In harmony, is it okay if there are consecutive 3rds in ii-V progression in two different bars?
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Consecutive 5ths, and octaves are a big no-no when doing voice leading and counterpoint, however consecutive 3rds and 6ths are fine (at least in moderation).
The reason for the distinction is when you have consecutive 5ths or octaves the voices that are in parallel sound like one unit and take away from the independence aspect of voice leading due to the purity of perfect intervals. 3rds and 6ths on the other hand still retain some independence in parallel due to the nature of the intervals.
The forbidden parallels regard most of the perfect consonances: unisons, fifths, and octaves. (Fourths are also perfect consonances, but parallel fourths are acceptable.)
But thirds and sixths are imperfect consonants and thus are not included in any rules regarding forbidden parallels.
Now, there's a broad rule in composition that you don't do the same thing more than three days in a row. So if you have parallel thirds, break them off before the fourth iteration. But this is a very soft rule and more of a recommendation than anything.
Lastly, the only thing to watch out for is the motion into the B chord on the downbeat. This is a very esoteric rule: between the soprano and bass, you have similar motion into a perfect fifth. When such similar motion has the soprano moving by step, this is okay. But if the soprano moves by leap, we call these "similar fifths," and some people (not all!) consider these forbidden.
PS: Note that you actually have three instances of consecutive thirds in this example: