213edo
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Prime factorization
3 × 71
Step size
5.6338¢
Fifth
125\213 (704.225¢)
Semitones (A1:m2)
23:14 (129.6¢ : 78.87¢)
Dual sharp fifth
125\213 (704.225¢)
Dual flat fifth
124\213 (698.592¢)
Dual major 2nd
36\213 (202.817¢) (→12\71)
Consistency limit
7
Distinct consistency limit
7
← 212edo | 213edo | 214edo → |
213edo is the equal division of the octave into 213 parts of 5.6338 cents each. It is (uniquely) consistent through the 7-odd-limit and tempers out the following commas up to the 13-limit: [3 -10 11⟩ in the 5-limit; [6 -5 -4 4⟩, [10 -11 2 1⟩ and 6144 / 6125 in the 7-limit; 896/891 in the 11-limit; [12 -7 0 1 0 -1⟩, 325 / 324, 352 / 351 and 364 / 363 in the 13-limit. The patent val for 213-EDO is <213 338 495 598|. The general approximations to pure 3- and 5-limit intervals are quite bad, but 7-limit intervals are slightly better tuned. However, intervals involving a factor of 5/3 or 3/5 are quite well approximated. Thus it makes sense to view this as a 2.5/3.7 subgroup temperament.