All the scale diagrams I've seen are shown in E standard tuning.
Would the scale shape change in another tuning, like Drop D for example? Alternatively, do I just keep the same scale shape regardless of tuning?
Note: I'm showing a bass guitar diagram because that's what I play, but I imagine this would be the same for most fretted instruments.
Yes, scale and chord shapes do change if you use an alternate tuning. If the open note was an "E" but has been changed, then all of the other notes on that string will move to other positions and you'll need to play a different "shape" to reach those new positions.
In this sort of situation the best thing to do is get a piece of paper and draw a new fretboard diagram with the notes written in their new positions, and the scale's notes circled to remind you of the new shape. With a bit of practice you'll re-learn the new intervals for the tunings you use frequently.
Yes, they would change. Try to think of the notes not on the fret, but on the specific position on the string. So, if you lower the tuning on that string, let's say by a whole tone, the note that was on the 5th fret would move up to the 7th fret. Similarly if you tune your strings up.
If you tune the whole bass/guitar a whole tone lower, then the fingerings wouldn't change per se, but everything would be a whole tone lower. But if you change the tuning a lot, like you tune your E to a D, and leave the other 3 strings as they are, then the fingerings would change a bit more.
The same goes if you try some other tuning as well (like for instance tuning in fifths like Tim said)
Yes. If the guitar was tuned to just drop D, then all the scale notes on the bottom string would need to be fretted 2 frets higher. With other tunings, because the open string notes have changed, and also changed in relation to each other then adjustments would have to be made all over.
The same scenario would happen on bass, although the most usual change of tuning seems to be a fifth between strings instead of a fourth, thus changing the fingering and fretting of scale notes.
