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Downtuning the bass, what changes in theory?

Well, I don't really read music very well, but I can't possibly see why the stave should change, it's the same no matter what tuning or instrument you are playing. The only thing that changes is where on the fretboard you have to place your fingers to get the same note.
 
I'm getting more and more used to my bass, tuned DGCF. But now I wanna read music notes. Is there anything that changes...?

Assuming that you only play with guitarists (no piano, woodwind or brasswind instruments), it depends on the guitar player(s)' tuning. If the guitars are also tuned one full step below standard (as your bass is), you can play exactly what's written without changing anything. The only difference is that the music will sound one full step lower than originally intended. Unless your singer complains about it because the new tuning is out of his/her range, it shouldn't mean any kind of inconvenience.

But if your guitarist invariably works with standard tuning and the sheet music for all instruments is intended for standard tuning, your only option (aside from returning to standard tuning, of course) is to play everything two frets higher than "normal". Example: If there's a low F on your sheet music, which is supposed to be played on the E string, 1st fret, you should play it on the 3rd fret, where a G would normally be located (you'll hear an F). Now, if you find it uncomfortable to play different notes (actually different positions) than written, you can retranscribe your part one full step higher (including the key signature) with the annotation "tune bass down one step (DGCF)". That way you'll play exactly what's written. It just will sound one full step lower.
 
Alvaro Martín Gómez A.;13074740 said:
Assuming that you only play with guitarists (no piano, woodwind or brasswind instruments), it depends on the guitar player(s)' tuning. If the guitars are also tuned one full step below standard (as your bass is), you can play exactly what's written without changing anything. The only difference is that the music will sound one full step lower than originally intended. Unless your singer complains about it because the new tuning is out of his/her range, it shouldn't mean any kind of inconvenience.

But if your guitarist invariably works with standard tuning and the sheet music for all instruments is intended for standard tuning, your only option (aside from returning to standard tuning, of course) is to play everything two frets higher than "normal". Example: If there's a low F on your sheet music, which is supposed to be played on the E string, 1st fret, you should play it on the 3rd fret, where a G would normally be located (you'll hear an F). Now, if you find it uncomfortable to play different notes (actually different positions) than written, you can retranscribe your part one full step higher (including the key signature) with the annotation "tune bass down one step (DGCF)". That way you'll play exactly what's written. It just will sound one full step lower.

Thanks for the info! Yes as far as I'm playing, it's only with a guitar player. We both have some financial problems, so it'll take a while before we get some equipment to play in a band. But that doesn't matter for us. We already have a lot of fun together :p

We both like the tuning a lot, standard was just to ''standard'' and we're both not really in those Drop down thingy's (i.e. Drop D, Drop C, etc. etc.)