a multiplicative operation is a mapping in which the argument is multiplied . multiplication originated intuitively in interval expansion, including tone row order number rotation, for example in the music of béla bartók and alban berg . pitch number rotation, "fünferreihe" or "five-series" and "siebenerreihe" or "seven-series", was first described by ernst krenek in "über neue musik" (; ). princeton-based theorists, including james k. , godfrey , and hubert s. "were the first to discuss and adopt them, not only with regards to twelve-tone series" .