How can I use inverse or negative wildcards when pattern matching in a unix/linux shell?

In Bash you can do it by enabling the extglob option, like this (replace ls with cp and add the target directory, of course)

~/foobar> shopt extglob
extglob        off
~/foobar> ls
abar  afoo  bbar  bfoo
~/foobar> ls !(b*)
-bash: !: event not found
~/foobar> shopt -s extglob  # Enables extglob
~/foobar> ls !(b*)
abar  afoo
~/foobar> ls !(a*)
bbar  bfoo
~/foobar> ls !(*foo)
abar  bbar

You can later disable extglob with

shopt -u extglob

The extglob shell option gives you more powerful pattern matching in the command line.

You turn it on with shopt -s extglob, and turn it off with shopt -u extglob.

In your example, you would initially do:

$ shopt -s extglob
$ cp !(*Music*) /target_directory

The full available extended globbing operators are (excerpt from man bash):

If the extglob shell option is enabled using the shopt builtin, several extended pattern matching operators are recognized.A pattern-list is a list of one or more patterns separated by a |. Composite patterns may be formed using one or more of the following sub-patterns:

• ?(pattern-list)
  Matches zero or one occurrence of the given patterns
• *(pattern-list)
  Matches zero or more occurrences of the given patterns
• +(pattern-list)
  Matches one or more occurrences of the given patterns
• @(pattern-list)
  Matches one of the given patterns
• !(pattern-list)
  Matches anything except one of the given patterns

So, for example, if you wanted to list all the files in the current directory that are not .c or .h files, you would do:

$ ls -d !(*@(.c|.h))

Of course, normal shell globing works, so the last example could also be written as:

$ ls -d !(*.[ch])

Not in bash (that I know of), but:

cp `ls | grep -v Music` /target_directory

I know this is not exactly what you were looking for, but it will solve your example.