Tools for Music Information Retrieval and Playing - Intelligent Music Information Systems: Tools and Methodologies - page 137

Figure 23. Overview of the Beat tracking system proposed in (Goto, 2001)

reliable one. It should be noted in Figure 23 that
the drums line is not mandatory, but it helps the
algorithm furnishing more information.
In Figure 24 we present the algorithm results
on music without drums and in Figure 25 we
present the results on music with drums.
Goto (2001) proposes a quantitative measure
of the rhythmic difficulty, called the power-dif-
ference measure (see also Goto (1999) for further
information) that considers differences between
the power on beats and the power on other posi-
tions. This measure is defined as the mean of all the
normalized power difference ${diff}_{pow}(n)$
in the song:

onset-time vectors, the model determines the inter-
beat interval and predicts the next beat time. The
output of this stage is the provisional beat times
vector. The provisional beat times obtained is just
a single hypothesis of the quarter-note level.
To calculate the chord-changes, the frequency
spectrum is sliced into the point indicated by the
provisional beat times component. In this point
the dominant frequencies of the spectrum are
estimated by using a histogram of frequency
components. Chord-change possibilities are then
obtained by comparing dominant frequencies be-
tween adjacent point indicated by the provisional
beat times element.
The drum patterns are restricted to bass drum
and snare. A drum-sound finder detects the onset
time of the bass drum; the onset time of the snare
is found using a noise detector.
The second step handled ambiguous situations
when the beat-tracking cues are interpreted; a
multiple-agent model in which multiple agents
examine various hypotheses of the beat structure
in parallel was developed. Each agent uses it's
own strategy and makes various hypotheses. The
agent manager gathers all hypotheses and then
determines the final output on the basis of the most

Figure 24. Histogram for 40 songs without drum-
sounds (Wang, 2001)