Transferring music folder to external hard drive

It somewhat depends on where things are now. If your Music library started out as an iTunes library then see Managing your Mac media libraries - Apple Community for advice on manipulating the library into a more typical layout for Music first. Once that is done the easiest method is to move the entire folder from ~/Music/Music to <Ext. Volume>/Music then option-start-Music, click Choose Library... and select <Ext. Volume>/Music/Music Library.musiclibrary.

An alternative approach would be to move/copy just the .musiclibrary package to <Ext. Volume>/Music/Music Library.musiclibrary, option-start-Music to select it, reset the media folder in Music's settings/preferences to <Ext. Volume>/Music/Media, then use File > Library > Organize Library to Consolidate Files which would copy everything in. You would then go back and manually clean up the internal drive.

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