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