212edo: Difference between revisions

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The 212 equal temperament divides the octave into 212 equal parts of 5.660 cents each. 212 = 4 * 53, and it tempers out the same commas (32805/32768, 15625/15552 and 1600000/1594323) as 53 in the [[~~5-limit|~~5-limit]]. In the [[~~7-limit|~~7-limit]] it tempers out 2401/2400; in the [[~~11-limit|~~11-limit]] 385/384 and 1375/1372; and in the [[13-limit|13-limit]] 325/324, 625/624, 676/675 and 1001/1000. It is the [[~~Optimal_patent_val|~~optimal patent val]] for 7 and 13 limit [[~~Kleismic_family~~|quadritikleismic temperament]], and the 13-limit rank three [[~~Breed_family~~#Agni|agni temperament]]. Also, using 212bb val (where fifth is flattened by single step, ~~app.~~ 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone.

The '''212 equal temperament''' divides the octave into 212 equal parts of 5.660 cents each. 212 = 4 × 53, and it tempers out the same commas ([[32805/32768]], [[15625/15552]] and [[1600000/1594323]]) as 53 in the [[5-limit]]. In the [[7-limit]] it tempers out [[2401/2400]]; in the [[11-limit]] [[385/384]] and 1375/1372; and in the [[13-limit|13-limit]] [[325/324]], 625/624, 676/675 and 1001/1000. 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]]. 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.

[[Category:Edo]]

[[Category:53edo]]

[[Category:~~agni~~]]

[[Category:Agni]]

[[Category:~~edo]]~~

[[Category:Quadritikleismic]]

~~[[Category:quadritikleismic~~]]

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-The 212 equal temperament divides the octave into 212 equal parts of 5.660 cents each. 212 = 4 * 53, and it tempers out the same commas (32805/32768, 15625/15552 and 1600000/1594323) as 53 in the [[5-limit|5-limit]]. In the [[7-limit|7-limit]] it tempers out 2401/2400; in the [[11-limit|11-limit]] 385/384 and 1375/1372; and in the [[13-limit|13-limit]] 325/324, 625/624, 676/675 and 1001/1000. It is the [[Optimal_patent_val|optimal patent val]] for 7 and 13 limit [[Kleismic_family|quadritikleismic temperament]], and the 13-limit rank three [[Breed_family#Agni|agni temperament]]. Also, using 212bb val (where fifth is flattened by single step, app. 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone.
+The '''212 equal temperament''' divides the octave into 212 equal parts of 5.660 cents each. 212 = 4 × 53, and it tempers out the same commas ([[32805/32768]], [[15625/15552]] and [[1600000/1594323]]) as 53 in the [[5-limit]]. In the [[7-limit]] it tempers out [[2401/2400]]; in the [[11-limit]] [[385/384]] and 1375/1372; and in the [[13-limit|13-limit]] [[325/324]], 625/624, 676/675 and 1001/1000. 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]]. 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.
+[[Category:Edo]]
 [[Category:53edo]]
-[[Category:agni]]
+[[Category:Agni]]
-[[Category:edo]]
+[[Category:Quadritikleismic]]
-[[Category:quadritikleismic]]