This paper presents a novel approach to music representation learning. Triplet loss based networks have become popular for representation learning in various multimedia retrieval domains. Yet, one of the most crucial parts of this approach is the appropriate selection of triplets, which is indispensable, considering that the number of possible triplets grows cubically. We present an approach to harness multi-tag annotations for triplet selection, by using Latent Semantic Indexing to project the tags onto a high-dimensional space. From this we estimate tag-relatedness to select hard triplets. The approach is evaluated in a multi-task scenario for which we introduce four large multi-tag annotations for the Million Song Dataset for the music properties genres, styles, moods, and themes.