Some pieces of music do not begin on the first beat of the bar. Any notes which come before the first full bar are called lead-in notes (or pick-up notes). When lead-in notes are used, the last bar is also incomplete. The notes in the lead-in and the notes in the last bar always add up to one full bar. Here is an example.
As well as the use of lead-ins, another common variation to the number of bars is the use of first and second endings. The piece is first played using the first ending ( Z ); it is then repeated using the second ending ( X ) instead of the first. This saves a lot of space in written music. First and second endings may be used at the end of a piece, or at the end of a verse (in a song) or section.
Note the slight variation in the first and second endings.