Distances on symbolic musical sequences are needed for a variety of applications, from music retrieval to automatic music generation. These musical sequences belong to a given corpus (or style) and it is obvious that a good distance on musical sequences should take this information into account; being able to define a distance ex nihilo which could be applicable to all music styles seems implausible. A distance could also be invariant under some transformations, such as transpositions, so that it can be used as a distance between musical motives rather than musical sequences. However, to our knowledge, none of the approaches to devise musical distances seem to address these issues. This paper introduces a method to build transposition-invariant distances on symbolic musical sequences which are learned from data. It is a hybrid distance which combines learned feature representations of musical sequences with a handcrafted rank distance. This distance depends less on the musical encoding of the data than previous methods and gives perceptually good results. We demonstrate its efficiency on the dataset of chorale melodies by J.S. Bach.