| To an extent, this effect is always present. But it could be more severe if the new D string is a higher tension string than the original set. It is best to try to get the strings to about the same tension across the board. Sometimes it is necessary to mix higher tensions to even them out in response.
It is not uncommon when bringing all the strings up to tension to have to go back and re-tune them a couple of times until the instrument has flexed to it's equilibrium point. An instrument under tension is compressed a bit longitudinally. If was too resistant to the tension it wouldn't sound too good.
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