I have a regular, 4-string bass, tuned EADG.
I tune my bass down one half-step.
I play the open string on the 4th (top) string.
What note am I playing?
on the question of Eb vs D#, it's actually context dependent based on the music you are playing. in a given musical moment, there is correct and incorrect answer as to how to spell the note.
for the most part, we would call it Eb since the standard tuning is E and we've lowered it.
interestingly, though, once you've tuned down the instrument is now transposing - the way a trumpet or saxophone would. so if you're tuned down it's fine and common practice to still "think" in the original keys.
when a classical bassist plays a solo, often the bass is tuned up a whole step (A E B F# from high to low.) but their music, and thinking, is still in standard tuning, if that makes sense.
. Everyone had a good laugh at the group leader's expense after the show
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