Beat tracking is an important initial step in computer emulation of human music understanding, since beats are fundamental to the perception of Western music. Even if a person cannot completely segregate and identify every sound component, he can nevertheless track musical beats and keep time to music by hand-clapping or foot-tapping. We therefore first build a computational model of beat perception and then extend the model, just as a person recognizes higher-level musical events on the basis of beats.
Most previous beat tracking systems [Dannenberg and Mont-Reynaud, 1987] [Allen and Dannenberg, 1990] [Rosenthal, 1992] [Desain and Honing, 1994] have dealt with MIDI as their input. Their reliance on MIDI, however, limited the input source to electronic instruments. Those systems generally dealt with classical works, in particular piano solo. Although some systems [Katayose et al., 1989] [Vercoe, 1994] dealt with audio signals, they were not able to process music played on ensembles of a variety of instruments, especially drums.
Our beat tracking system, called BTS,
processes monaural acoustic signals
that contain sounds of various instruments in real time.
BTS deals with popular music
in which drums maintain the beat.
Not only does
BTS predict the temporal position of the next beat (beat time);
it also determines whether the beat is strong or weak (beat type)
.
In other words, BTS can track beats at the half-note level.
Our previous system (PreBTS) [Goto and Muraoka, 1994] based on multiple-agent architecture had the following problems: (1) PreBTS assumed only the case where a bass drum and a snare drum usually sounded on the strong and weak beats, respectively. (2) PreBTS sometimes failed to infer correct beat type when characteristic frequencies of drum-sounds were not acquired correctly. (3) PreBTS implemented a mechanism for correcting a typical beat-tracking error, which consisted of having agent-pairs track alternative hypotheses that differed only in phase. Though effective, this system was nevertheless not sufficiently flexible for certain situations. (4) PreBTS occasionally made double-tempo or half-tempo errors.
Our solutions to these problems are outlined as follows:
(1)
BTS leverages musical knowledge
represented as pre-registered drum patterns
of the bass drum and the snare drum.
These patterns represent
how drum-sounds are used in a large class of popular music.
The results of matching
these patterns with the currently detected drum pattern
make it possible to determine the beat type
and which note-value a beat corresponds to.
(2)
To improve the method of detecting the snare drum,
BTS finds noise components
that are widely distributed along the frequency axis,
since such a frequency profile is typical of the snare drum.
(3)
Multiple agents
that track beats according to different strategies
utilize auto- and cross-correlation
of detected onset times to predict the next beat.
Each agent first calculates an inter-beat interval,
and then determines the appro- priate beat position
by evaluating every beat-position possibility
that the obtained inter-beat interval could support.
(4)
Agents are grouped into pairs;
in each pair one agent tries to track beats
at a relatively higher tempo and the other tracks them at a lower tempo.
These two agents then inhibit each other.
This enables one agent to track the correct beats
even if the other agent tracks beats with double or half the correct tempo.
To perform this computationally-intensive task in real time, BTS has been implemented on a parallel computer, the Fujitsu AP1000. In our experiment with eight pre-registered drum patterns, BTS correctly tracked beats in 42 out of 44 songs sampled from compact discs. Moreover, we have developed an application with BTS that displays a computer graphics dancer whose motion changes with musical beats in real time.
Masataka Goto