An extended Boolean network model is investigated as a possible medium in which a human composer can write music. A Boolean network is a simple discrete-time dynamical system whose state is characterised by the states of its constituent Boolean-valued vertices. The evolution of the system is predetermined by an initial state and the properties of the activation functions associated with each vertex. By associating musical events with the states of the system, its trajectory from a particular start state can be interpreted as a piece of tonal music. The primary source of interest in composing music using a deterministic dynamical system is the dependence of the musical result on the initial conditions. This paper explores the possibility of producing musically interesting variations on a given melodic phrase by changing the initial conditions from which the generating dynamical system is started.