212edo: Difference between revisions
m cleanup (grammar), "X temperament" doesn't take "the" Tags: Mobile edit Mobile web edit |
Expansion |
||
| Line 1: | Line 1: | ||
'''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]] | '''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. | |||
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]]. 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:Edo]] | ||
Revision as of 08:00, 13 October 2020
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 harmonics with 53edo, but the mapping differs for 7 and 11. 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, 390625/388962 and 4802000/4782969; in the 11-limit 385/384, 1375/1372, 6250/6237, 9801/9800 and 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 quadritikleismic temperament, and the 13-limit rank three 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.