Music and notation from the 15th century are examined and the meanings of cut signatures in musical practice from Dufay to Desprez are ascertained. A detailed examination of notational developments in the 14th century is followed by an analysis of new notational features in the early 15th century, and of the behavior of the earliest works that exhibited cut signatures. Statements in the treatises of Tinctoris pertaining to the relationship between mensuration and tempo are examined. A comprehensive survey of theoretical writings from c. 1490 to 1550 is followed by a review of editorial practices in published modern editions of selected works from the 15th-century repertoire. A purely proportional or mathematical understanding of the relationships between uncut and cut signatures is contested. [RILM-abbrev]