Scala analysis: myna15br3
Myna[15] with a brat of 3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39.635 cents 39.634520 2: 79.269 cents 79.269040 3: 118.904 cents 118.903559 4: 309.909 cents 309.908630 5: 349.543 cents 349.543150 6: 389.178 cents 389.177670 7: 580.183 cents 580.182740 8: 619.817 cents 619.817260 9: 659.452 cents 659.451780 10: 699.086 cents 699.086300 11: 890.091 cents 890.091370 12: 929.726 cents 929.725890 13: 969.360 cents 969.360410 14: 1008.995 cents 1008.994929 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 191.0051 cents 191.0051 1: 39.6345 cents 39.6345 2: 39.6345 cents 39.6345 3: 39.6345 cents 39.6345 4: 191.0051 cents 191.0051 5: 39.6345 cents 39.6345 6: 39.6345 cents 39.6345 7: 191.0051 cents 191.0051 8: 39.6345 cents 39.6345 9: 39.6345 cents 39.6345 10: 39.6345 cents 39.6345 11: 191.0051 cents 191.0051 12: 39.6345 cents 39.6345 13: 39.6345 cents 39.6345 14: 39.6345 cents 39.6345 15: 191.0051 cents 191.0051
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 39.63452 cents 1: 4 191.00507 cents 2: 7 79.26904 cents 2: 8 230.63959 cents 3: 3 118.90356 cents 3: 12 270.27411 cents 4: 14 309.90863 cents 4: 1 461.27918 cents 5: 10 349.54315 cents 5: 5 500.91370 cents 6: 6 389.17767 cents 6: 9 540.54822 cents 7: 2 428.81219 cents 7: 13 580.18274 cents 8: 13 619.81726 cents 8: 2 771.18781 cents 9: 9 659.45178 cents 9: 6 810.82233 cents 10: 5 699.08630 cents 10: 10 850.45685 cents 11: 1 738.72082 cents 11: 14 890.09137 cents 12: 12 929.72589 cents 12: 3 1081.09644 cents 13: 8 969.36041 cents 13: 7 1120.73096 cents 14: 4 1008.99493 cents 14: 11 1160.36548 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 12 13 14 15 0.0 : 39.6 79.3 118.9 309.9 349.5 389.2 580.2 619.8 659.5 699.1 890.1 929.7 969.4 1009.0 1200.0 39.6 : 39.6 79.3 270.3 309.9 349.5 540.5 580.2 619.8 659.5 850.5 890.1 929.7 969.4 1160.4 1200.0 79.3 : 39.6 230.6 270.3 309.9 500.9 540.5 580.2 619.8 810.8 850.5 890.1 929.7 1120.7 1160.4 1200.0 118.9 : 191.0 230.6 270.3 461.3 500.9 540.5 580.2 771.2 810.8 850.5 890.1 1081.1 1120.7 1160.4 1200.0 309.9 : 39.6 79.3 270.3 309.9 349.5 389.2 580.2 619.8 659.5 699.1 890.1 929.7 969.4 1009.0 1200.0 349.5 : 39.6 230.6 270.3 309.9 349.5 540.5 580.2 619.8 659.5 850.5 890.1 929.7 969.4 1160.4 1200.0 389.2 : 191.0 230.6 270.3 309.9 500.9 540.5 580.2 619.8 810.8 850.5 890.1 929.7 1120.7 1160.4 1200.0 580.2 : 39.6 79.3 118.9 309.9 349.5 389.2 428.8 619.8 659.5 699.1 738.7 929.7 969.4 1009.0 1200.0 619.8 : 39.6 79.3 270.3 309.9 349.5 389.2 580.2 619.8 659.5 699.1 890.1 929.7 969.4 1160.4 1200.0 659.5 : 39.6 230.6 270.3 309.9 349.5 540.5 580.2 619.8 659.5 850.5 890.1 929.7 1120.7 1160.4 1200.0 699.1 : 191.0 230.6 270.3 309.9 500.9 540.5 580.2 619.8 810.8 850.5 890.1 1081.1 1120.7 1160.4 1200.0 890.1 : 39.6 79.3 118.9 309.9 349.5 389.2 428.8 619.8 659.5 699.1 890.1 929.7 969.4 1009.0 1200.0 929.7 : 39.6 79.3 270.3 309.9 349.5 389.2 580.2 619.8 659.5 850.5 890.1 929.7 969.4 1160.4 1200.0 969.4 : 39.6 230.6 270.3 309.9 349.5 540.5 580.2 619.8 810.8 850.5 890.1 929.7 1120.7 1160.4 1200.0 1009.0: 191.0 230.6 270.3 309.9 500.9 540.5 580.2 771.2 810.8 850.5 890.1 1081.1 1120.7 1160.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.6345 .. 191.0051 cents 151.37055 cents 39.63452 cents 2: 79.2690 .. 230.6396 cents 151.37055 cents -111.73603 cents 3: 118.9036 .. 270.2741 cents 151.37055 cents -111.73603 cents 4: 309.9086 .. 461.2792 cents 151.37055 cents 39.63452 cents 5: 349.5431 .. 500.9137 cents 151.37055 cents -111.73603 cents 6: 389.1777 .. 540.5482 cents 151.37055 cents -111.73603 cents 7: 428.8122 .. 580.1827 cents 151.37055 cents -111.73603 cents 8: 619.8173 .. 771.1878 cents 151.37055 cents 39.63452 cents 9: 659.4518 .. 810.8223 cents 151.37055 cents -111.73603 cents 10: 699.0863 .. 850.4569 cents 151.37055 cents -111.73603 cents 11: 738.7208 .. 890.0914 cents 151.37055 cents -111.73603 cents 12: 929.7259 .. 1081.0964 cents 151.37055 cents 39.63452 cents 13: 969.3604 .. 1120.7310 cents 151.37055 cents -111.73603 cents 14: 1008.9949 .. 1160.3655 cents 151.37055 cents -111.73603 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 39.63452 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 191.00507 cents Average / Smallest step : 2.018443 Largest / Average step : 2.387563 Largest / Smallest step : 4.819159 Median interval of one step : 39.63452 cents, amount: 11 Most common interval of one step : 39.63452 cents, amount: 11 Least squares average step : 75.40192 cents, oct.: 1131.02874 cents Scale is not proper Scale has Myhill's property chromas: 151.37055 cents and 111.73603 cents, ratio: 1.354716 generators: 4 of 309.90863 cents and 11 of 890.09137 cents ET pair of linear temperament : 27&31 Scale is distributional even Scale is a mode of a 2180-tone equal temperament with octave 1200.000 cents degrees: 72 144 216 563 635 707 1054 1126 1198 1270 1617 1689 1761 1833 2180 generators: 563 and 1617 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAABAAABAAAB Step pattern size order : SSSLSSLSSSLSSSL Scale is a Constant Structure, by a margin of 32.46699 cents Scale diversity : 1.227982 Lumma stability : 0.165144 Lumma impropriety factor : 0.570626 Rothenberg efficiency : 0.711111 redundancy: 0.288889 Efficiency x scale size : 10.666667 Number of different interval sizes : 28 = 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 : 32.46699 cents Most common intervals : 309.90863 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 309.909 619.817 cents Most common triad is 0.0 309.909 890.091 cents, amount: 13 Number of recognisable fifths : 5, average 699.0863 cents Formal octave complements present : 5 = 33.3333% Limited inverse transpositions : 10 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 12-13 -- Rational properties --
FIT/MODE
15: 0 1 0 3 0 1 2 1 0 1 2 1 0 1 2 N SD: 22.9120 c. M: 39.6345 c. 16: 1 0 1 2 1 0 3 0 1 0 3 0 1 0 3 N SD: 21.5403 c. M:-35.3655 c. 18: 1 0 1 3 0 1 3 0 1 1 2 1 1 0 3 N SD: 19.3531 c. M:-34.2470 c. 19: 1 0 1 3 1 0 3 1 0 1 3 1 0 1 3 N T3 SD: 15.8662 c. M:-29.4042 c. 21: 1 0 1 3 1 1 3 1 1 0 4 0 1 1 3 N SD: 15.9116 c. M:-26.2625 c. 22: 1 0 1 4 0 1 4 0 1 1 3 1 1 0 4 N SD: 16.1089 c. M: 27.1767 c. 24: 1 1 0 4 1 1 4 0 1 1 4 1 0 1 4 N S SD: 14.0253 c. M:-20.7310 c. 27: 1 1 1 4 1 1 4 1 1 1 4 1 1 1 4 N M DE S SD: 7.9461 c. M:-14.4298 c. 31: 1 1 1 5 1 1 5 1 1 1 5 1 1 1 5 N M DE S SD: 1.5279 c. M: 2.7745 c. 89: 3 3 3 14 3 3 14 3 3 3 14 3 3 3 14 N M DE S SD: 1.3463 c. M:-2.4448 c. 120: 4 4 4 19 4 4 19 4 4 4 19 4 4 4 19 N M DE S SD: 0.6038 c. M:-1.0964 c. 151: 5 5 5 24 5 5 24 5 5 5 24 5 5 5 24 N M DE S SD: 0.1662 c. M:-0.3017 c. 182: 6 6 6 29 6 6 29 6 6 6 29 6 6 6 29 N M DE S SD: 0.1224 c. M: 0.2222 c. 333: 11 11 11 53 11 11 53 11 11 11 53 11 11 11 53 N M DE S SD: 0.0085 c. M:-0.0154 c. 1514: 50 50 50 241 50 50 241 50 50 50 241 50 50 50 241 N M DE S SD: 0.0073 c. M: 0.0132 c. 1847: 61 61 61 294 61 61 294 61 61 61 294 61 61 61 294 N M DE S SD: 0.0044 c. M: 0.0081 c. 2180: 72 72 72 347 72 72 347 72 72 72 347 72 72 72 347 N M DE S SD: 0.0025 c. M: 0.0045 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 x 3 x x x x 4 S SD: 1.4344 cents 3 x x x x x x 4 x x x 5 x x x 6 S SD: 27.4458 cents 4 x x x x x 5 x x x 6 x x 7 x 8 S SD: 1.0222 cents 5 x x x 6 x x 7 x x x 8 x x 9:10 S SD: 15.4273 cents 6 x x x 7 x x 8 x x 9:10 x x 11:12 S SD: 16.8898 cents 7 x x x 8 x 9 x 10 x x x 12 x 13:14 S SD: 18.4509 cents 8 x x 9 x x 10:11 x x 12:13 x 14 x 16 S SD: 14.6612 cents 9 x x 10 x 11 x x 13 x x 15 x x 16:18 SD: 11.2033 cents 10 x x 11:12 x 13:14 x x 15 x 17 x 18:20 SD: 10.1538 cents 11 x x 12:13 x 14:15 x 16 x 18:19 x 20:22 S SD: 9.0106 cents 12 x x 13:14 x 15 x 17 x 18:20 x 21 x 24 SD: 6.3388 cents 13 x x 14 x 16 x 18 x 19 x x 22:23 x 26 SD: 4.8902 cents 14 x x 15 x 17:18 x 20 x 21:23:24 x 25:28 SD: 6.3623 cents 15 x x 16:18 x 19:21 x 22 x 25 x 26:27:30 SD: 3.3419 cents 16 x x 17:19 x 20:22:23 x 24:27 x 28:29:32 SD: 4.4069 cents 17 x 18 x 20:21 x 24 x 25 x 28:29:30 x 34 SD: 5.8017 cents 18 x 19 x x 22:23:25:26 x 27:30:31 x 32:36 SD: 4.6898 cents 19 x 20 x x 23:24 x 27:28 x 32 x 33:34:38 SD: 3.9904 cents 20 x 21 x 24 x 25:28 x 29:30:33:34:35:36:40 SD: 2.9821 cents 21 x 22 x 25 x 26:29:30:31 x 35:36:37:38:42 SD: 3.6484 cents 22 x 23:24:26:27:28:31 x 32:33:37:38 x 39:44 SD: 4.7607 cents 23 x 24:25 x 28:29:32:33:34 x 38:39:40:41:46 SD: 3.8847 cents 24 x 25:26:29 x 30 x 34:35:36:40:41:42:43:48 SD: 2.8301 cents 25 x 26:27:30 x 31:35:36:37 x 42:43:44:45:50 SD: 3.1916 cents 26 x 27:28:31:32:33:36:37:38:39:43:44:46:47:52 SD: 3.6840 cents 27 x 28:29:32:33:34:38:39 x 40:45:46:47:48:54 SD: 3.2172 cents 28 x 29:30:33:34:35:39:40:41:42:47:48:49:50:56 SD: 2.5939 cents 29:30 x 31:35 x 36:41 x 42:43:48:50:51:52:58 SD: 4.0814 cents 30:31 x 32:36:37:38:42:43:44:45:50:51:53:54:60 SD: 2.7514 cents 31:32 x 33:37:38:39:43:44:45:46:52:53:54:56:62 SD: 2.8452 cents 32:33 x 34:38:39:40:45:46:47:48:54:55:56:57:64 SD: 2.4865 cents 33:34 x 35:39:40:41:46:47:48:49:55:56:58:59:66 SD: 3.2132 cents 34:35:36 x 41:42:43:48:49:50:51:57:58:60:61:68 SD: 3.2271 cents 35:36:37 x 42:43:44:49:50:51:52:59:60:61:63:70 SD: 2.3628 cents 37:38:39:40:44:45:46:52:53:54:55:62:63:65:66:74 SD: 2.3558 cents 39:40:41:42:47:48:49:55:56:57:58:65:67:68:70:78 SD: 2.1358 cents 40:41:42:43:48:49:50:56:57:59:60:67:68:70:72:80 SD: 1.5833 cents 56:57:59:60:67:69:70:78:80:82:84:94:96:98:100:112 SD: 1.4790 cents 58:59:61:62:69:71:73:81:83:85:87:97:99:102:104:116 SD: 1.4086 cents 67:69:70:72:80:82:84:94:96:98:100:112:115:117:120:134 SD: 1.1799 cents 72:74:75:77:86:88:90:101:103:105:108:120:123:126:129:144 SD: 1.1174 cents 76:78:80:81:91:93:95:106:109:111:114:127:130:133:136:152 SD: 1.0930 cents 80:82:84:86:96:98:100:112:114:117:120:134:137:140:143:160 SD: 0.9517 cents 82:84:86:88:98:100:103:115:117:120:123:137:140:144:147:164 SD: 0.9400 cents 86:88:90:92:103:105:108:120:123:126:129:144:147:151:154:172 SD: 0.7040 cents 123:126:129:132:147:151:154:172:176:180:184:206:210:215:220:246 SD: 0.6479 cents 125:128:131:134:150:153:157:175:179:183:187:209:214:219:224:250 SD: 0.6195 cents 128:131:134:137:153:157:160:179:183:187:192:214:219:224:229:256 SD: 0.4750 cents 168:172:176:180:201:206:210:235:240:246:252:281:287:294:301:336 SD: 0.4541 cents 169:173:177:181:202:207:212:236:242:247:253:283:289:296:303:338 SD: 0.4233 cents 179:183:187:192:214:219:224:250:256:262:268:299:306:313:321:358 SD: 0.4203 cents 183:187:192:196:219:224:229:256:262:268:274:306:313:320:328:366 SD: 0.3731 cents 209:214:219:224:250:256:262:292:299:306:313:349:358:366:374:418 SD: 0.3485 cents 211:216:221:226:252:258:264:295:302:309:316:353:361:369:378:422 SD: 0.2739 cents 254:260:266:272:304:311:318:355:363:372:380:425:435:445:455:508 SD: 0.2728 cents 281:288:294:301:336:344:352:393:402:411:421:470:481:492:503:562 SD: 0.2620 cents 296:303:310:317:354:362:371:414:423:433:443:495:506:518:530:592 SD: 0.2484 cents 297:304:311:318:355:363:372:415:425:435:445:497:508:520:532:594 SD: 0.2386 cents 321:328:336:344:384:393:402:449:459:470:481:537:549:562:575:642 SD: 0.2182 cents 336:344:352:360:402:411:421:470:481:492:503:562:575:588:602:672 SD: 0.2087 cents 341:349:357:365:408:417:427:477:488:499:511:570:583:597:611:682 SD: 0.1981 cents 381:390:399:408:456:466:477:533:545:558:571:637:652:667:682:762 SD: 0.1979 cents 384:393:402:411:459:470:481:537:549:562:575:642:657:672:688:768 SD: 0.1552 cents 425:435:445:455:508:520:532:594:608:622:636:711:727:744:761:850 SD: 0.1542 cents 464:475:486:497:555:568:581:649:664:679:695:776:794:812:831:928 SD: 0.1287 cents 550:563:576:589:658:673:689:769:787:805:824:920:941:963:985:1100 SD: 0.1268 cents 595:609:623:637:712:728:745:832:851:871:891:995:1018:1042:1066:1190 SD: 0.1161 cents