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