Scala analysis: xen18-erlich-nautilus-09

1L 8s MOS for Nautilus, L=538.90, s=82.97

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         82.970 cents      82.970000
  2:        165.940 cents     165.940000
  3:        248.910 cents     248.910000
  4:        331.880 cents     331.880000
  5:        870.780 cents     870.780000
  6:        953.750 cents     953.750000
  7:       1036.720 cents    1036.720000
  8:       1119.690 cents    1119.690000
  9:       1202.660 cents    1202.660000
SHOW/INTERVAL
  0:         82.9700 cents     82.9700
  1:         82.9700 cents     82.9700
  2:         82.9700 cents     82.9700
  3:         82.9700 cents     82.9700
  4:         82.9700 cents     82.9700
  5:        538.9000 cents    538.9000
  6:         82.9700 cents     82.9700
  7:         82.9700 cents     82.9700
  8:         82.9700 cents     82.9700
  9:         82.9700 cents     82.9700
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   8 82.97000 cents
  1:   1 538.90000 cents
  2:   7 165.94000 cents
  2:   2 621.87000 cents
  3:   6 248.91000 cents
  3:   3 704.84000 cents
  4:   5 331.88000 cents
  4:   4 787.81000 cents
  5:   4 414.85000 cents
  5:   5 870.78000 cents
  6:   3 497.82000 cents
  6:   6 953.75000 cents
  7:   2 580.79000 cents
  7:   7 1036.72000 cents
  8:   1 663.76000 cents
  8:   8 1119.69000 cents
Highest number of different intervals for one interval class: 2
Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6     7      8      9     
 0.0   : 83.0  165.9 248.9 331.9 870.8 953.8 1036.7 1119.7 1202.7
 83.0  : 83.0  165.9 248.9 787.8 870.8 953.8 1036.7 1119.7 1202.7
 165.9 : 83.0  165.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7
 248.9 : 83.0  621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7
 331.9 : 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7
 870.8 : 83.0  165.9 248.9 331.9 414.9 497.8 580.8  663.8  1202.7
 953.8 : 83.0  165.9 248.9 331.9 414.9 497.8 580.8  1119.7 1202.7
 1036.7: 83.0  165.9 248.9 331.9 414.8 497.8 1036.7 1119.7 1202.7
 1119.7: 83.0  165.9 248.9 331.9 414.9 953.8 1036.7 1119.7 1202.7
 1202.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  82.9700   .. 538.9000 cents      455.93000 cents                    82.97000 cents
  2:  165.9400  .. 621.8700 cents      455.93000 cents                   -372.96000 cents
  3:  248.9100  .. 704.8400 cents      455.93000 cents                   -372.96000 cents
  4:  331.8800  .. 787.8100 cents      455.93000 cents                   -372.96000 cents
  5:  414.8500  .. 870.7800 cents      455.93000 cents                   -372.96000 cents
  6:  497.8200  .. 953.7500 cents      455.93000 cents                   -372.96000 cents
  7:  580.7900  .. 1036.7200 cents     455.93000 cents                   -372.96000 cents
  8:  663.7600  .. 1119.6900 cents     455.93000 cents                   -372.96000 cents
SHOW DATA
Number of notes                     : 9
-- Interval properties --
Smallest interval                   : 82.97000 cents, class 1
Average step (divided formal octave): 133.6289 cents
Largest one step interval           : 538.90000 cents
Average / Smallest step             : 1.610569
Largest / Average step              : 4.032811
Largest / Smallest step             : 6.495119
Median interval of one step         : 82.97000 cents, amount: 8
Most common interval of one step    : 82.97000 cents, amount: 8
Least squares average step          : 138.96140 cents, oct.:  1250.65263 cents
Scale is not proper
Scale has Myhill's property
  chromas: 455.93000 cents and 372.96000 cents, ratio: 1.222464
  generators: 1 of 82.97000 cents and 8 of 1119.69000 cents
ET pair of linear temperament       : 14&29
Scale is distributional even
Scale is a mode of a 1435-tone equal temperament with octave  1202.660 cents
  degrees: 99 198 297 396 1039 1138 1237 1336 1435
  generators: 99 and 1336
Number of contiguous 1-step segments: 0
Step pattern alph. order: AAAABAAAA
Step pattern size order : SSSSLSSSS
Scale is a Constant Structure, by a margin of 41.08000 cents
Scale diversity                     : 1.255706
Lumma stability                     : 0.137977
Lumma impropriety factor            : 0.724045
Rothenberg efficiency               : 0.740741   redundancy: 0.259259
Efficiency x scale size             : 6.666667
Number of different interval sizes  : 16 = 2.00000 / class
Number of one step interval sizes   : 2
Highest interval variety            : 2
Mean interval variety               : 2.00000 = 2
Median interval variety             : 2
Lowest interval variety             : 2
Smallest interval difference        : 41.08000 cents
Most common intervals               : 82.97000 cents & inv., amount: 8
Scale is a chain of 4 triads 0.0 331.880 1119.690 cents
Number of recognisable fifths       : 3, average 704.8400 cents
Number of recognisable fourths      : 3, average 497.8200 cents
Scale contains two identical disjunct pentachords
Formal octave complements present   : 9 = 100.0000%
2/1 octave complements present      : 0 = 0.0000%
Inversional symmetry on degrees     :
 0
Inversional symmetry on intervals   :
 4-5
-- Rational properties --
FIT/MODE
  9:  0 1 0 1 4 1 0 1 1   N        SD: 69.3814 c. M: 115.2811 c. 
 10:  1 0 1 1 4 1 1 0 1   N      I SD: 31.2109 c. M:-45.6740 c. 
 13:  1 1 1 1 5 1 1 1 1   N M DE I SD: 24.6381 c. M:-38.1692 c. 
 14:  1 1 1 1 6 1 1 1 1   N M DE I SD: 7.5763 c. M:-11.7371 c. 
 15:  1 1 1 1 7 1 1 1 1   N M DE I SD: 7.2106 c. M:-11.1707 c. 
 29:  2 2 2 2 13 2 2 2 2   N M DE I SD: 0.0721 c. M:-0.1117 c. 
 768: 53 53 53 53 344 53 53 53 53   N M DE I SD: 0.0673 c. M:-0.1043 c. 
 797: 55 55 55 55 357 55 55 55 55   N M DE I SD: 0.0622 c. M:-0.0964 c. 
 826: 57 57 57 57 370 57 57 57 57   N M DE I SD: 0.0575 c. M:-0.0891 c. 
 855: 59 59 59 59 383 59 59 59 59   N M DE I SD: 0.0531 c. M:-0.0823 c. 
 884: 61 61 61 61 396 61 61 61 61   N M DE I SD: 0.0490 c. M:-0.0759 c. 
 913: 63 63 63 63 409 63 63 63 63   N M DE I SD: 0.0452 c. M:-0.0700 c. 
 942: 65 65 65 65 422 65 65 65 65   N M DE I SD: 0.0416 c. M:-0.0644 c. 
 971: 67 67 67 67 435 67 67 67 67   N M DE I SD: 0.0382 c. M:-0.0591 c. 
 1000: 69 69 69 69 448 69 69 69 69   N M DE I SD: 0.0350 c. M:-0.0542 c. 
 1029: 71 71 71 71 461 71 71 71 71   N M DE I SD: 0.0319 c. M:-0.0495 c. 
 1058: 73 73 73 73 474 73 73 73 73   N M DE I SD: 0.0291 c. M:-0.0451 c. 
 1087: 75 75 75 75 487 75 75 75 75   N M DE I SD: 0.0264 c. M:-0.0409 c. 
 1116: 77 77 77 77 500 77 77 77 77   N M DE I SD: 0.0238 c. M:-0.0369 c. 
 1145: 79 79 79 79 513 79 79 79 79   N M DE I SD: 0.0214 c. M:-0.0332 c. 
 1174: 81 81 81 81 526 81 81 81 81   N M DE I SD: 0.0191 c. M:-0.0296 c. 
 1203: 83 83 83 83 539 83 83 83 83   N M DE I SD: 0.0169 c. M:-0.0262 c. 
 1232: 85 85 85 85 552 85 85 85 85   N M DE I SD: 0.0148 c. M:-0.0229 c. 
 1261: 87 87 87 87 565 87 87 87 87   N M DE I SD: 0.0128 c. M:-0.0198 c. 
 1290: 89 89 89 89 578 89 89 89 89   N M DE I SD: 0.0109 c. M:-0.0169 c. 
 1319: 91 91 91 91 591 91 91 91 91   N M DE I SD: 0.0091 c. M:-0.0140 c. 
 1348: 93 93 93 93 604 93 93 93 93   N M DE I SD: 0.0073 c. M:-0.0113 c. 
 1377: 95 95 95 95 617 95 95 95 95   N M DE I SD: 0.0056 c. M:-0.0087 c. 
 1406: 97 97 97 97 630 97 97 97 97   N M DE I SD: 0.0040 c. M:-0.0063 c. 
 1435: 99 99 99 99 643 99 99 99 99   N M DE I SD: 0.0025 c. M:-0.0039 c. 
 1464: 101 101 101 101 656 101 101 101 101   N M DE I SD: 0.0010 c. M:-0.0016 c. 
 1493: 103 103 103 103 669 103 103 103 103   N M DE I SD: 0.0004 c. M: 0.0006 c. 
FIT/HARMONIC
 1 x x x x x x x x 2  S SD: 2.6600 cents
 2 x x x x 3 x x x 4  S SD: 84.4230 cents
 3 x x x 4:5 x x x 6  S SD: 55.5800 cents
 4 x x x 5 x 7 x x 8    SD: 18.8485 cents
 5 x x x 6:8 x 9 x 10  S SD: 15.6048 cents
 6 x x 7 x 10 x 11 x 12    SD: 6.4899 cents
 7 x x 8 x x 12:13 x 14  S SD: 11.0978 cents
 8 x 9 x 10:13:14 x 15:16    SD: 13.4800 cents
 9 x 10 x 11:15 x 16:17:18    SD: 8.6635 cents
 10 x 11 x 12 x 17:18:19:20    SD: 7.3448 cents
 11 x 12:13 x 18:19:20:21:22    SD: 6.7857 cents
 12 x 13:14:15:20:21:22:23:24  S SD: 8.5304 cents
 13 x 14:15:16:22:23:24:25:26    SD: 9.4437 cents
 14:15 x 16:17:23:24:25:27:28    SD: 7.5085 cents
 15:16 x 17:18:25:26:27:29:30    SD: 7.0223 cents
 16:17:18 x 19:26:28:29:31:32    SD: 8.7938 cents
 17:18:19:20:21:28:29:31:32:34    SD: 7.6102 cents
 18:19:20:21:22:30:31:33:34:36    SD: 4.7221 cents
 19:20:21:22:23:31:33:35:36:38    SD: 3.9732 cents
 20:21:22:23:24:33:35:36:38:40    SD: 3.5169 cents
 33:35:36:38:40:55:57:60:63:66    SD: 3.2697 cents
 37:39:41:43:45:61:64:67:71:74    SD: 2.7069 cents
 38:40:42:44:46:63:66:69:73:76    SD: 1.8320 cents
 57:60:63:66:69:94:99:104:109:114    SD: 1.4590 cents
 76:80:84:88:92:126:132:138:145:152    SD: 1.4121 cents
 77:81:85:89:93:127:134:140:147:154    SD: 1.3023 cents
 78:82:86:90:94:129:135:142:149:156    SD: 1.2516 cents
 79:83:87:91:96:131:137:144:151:158    SD: 1.0883 cents
 90:94:99:104:109:149:156:164:172:180    SD: 1.0083 cents
 98:103:108:113:119:162:170:178:187:196    SD: 0.8581 cents
 99:104:109:114:120:164:172:180:189:198    SD: 0.8232 cents
 118:124:130:136:143:195:205:215:225:236    SD: 0.7484 cents
 122:128:134:141:148:202:212:222:233:244    SD: 0.7220 cents
 141:148:155:163:171:233:245:257:269:282    SD: 0.6893 cents
 142:149:156:164:172:235:246:258:271:284    SD: 0.6514 cents
 161:169:177:186:195:266:279:293:307:322    SD: 0.5432 cents
 180:189:198:208:218:298:312:328:344:361    SD: 0.5330 cents
 188:197:207:217:228:311:326:342:359:377    SD: 0.4262 cents
 199:209:219:230:241:329:345:362:380:399    SD: 0.3831 cents
 227:238:250:262:275:375:394:413:433:455    SD: 0.3706 cents
 245:257:270:283:297:405:425:446:468:491    SD: 0.3410 cents
 246:258:271:284:298:407:427:448:470:493    SD: 0.3093 cents
 265:278:292:306:321:438:460:482:506:531    SD: 0.3030 cents
 289:303:318:334:350:478:501:526:552:579    SD: 0.2784 cents
 309:324:340:357:374:511:536:562:590:619    SD: 0.2588 cents
 349:366:384:403:423:577:605:635:666:699    SD: 0.2409 cents
 350:367:385:404:424:579:607:637:668:701    SD: 0.1978 cents
 387:406:426:447:469:640:671:704:739:775    SD: 0.1930 cents
 388:407:427:448:470:642:673:706:741:777    SD: 0.1461 cents
 407:427:448:470:493:673:706:741:777:815    SD: 0.1038 cents