There are two known Ringer scales based on 311edo. Both include the complete mode 234 of the harmonic series (234afdo) using non-patent vals 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'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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Scale as chord:
936:940:941:943:944:948:950:952:954:956:958:960:962:
964:966:968:970:972:974:976:980:982:984:986:988:990:
992:994:996:1000:1002:1004:1006:1008:1010:1012:1016:1018:1020:
1022:1024:1026:1028:1030:1032:1036:1038:1040:1042:1044:1048:1050:
1052:1054:1056:1060:1063:1064:1066:1068:1070:1072:1076:1078:1080:
1082:1084:1088:1090:1092:1096:1097:1100:1102:1104:1108:1110:1112:
1114:1116:1120:1122:1124:1128:1130:1132:1134:1136:1140:1142:1144:
1148:1150:1152:1156:1158:1160:1162:1164:1168:1170:1172:1176:1178:
1180:1184:1186:1188:1192:1194:1196:1200:1202:1204:1208:1210:1212:
1216:1218:1220:1224:1226:1228:1232:1234:1236:1240:1244:1246:1248:
1252:1254:1256:1260:1264:1266:1268:1272:1274:1276:1280:1282:1284:
1288:1292:1294:1296:1300:1304:1306:1308:1312:1316:1318:1320:1324:
1326:1328:1332:1336:1338:1340:1344:1348:1350:1352:1356:1360:1362:
1364:1368:1372:1374:1376:1380:1384:1388:1390:1392:1396:1400:1402:
1404:1408:1412:1414:1416:1420:1424:1428:1432:1434:1436:1440:1444:
1448:1450:1452:1456:1460:1462:1464:1468:1472:1476:1480:1484:1486:
1488:1492:1496:1500:1504:1506:1508:1512:1516:1520:1524:1526:1528:
1532:1536:1540:1544:1546:1548:1552:1556:1560:1564:1568:1572:1576:
1580:1582:1584:1588:1592:1596:1600:1604:1606:1608:1612:1616:1620:
1624:1628:1632:1636:1640:1644:1646:1648:1652:1656:1660:1664:1668:
1672:1676:1680:1684:1688:1692:1696:1700:1702:1704:1708:1712:1716:
1720:1724:1728:1732:1736:1740:1744:1748:1752:1756:1760:1764:1768:
1772:1776:1780:1784:1788:1792:1796:1800:1804:1808:1812:1816:1820:
1824:1828:1832:1836:1840:1844:1848:1852:1856:1860:1864:1868:1872
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Reduced to mode 234:
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:
263:527/2:264:265:1063/4:266:533/2:267:535/2:268:269:539/2:270:
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:
663/2:332:333:334:669/2:335:336:337:675/2:338:339:340:681/2:
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:
395:791/2:396:397:398:399:400:401:803/2:402:403:404:405:
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
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Ringer 311[+61, −67]
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Scale as chord:
936:940:941:943:944:948:950:952:954:956:958:960:962:
964:966:968:970:972:974:976:980:982:984:986:988:990:
992:994:996:1000:1002:1004:1006:1008:1010:1012:1016:1018:1020:
1022:1024:1026:1028:1030:1032:1036:1038:1040:1042:1044:1048:1050:
1052:1054:1056:1060:1061:1064:1066:1068:1072:1074:1076:1078:1080:
1082:1084:1088:1090:1092:1096:1097:1100:1102:1104:1108:1110:1112:
1114:1116:1120:1122:1124:1128:1130:1132:1134:1136:1140:1142:1144:
1148:1150:1152:1156:1158:1160:1162:1164:1168:1170:1172:1176:1178:
1180:1184:1186:1188:1192:1194:1196:1200:1202:1204:1208:1210:1212:
1216:1218:1220:1224:1226:1228:1232:1234:1236:1240:1244:1246:1248:
1252:1254:1256:1260:1264:1266:1268:1272:1274:1276:1280:1282:1284:
1288:1292:1294:1296:1300:1304:1306:1308:1312:1316:1318:1320:1324:
1326:1328:1332:1336:1340:1341:1344:1348:1350:1352:1356:1360:1362:
1364:1368:1372:1374:1376:1380:1384:1388:1390:1392:1396:1400:1402:
1404:1408:1412:1414:1416:1420:1424:1428:1432:1434:1436:1440:1444:
1448:1450:1452:1456:1460:1462:1464:1468:1472:1476:1480:1484:1486:
1488:1492:1496:1500:1504:1506:1508:1512:1516:1520:1524:1526:1528:
1532:1536:1540:1544:1546:1548:1552:1556:1560:1564:1568:1572:1576:
1580:1582:1584:1588:1592:1596:1600:1604:1608:1610:1612:1616:1620:
1624:1628:1632:1636:1640:1644:1646:1648:1652:1656:1660:1664:1668:
1672:1676:1680:1684:1688:1692:1696:1700:1702:1704:1708:1712:1716:
1720:1724:1728:1732:1736:1740:1744:1748:1752:1756:1760:1764:1768:
1772:1776:1780:1784:1788:1792:1796:1800:1804:1808:1812:1816:1820:
1824:1828:1832:1836:1840:1844:1848:1852:1856:1860:1864:1868:1872
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Reduced to mode 234:
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:
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