Labeling a music recording according to its genre is an intuitive and familiar way to describe its content. Music genres are valuable information, especially for music organization, personalized listening experience, and playlist generation. Automatically classifying music genres is a challenging endeavor due to the inherent ambiguity and subjectivity. Most efforts on music genre classification consider the complete independence between labels. However, music genres typically respect a hierarchical structure based on the influences or origins of each style. Conversely, many of the methods available for hierarchical classification are based on assumptions about the class hierarchy, such as the need for multiple children in each hierarchy's node, which may limit their use in music applications. Also, the local classifier per node approach that would be the most suitable for this scenario is costly regarding time and memory. In this paper, we present two local hierarchical classification approaches and show how to combine them to obtain a single one that is more robust and faithful to the music genre classification scenario. We evaluate our proposal in a music dataset hierarchically labeled with 120 music genres. As shown, compared to state-of-the-art approaches, our approach has a lower computational cost and can achieve competitive performances.