Consider the following contrasting period [from Beethoven, Sonata Op. 13, II]:
Here, as in a parallel period, there are two phrases. The first phrase ends with a relatively inconclusive cadence (a half cadence in the tonic key) which is answered by a perfect authentic cadence at the end of the second phrase. Even though the two phrases of the theme are not similar, they do form a unit of musical meaning unified by harmonic structure; the contrasting surface design of the two phrases makes them complement each other. We might represent a contrasting period analytically as
By representing the two phrases as "a" and "b," we indicate that they are dissimilar with respect to their surface design. The double bar after b shows that this is nevertheless a period.