For a while I was playing in a couple bands , one in E and one in Eb. What I noticed was that when I went to Eb , if I didn't drop the tuning below Eb and bring it up to key , the bass would go out of tune a couple times. After a couple re-tunes , everything seemed OK and I had no more problems till I re-tuned. Standard practice for tuning any guitar is to bring it up to tune , never down. This is because the strings won't completly relax on the nut and the bridge and as they do , the instrument will go slightly out of tune. Making sure I took the tuning down below Eb and then brought it up took care of most of the problem. I didn't have to change anything as far as stringing. I have noticed with both guitars and bass that changing tuning usually will require a re-tune or two (although not as quickly if brought UP to tune) regardless of the technique used to tune them. Hope this helps.