311edo/Ringer 311: Difference between revisions

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There are two known [[Ringer scale]]s based on 311edo. Both include the complete mode 234 of the harmonic series using non-[[patent val]]s of 311edo, which is believed to be the highest possible complete harmonic series mode mapped by a 311-form. However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167, which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a temperament~~; it~~'s unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).

There are two known [[Ringer scale]]s based on [[311edo]]. Both include the complete mode 234 [[Overtone scale|of the harmonic series]] ([[234afdo]]) using non-[[patent val]]s of 311edo, which is believed to be the highest possible complete harmonic series mode mapped by a 311-form.

However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167 ([[167afdo]]), which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a [[temperament]]).

It's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).

==== Ringer 311[+61] ====

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==== Ringer 311[+61, &~~minus~~;67] ====

==== Ringer 311[+61, −67] ====

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234:235:941/4:943/4:236:237:475/2:238:477/2:239:479/2:240:481/2: 241:483/2:242:485/2:243:487/2:244:245:491/2:246:493/2:247:495/2: 248:497/2:249:250:501/2:251:503/2:252:505/2:253:254:509/2:255: 511/2:256:513/2:257:515/2:258:259:519/2:260:521/2:261:262:525/2: 263:527/2:264:265:1061/4:266:533/2:267:268:537/2:269:539/2:270: 541/2:271:272:545/2:273:274:1097/4:275:551/2:276:277:555/2:278: 557/2:279:280:561/2:281:282:565/2:283:567/2:284:285:571/2:286: 287:575/2:288:289:579/2:290:581/2:291:292:585/2:293:294:589/2: 295:296:593/2:297:298:597/2:299:300:601/2:301:302:605/2:303: 304:609/2:305:306:613/2:307:308:617/2:309:310:311:623/2:312: 313:627/2:314:315:316:633/2:317:318:637/2:319:320:641/2:321: 322:323:647/2:324:325:326:653/2:327:328:329:659/2:330:331: 663/2:332:333:334:335:1341/4:336:337:675/2:338:339:340:681/2: 341:342:343:687/2:344:345:346:347:695/2:348:349:350:701/2: 351:352:353:707/2:354:355:356:357:358:717/2:359:360:361: 362:725/2:363:364:365:731/2:366:367:368:369:370:371:743/2: 372:373:374:375:376:753/2:377:378:379:380:381:763/2:382: 383:384:385:386:773/2:387:388:389:390:391:392:393:394: 395:791/2:396:397:398:399:400:401:402:805/2:403:404:405: 406:407:408:409:410:411:823/2:412:413:414:415:416:417: 418:419:420:421:422:423:424:425:851/2:426:427:428:429: 430:431:432:433:434:435:436:437:438:439:440:441:442: 443:444:445:446:447:448:449:450:451:452:453:454:455: 456:457:458:459:460:461:462:463:464:465:466:467:468:

[[Category:Just intonation scales]]

[[Category:Pages with mostly numerical content]][[Category:311edo]]

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-There are two known [[Ringer scale]]s based on 311edo. Both include the complete mode 234 of the harmonic series using non-[[patent val]]s of 311edo, which is believed to be the highest possible complete harmonic series mode mapped by a 311-form. However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167, which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a temperament; it's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).
+{{breadcrumb}}
+There are two known [[Ringer scale]]s based on [[311edo]]. Both include the complete mode 234 [[Overtone scale|of the harmonic series]] ([[234afdo]]) using non-[[patent val]]s of 311edo, which is believed to be the highest possible complete harmonic series mode mapped by a 311-form.
+However, if one is looking for a Ringer scale, [[217edo#Ringer_217|217edo's corresponding Ringer 217]] may be preferred due to mapping all of mode 167 ([[167afdo]]), which is exceptional for its size (as a Ringer scale), just as [[311edo]] is exceptional for its size (as an [[edo]] interpreted as a [[temperament]]).
+It's unknown whether Ringer 311 possesses any special properties that are not a direct result of 311edo's special properties as a temperament).
 ==== Ringer 311[+61] ====
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 {{col-end}}
-==== Ringer 311[+61, &minus;67] ====
+==== Ringer 311[+61,&nbsp;−67] ====
 {{col-begin}}
 {{col-break}}
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 :235:<b>941/4</b>:<b>943/4</b>:236:237:<b>475/2</b>:238:<b>477/2</b>:239:<b>479/2</b>:240:<b>481/2</b>:<br />241:<b>483/2</b>:242:<b>485/2</b>:243:<b>487/2</b>:244:245:<b>491/2</b>:246:<b>493/2</b>:247:<b>495/2</b>:<br />248:<b>497/2</b>:249:250:<b>501/2</b>:251:<b>503/2</b>:252:<b>505/2</b>:253:254:<b>509/2</b>:255:<br /><b>511/2</b>:256:<b>513/2</b>:257:<b>515/2</b>:258:259:<b>519/2</b>:260:<b>521/2</b>:261:262:<b>525/2</b>:<br />263:<b>527/2</b>:264:265:<b>1061/4</b>:266:<b>533/2</b>:267:268:<b>537/2</b>:269:<b>539/2</b>:270:<br /><b>541/2</b>:271:272:<b>545/2</b>:273:274:<b>1097/4</b>:275:<b>551/2</b>:276:277:<b>555/2</b>:278:<br /><b>557/2</b>:279:280:<b>561/2</b>:281:282:<b>565/2</b>:283:<b>567/2</b>:284:285:<b>571/2</b>:286:<br />287:<b>575/2</b>:288:289:<b>579/2</b>:290:<b>581/2</b>:291:292:<b>585/2</b>:293:294:<b>589/2</b>:<br />295:296:<b>593/2</b>:297:298:<b>597/2</b>:299:300:<b>601/2</b>:301:302:<b>605/2</b>:303:<br />304:<b>609/2</b>:305:306:<b>613/2</b>:307:308:<b>617/2</b>:309:310:311:<b>623/2</b>:312:<br />313:<b>627/2</b>:314:315:316:<b>633/2</b>:317:318:<b>637/2</b>:319:320:<b>641/2</b>:321:<br />322:323:<b>647/2</b>:324:325:326:<b>653/2</b>:327:328:329:<b>659/2</b>:330:331:<br /><b>663/2</b>:332:333:334:335:<b>1341/4</b>:336:337:<b>675/2</b>:338:339:340:<b>681/2</b>:<br />341:342:343:<b>687/2</b>:344:345:346:347:<b>695/2</b>:348:349:350:<b>701/2</b>:<br />351:352:353:<b>707/2</b>:354:355:356:357:358:<b>717/2</b>:359:360:361:<br />362:<b>725/2</b>:363:364:365:<b>731/2</b>:366:367:368:369:370:371:<b>743/2</b>:<br />372:373:374:375:376:<b>753/2</b>:377:378:379:380:381:<b>763/2</b>:382:<br />383:384:385:386:<b>773/2</b>:387:388:389:390:391:392:393:394:<br />395:<b>791/2</b>:396:397:398:399:400:401:402:<b>805/2</b>:403:404:405:<br />406:407:408:409:410:411:<b>823/2</b>:412:413:414:415:416:417:<br />418:419:420:421:422:423:424:425:<b>851/2</b>:426:427:428:429:<br />430:431:432:433:434:435:436:437:438:439:440:441:442:<br />443:444:445:446:447:448:449:450:451:452:453:454:455:<br />456:457:458:459:460:461:462:463:464:465:466:467:468:
 {{col-end}}
+[[Category:Just intonation scales]]
+[[Category:Pages with mostly numerical content]][[Category:311edo]]