Okay it's more complicated and you're all right in a way, this is the UK law (or at least my understanding of it) by the way it varies in different countries:
The
composer of a piece of music holds the copyright to that piece (or at least his relatives do) until the end of the 70th year after their death: this means that one cannot play (in public), write down or alter their music without their permission.
The
arranger or editor of a piece of sheet music owns the copyright to their arrangement of a piece of music for 25 years, so you cannot photocopy written music that contains an editor's alterations for 25 years from publication without their permission. So it's legal to copy, say, Beethoven Sonata editions that were transcribed more than 25 years ago (there are some at
The Sheet Music Archive) but you can't copy the latest ABRSM ones.
The
performer of any recorded music maintains copyright to that recording for 50 years from the date of the recording. So you can copy freely recordings that were made over 50 years ago (provided the composer of the pieces has been dead at least 70 years).
Often performers sign away their copyright rights to record labels, and editors to pulishers so they're usually the people who technically have the copyright.