Anacrusis or Up Beat

An anacrusis, also known as an up beat, is when a piece of music does not start on the first beat of the bar. In the example below, the music starts on the second half of the fourth beat. So, the last bar will contain three and a half beats to make this bar complete to four beats. If the first bar is incomplete, then the final bar will be incomplete.

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In the next example, the music starts on the fourth beat, so the final bar contains only three beats.

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Brown, James Murray. A Handbook Of Musical Knowledge. London: Trinity College of Music, 1987. Print, p. 24.