"Familiar relationships between sets of musical notes, such as transposition between chords, directly translate into geometrical structures such as this Möbius strip — where each dot represents a whole class of equivalent two-note chords — or into more complex structures with many dimensions.
Composers have an understanding of these geometries without realizing it, says music theorist Dmitri Tymoczko of Princeton University. "Musicians like Chopin had a very direct, intuitive understanding of these spaces at a time when mathematicians still didn't know much about high-dimensional geometry," he says."
Full story here in Science News I think the intuitive geometric sense of those who work with music accounts for the argument, "I am in shape!! Round is a shape...".