ï~~An Auditory-Motor Model of Beat Induction
Neil Todd
Department of Music
Sheffield University
Sheffield, S10 2TN
UK
Chris Lee
Department of Music
City University
London, EC1V OHB
UK
Abstract
A model of beat induction is presented which attempts to simulate the processes involved in the auditory
system which give rise to the percept of a beat. The input to the model is an audio signal and the output is a
visual representation of the rhythm in form of a rhythmogram. Rhythmograms are of two kinds (1) timedomain rhythmograms, which resemble Lerdahl and Jackendoff's time-span reductions and (2) frequencydomain rhythmograms, which resemble Lerdahl and Jackendoff's metrical grids. [Research supported by a
grant from the MRC.]
1 Overview
system which is necessary in order to plan action in
advance. The time-domain process can also be
thought of as a kind of sensory memory since it is
able to account for a number of associated phenomena
such as temporal integration and backward masking.
2 Temporal Analysis
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model of beat induction.
Figure 1. A
Figure 1 shows an overview of the model which has
the following main components. (1) An auditory
periphery simulated with a cochlear model in
conjunction with an array of hair-cells; (2) a timedomain process, triggered by onsets, which carries
out a temporal segmentation of the activity in the
auditory nerve and gives information on the (i) stress
or loudness and (ii) the grouping of the neural events;
(3) a frequency-domain process, which carries out a
periodicity analysis and gives information on the
periodicity content of the rhythm; and (4) a sensorymotor filter which selects a tactus from the metrical
harmonics. The sensory-motor process is a
representation of the dynamic properties of the motor
Figure 2. A time-domain rhythmogram.
Figure 2 shows the response of the time-domain
analysis to a simple rhythm constructed from 50ms
tone bursts with inter-onset intervals of 250ms and
500ms. Note that this has captured the principle of
grouping by temporal proximity since the tone bursts
have been clearly grouped in threes. Further, the last
event in a group is represented as more important
thus also capturing the well documented phenomenon
of interval produced accents. This last feature is vital
for determining the phase of the metrical grid. The
degree of relative accent is dependent on the relative
and absolute intervals between events and thus on the
overall tempo.
3 Periodicity Analysis
Figure 3 shows the response of the frequency-domain
analysis to the same rhythm. The naturalness of
placing pitch and rhythm in the same map is evident.
Foot-tapping
88
ICMC Proceedings 1994
