212edo: Difference between revisions

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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 ([[15625/15552]], [[32805/32768]], ~~and~~ [[amity comma|1600000/1594323]]) as 53edo in the [[5-limit]].

It tempers out the same commas ([[15625/15552]], [[32805/32768]], [[amity comma|1600000/1594323]], etc.) as 53edo in the [[5-limit]].

In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[~~dimcomp comma|~~dimcomp comma]]), and 4802000/4782969 ([[~~canousma|~~canousma]]).

In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]).

In the [[11-limit]], 385/384 ([[keenanisma]]), 1375/1372 ([[moctdel comma]]), 6250/6237 ([[liganellus comma]]), 9801/9800 ([[kalisma]]) and 14641/14580 ([[semicanousma]]).

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In the [[13-limit]], 325/324 ([[marveltwin comma]]), 625/624 ([[tunbarsma]]), 676/675 ([[island comma]]), 1001/1000 ([[sinbadma]]), 1716/1715 ([[lummic comma]]), 2080/2079 ([[ibnsinma]]).

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.

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]], the 7-limit rank-3 [[Kleismic rank three family #Kleismic|kleismic temperament]], and the 13-limit rank-3 [[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.

=== Prime intervals ===

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[[Category:Equal divisions of the octave]]

[[Category:53edo]]

[[Category:Kleismic]]

[[Category:Agni]]

[[Category:Quadritikleismic]]

@@ Line 5: / Line 5: @@
 = 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 ([[15625/15552]], [[32805/32768]], and [[amity comma|1600000/1594323]]) as 53edo in the [[5-limit]].
+It tempers out the same commas ([[15625/15552]], [[32805/32768]], [[amity comma|1600000/1594323]], etc.) as 53edo in the [[5-limit]].
-In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma|dimcomp comma]]), and 4802000/4782969 ([[canousma|canousma]]).
+In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]).
 In the [[11-limit]], 385/384 ([[keenanisma]]), 1375/1372 ([[moctdel comma]]), 6250/6237 ([[liganellus comma]]), 9801/9800 ([[kalisma]]) and 14641/14580 ([[semicanousma]]).
@@ Line 13: / Line 13: @@
 In the [[13-limit]], 325/324 ([[marveltwin comma]]), 625/624 ([[tunbarsma]]), 676/675 ([[island comma]]), 1001/1000 ([[sinbadma]]), 1716/1715 ([[lummic comma]]), 2080/2079 ([[ibnsinma]]).
-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.
+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]], the 7-limit rank-3 [[Kleismic rank three family #Kleismic|kleismic temperament]], and the 13-limit rank-3 [[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.
 === Prime intervals ===
@@ Line 20: / Line 20: @@
 [[Category:Equal divisions of the octave]]
 [[Category:53edo]]
+[[Category:Kleismic]]
 [[Category:Agni]]
 [[Category:Quadritikleismic]]