If you're moving more than a few gigs of music files, my personal preference would be to do it like this:
1. Move the entire music structure as is, to your new drive. I would not change the structure at ALL during this. As an example, let's say your current music files are in:
[your user directory]/Music/FLAC/[Albums and Artists go here]
...and let's say your new drive is at /Volumes/BigThunderBolt
I would move them such that the new path is:
/Volumes/BigThunderBolt/Music/FLAC/[Albums and Artists go here]
You could drag and drop to copy these files over. Or you could use rsync if you're familiar. I would use rsync, but it's use is WAY beyond this discussion.
2. Now that your files are moved, you need to update MC to the new location. We do this with the Rename, Move, and Copy tool, set to Update Mode. This mode just changes the place that MC points to for each file. It doesn't try to move any files. Just updates their database pointers. Because we already moved all the files in step 1.
A. Select some files. I would do a few as a test and later do larger batches, or all at once.
B. Open RM&C. Set it to Update mode.
C. Uncheck Directories, and Filename. Check Find and Replace.
D. In the Find and Replace boxes, type in something like this:
Find: /Users/Your User Name/
Replace: /Volumes/BigThunderBolt/
E. Look in the Preview Pane to the right and check to see what the tool is going to do. It should show you the new paths to the new files. Check these to make sure the new paths look correct. If not, adjust your find and replace rule until the new directory structure matches what you actually have on disk.
F. Press OK and let it do the updates.
G. Check your work. Play a few files that you just moved, to make sure the update worked correctly.
H. Repeat from step A with a larger group of files if you were successful.
You could do the whole thing including the actual file moves using RM&C, but I'm not super comfortable with that myself because it doesn't show status during the file moves or copies. That's just my preference. Read up on the link above to learn about the RM&C tool. It's pretty great. Do whatever makes you comfortable. This is just how I would do it.
Good luck.
Brian.