Pitch standardization didn't become a thing until a couple decades after that piece was written. Schumann wrote that piece in 1849, and the first attempt to create a standardized tuning pitch was in France in 1859 which established the A above middle C as 435 cycles per second (later named Hertz). Prior to this, most orchestras relied on whatever tuning fork or instrument happened to be present in that orchestras performance space. This could have been anywhere between 400 and 450 Hertz.