In research on word recognition, it has been shown that word beginnings have higher information content for word identification than word endings; this asymmetric information distribution within words has been argued to be due to the communicative pressure to allow words in speech to be recognized as early as possible. Through entropy analysis using two representative datasets from Wikifonia and the Essen folksong corpus, we show that musical segments also have higher information content (i.e., higher entropy) in segment beginnings than endings. Nevertheless, this asymmetry was not as dramatic as that found within words, and the highest information content was observed in the middle of the segments (i.e., an inverted U pattern). This effect may be because the first and last notes of a musical segment tend to be tonally stable, with more flexibility in the first note for providing the initial context. The asymmetric information distribution within words has been shown to be an important factor accounting for various asymmetric effects in word reading, such as the left-biased preferred viewing location and optimal viewing position effects. Similarly, the asymmetric information distribution within musical segments is a potential factor that can modulate music reading behavior and should not be overlooked.