The Effects of Network Delay on Tempo in Musical Performance Peter F. Driessen, Thomas E. Darcie, and Bipin Pillay Department of Electrical and Computer Engineering University of Victoria Victoria, BC Canada V8W 3P6 peter@ece.uvic.ca {tdarcie, bipin}@uvic.ca Internet-based collaborative networking applica- tions, such as instant messaging, voice-over-IP telephony, and social networking, have displaced traditional communication services and redefined social interaction. The Internet has also trans- formed the music industry, revolutionizing the way music is distributed and marketed. Yet despite these two powerful trends, the intersection—where collaboration and music meet in online music- making—has remained merely a curiosity. Why? Artistically pleasing online audio collaboration requires network delay less than that encountered typically in the Internet. The bandwidth required for high-quality audio exceeds the bandwidth that is generally available on consumer-oriented broad- band access (cable and digital subscriber line [DSL]) systems. The emergence of Web 2.0, broadly defined as Web-based communities such as social-networking sites that facilitate sharing of ideas among Web users, has been significant for many existing online communities. One such community, made up of real-time Web-based music collaborators using sys- tems for networked musical performance (NMP), is in its infancy. An online NMP application lets musicians from across the globe play together over the Internet, as if they were together in a studio. With online music-making (either improvisatory or strictly notated), musicians can create ensembles without location bounds, searching for musicians around the world. The quality of the user’s experi- ence is critical to the success of this Web application. However, because performing artists are highly sen- sitive to delay, network latency affects the quality of the user experience of online music-making. To achieve a good user experience the latency over the network has to be within reasonable bounds. If the delay is excessive, then the musicians will not be Computer Music Journal, 35:1, pp. 76–89, Spring 2011 c  2011 Massachusetts Institute of Technology. able to maintain a consistent tempo. We seek to find out how the tempo of two musicians performing together via a network varies as a function of fixed network delay. Future work may consider the more general case of more than two musicians and/or variable network delay. Two musicians making music online will inde- pendently generate rhythmic patterns. Entrainment refers to an interaction between autonomous rhyth- mic processes such that they adjust to a common tempo or related tempi. Two oscillators, like two rhythmic processes, may synchronize, but other phase relationships are also possible. Entrainment and synchronization arise in many different con- texts, where there is interaction (or coupling) between oscillators, where the oscillator may be designed for a particular purpose (e. g., electronic oscillator), or occur naturally (e. g., neural oscilla- tors). Mathematical models of electronic and neural oscillators have been developed and are used to predict behavior by analysis or simulation. We are particularly interested in models for coupled oscillators with a time delay between them. One such model was developed for geographically separated oscillators with delay compensation (an- ticipation). An equivalent model was developed for mutual entrainment of two limit-cycle oscillators with time-delayed coupling. We will show that both models make the same prediction: For delays that are a small fraction of the tempo period, the mean tempo in beats per minute (BPM), or beats per second, decreases by approximately half the tempo times the delay in seconds. This result is also relevant when musicians are far apart on a stage (e. g., the opposite ends of an opera stage), as each meter of separation adds about 3 msec of delay. This article is organized as follows. We begin with a review of previous work on network musical performance systems and musical collaboration at a distance with delay. We also review previous work on entrainment and coupled oscillators. We develop 76 Computer Music Journal