This article addresses the relation between Andean 'traditional music' and circulations of people, objects, ideas and sounds. Although many studies on Andean indigenous music have explored such circulations, scholars still tend to understand musical practices in terms of 'cultures'. The case of indigenous music from Otavalo, in the Ecuadorian Andes, encourages us to go beyond this approach. I make two arguments. First, by conceiving of the translocal/transnational flows that have shaped 'traditional music' from Otavalo through the concepts of 'network' and 'music world', I unsettle the link - underlying previous approaches - between a specific people, music and place. Second, through the concepts of 'assemblage' and 'mediation', I closely look at processes of 'traditionalisation' and 'indigenisation' to show how, in the context of multiple circulations, social actors nevertheless produce a specific link between people, music and place in order to make a musical practice 'traditional' and/or 'indigenous'.