Compositions in which time is constantly modulated abound in new music since 1950. Even within one single movement, the tempo can fluctuate continuously. This necessitates both a logical transition between successive tempi and an overall temporal framework. A composition with flexible tempi thus resembles a polytopic clockwork that shows time in different places, yet being based on one and the same underlying time system. The new music research group at K.U.Leuven’s musicology department recently launched an new project with the aim of systematically investigating the notation and above all the structural and formal significance of tempo relationships in contemporary music. It proposes an analysis of the works and theories of composers such as Elliott Carter, Karlheinz Stockhausen, Karel Goeyvaerts, Milton Babbitt, John Cage and Harrison Birtwistle who have all developed sophisticated techniques to organize time and tempo relationships. Special attention is devoted to Carter’s technique of so-called ‘metric modulation’, enabling a flexible and smooth, yet very accurate transition from one tempo to the next. For methodological reasons, a study of this topic from the viewpoint of so-called ‘cognitive musicology’ -including music psychological research into reproduction and perception of tempo- will not be carried out in this project. This is why a presentation of this topic in the context of RPPW could be the more rewarding: several examples of the importance of tempo relationships in contemporary music will be presented, after which possible contributions by cognitive musicology to this research field can be discussed.