Statistical modeling and analysis have been applied to different music
related fields. One of them is sound synthesis and analysis. Sound can be
represented as a real-valued function of time. This function can be
sampled at
a small enough rate so that the resulting discrete version is a good
approximation of
the continuous one. This permits one to study musical sounds as a discrete
time series, an entity for which  many statistical techniques are
available. Physical modeling suggests that many musical instruments'
sounds may be 
characterized by a 
deterministic periodic and stochastic signal model. 
In this paper the interest is in separating these two elements of
the sound and finding parametric representations with musical
meaning. To do so a local harmonic model  that tracks  changes
in pitch and in the amplitudes of the harmonics is fit. Deterministic
changes
in the signal, such as pitch change, suggest that different temporal
window sizes 
should be considered. Ways to choose appropriate window sizes are
studied. Amongst other things our analysis provides estimates of the
harmonic
signal and of the noise signal. Different musical composition
applications may be based on the estimates.