All of the patterns covered in the Lessons 1 through 5 of The Fundamentals of Rhythm have started on beat one. However, patterns and phrases can also include notes that occur before the first full measure. These notes are called anachronism or pickup notes. An incomplete measure at the beginning of a piece of music is called a pickup measure.
To properly count the beats of a pickup measure, we count backwards from the end of the measure. For example, if we are in 4/4 and there is a pickup note of one quarter note, we count that note as beat 4, not beat 1.
When a piece of music has a pickup measure, the last measure will not have the full number of beats. The number of beats in the last measure will be reduced by the number of beats in the pickup measure. In the example below, there is a pickup measure of one beat. Therefore, the last measure of that piece will only have three beats.