Many studies have presented computational models of musical structure, as an important aspect of musicological analysis. However, the use of grammar-based compressors to automatically recover such information is a relatively new and promising technique. We investigate their performance extensively using a collection of nearly 8000 scores, on tasks including error detection, classification, and segmentation, and compare this with a range of more traditional compressors. Further, we detail a novel method for locating transcription errors based on grammar compression. Despite its lack of domain knowledge, we conclude that grammar-based compression offers competitive performance when solving a variety of musicological tasks.