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, ~~the 212b~~ 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|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.

[[Category:53]]

[[Category:53edo]]

[[Category:agni]]

[[Category:edo]]

[[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, the 212b 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|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.
-[[Category:53]]
+[[Category:53edo]]
 [[Category:agni]]
 [[Category:edo]]
 [[Category:quadritikleismic]]