212edo: Difference between revisions

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'''212 equal temperament''' divides the octave into 212 equal parts of 5.660 cents each.

212 = 4 × 53, and it shares the 3rd, 5th, and 13th [[Overtone series|harmonics]] with [[53edo]], but the mapping differs for 7 and 11. It tempers out the same commas ([[32805/32768]], [[15625/15552]] and [[amity comma|1600000/1594323]]) as 53 in the [[5-limit]]. In the [[7-limit]] it tempers out [[2401/2400]], [[dimcomp comma|390625/388962]] and [[canousma|4802000/4782969]]; in the [[11-limit]] [[385/384]], 1375/1372, 6250/6237, 9801/9800 and [[semicanousma|14641/14580]]; and in the [[13-limit]] [[325/324]], 625/624, 676/675 and 1001/1000.

212 = 4 × 53, and it shares the 3rd, 5th, and 13th [[Overtone series|harmonics]] with [[53edo]], but the mapping differs for 7 and 11. It tempers out the same commas ([[32805/32768]], [[15625/15552]] and [[amity comma|1600000/1594323]]) as 53 in the [[5-limit]]. In the [[7-limit]] it tempers out [[2401/2400]], [[dimcomp comma|390625/388962]] and [[canousma|4802000/4782969]]; in the [[11-limit]] [[385/384]], 1375/1372, 6250/6237, [[9801/9800]] and [[semicanousma|14641/14580]]; and in the [[13-limit]] [[325/324]], 625/624, 676/675 and 1001/1000.

It is distinctly [[consistent]] in the [[15-odd-limit]] with harmonics of 3 through 13 all tuned flat. It is the [[optimal patent val]] for 7 and 13 limit [[Kleismic family #Quadritikleismic|quadritikleismic temperament]], and the 13-limit rank three [[Breed family #Agni|agni temperament]]. 212gh val shows some potential beyond 15-odd-limit. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone.

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 '''212 equal temperament''' divides the octave into 212 equal parts of 5.660 cents each.
-= 4 × 53, and it shares the 3rd, 5th, and 13th [[Overtone series|harmonics]] with [[53edo]], but the mapping differs for 7 and 11. It tempers out the same commas ([[32805/32768]], [[15625/15552]] and [[amity comma|1600000/1594323]]) as 53 in the [[5-limit]]. In the [[7-limit]] it tempers out [[2401/2400]], [[dimcomp comma|390625/388962]] and [[canousma|4802000/4782969]]; in the [[11-limit]] [[385/384]], 1375/1372, 6250/6237, 9801/9800 and [[semicanousma|14641/14580]]; and in the [[13-limit]] [[325/324]], 625/624, 676/675 and 1001/1000.
+= 4 × 53, and it shares the 3rd, 5th, and 13th [[Overtone series|harmonics]] with [[53edo]], but the mapping differs for 7 and 11. It tempers out the same commas ([[32805/32768]], [[15625/15552]] and [[amity comma|1600000/1594323]]) as 53 in the [[5-limit]]. In the [[7-limit]] it tempers out [[2401/2400]], [[dimcomp comma|390625/388962]] and [[canousma|4802000/4782969]]; in the [[11-limit]] [[385/384]], 1375/1372, 6250/6237, [[9801/9800]] and [[semicanousma|14641/14580]]; and in the [[13-limit]] [[325/324]], 625/624, 676/675 and 1001/1000.
 It is distinctly [[consistent]] in the [[15-odd-limit]] with harmonics of 3 through 13 all tuned flat. It is the [[optimal patent val]] for 7 and 13 limit [[Kleismic family #Quadritikleismic|quadritikleismic temperament]], and the 13-limit rank three [[Breed family #Agni|agni temperament]]. 212gh val shows some potential beyond 15-odd-limit. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone.