These models assume that there is an internal clock somewhere in the brain that produces steady intervals and allows us to tap regular intervals, either when synchronizing to a metronome or when continuing the isochronous beat after the metronome fades out. The mechanism has sources of noise (usually motor noise, e.g. the movement of the finger as cited above) and so a timing error creeps up, and unless there is an error correction mechanism, the error grows and timekeeping fails. The error correction mechanism in these two cases simply takes the perceived asynchrony in the previous beat, adds the interval that the internal clock produces, adds or subtracts a little bit, depending on whether the previous tap was early or late and then executes the next tap, etc. The phase error correction (if one beat is slightly misaligned) is thought to be subconscious and automatic (Stephan et al. 2002), whilst period error correction (tempo changes to faster or slower) requires conscious control.
Bispham describes interacting phase and period error correction mechanisms as forming the basic temporal framework for real-time interpersonal musical behaviours. (Op. cit. p. 130) Thaut (2005) writing on rhythm, music, and the brain argues that period is a key concept in timekeeping and that periodicity and the ability to adjust the period are central for interaction.
However, current phase error correction models pose a problem as they do not seem to work for situations where there are two, mutually adapting agents as in Himberg experiments (2011). This may be because they are simple descriptions of what goes on when an individual adjusts to a metronome and do not extend beyond that to the mutual, real-time adaptation and communication process with its complex dynamics, information, and emotion. In principle, the phase error correction/period error correction models that have been postulated for human timekeeping and synchronization should apply for two person interaction, but tests by Himberg show that more work needs to be done to improve them for them to work.
The dynamic systems models, the coupled oscillator models that Shockley et al. (1983), Marsh et al. (2009), and others have applied to entrainment capture the process of interpersonal synchrony much better. The dynamic systems model is not concerned with phase correction or period correction, as it does not deal with the constant adjustment of individual tap timings, but rather with interaction and the constant push and pull between the ‘oscillators’ (people). Most importantly, it seems that dynamic systems theories and models are able to handle verbal, non-verbal, musical performance, and dance, equally well, and they work with continuous data as well as discrete data, handling the great changes of pace, differing periodicities, and metrical levels that are present in real interactions.
Error correction has been considered outside of music psychology, in the study of everyday conversations and interactions with others, where we self-correct to be in time with others by gauging the intervals. Conversation analysts speak of ‘self-repair’ (Good 1990) as being essential to the maintenance of the ‘turn’. Edward T Hall (1983) drew upon the feedback metaphor to speak about knowing the proper interval for corrective action as the feedback rhythm. However, there is little work on error correction as a rhythmic property in human interaction and the dynamic systems model provides a more appropriate analysis of timekeeping in human engagement.