Scala analysis: xen18-erlich-keemun-11

4L 7s MOS for Keemun, L=181.50, s=68.17

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         68.170 cents      68.170000
  2:        249.670 cents     249.670000
  3:        317.840 cents     317.840000
  4:        386.010 cents     386.010000
  5:        567.510 cents     567.510000
  6:        635.680 cents     635.680000
  7:        817.180 cents     817.180000
  8:        885.350 cents     885.350000
  9:        953.520 cents     953.520000
 10:       1135.020 cents    1135.020000
 11:       1203.190 cents    1203.190000
SHOW/INTERVAL
  0:         68.1700 cents     68.1700
  1:         68.1700 cents     68.1700
  2:        181.5000 cents    181.5000
  3:         68.1700 cents     68.1700
  4:         68.1700 cents     68.1700
  5:        181.5000 cents    181.5000
  6:         68.1700 cents     68.1700
  7:        181.5000 cents    181.5000
  8:         68.1700 cents     68.1700
  9:         68.1700 cents     68.1700
 10:        181.5000 cents    181.5000
 11:         68.1700 cents     68.1700
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   7 68.17000 cents
  1:   4 181.50000 cents
  2:   3 136.34000 cents
  2:   8 249.67000 cents
  3:  10 317.84000 cents
  3:   1 431.17000 cents
  4:   6 386.01000 cents
  4:   5 499.34000 cents
  5:   2 454.18000 cents
  5:   9 567.51000 cents
  6:   9 635.68000 cents
  6:   2 749.01000 cents
  7:   5 703.85000 cents
  7:   6 817.18000 cents
  8:   1 772.02000 cents
  8:  10 885.35000 cents
  9:   8 953.52000 cents
  9:   3 1066.85000 cents
 10:   4 1021.69000 cents
 10:   7 1135.02000 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      10     11    
 0.0   : 68.2  249.7 317.8 386.0 567.5 635.7 817.2 885.3 953.5  1135.0 1203.2
 68.2  : 181.5 249.7 317.8 499.3 567.5 749.0 817.2 885.3 1066.8 1135.0 1203.2
 249.7 : 68.2  136.3 317.8 386.0 567.5 635.7 703.8 885.4 953.5  1021.7 1203.2
 317.8 : 68.2  249.7 317.8 499.3 567.5 635.7 817.2 885.3 953.5  1135.0 1203.2
 386.0 : 181.5 249.7 431.2 499.3 567.5 749.0 817.2 885.3 1066.8 1135.0 1203.2
 567.5 : 68.2  249.7 317.8 386.0 567.5 635.7 703.8 885.4 953.5  1021.7 1203.2
 635.7 : 181.5 249.7 317.8 499.3 567.5 635.7 817.2 885.3 953.5  1135.0 1203.2
 817.2 : 68.2  136.3 317.8 386.0 454.2 635.7 703.8 772.0 953.5  1021.7 1203.2
 885.3 : 68.2  249.7 317.8 386.0 567.5 635.7 703.9 885.3 953.5  1135.0 1203.2
 953.5 : 181.5 249.7 317.8 499.3 567.5 635.7 817.2 885.4 1066.8 1135.0 1203.2
 1135.0: 68.2  136.3 317.8 386.0 454.2 635.7 703.8 885.3 953.5  1021.7 1203.2
 1203.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  68.1700   .. 181.5000 cents      113.33000 cents                    68.17000 cents
  2:  136.3400  .. 249.6700 cents      113.33000 cents                   -45.16000 cents
  3:  317.8400  .. 431.1700 cents      113.33000 cents                    68.17000 cents
  4:  386.0100  .. 499.3400 cents      113.33000 cents                   -45.16000 cents
  5:  454.1800  .. 567.5100 cents      113.33000 cents                   -45.16000 cents
  6:  635.6800  .. 749.0100 cents      113.33000 cents                    68.17000 cents
  7:  703.8500  .. 817.1800 cents      113.33000 cents                   -45.16000 cents
  8:  772.0200  .. 885.3500 cents      113.33000 cents                   -45.16000 cents
  9:  953.5200  .. 1066.8500 cents     113.33000 cents                    68.17000 cents
 10:  1021.6900 .. 1135.0200 cents     113.33000 cents                   -45.16000 cents
SHOW DATA
Number of notes                     : 11
-- Interval properties --
Smallest interval                   : 68.17000 cents, class 1
Average step (divided formal octave): 109.3809 cents
Largest one step interval           : 181.50000 cents
Average / Smallest step             : 1.604531
Largest / Average step              : 1.659339
Largest / Smallest step             : 2.662461
Median interval of one step         : 68.17000 cents, amount: 7
Most common interval of one step    : 68.17000 cents, amount: 7
Least squares average step          : 110.05283 cents, oct.:  1210.58109 cents
Scale is not proper
Scale has Myhill's property
  chromas: 113.33000 cents and 45.16000 cents, ratio: 2.509522
  generators: 3 of 317.84000 cents and 8 of 885.35000 cents
ET pair of linear temperament       : 15&19
Scale is distributional even
Scale is a mode of a 1306-tone equal temperament with octave  1203.190 cents
  degrees: 74 271 345 419 616 690 887 961 1035 1232 1306
  generators: 345 and 961
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABAABABAABA
Step pattern size order : SLSSLSLSSLS
Scale is a Constant Structure, by a margin of 23.01000 cents
Scale diversity                     : 1.239234
Lumma stability                     : 0.283289
Lumma impropriety factor            : 0.225201
Rothenberg efficiency               : 0.727273   redundancy: 0.272727
Efficiency x scale size             : 8.000000
Number of different interval sizes  : 20 = 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        : 23.01000 cents
Most common intervals               : 317.84000 cents & inv., amount: 10
Scale is a chain of 5 triads 0.0 386.010 885.350 cents
Most common triad is 0.0 317.840 885.350 cents, amount: 9
Number of recognisable fifths       : 5, average 703.8500 cents
Number of recognisable fourths      : 5, average 499.3400 cents
Scale contains two identical conjunct hexachords 
Formal octave complements present   : 11 = 100.0000%
2/1 octave complements present      : 0 = 0.0000%
Inversional symmetry on degrees     :
 0
Inversional symmetry on intervals   :
 5-6
-- Rational properties --
FIT/MODE
 11:  1 1 1 1 1 1 1 1 1 1 1  SP B ME I SD: 32.5801 c. M: 51.5136 c. 
 13:  1 2 0 1 2 1 2 1 0 2 1   N   T3 I SD: 24.8290 c. M: 40.1808 c. 
 15:  1 2 1 1 2 1 2 1 1 2 1   P M ME I SD: 9.5206 c. M: 15.0533 c. 
 19:  1 3 1 1 3 1 3 1 1 3 1   N M DE I SD: 3.8297 c. M: 6.0553 c. 
 34:  2 5 2 2 5 2 5 2 2 5 2   N M DE I SD: 2.0601 c. M: 3.2574 c. 
 53:  3 8 3 3 8 3 8 3 3 8 3   N M DE I SD: 0.0513 c. M: 0.0811 c. 
 723: 41 109 41 41 109 41 109 41 41 109 41   N M DE I SD: 0.0480 c. M: 0.0759 c. 
 776: 44 117 44 44 117 44 117 44 44 117 44   N M DE I SD: 0.0412 c. M: 0.0651 c. 
 829: 47 125 47 47 125 47 125 47 47 125 47   N M DE I SD: 0.0353 c. M: 0.0558 c. 
 882: 50 133 50 50 133 50 133 50 50 133 50   N M DE I SD: 0.0301 c. M: 0.0476 c. 
 935: 53 141 53 53 141 53 141 53 53 141 53   N M DE I SD: 0.0255 c. M:-0.0403 c. 
 988: 56 149 56 56 149 56 149 56 56 149 56   N M DE I SD: 0.0213 c. M: 0.0338 c. 
 1041: 59 157 59 59 157 59 157 59 59 157 59   N M DE I SD: 0.0176 c. M:-0.0279 c. 
 1094: 62 165 62 62 165 62 165 62 62 165 62   N M DE I SD: 0.0143 c. M: 0.0226 c. 
 1147: 65 173 65 65 173 65 173 65 65 173 65   N M DE I SD: 0.0113 c. M: 0.0178 c. 
 1200: 68 181 68 68 181 68 181 68 68 181 68   N M DE I SD: 0.0085 c. M: 0.0135 c. 
 1253: 71 189 71 71 189 71 189 71 71 189 71   N M DE I SD: 0.0060 c. M: 0.0095 c. 
 1306: 74 197 74 74 197 74 197 74 74 197 74   N M DE I SD: 0.0037 c. M: 0.0058 c. 
 1359: 77 205 77 77 205 77 205 77 77 205 77   N M DE I SD: 0.0015 c. M: 0.0024 c. 
 1412: 80 213 80 80 213 80 213 80 80 213 80   N M DE I SD: 0.0005 c. M: 0.0007 c. 
FIT/HARMONIC
 1 x x x x x x x x x x 2  S SD: 3.1900 cents
 2 x x x x x 3 x x x x 4  S SD: 33.1759 cents
 3 x x x x 4 x x 5 x x 6  S SD: 23.1818 cents
 4 x x x 5 x 6 x x 7 x 8  S SD: 17.0237 cents
 5 x x 6 x 7 x 8 x 9 x 10  S SD: 13.2031 cents
 6 x 7 x x 8:9 x 10 x x 12  S SD: 19.5190 cents
 7 x 8 x 9 x 10:11 x 12:13:14  S SD: 13.3399 cents
 8 x 9 x 10:11:12:13 x 14:15:16  S SD: 12.3262 cents
 9 x 10:11 x x 13:14:15:16:17:18    SD: 13.1749 cents
 10 x x 12:13:14 x 16:17 x 19:20    SD: 11.5880 cents
 11:12 x 13:14:15:16 x 18:19:21:22    SD: 11.7034 cents
 12:13:14 x 15 x 17:19:20:21:23:24    SD: 9.3684 cents
 13:14:15 x 16:18:19:21:22:23:25:26    SD: 8.2478 cents
 15:16:17:18:19:21:22:24:25:26:29:30    SD: 6.1448 cents
 17:18:20 x 21:24:25:27:28:29:33:34    SD: 7.7463 cents
 18:19:21:22:23:25:26:29:30:31:35:36    SD: 5.5966 cents
 19:20:22:23:24:26:27:30:32:33:37:38    SD: 5.4977 cents
 20:21:23:24:25:28:29:32:33:35:39:40    SD: 3.6980 cents
 25:26:29:30:31:35:36:40:42:43:48:50    SD: 2.7575 cents
 39:41:45:47:49:54:56:63:65:68:75:78    SD: 2.6165 cents
 40:42:46:48:50:56:58:64:67:69:77:80    SD: 2.5503 cents
 41:43:47:49:51:57:59:66:68:71:79:82    SD: 2.4532 cents
 43:45:50:52:54:60:62:69:72:75:83:86    SD: 2.3910 cents
 44:46:51:53:55:61:64:71:73:76:85:88    SD: 2.2203 cents
 45:47:52:54:56:62:65:72:75:78:87:90    SD: 1.6697 cents
 52:54:60:62:65:72:75:83:87:90:100:104    SD: 1.6595 cents
 56:58:65:67:70:78:81:90:93:97:108:112    SD: 1.6195 cents
 64:67:74:77:80:89:92:103:107:111:123:128    SD: 1.5427 cents
 65:68:75:78:81:90:94:104:108:113:125:130    SD: 1.4215 cents
 69:72:80:83:86:96:100:111:115:120:133:138    SD: 1.3729 cents
 70:73:81:84:87:97:101:112:117:121:135:140    SD: 1.3277 cents
 72:75:83:87:90:100:104:115:120:125:139:144    SD: 1.2432 cents
 75:78:87:90:94:104:108:120:125:130:144:150    SD: 1.1542 cents
 79:82:91:95:99:110:114:127:132:137:152:158    SD: 1.0785 cents
 93:97:107:112:116:129:134:149:155:161:179:186    SD: 1.0613 cents
 95:99:110:114:119:132:137:152:158:165:183:190    SD: 0.9275 cents
 103:107:119:124:129:143:149:165:172:179:198:206    SD: 0.8325 cents
 108:112:125:130:135:150:156:173:180:187:208:216    SD: 0.7831 cents
 121:126:140:145:151:168:175:194:202:210:233:242    SD: 0.7303 cents
 124:129:143:149:155:172:179:199:207:215:239:248    SD: 0.4754 cents
 180:187:208:216:225:250:260:289:300:312:347:361    SD: 0.4575 cents
 193:201:223:232:241:268:279:309:322:335:372:387    SD: 0.4458 cents
 199:207:230:239:249:276:287:319:332:345:383:399    SD: 0.3563 cents
 219:228:253:263:274:304:316:351:365:380:422:439    SD: 0.2888 cents
 252:262:291:303:315:350:364:404:420:437:485:505    SD: 0.2659 cents
 297:309:343:357:371:412:429:476:495:515:572:595    SD: 0.2054 cents
 421:438:486:506:526:584:608:675:702:730:811:844    SD: 0.1918 cents
 446:464:515:536:557:619:644:715:744:774:859:894    SD: 0.1796 cents
 451:469:521:542:564:626:651:723:752:782:869:904    SD: 0.1489 cents
 476:495:550:572:595:661:687:763:794:826:917:954    SD: 0.1471 cents
 516:537:596:620:645:716:745:827:860:895:994:1034    SD: 0.1417 cents
 521:542:602:626:651:723:752:835:869:904:1004:1044    SD: 0.1228 cents
 572:595:661:687:715:794:826:917:954:992:1102:1146    SD: 0.1140 cents