Scala analysis: xen18-erlich-augmented-15
12L 3s MOS for Augmented, L=93.15, s=26.42
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.150 cents 93.150000 2: 186.300 cents 186.300000 3: 212.720 cents 212.720000 4: 305.870 cents 305.870000 5: 399.020 cents 399.020000 6: 492.170 cents 492.170000 7: 585.320 cents 585.320000 8: 611.740 cents 611.740000 9: 704.890 cents 704.890000 10: 798.040 cents 798.040000 11: 891.190 cents 891.190000 12: 984.340 cents 984.340000 13: 1010.760 cents 1010.760000 14: 1103.910 cents 1103.910000 15: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 93.1500 cents 93.1500 1: 93.1500 cents 93.1500 2: 93.1500 cents 93.1500 3: 26.4200 cents 26.4200 4: 93.1500 cents 93.1500 5: 93.1500 cents 93.1500 6: 93.1500 cents 93.1500 7: 93.1500 cents 93.1500 8: 26.4200 cents 26.4200 9: 93.1500 cents 93.1500 10: 93.1500 cents 93.1500 11: 93.1500 cents 93.1500 12: 93.1500 cents 93.1500 13: 26.4200 cents 26.4200 14: 93.1500 cents 93.1500 15: 93.1500 cents 93.1500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 26.42000 cents 1: 12 93.15000 cents 2: 6 119.57000 cents 2: 9 186.30000 cents 3: 9 212.72000 cents 3: 6 279.45000 cents 4: 12 305.87000 cents 4: 3 372.60000 cents 5: 15 399.02000 cents 6: 3 425.44000 cents 6: 12 492.17000 cents 7: 6 518.59000 cents 7: 9 585.32000 cents 8: 9 611.74000 cents 8: 6 678.47000 cents 9: 12 704.89000 cents 9: 3 771.62000 cents 10: 15 798.04000 cents 11: 3 824.46000 cents 11: 12 891.19000 cents 12: 6 917.61000 cents 12: 9 984.34000 cents 13: 9 1010.76000 cents 13: 6 1077.49000 cents 14: 12 1103.91000 cents 14: 3 1170.64000 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 : 93.2 186.3 212.7 305.9 399.0 492.2 585.3 611.7 704.9 798.0 891.2 984.3 1010.8 1103.9 1197.1 93.2 : 93.2 119.6 212.7 305.9 399.0 492.2 518.6 611.7 704.9 798.0 891.2 917.6 1010.8 1103.9 1197.1 186.3 : 26.4 119.6 212.7 305.9 399.0 425.4 518.6 611.7 704.9 798.0 824.5 917.6 1010.8 1103.9 1197.1 212.7 : 93.2 186.3 279.4 372.6 399.0 492.2 585.3 678.5 771.6 798.0 891.2 984.3 1077.5 1170.6 1197.1 305.9 : 93.2 186.3 279.5 305.9 399.0 492.2 585.3 678.5 704.9 798.0 891.2 984.3 1077.5 1103.9 1197.1 399.0 : 93.2 186.3 212.7 305.9 399.0 492.2 585.3 611.7 704.9 798.0 891.2 984.3 1010.8 1103.9 1197.1 492.2 : 93.2 119.6 212.7 305.9 399.0 492.2 518.6 611.7 704.9 798.0 891.2 917.6 1010.8 1103.9 1197.1 585.3 : 26.4 119.6 212.7 305.9 399.0 425.4 518.6 611.7 704.9 798.0 824.5 917.6 1010.8 1103.9 1197.1 611.7 : 93.2 186.3 279.5 372.6 399.0 492.2 585.3 678.5 771.6 798.0 891.2 984.3 1077.5 1170.6 1197.1 704.9 : 93.2 186.3 279.4 305.9 399.0 492.2 585.3 678.5 704.9 798.0 891.2 984.3 1077.5 1103.9 1197.1 798.0 : 93.2 186.3 212.7 305.9 399.0 492.2 585.3 611.7 704.9 798.0 891.2 984.3 1010.8 1103.9 1197.1 891.2 : 93.2 119.6 212.7 305.9 399.0 492.2 518.6 611.7 704.9 798.0 891.2 917.6 1010.8 1103.9 1197.1 984.3 : 26.4 119.6 212.7 305.9 399.0 425.4 518.6 611.7 704.9 798.0 824.5 917.6 1010.8 1103.9 1197.1 1010.8: 93.2 186.3 279.5 372.6 399.0 492.2 585.3 678.5 771.6 798.0 891.2 984.3 1077.5 1170.6 1197.1 1103.9: 93.1 186.3 279.4 305.9 399.0 492.2 585.3 678.5 704.9 798.0 891.2 984.3 1077.5 1103.9 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4200 .. 93.1500 cents 66.73000 cents 26.42000 cents 2: 119.5700 .. 186.3000 cents 66.73000 cents 26.42000 cents 3: 212.7200 .. 279.4500 cents 66.73000 cents 26.42000 cents 4: 305.8700 .. 372.6000 cents 66.73000 cents 26.42000 cents 5: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 26.42000 cents 6: 425.4400 .. 492.1700 cents 66.73000 cents 26.42000 cents 7: 518.5900 .. 585.3200 cents 66.73000 cents 26.42000 cents 8: 611.7400 .. 678.4700 cents 66.73000 cents 26.42000 cents 9: 704.8900 .. 771.6200 cents 66.73000 cents 26.42000 cents 10: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 26.42000 cents 11: 824.4600 .. 891.1900 cents 66.73000 cents 26.42000 cents 12: 917.6100 .. 984.3400 cents 66.73000 cents 26.42000 cents 13: 1010.7600 .. 1077.4900 cents 66.73000 cents 26.42000 cents 14: 1103.9100 .. 1170.6400 cents 66.73000 cents 26.42000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 26.42000 cents, class 1 Average step (divided formal octave): 79.8040 cents Largest one step interval : 93.15000 cents Average / Smallest step : 3.020590 Largest / Average step : 1.167235 Largest / Smallest step : 3.525738 Median interval of one step : 93.15000 cents, amount: 12 Most common interval of one step : 93.15000 cents, amount: 12 Least squares average step : 79.64256 cents, oct.: 1194.63835 cents Scale is strictly proper Scale has 3 repeating blocks of 5 notes Blocks have Myhill's property chromas: 66.73000 cents and 40.31000 cents, ratio: 1.655420 generators: 1 of 93.15000 cents and 4 of 305.87000 cents ET pair of linear temperament : 39&51 Scale is distributional even Scale is a mode of a 861-tone equal temperament with octave 1197.060 cents degrees: 67 134 153 220 287 354 421 440 507 574 641 708 727 794 861 Least number of segments generator : 431 of 599.225 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 641 of 891.191 cents and inv. generated superset size: 579 = 564 more = 3860.000% 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 26.42000 cents Scale diversity : 1.149310 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.331061 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 : 26.42000 cents Most common intervals : 399.02000 cents & inv., amount: 15 Most common triad is 0.0 399.020 798.040 cents, amount: 15 Number of recognisable fifths : 12, average 704.8900 cents Number of recognisable fourths : 12, average 492.1700 cents Formal octave complements present : 15 = 100.0000% 2/1 octave complements present : 0 = 0.0000% 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: 18.8741 c. M: 26.6920 c. 17: 1 2 0 1 2 1 1 1 1 1 2 1 0 2 1 N D3 I SD: 19.1929 c. M: 24.9459 c. 18: 1 2 0 2 1 1 2 0 2 1 1 2 0 2 1 P B D3 I SD: 18.8101 c. M: 26.6467 c. 19: 1 2 0 2 1 2 1 1 1 2 1 2 0 2 1 N D3 I SD: 18.1776 c. M: 30.1468 c. 20: 2 1 1 1 2 1 2 0 2 1 2 1 1 1 2 N D3 I SD: 17.3490 c. M: 26.6920 c. 21: 2 1 1 1 2 2 1 1 1 2 2 1 1 1 2 N B D3 I SD: 16.3559 c. M: 20.8557 c. 22: 2 1 1 2 1 2 2 0 2 2 1 2 1 1 2 P D3 I SD: 15.2134 c. M: 23.0645 c. 23: 2 2 0 2 2 1 2 1 2 1 2 2 0 2 2 N I SD: 15.0099 c. M: 23.7552 c. 24: 2 2 0 2 2 2 2 0 2 2 2 2 0 2 2 P B DE I SD: 9.3409 c. M: 13.2100 c. 27: 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 SP B ME I SD: 6.3341 c. M: 8.9578 c. 39: 3 3 1 3 3 3 3 1 3 3 3 3 1 3 3 SP B DE I SD: 1.5110 c. M: 2.1369 c. Augmented-15 51: 4 4 1 4 4 4 4 1 4 4 4 4 1 4 4 SP B DE I SD: 1.0424 c. M: 1.4741 c. Augmented-15 90: 7 7 2 7 7 7 7 2 7 7 7 7 2 7 7 SP B DE I SD: 0.0641 c. M: 0.0907 c. Augmented-15 501: 39 39 11 39 39 39 39 11 39 39 39 39 11 39 39 SP B DE I SD: 0.0485 c. M: 0.0686 c. 591: 46 46 13 46 46 46 46 13 46 46 46 46 13 46 46 SP B DE I SD: 0.0314 c. M: 0.0444 c. 681: 53 53 15 53 53 53 53 15 53 53 53 53 15 53 53 SP B DE I SD: 0.0188 c. M: 0.0265 c. 771: 60 60 17 60 60 60 60 17 60 60 60 60 17 60 60 SP B DE I SD: 0.0091 c. M: 0.0128 c. 861: 67 67 19 67 67 67 67 19 67 67 67 67 19 67 67 SP B DE I SD: 0.0014 c. M: 0.0020 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 2.9400 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 2.0771 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 3.1592 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 5.1198 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 4.0177 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 9.2939 cents 7 x x 8 x 9 x x 10 x 11:12 x x 13:14 S SD: 9.8155 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.6065 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 6.7520 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 5.5795 cents 11 x 12 x 13:14:15 x 16 x 17:18:19:20:21:22 S SD: 9.5414 cents 12:13 x x 14:15:16 x 17:18:19:20:21:22:23:24 S SD: 6.5403 cents 13:14 x 15 x 16:17:18:19:20:21:22:23 x 25:26 SD: 8.8322 cents 14:15 x 16:17:18:19 x 20:21:22:23 x 25:26:28 SD: 6.9557 cents 15:16 x 17:18:19:20:21 x 23:24:25:26:27:28:30 SD: 4.7155 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:30:32 SD: 4.5474 cents 17:18:19 x 20:21:23:24 x 26:27:28:30 x 32:34 SD: 5.6926 cents 18:19:20 x 21:23:24:25:26:27:29:30:32 x 34:36 SD: 4.9142 cents 19:20:21 x 23:24:25 x 27:29:30:32 x 34:36:38 SD: 3.8052 cents 20:21:22:23:24:25:27:28 x 30:32:33:35:36:38:40 SD: 4.2787 cents 22:23 x 25:26:28:29:31 x 33:35:37:39 x 42:44 SD: 3.3713 cents 23:24 x 26:27:29:31:32:33:35:36:38 x 41:44:46 SD: 4.9197 cents 24:25 x 27:29:30:32 x 34:36:38:40:42:43:45:48 SD: 3.3399 cents 25:26:28 x 30:31:33:35:36:38:40:42:44:45:47:50 SD: 3.8887 cents 26:27:29 x 31:33:35:36:37:39:41:44:46:47:49:52 SD: 3.7175 cents 27:28:30:31:32:34:36:38 x 41:43:45:48 x 51:54 SD: 3.7944 cents 28:30:31:32:33:35:37:39:40:42:44:47:49:50:53:56 SD: 3.3962 cents 29:31:32:33:35:37:39 x 41:44:46:49:51:52:55:58 SD: 3.9123 cents 30:32:33:34:36:38:40:42:43:45:48:50:53:54:57:60 SD: 2.6657 cents 31:33 x 35:37:39:41:43:44:47:49:52:55:56:59:62 SD: 2.6049 cents 32:34 x 36:38:40:43:45:46:48:51:54 x 57:61:64 SD: 3.1969 cents 33:35:37 x 39:42:44:46:47:50:52:55:58:59:62:66 SD: 2.8498 cents 34:36:38 x 41:43:45:48 x 51:54:57:60:61:64:68 SD: 2.1261 cents 37:39:41:42:44:47:49:52:53:56:59:62:65:66:70:74 SD: 2.0765 cents 40:42 x 45:48:50:53:56:57:60:63:67:71:72:76:80 SD: 1.9971 cents 41:43:46 x 49:52:54:57:58:62:65:69:72:74:78:82 SD: 2.8324 cents 42:44:47 x 50:53:56:59:60:63:67:70:74:75:79:84 SD: 1.8580 cents 46:49:51:52:55:58:61 x 65:69:73:77:81:82:87:92 SD: 1.8470 cents 49:52 x 55:58:62:65:69:70:74:78:82:87:88:93:98 SD: 2.1154 cents 50:53:56:57:60:63:66:70:71:75:79:84:88:90:95:100 SD: 1.9452 cents 51:54:57:58:61:64:68:72:73:77:81:85:90:91:96:102 SD: 1.8382 cents 52:55:58:59:62:65:69:73:74:78:82:87:92:93:98:104 SD: 1.3599 cents 55:58:61:62:66:69:73:77:78:83:87:92:97:99:104:110 SD: 1.3503 cents 62:65:69:70:74:78:82:87:88:93:98:104:109:111:117:124 SD: 1.3093 cents 67:71:75:76:80:84:89:94:95:101:106:112:118:120:127:134 SD: 1.2759 cents 68:72:76:77:81:86:90:95:97:102:108:114:120:122:129:136 SD: 1.1633 cents 70:74:78:79:84:88:93:98:100:105:111:117:124:126:132:140 SD: 1.1506 cents 73:77:81:83:87:92:97:102:104:110:116:122:129:131:138:146 SD: 1.0220 cents 77:81:86:87:92:97:102:108:110:116:122:129:136:138:146:154 SD: 0.8837 cents 89:94:99:101:106:112:118:125:127:134:141:149:157:160:168:178 SD: 0.8398 cents 92:97:102:104:110:116:122:129:131:138:146:154:162:165:174:184 SD: 0.7745 cents 104:110:116:118:124:131:138:146:148:156:165:174:184:186:197:208 SD: 0.7414 cents 107:113:119:121:128:135:142:150:152:161:170:179:189:192:202:214 SD: 0.6749 cents 123:130:137:139:147:155:163:172:175:185:195:206:217:221:233:246 SD: 0.6640 cents 125:132:139:141:149:157:166:175:178:188:198:209:221:224:237:250 SD: 0.6403 cents 130:137:145:147:155:164:173:182:185:195:206:218:230:233:246:260 SD: 0.6154 cents 131:138:146:148:156:165:174:184:187:197:208:219:231:235:248:262 SD: 0.5973 cents 139:147:155:157:166:175:185:195:198:209:220:233:245:249:263:278 SD: 0.5784 cents 140:148:156:158:167:176:186:196:199:210:222:234:247:251:265:280 SD: 0.5575 cents 149:157:166:168:178:188:198:209:212:224:236:249:263:267:282:297 SD: 0.5528 cents 159:168:177:180:190:200:211:223:226:239:252:266:281:285:301:317 SD: 0.4432 cents 177:187:197:200:211:223:235:248:252:266:281:296:313:317:335:353 SD: 0.3897 cents 201:212:224:227:240:253:267:282:286:302:319:336:355:360:380:401 SD: 0.3238 cents 213:225:237:241:254:268:283:299:303:320:338:356:376:382:403:425 SD: 0.3187 cents 231:244:257:261:276:291:307:324:329:347:366:387:408:414:437:461 SD: 0.3064 cents 238:251:265:269:284:300:316:334:339:358:377:398:420:427:450:475 SD: 0.3060 cents 239:252:266:270:285:301:318:335:340:359:379:400:422:429:452:477 SD: 0.3007 cents 253:267:282:286:302:319:336:355:360:380:401:423:447:454:479:505 SD: 0.2932 cents 273:288:304:309:326:344:363:383:389:410:433:457:482:489:517:545 SD: 0.2737 cents 274:289:305:310:327:345:364:384:390:412:434:458:484:491:518:547 SD: 0.2602 cents 289:305:322:327:345:364:384:405:411:434:458:484:510:518:547:577 SD: 0.2506 cents 290:306:323:328:346:365:385:407:413:436:460:485:512:520:549:579 SD: 0.2019 cents 328:346:365:371:391:413:436:460:467:493:520:549:579:588:621:655 SD: 0.1893 cents 343:362:382:388:409:432:456:481:488:515:544:574:606:615:649:685 SD: 0.1832 cents 398:420:443:450:475:501:529:558:567:598:631:666:703:714:753:795 SD: 0.1397 cents 502:530:559:568:599:632:667:704:715:754:796:840:886:900:950:1002 SD: 0.1314 cents 529:558:589:598:631:666:703:742:753:795:839:885:934:948:1001:1056 SD: 0.1169 cents 575:607:640:650:686:724:764:806:819:864:912:962:1015:1031:1088:1148 SD: 0.1150 cents 581:613:647:657:693:732:772:815:827:873:921:972:1026:1042:1099:1160 SD: 0.1134 cents 599:632:667:677:715:754:796:840:853:900:950:1002:1058:1074:1133:1196 SD: 0.1047 cents