217edo: Difference between revisions

Line 182:

* [[Cotoneum41]]

== Detemperaments ==

=== Ringer 217 ===

217edo is the basis for an exceptional Ringer scale that maps an unusually large amount of the harmonic series compared to other edos in this size range. Specifically, it maps the complete mode 167 of the harmonic series, corresponding to the ''entire'' 333-odd-limit. As 217 = 31 * 7, this can be used to derive 7 possible 31nejis.

<pre>

167:168:337/2:169:339/2:170:341/2:171:687/4:172:173:347/2:174:349/2:175:351/2:176:353/2:177:178:357/2:179:359/2:180:361/2:181:182:365/2:183:367/2:184:369/2:185:186:373/2:187:375/2:188:189:379/2:190:191:383/2:192:385/2:193:194:389/2:195:196:393/2:197:395/2:198:199:399/2:200:401/2:201:202:203:813/4:204:409/2:205:206:413/2:207:208:417/2:209:210:421/2:211:212:425/2:213:214:429/2:215:216:217:435/2:218:219:439/2:220:221:443/2:222:223:224:449/2:225:226:227:455/2:228:229:459/2:230:231:232:465/2:233:234:469/2:235:236:237:238:239:479/2:240:241:483/2:242:243:244:245:491/2:246:247:248:497/2:249:250:251:252:505/2:253:254:255:256:257:515/2:258:259:260:261:262:263:527/2:264:265:266:267:535/2:268:269:270:271:272:273:274:549/2:275:276:277:278:279:280:281:563/2:282:283:284:285:286:287:288:289:290:291:292:293:294:589/2:295:296:297:298:299:300:301:302:303:304:305:306:307:308:309:310:311:312:313:314:315:316:317:318:319:320:321:322:323:324:325:326:327:328:329:330:331:332:333:334

</pre>

==== Deriving 31nejis ====

This section shows how one can programmatically derive the 7 possible 31nejis aforementioned through use of [[User:Godtone]]'s [[User:Godtone#My_Python_3_code|copyleft Python 3 code]]:

>>> r217text = '[paste the above Ringer 217 data here]'

>>> r217=toneji(r217text) # r217

>>> r31s = [ [r217[7*i+j] for i in range(31)]+[r217[j]*2] for j in range(7) ]

>>> r31s2 = [ toneji(':'.join([ str(h) for h in r31 ]),True) for r31 in r31s ]

>>> for i in range(7):

print(str(i)+'th: ',':'.join([ str(h) for h in r31s2[i] ]))

0th: 274:280:286:293:299:306:313:320:327:334:342:350:358:366:374:383:392:400:409:418:428:438:448:458:468:479:490:500:512:524:535:548

1th: 351:359:367:375:384:393:401:410:420:429:439:449:459:469:480:491:502:514:526:536:549:562:574:588:600:614:628:642:656:672:687:702

2th: 301:308:315:322:329:337:344:352:360:368:376:385:394:402:412:421:430:440:450:460:470:482:492:504:515:527:538:550:563:576:589:602

3th: 258:264:270:276:282:289:295:302:309:316:323:330:338:346:353:361:369:378:386:395:404:413:422:432:442:452:462:472:483:494:505:516

4th: 227:232:237:242:248:253:259:265:271:277:283:290:296:303:310:317:324:331:339:347:354:362:370:379:388:396:406:414:424:434:443:454

5th: 416:425:435:444:455:465:476:486:497:508:520:532:544:556:568:582:594:608:622:636:650:664:680:696:712:728:744:760:778:796:813:832

6th: 213:218:223:228:233:239:244:249:255:261:267:273:279:285:292:298:305:312:319:326:333:341:349:357:365:373:382:390:399:408:417:426

>>> # using the below code can be used to show that only the 0th and 1th 31nejis are mapped correctly by 31edo's patent val

>>> for i in range(7): # (output omitted to avoid spam)

print(str(i)+'th:\n')

worstneji(r31s2[i],9)

print('\n'*2)

</syntaxhighlight>

[[Category:Arch]]

[[Category:Birds]]

[[Category:Cotoneum]]

@@ Line 182: / Line 182: @@
 * [[Cotoneum41]]
+== Detemperaments ==
+=== Ringer 217 ===
+edo is the basis for an exceptional Ringer scale that maps an unusually large amount of the harmonic series compared to other edos in this size range. Specifically, it maps the complete mode 167 of the harmonic series, corresponding to the ''entire'' 333-odd-limit. As 217 = 31 * 7, this can be used to derive 7 possible 31nejis.
+<pre>
+:168:337/2:169:339/2:170:341/2:171:687/4:172:173:347/2:174:349/2:175:351/2:176:353/2:177:178:357/2:179:359/2:180:361/2:181:182:365/2:183:367/2:184:369/2:185:186:373/2:187:375/2:188:189:379/2:190:191:383/2:192:385/2:193:194:389/2:195:196:393/2:197:395/2:198:199:399/2:200:401/2:201:202:203:813/4:204:409/2:205:206:413/2:207:208:417/2:209:210:421/2:211:212:425/2:213:214:429/2:215:216:217:435/2:218:219:439/2:220:221:443/2:222:223:224:449/2:225:226:227:455/2:228:229:459/2:230:231:232:465/2:233:234:469/2:235:236:237:238:239:479/2:240:241:483/2:242:243:244:245:491/2:246:247:248:497/2:249:250:251:252:505/2:253:254:255:256:257:515/2:258:259:260:261:262:263:527/2:264:265:266:267:535/2:268:269:270:271:272:273:274:549/2:275:276:277:278:279:280:281:563/2:282:283:284:285:286:287:288:289:290:291:292:293:294:589/2:295:296:297:298:299:300:301:302:303:304:305:306:307:308:309:310:311:312:313:314:315:316:317:318:319:320:321:322:323:324:325:326:327:328:329:330:331:332:333:334
+</pre>
+==== Deriving 31nejis ====
+This section shows how one can programmatically derive the 7 possible 31nejis aforementioned through use of [[User:Godtone]]'s [[User:Godtone#My_Python_3_code|copyleft Python 3 code]]:
+<syntaxhighlight lang="python">
+>>> r217text = '[paste the above Ringer 217 data here]'
+>>> r217=toneji(r217text) # r217
+>>> r31s = [ [r217[7*i+j] for i in range(31)]+[r217[j]*2] for j in range(7) ]
+>>> r31s2 = [ toneji(':'.join([ str(h) for h in r31 ]),True) for r31 in r31s ]
+>>> for i in range(7):
+  print(str(i)+'th: ',':'.join([ str(h) for h in r31s2[i] ]))
+th:  274:280:286:293:299:306:313:320:327:334:342:350:358:366:374:383:392:400:409:418:428:438:448:458:468:479:490:500:512:524:535:548
+th:  351:359:367:375:384:393:401:410:420:429:439:449:459:469:480:491:502:514:526:536:549:562:574:588:600:614:628:642:656:672:687:702
+th:  301:308:315:322:329:337:344:352:360:368:376:385:394:402:412:421:430:440:450:460:470:482:492:504:515:527:538:550:563:576:589:602
+th:  258:264:270:276:282:289:295:302:309:316:323:330:338:346:353:361:369:378:386:395:404:413:422:432:442:452:462:472:483:494:505:516
+th:  227:232:237:242:248:253:259:265:271:277:283:290:296:303:310:317:324:331:339:347:354:362:370:379:388:396:406:414:424:434:443:454
+th:  416:425:435:444:455:465:476:486:497:508:520:532:544:556:568:582:594:608:622:636:650:664:680:696:712:728:744:760:778:796:813:832
+th:  213:218:223:228:233:239:244:249:255:261:267:273:279:285:292:298:305:312:319:326:333:341:349:357:365:373:382:390:399:408:417:426
+>>> # using the below code can be used to show that only the 0th and 1th 31nejis are mapped correctly by 31edo's patent val
+>>> for i in range(7): # (output omitted to avoid spam)
+  print(str(i)+'th:\n')
+  worstneji(r31s2[i],9)
+  print('\n'*2)
+</syntaxhighlight>
 [[Category:Arch]]
 [[Category:Birds]]
 [[Category:Cotoneum]]