SP SD: 1.9581 c. M:-3.7884 c. 198: 18 27 15 26 15 26 14 20 17 20 SP SD: 1.8294 c. M: 3.0303 c. 219: 20 30 17 28 16 29 16 22 19 22 SP SD: 1.8378 c. M: 2.8630 c. 220: 20 30 17 29 16 29 16 22 19 22 SP SD: 1.0417 c. M:-2.2364 c. 289: 26 40 22 38 21 38 21 29 25 29 SP SD: 1.1414 c. M: 1.8131 c. 295: 27 40 23 38 22 39 21 30 26 29 SP SD: 1.1212 c. M: 2.1322 c. 331: 30 45 26 43 24 44 24 33 29 33 SP SD: 0.9889 c. M: 1.9154 c. 342: 31 47 26 45 25 45 25 34 30 34 SP SD: 0.9102 c. M: 1.6023 c. 375: 34 51 29 49 28 49 27 38 33 37 SP SD: 1.0579 c. M:-1.5387 c. 386: 35 53 30 50 28 51 28 39 34 38 SP SD: 0.9873 c. M:-1.6995 c. 393: 36 53 31 51 29 52 28 40 34 39 SP SD: 0.9467 c. M: 1.7074 c. 404: 37 55 31 53 29 54 29 41 35 40 SP SD: 0.9462 c. M: 1.8416 c. 423: 38 58 33 55 31 56 30 43 37 42 SP SD: 0.9779 c. M: 2.0733 c. 439: 40 60 34 57 32 58 32 44 38 44 SP SD: 0.8037 c. M: 1.6036 c. 450: 41 61 35 59 33 59 33 45 39 45 SP SD: 0.8625 c. M: 1.3467 c. 452: 41 62 35 59 33 60 32 46 39 45 SP SD: 0.9268 c. M:-1.9027 c. 453: 41 62 35 59 33 60 33 46 39 45 SP SD: 0.7004 c. M:-1.4172 c. 462: 42 63 36 60 34 61 33 47 40 46 SP SD: 0.4912 c. M: 1.1212 c. 515: 47 70 40 67 38 68 37 52 45 51 SP SD: 0.4094 c. M:-0.7165 c. 584: 53 80 45 76 43 77 42 59 51 58 SP SD: 0.4016 c. M: 0.7534 c. 682: 62 93 53 89 50 90 49 69 59 68 SP SD: 0.4233 c. M: 0.6804 c. 735: 67 100 57 96 54 97 53 74 64 73 SP SD: 0.3956 c. M:-0.6707 c. 804: 73 110 62 105 59 106 58 81 70 80 SP SD: 0.3054 c. M: 0.5970 c. 968: 88 132 75 126 71 128 70 98 84 96 SP SD: 0.2536 c. M:-0.4959 c. 1037: 94 142 80 135 76 137 75 105 90 103 SP SD: 0.2804 c. M: 0.4754 c. 1090: 99 149 84 142 80 144 79 110 95 108 SP SD: 0.2648 c. M:-0.4257 c. 1188: 108 162 92 155 87 157 86 120 103 118 SP SD: 0.1974 c. M:-0.3704 c. 1257: 114 172 97 164 92 166 91 127 109 125 SP SD: 0.1677 c. M: 0.2936 c. 1552: 141 212 120 202 114 205 112 157 135 154 SP SD: 0.1477 c. M: 0.3170 c. 1719: 156 235 133 224 126 227 124 174 149 171 SP SD: 0.1478 c. M: 0.2723 c. 1772: 161 242 137 231 130 234 128 179 154 176 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 x x 3 S SD: 72.2103 cents 2 x x x 3 x x 4 x 5:6 S SD: 40.0923 cents 3 x x 4 x 5 x 6:7 x 8 S SD: 21.9946 cents 4 x 5 x 6:7 x 8:9:10:11 S SD: 17.8357 cents 5 x 6:7:8 x x 10:12:13:14 S SD: 22.2015 cents 6:7 x 8:9:10 x 12:14:15:17 SD: 19.2254 cents 7:8:9:10:11:12:13:15:16:18:19 SD: 15.4388 cents 8:9:10:11:12:13:15:17:18:20:22 SD: 12.8796 cents 9:10:11:12:14:15:17:19:21:23:25 SD: 9.5635 cents 10:11:13:14:16:17:19:21:23:25:28 SD: 8.8381 cents 11:12:14:15:17:19:21:23:25:28:31 SD: 6.6856 cents 14:15:18:19:22:24:27:29:32:35:39 SD: 6.5358 cents 16:18:20:22:25:27:31:33:37:40:45 SD: 5.4614 cents 18:20:23:25:28:30:35:37:41:45:50 SD: 5.4289 cents 19:21:24:26:30:32:37:39:44:48:53 SD: 3.8215 cents 22:24:28:30:34:37:42:46:51:55:61 SD: 3.7225 cents 23:25:29:31:36:39:44:48:53:58:64 SD: 3.6217 cents 27:30:34:37:42:45:52:56:62:68:75 SD: 2.9083 cents 30:33:38:41:47:50:58:62:69:75:83 SD: 2.5465 cents 38:42:48:52:59:64:73:79:87:96:106 SD: 2.0989 cents 39:43:49:53:61:66:75:81:90:98:109 SD: 2.0379 cents 41:45:52:56:64:69:79:85:94:103:114 SD: 1.0374 cents 80:88:101:109:125:135:154:166:184:201:223 SD: 0.8573 cents 84:92:106:115:131:141:162:174:193:211:234 SD: 0.8110 cents 91:100:115:124:142:153:175:189:209:229:253 SD: 0.7593 cents 103:113:130:141:161:173:198:214:237:259:287 SD: 0.7488 cents 107:117:135:146:167:180:206:222:246:269:298 SD: 0.6920 cents 111:122:140:152:173:187:214:230:255:279:309 SD: 0.6850 cents 114:125:144:156:178:192:220:236:262:287:317 SD: 0.6826 cents 121:133:153:165:189:204:233:251:278:304:337 SD: 0.6771 cents 123:135:155:168:192:207:237:255:283:309:342 SD: 0.3542 cents 164:180:207:224:256:276:316:340:377:412:456 SD: 0.2456 cents 267:293:337:365:417:449:514:554:614:671:743 SD: 0.2412 cents 287:315:362:392:448:483:553:595:660:722:799 SD: 0.1958 cents 309:339:390:422:482:520:595:641:711:777:860 SD: 0.1824 cents 328:360:414:448:512:552:632:680:754:825:913 SD: 0.1641 cents 420:461:530:574:656:707:809:871:966:1056:1169 SD: 0.1480 cents 451:495:569:616:704:759:869:935:1037:1134:1255 SD: 0.1336 cents 473:519:597:646:738:796:911:981:1088:1189:1316 SD: 0.1180 cents 554:608:699:757:865:932:1067:1149:1274:1393:1542 SD: 0.1082 cents 595:653:751:813:929:1001:1146:1234:1369:1496:1656 SD: 0.0984 cents