In recent years, deep learning has achieved formidable results in creative computing. When it comes to music, one viable model for music generation are Transformer based models. However, while transformers models are popular for music generation, they often rely on annotated structural information. In this work, we inquire if the off-the-shelf Music Transformer models perform just as well on structural similarity metrics using only unannotated MIDI information. We show that a slight tweak to the most common representation yields small but significant improvements. We also advocate that searching for better unannotated musical representations is more cost-effective than producing large amounts of curated and annotated data.