# Oscillators and Tempo

## Some Facts about Tempo Perception

• Rhythm is built up out of the intervals between events. A model must first deal with these intervals.
• People are not very good at estimating the length of a single interval, but they are good at judging relative lengths of successive intervals.
• In the real world, patterns are not perfectly isochronous; the intervals between the events vary.
• Given a (more or less) isochronous sequence of events, people can predict with some accuracy when the next event will occur, and they can detect with some accuracy a change in tempo.
• People are better at estimating the time of the next event and at detecting a change in tempo the longer the sequence they have heard.
• People are better at estimating the time of the next event and at detecting a change in tempo when the tempo of the pattern is near their preferred tempo.
• When a pattern is faster than preferred tempo, people overestimate the interval to the next event.
• When a pattern is slower than preferred tempo, people underestimate the interval to the next event.

## Oscillator Model of Time Perception (McAuley)

• Oscillators with particular preferred (resting) periods couple with events in the world.
• Phase coupling: When an event is close enough the zero phase of an oscillator, the oscillator adjusts its phase in the direction of the event.

• Period coupling: Oscillators speed up or slow down in response to sequences of input events.

• Period decay: Oscillator periods continually decay back toward the resting periods of the oscillators (though they may never reach them because of the effects of coupling with an input pattern).

• Time as phase
• In the model time cannot be measured directly; rather time is represented in terms of the periods of oscillators.
• The model predicts an input event when an activated oscillator reaches its zero phase.
• Because of the effects of period decay, oscillator models exhibit the same general behaviors as people: best performance with tempos close to preferred tempo, underestimation for slower patterns, overestimation for faster patterns.

Last updated: 30 November 1995
URL: http://www.indiana.edu/~gasser/osc_tempo.html