Scala analysis: augene15br1

Augene[15] with a brat of 1

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         93.471 cents      93.470871
  2:        186.942 cents     186.941743
  3:        213.058 cents     213.058257
  4:        306.529 cents     306.529129
  5:        400.000 cents     400.000000
  6:        493.471 cents     493.470871
  7:        586.942 cents     586.941743
  8:        613.058 cents     613.058257
  9:        706.529 cents     706.529129
 10:        800.000 cents     800.000000
 11:        893.471 cents     893.470871
 12:        986.942 cents     986.941743
 13:       1013.058 cents    1013.058257
 14:       1106.529 cents    1106.529129
 15:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:         93.4709 cents     93.4709
  1:         93.4709 cents     93.4709
  2:         93.4709 cents     93.4709
  3:         26.1165 cents     26.1165
  4:         93.4709 cents     93.4709
  5:         93.4709 cents     93.4709
  6:         93.4709 cents     93.4709
  7:         93.4709 cents     93.4709
  8:         26.1165 cents     26.1165
  9:         93.4709 cents     93.4709
 10:         93.4709 cents     93.4709
 11:         93.4709 cents     93.4709
 12:         93.4709 cents     93.4709
 13:         26.1165 cents     26.1165
 14:         93.4709 cents     93.4709
 15:         93.4709 cents     93.4709
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   3 26.11651 cents
  1:  12 93.47087 cents
  2:   6 119.58739 cents
  2:   9 186.94174 cents
  3:   9 213.05826 cents
  3:   6 280.41261 cents
  4:  12 306.52913 cents
  4:   3 373.88349 cents
  5:  15 400.00000 cents
  6:   3 426.11651 cents
  6:  12 493.47087 cents
  7:   6 519.58739 cents
  7:   9 586.94174 cents
  8:   9 613.05826 cents
  8:   6 680.41261 cents
  9:  12 706.52913 cents
  9:   3 773.88349 cents
 10:  15 800.00000 cents
 11:   3 826.11651 cents
 11:  12 893.47087 cents
 12:   6 919.58739 cents
 12:   9 986.94174 cents
 13:   9 1013.05826 cents
 13:   6 1080.41261 cents
 14:  12 1106.52913 cents
 14:   3 1173.88349 cents
Highest number of different intervals for one interval class: 2
Average number of different intervals per interval class: 1.85714 = 13/7
SHOW/LINE/CENTS INTERVALS
         1    2     3     4     5     6     7     8     9     10    11    12    13     14     15    
 0.0   : 93.5 186.9 213.1 306.5 400.0 493.5 586.9 613.1 706.5 800.0 893.5 986.9 1013.1 1106.5 1200.0
 93.5  : 93.5 119.6 213.1 306.5 400.0 493.5 519.6 613.1 706.5 800.0 893.5 919.6 1013.1 1106.5 1200.0
 186.9 : 26.1 119.6 213.1 306.5 400.0 426.1 519.6 613.1 706.5 800.0 826.1 919.6 1013.1 1106.5 1200.0
 213.1 : 93.5 186.9 280.4 373.9 400.0 493.5 586.9 680.4 773.9 800.0 893.5 986.9 1080.4 1173.9 1200.0
 306.5 : 93.5 186.9 280.4 306.5 400.0 493.5 586.9 680.4 706.5 800.0 893.5 986.9 1080.4 1106.5 1200.0
 400.0 : 93.5 186.9 213.1 306.5 400.0 493.5 586.9 613.1 706.5 800.0 893.5 986.9 1013.1 1106.5 1200.0
 493.5 : 93.5 119.6 213.1 306.5 400.0 493.5 519.6 613.1 706.5 800.0 893.5 919.6 1013.1 1106.5 1200.0
 586.9 : 26.1 119.6 213.1 306.5 400.0 426.1 519.6 613.1 706.5 800.0 826.1 919.6 1013.1 1106.5 1200.0
 613.1 : 93.5 186.9 280.4 373.9 400.0 493.5 586.9 680.4 773.9 800.0 893.5 986.9 1080.4 1173.9 1200.0
 706.5 : 93.5 186.9 280.4 306.5 400.0 493.5 586.9 680.4 706.5 800.0 893.5 986.9 1080.4 1106.5 1200.0
 800.0 : 93.5 186.9 213.1 306.5 400.0 493.5 586.9 613.1 706.5 800.0 893.5 986.9 1013.1 1106.5 1200.0
 893.5 : 93.5 119.6 213.1 306.5 400.0 493.5 519.6 613.1 706.5 800.0 893.5 919.6 1013.1 1106.5 1200.0
 986.9 : 26.1 119.6 213.1 306.5 400.0 426.1 519.6 613.1 706.5 800.0 826.1 919.6 1013.1 1106.5 1200.0
 1013.1: 93.5 186.9 280.4 373.9 400.0 493.5 586.9 680.4 773.9 800.0 893.5 986.9 1080.4 1173.9 1200.0
 1106.5: 93.5 186.9 280.4 306.5 400.0 493.5 586.9 680.4 706.5 800.0 893.5 986.9 1080.4 1106.5 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  26.1165   .. 93.4709 cents       67.35436 cents                     26.11651 cents
  2:  119.5874  .. 186.9417 cents      67.35436 cents                     26.11651 cents
  3:  213.0583  .. 280.4126 cents      67.35436 cents                     26.11651 cents
  4:  306.5291  .. 373.8835 cents      67.35436 cents                     26.11651 cents
  5:  400.0000  .. 400.0000 cents      1/1, 0.0000 cents                  26.11651 cents
  6:  426.1165  .. 493.4709 cents      67.35436 cents                     26.11651 cents
  7:  519.5874  .. 586.9417 cents      67.35436 cents                     26.11651 cents
  8:  613.0583  .. 680.4126 cents      67.35436 cents                     26.11651 cents
  9:  706.5291  .. 773.8835 cents      67.35436 cents                     26.11651 cents
 10:  800.0000  .. 800.0000 cents      1/1, 0.0000 cents                  26.11651 cents
 11:  826.1165  .. 893.4709 cents      67.35436 cents                     26.11651 cents
 12:  919.5874  .. 986.9417 cents      67.35436 cents                     26.11651 cents
 13:  1013.0583 .. 1080.4126 cents     67.35436 cents                     26.11651 cents
 14:  1106.5291 .. 1173.8835 cents     67.35436 cents                     26.11651 cents
SHOW DATA
Number of notes                     : 15
-- Interval properties --
Smallest interval                   : 26.11651 cents, class 1
Average step (divided formal octave): 80.0000 cents
Largest one step interval           : 93.47087 cents
Average / Smallest step             : 3.063196
Largest / Average step              : 1.168386
Largest / Smallest step             : 3.578995
Median interval of one step         : 93.47087 cents, amount: 12
Most common interval of one step    : 93.47087 cents, amount: 12
Least squares average step          : 79.83705 cents, oct.:  1197.55569 cents
Scale is strictly proper
Scale has 3 repeating blocks of 5 notes
Blocks have Myhill's property
  chromas: 67.35436 cents and 41.23784 cents, ratio: 1.633314
  generators: 1 of 93.47087 cents and 4 of 306.52913 cents
ET pair of linear temperament       : 39&51
Scale is distributional even
Scale is a mode of a 873-tone equal temperament with octave  1200.000 cents
  degrees: 68 136 155 223 291 359 427 446 514 582 650 718 737 805 873
Least number of segments generator  : 437 of 600.687 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 514 of 706.529 cents and inv.
  generated superset size: 587 = 572 more = 3913.333%
Number of contiguous 1-step segments: 0
Step pattern alph. order: AABAAAABAAAABAA
Step pattern size order : LLSLLLLSLLLLSLL
Scale is a Constant Structure, by a margin of 26.11651 cents
Scale diversity                     : 1.145878
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.326456
Number of different interval sizes  : 26 = 1.85714 / class
Number of one step interval sizes   : 2
Highest interval variety            : 2
Mean interval variety               : 1.85714 = 13/7
Median interval variety             : 2
Lowest interval variety             : 1
Smallest interval difference        : 26.11651 cents
Most common intervals               : 400.00000 cents & inv., amount: 15
Most common triad is 0.0 400.000 800.000 cents, amount: 15
Number of recognisable fifths       : 12, average 706.5291 cents
Formal octave complements present   : 15 = 100.0000%
Limited transpositions              :
 5 10
Limited inverse transpositions      :
 5 10
Inversional symmetry on degrees     :
 0 5 10
Inversional symmetry on intervals   :
 2-3 7-8 12-13
-- Rational properties --
FIT/MODE
 15:  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  SP B ME I SD: 19.0507 c. M:-26.9417 c. 
 17:  1 2 0 1 2 1 1 1 1 1 2 1 0 2 1   N   D3 I SD: 19.2334 c. M:-24.8230 c. 
 18:  1 2 0 2 1 1 2 0 2 1 1 2 0 2 1   P B D3 I SD: 18.8572 c. M:-26.8042 c. 
 19:  1 2 0 2 1 2 1 1 1 2 1 2 0 2 1   N   D3 I SD: 18.2302 c. M:-30.3130 c. 
 22:  2 1 1 2 1 2 2 0 2 2 1 2 1 1 2   P   D3 I SD: 15.2811 c. M:-23.3054 c. 
 24:  2 2 0 2 2 2 2 0 2 2 2 2 0 2 2   P B DE I SD: 9.2336 c. M:-13.0583 c. 
 27:  2 2 1 2 2 2 2 1 2 2 2 2 1 2 2  SP B ME I SD: 6.4799 c. M:-9.1640 c. 
 39:  3 3 1 3 3 3 3 1 3 3 3 3 1 3 3  SP B DE I SD: 1.6450 c. M:-2.3264 c.  Augmented-15
 51:  4 4 1 4 4 4 4 1 4 4 4 4 1 4 4  SP B DE I SD: 0.9147 c. M:-1.2936 c.  Augmented-15
 90:  7 7 2 7 7 7 7 2 7 7 7 7 2 7 7  SP B DE I SD: 0.1945 c. M:-0.2751 c.  Augmented-15
 231: 18 18 5 18 18 18 18 5 18 18 18 18 5 18 18  SP B DE I SD: 0.0504 c. M:-0.0712 c. 
 321: 25 25 7 25 25 25 25 7 25 25 25 25 7 25 25  SP B DE I SD: 0.0183 c. M:-0.0259 c. 
 552: 43 43 12 43 43 43 43 12 43 43 43 43 12 43 43  SP B DE I SD: 0.0105 c. M:-0.0148 c. 
 873: 68 68 19 68 68 68 68 19 68 68 68 68 19 68 68  SP B DE I SD: 0.0001 c. M:-0.0002 c. 
FIT/HARMONIC
 1 x x x x x x x x x x x x x x 2  S SD: 0.0000 cents
 2 x x x x x x x x 3 x x x x x 4  S SD: 2.2871 cents
 3 x x x x x 4 x x x x 5 x x x 6  S SD: 3.3986 cents
 4 x x x x 5 x x x 6 x x 7 x x 8  S SD: 5.7902 cents
 5 x x x 6 x x 7 x x 8 x x 9 x 10  S SD: 3.5245 cents
 6 x x x 7 x 8 x x 9 x 10 x 11 x 12  S SD: 9.1525 cents
 7 x x 8 x 9 x x 10 x 11:12 x x 13:14  S SD: 9.7635 cents
 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16  S SD: 7.7712 cents
 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18  S SD: 6.7544 cents
 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20  S SD: 5.4856 cents
 11 x 12 x 13:14:15 x 16 x 17:18:19:20:21:22  S SD: 9.6267 cents
 12:13 x x 14:15:16 x 17:18:19:20:21:22:23:24  S SD: 6.4967 cents
 13:14 x 15 x 16:17:18:19:20:21:22:23 x 25:26    SD: 8.6592 cents
 14:15 x 16:17:18:19 x 20:21:22:23 x 25:27:28    SD: 6.9077 cents
 15:16 x 17:18:19:20:21 x 23:24:25 x 27:28:30    SD: 4.2832 cents
 16:17 x 18:19:20:21:22:23:24:25:27:28:29:30:32    SD: 4.7153 cents
 17:18:19 x 20:21:23:24 x 26:27:28:30:31:32:34    SD: 5.6792 cents
 18:19:20 x 21:23:24:25:26:27:29:30:32 x 34:36    SD: 4.8478 cents
 19:20:21 x 23:24:25 x 27:29:30:32 x 34:36:38    SD: 3.7502 cents
 22:23 x 25:26:28:29:31 x 33:35:37:39 x 42:44    SD: 3.2148 cents
 23:24 x 26:27:29:31:32:33:35:37:39 x 41:44:46    SD: 4.8327 cents
 24:25 x 27:29:30:32 x 34:36:38:40:42:43:45:48    SD: 3.5712 cents
 25:26:28 x 30:32:33:35:36:38:40:42:44:45:47:50    SD: 3.8527 cents
 26:27:29 x 31:33:35:36:37:39:41:44:46:47:49:52    SD: 3.6791 cents
 27:29:30:31:32:34:36:38 x 41:43:45:48 x 51:54    SD: 3.7060 cents
 28:30:31:32:33:35:37:39:40:42:44:47 x 50:53:56    SD: 3.5969 cents
 29:31:32:33:35:37:39:41 x 44:46:49:51:52:55:58    SD: 3.7702 cents
 30:32:33:34:36:38:40:42:43:45:48:50:53:54:57:60    SD: 2.5624 cents
 31:33 x 35:37:39:41 x 44:47:49:52:55:56:59:62    SD: 2.2114 cents
 32:34 x 36:38:40:43:45:46:48:51:54:57 x 61:64    SD: 3.0173 cents
 33:35:37 x 39:42:44:46:47:50:52:55:58:59:63:66    SD: 2.9509 cents
 34:36:38 x 41:43:45:48 x 51:54:57:60:61:64:68    SD: 2.1084 cents
 36:38:40:41:43:45:48 x 51:54:57:60:64:65:68:72    SD: 2.0359 cents
 40:42 x 45:48:50:53:56:57:60:63:67:71:72:76:80    SD: 1.9995 cents
 41:43:46 x 49:52:55 x 58:62:65:69:73:74:78:82    SD: 2.6843 cents
 42:44:47:48:50:53:56:59:60:63:67:70:74:75:80:84    SD: 2.1209 cents
 43:45:48:49:51:54:57:60:61:65:68:72:76:77:81:86    SD: 2.1054 cents
 45:47:50:51:54:57:60:63:64:68:71:75:80:81:85:90    SD: 2.0868 cents
 46:49:51:52:55:58:61:65:66:69:73:77:81:83:87:92    SD: 1.8842 cents
 49:52:55 x 58:62:65:69:70:74:78:82:87:88:93:98    SD: 1.9315 cents
 51:54:57:58:61:64:68:72:73:77:81:85:90:92:97:102    SD: 1.6989 cents
 52:55:58:59:62:66:69:73:74:78:83:87:92:93:99:104    SD: 1.4349 cents
 57:60 x 64:68:72:76:80:81:86:90:96:101:102:108:114    SD: 1.5702 cents
 58:61:65:66:69:73:77:81:83:87:92:97:103:104:110:116    SD: 1.5302 cents
 61:64:68:69:73:77:81:86:87:92:97:102:108:110:116:122    SD: 1.2513 cents
 68:72:76:77:81:86:90:95:97:102:108:114:120:122:129:136    SD: 1.1544 cents
 69:73:77:78:82:87:92:97:98:104:110:116:122:124:131:138    SD: 1.0855 cents
 70:74:78:79:84:88:93:98:100:105:111:117:124:126:133:140    SD: 1.0612 cents
 77:81:86:87:92:97:102:108:110:116:122:129:136:138:146:154    SD: 0.8390 cents
 87:92:97:98:104:110:116:122:124:131:138:146:154:156:165:174    SD: 0.8192 cents
 97:102:108:110:116:122:129:136:138:146:154:163:172:174:184:194    SD: 0.8161 cents
 104:110:116:118:124:131:138:146:148:156:165:174:184:187:197:208    SD: 0.6946 cents
 107:113:119:121:128:135:142:150:152:161:170:179:189:192:203:214    SD: 0.6447 cents
 123:130:137:139:147:155:164:173:175:185:195:206:218:221:233:246    SD: 0.5778 cents
 124:131:138:140:148:156:165:174:177:186:197:208:219:223:235:248    SD: 0.5676 cents
 139:147:155:157:166:175:185:195:198:209:221:233:246:250:263:278    SD: 0.4791 cents
 151:159:168:171:180:190:201:212:215:227:240:253:267:271:286:302    SD: 0.4666 cents
 160:169:178:181:191:202:213:225:228:241:254:268:283:287:303:320    SD: 0.4460 cents
 161:170:179:182:192:203:214:226:229:242:256:270:285:289:305:322    SD: 0.4385 cents
 176:186:196:199:210:222:234:247:251:265:279:295:311:316:333:352    SD: 0.3698 cents
 181:191:202:205:216:228:241:254:258:272:287:303:320:325:343:362    SD: 0.3633 cents
 191:202:213:216:228:241:254:268:272:287:303:320:338:343:362:382    SD: 0.3565 cents
 200:211:223:226:239:252:266:281:285:301:317:335:354:359:379:400    SD: 0.3179 cents
 216:228:241:244:258:272:287:303:308:325:343:362:382:388:409:432    SD: 0.3092 cents
 228:241:254:258:272:287:303:320:325:343:362:382:403:409:432:456    SD: 0.2628 cents
 273:288:304:309:326:344:363:383:389:411:433:457:483:490:517:546    SD: 0.2465 cents
 288:304:321:326:344:363:383:404:410:433:457:483:509:517:546:576    SD: 0.2456 cents
 289:305:322:327:345:364:384:406:412:435:459:484:511:519:548:578    SD: 0.2245 cents
 327:345:364:370:390:412:435:459:466:492:519:548:578:587:620:654    SD: 0.1911 cents
 342:361:381:387:408:431:455:480:487:514:543:573:605:614:648:684    SD: 0.1638 cents
 397:419:442:449:474:500:528:557:566:597:630:665:702:713:752:794    SD: 0.1404 cents
 419:442:467:474:500:528:557:588:597:630:665:702:741:752:794:838    SD: 0.1205 cents
 542:572:604:613:647:683:721:761:772:815:860:908:958:973:1027:1084    SD: 0.1166 cents
 543:573:605:614:648:684:722:762:774:817:862:910:960:975:1029:1086    SD: 0.0984 cents