The Value of Mathematical and Musical Notation

Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience.  —Keith Devlin, Mathematics: The Science of Patterns 

Both mathematical and musical notation point to universes quite different from the one in which ordinary language functions so well. But, in each too, there is genius in the very notation that has developed for giving representation to ideas that seem to lie beyond ordinary language. There are times in mathematics when the similarities in notation is the first clue to a deeper relationship. Similarly musical notation not only created a structure within which Western music could develop but also shows something other than just the sounds being made. It indicates how the various elements stand in relation to one another, how sound creates a space, it shows how different musical voices move against and through each other. The notation in both subjects can make visible the hidden connections within each subject that reveal hidden connections among outside phenomenon.  —Edward Rothstein, Emblems of Mind