Music similarity search is useful for a variety of creative tasks such as replacing one music recording with another recording with a similar "feel", a common task in video editing. For this task, it is typically necessary to define a similarity metric to compare one recording to another. Music similarity, however, is hard to define and depends on multiple simultaneous notions of similarity (i.e. genre, mood, instrument, tempo). While prior work ignore this issue, we embrace this idea and introduce the concept of multidimensional similarity and unify both global and specialized similarity metrics into a single, semantically disentangled multidimensional similarity metric. To do so, we adapt a variant of deep metric learning called conditional similarity networks to the audio domain and extend it using track-based information to control the specificity of our model. We evaluate our method and show that our single, multidimensional model outperforms both specialized similarity spaces and alternative baselines. We also run a user-study and show that our approach is favored by human annotators as well.