Biomedical Engineering Reference
In-Depth Information
6 Complex Oscillations
To describe the songs of birds using the songs of the canary and the chingolo
as the only examples might seem suspicious. We are all familiar with the wide
range of timbre that birds can show in their songs. Can they all be described
in terms of the simple mechanisms presented so far? The answer is negative,
as we shall discuss in this chapter. Unavoidably, we shall have to introduce
more subtle effects in order to widen the spectrum of phenomena that are
presented by different species and under different circumstances.
6.1 Complex Sounds
6.1.1 Instructions vs. Mechanics
The spectral description of the song of some birds reveals the existence of
phenomena more complex than the ones studied so far. In Fig. 6.1, two sono-
grams are displayed. They correspond to the songs of the eastern slaty thrush
(
Turdus subalaris
) [Straneck 1990a] and the grassland sparrow (
Ammodramus
humeralis
) [Straneck 1990b]. They are more complicated than the sonograms
described in the previous chapters.
In Fig. 6.1a, above the curve representing the fundamental frequency,
there is a second curve which has little in common with the first curve. It
neither begins nor ends when the first curve does, and the frequency values do
not correspond to multiples of those of the first curve, i.e., the second curve
does not represent a harmonic of the first one. The completely different way
in which these curves behave is a signature of the fact that the bird has used
both sources in an independent way in order to generate its vocalization.
Compared with Fig. 6.1a, Fig. 6.1b is misleadingly simple. Notice that
there is a qualitative change in the shape of the sonogram, indicated by the
arrow. The line that corresponds to the time evolution of what was the lowest
frequency at the beginning of the vocalization appears to be accompanied
after some time by new curves at its sides. Have we seen sonograms like
this one before? No, since these new “parallel” curves are not harmonics of
the previous fundamental frequency. Recall that the harmonic frequencies
are lines parallel to the curve representing the fundamental frequency (the
lowest curve) that are located at multiples of the fundamental frequency. In
