Vocal production mechanisms in the budgerigar (Melopsittacus undulatus): The presence and implications of amplitude modulation

Abstract

In this paper acoustic evidence is presented for the presence of amplitude modulation in budgerigar (Melopsittacus undulatus) contact calls and learned English vocalizations. Previously, acoustic analyses of budgerigar vocalizations have consisted solely of visual inspection of spectrograms or power spectra (derived from Fourier transformation). Such analyses have led researchers to conclude that budgerigar vocalizations are primarily frequency-modulated, harmonic vocalizations. Although budgerigar calls have been shown to contain regions that are modulated in amplitude, the implications of this fact have been largely ignored. Amplitude modulation, the nonlinear interaction between two separate signals that results in the creation of new, heterodyne (sum and difference) frequencies, can produce a very complex Fourier spectrum that may resemble that produced by a harmonic vocalization. In this paper, the acoustic principles necessary for identifying amplitude modulation present in signals are outlined, and followed by data demonstrating that amplitude modulation is a prominent feature not only of natural budgerigar contact calls, but also of their learned English vocalizations. It is illustrated how analyzing a vocalization that contains amplitude modulation as if it were harmonic can result in misinterpretations of the acoustic and physical properties of the sound and sound source. The implications of amplitude modulation for studies of the ontogenetic, physical, and neural basis of budgerigar vocalizations are discussed, and a potential model for how the budgerigar syrinx may function to produce amplitude modulation is proposed.

Full text

Vocal production mechanisms in the budgerigar
(Melopsittacus undulatus): The presence and implications
of amplitude modulation
Pamela Banta Lavenex
a)
Program in Neuroscience, 611 Gould-Simpson, University of Arizona, Tucson, Arizona 85721
~Received 1 September 1998; revised 1 April 1999; accepted 9 April 1999!
In this paper acoustic evidence is presented for the presence of amplitude modulation in budgerigar
~Melopsittacus undulatus! contact calls and learned English vocalizations. Previously, acoustic
analyses of budgerigar vocalizations have consisted solely of visual inspection of spectrograms or
power spectra ~derived from Fourier transformation!. Such analyses have led researchers to
conclude that budgerigar vocalizations are primarily frequency-modulated, harmonic vocalizations.
Although budgerigar calls have been shown to contain regions that are modulated in amplitude, the
implications of this fact have been largely ignored. Amplitude modulation, the nonlinear interaction
between two separate signals that results in the creation of new, heterodyne ~sum and difference!
frequencies, can produce a very complex Fourier spectrum that may resemble that produced by a
harmonic vocalization. In this paper, the acoustic principles necessary for identifying amplitude
modulation present in signals are outlined, and followed by data demonstrating that amplitude
modulation is a prominent feature not only of natural budgerigar contact calls, but also of their
learned English vocalizations. It is illustrated how analyzing a vocalization that contains amplitude
modulation as if it were harmonic can result in misinterpretations of the acoustic and physical
properties of the sound and sound source. The implications of amplitude modulation for studies of
the ontogenetic, physical, and neural basis of budgerigar vocalizations are discussed, and a potential
model for how the budgerigar syrinx may function to produce amplitude modulation is proposed.
© 1999 Acoustical Society of America. @S0001-4966~99!03607-3#
PACS numbers: 43.80.Ka @WWLA#
INTRODUCTION
A. Budgerigar vocal mechanisms
Natural budgerigar ~parakeet! vocalizations, including
contact calls and some warble song elements, have been de-
scribed and investigated as frequency-modulated, harmonic
signals ~Heaton et al., 1995; Brittan-Powell et al., 1997a,b!.
Studies have examined the ontogeny of spectrally repre-
sented frequency modulations in calls ~Brittan-Powell et al.,
1997a; Hall et al., 1997!, the effects of syringeal denervation
on spectral characteristics of calls ~Heaton et al., 1995; Shea
et al., 1997!, and whether production in helium alters spec-
tral features of calls produced by syringeal denervated and
normal budgerigars ~Brittan-Powell et al., 1997b!. Acoustic
features of budgerigar vocalizations have been compared to
those of Gray parrots ~Psittacus erithacus, Turney et al.,
1994!, and humans ~Silaeva, 1998!. These studies, however,
analyzed only the frequency spectra derived via Fourier tech-
niques, specifically, frequency by time ‘‘spectrograms’’ or
amplitude by frequency ‘‘power spectra.’’
Budgerigar contact calls, however, also display signifi-
cant modulation in amplitude ~Dooling and Searcy, 1981,
1985!. A call may contain several frequency changes, but
amplitude fluctuations are ubiquitous and easily identified in
displays of both the gross temporal envelope and amplitude
waveform @Fig. 1~A! and ~B!, respectively; amplitude by
time representations of the signal#. As demonstrated here,
some of this amplitude fluctuation is due to nonlinear ampli-
tude modulation. When amplitude modulation is present in a
signal, its Fourier spectrum contains additional frequency
components that are produced not by the primary source~s!,
but rather by nonlinear interactions between two originally
independent signals ~Nowicki and Capranica, 1986a, b;
Bradbury and Vehrencamp, 1998!. To date, no study of bud-
gerigar calls or warble song has explained the complex array
of observed spectral components, investigated whether the
observed spectral components are generated by a mechanism
of amplitude modulation, nor examined how amplitude
modulation develops ontogenetically, is produced, or is af-
fected by perturbations of the vocal production system ~e.g.,
neural or mechanical!. Given the spectral complexity of vo-
calizations that can be produced by amplitude modulation,
perturbations affecting that modulation may be difficult or
impossible to detect in a cursory inspection of a Fourier
spectrum ~either spectrograms or power spectra!. Indeed,
cursory analyses of vaguely harmonic-like signals have led
to inaccurate interpretations of the acoustic, physical, and
neural mechanisms underlying avian vocalizations that con-
tain amplitude modulation @e.g., in chickadees ~Greenewalt,
1968!, and in budgerigars ~Heaton et al., 1995 and Brauth
et al., 1997!#.
The fact that budgerigars produce amplitude-modulated
signals is itself significant. Budgerigars have a syrinx with
one set of opposable membranes @like all parrots, but unlike
a!
Present address: Pamela Banta Lavenex, Ph.D., Neurobiology, Physiology
and Behavior, 196 Briggs Hall, University of California at Davis, Davis,
CA 95616; Electronic mail: pabanta@ucdavis.edu
491 491J. Acoust. Soc. Am. 106 (1), July 1999 0001-4966/99/106(1)/491/15/$15.00 © 1999 Acoustical Society of America

passerine birds that have a bipartite syrinx with two sets of
membranes ~Evans, 1969; Nottebohm, 1976; Gaunt and
Gaunt, 1985; Suthers, 1997!#, and only two pair of intrinsic
syringeal muscles ~Evans, 1969; Gaunt and Gaunt, 1985!.
Moreover, parrots are thought not to have independent con-
trol of their syringeal membranes ~Nottebohm, 1976; Heaton
et al., 1995; Brittan-Powell et al., 1997b; Brauth et al.,
1997!. Learning how budgerigars produce two independent
source signals that interact nonlinearly to produce amplitude
modulation will further our understanding of syringeal
mechanisms that underlie complex avian vocal productions.
In this paper, I show that budgerigars produce amplitude
modulation both in their natural contact calls and when mim-
icking human vowel sounds. First, I redescribe key acoustic
and spectral features that allow identification of a sound pro-
duced by amplitude modulation, and how nonlinear interac-
tions generate new frequencies. I use the term ‘‘redescribe’’
intentionally, because I review material from two overlooked
papers by Nowicki and Capranica ~1986a, b! on the exis-
tence and implications of amplitude modulation in avian vo-
calizations. Moreover, because a thorough understanding of
acoustic principles is necessary to evaluate the vocalizations
I present, I also describe two other signal types that must be
distinguished from amplitude-modulated ones in the analysis
of any vocalizations: Vocalizations known as harmonic, and
those produced from a linear interaction ~or beating! between
harmonic signals.
B. Acoustic characteristics of signals containing
harmonics, amplitude modulation, and beating
The relationship between the amplitude waveform and
its Fourier spectrum is critical for understanding the physical
nature of any sound. The amplitude waveform is the true
representation of a signal in the time domain, and is free of
mathematical transformation. The wave shape of the ampli-
tude waveform displays how frequency, amplitude, and
phase of a signal vary with time. A Fourier transformation,
by definition, transforms the signal into the frequency do-
main. A Fourier analysis decomposes each user-specified
time window of an amplitude waveform into a series of pure
sinusoids that, when added, produce the observed waveform.
For any signal, conclusions based on independent analyses of
time and frequency domains must concur. I thus describe the
relationship between time and frequency domains for signals
that contain harmonics, amplitude modulation, and beating.
1. Harmonics
A harmonic signal is one in which the amplitude wave-
form repeats itself exactly ~i.e., is periodic!. A pure tone or
sinusoid ~a signal composed of only one frequency! is the
simplest form of harmonic sound, and is represented in a
Fourier spectrum ~i.e., either a spectrogram or a power spec-
trum! by a single component at the frequency the waveform
repeats; this frequency is known as the fundamental fre-
quency.
More complex, nonsinusoidal harmonic waveforms ~sig-
nals composed of multiple frequencies, termed multi-
frequency harmonic signals! are represented in a Fourier
spectrum by an array of evenly spaced energy components
~also known as a harmonic ‘‘stack’’ in a spectrogram!. The
fundamental frequency of the vocalization ~known as the
first harmonic! is usually the lowest frequency component;
successive frequency components are located at exact-integer
multiples of the fundamental. A multi-frequency harmonic
vocalization with a waveform that repeats every 5 ms thus
has a fundamental frequency of 200 Hz and component fre-
quencies at 200, 400, 600 Hz, n3 200Hz, the fundamental
may also be calculated as the highest common denominator
of the component frequencies. A sound is classified as ‘‘har-
monic’’ because, and only because, it repeats exactly in the
time domain. Perfectly harmonic biological signals ~i.e.,
where repetition is exact from one period to the next!, how-
ever, are rare, and some fluctuation usually exists in their
periodicity. This fluctuation, or ‘‘quasi-periodicity’’ ~Titze,
1994!, can cause higher harmonics in natural signals to be at
near rather than exact-integer multiples of the fundamental
frequency ~e.g., if a fundamental frequency is 20062 Hz, the
first several harmonics would be at close multiples of 200,
but the 10th harmonic could be located at 2000620 Hz!.
Figure 2~A! shows the amplitude waveform of a repre-
sentative multi-frequency harmonic signal with a fundamen-
tal frequency of 183 Hz, and Fig. 3~A! is a schematic of the
power spectrum ~a representation of the signal after Fourier
transformation! that would be generated by this signal. The
waveform repeats identically every 5.5 ms, and the harmon-
ics of the fundamental frequency are at 366, 549, and 732 Hz
in the power spectrum.
2. Amplitude modulation
An amplitude-modulated vocalization is produced when
one signal, the carrier signal, is modulated in amplitude by a
second, the modulating signal. In general, the carrier signal
has the greater frequency, and is modulated by the lower
FIG. 1. A budgerigar’s contact call ~Forest!. ~A! The entire amplitude en-
velope. ~B! Amplitude waveform of a 20-ms expanded time window from
the call in ~A!~173–193 ms! showing aperiodic fluctuations of the ampli-
tude. Note the extensive modulation of amplitude that occurs throughout the
call.
492 492J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

frequency modulating signal. Because modulation is a non-
linear process ~modeled by multiplication of sinusoids repre-
sented by polynomials, see below!, interactions between the
carrier and modulating signals create new frequencies not
present in either initial signal. When subject to Fourier trans-
formation, the new components are represented as hetero-
dyne sidebands ~sum and difference frequencies! in the spec-
trum. Thus, two source signals ~periodic or aperiodic!
interact nonlinearly to produce a resultant output waveform
that is not a harmonic series ~i.e., it has no single fundamen-
tal frequency!, and should not be represented by a harmonic
array of components. The Fourier spectrum contains a set of
component frequencies that, when summed, produce the ob-
served waveform, but those components are not integer mul-
tiples of a fundamental frequency. Ascribing their origin to a
simple harmonic process is incorrect and misleading regard-
ing the acoustic nature of the signal and the physical nature
of the source.
The process of amplitude modulation is not synonymous
or analogous to the simple variation in amplitude of a signal
with time that can be observed in a display of the gross
temporal envelope @Fig. 1~A!#. Such modulations may or
may not be due to the nonlinear process of amplitude modu-
lation, but no conclusions can be drawn from this level of
analysis. Amplitude modulation occurs uniquely when two
signals interact nonlinearly and as a result produce new het-
erodyne sideband components and a waveform that increases
and decreases in amplitude. Some linear processes ~e.g.,
simple summation that occurs during beating!, can also pro-
duce a waveform that appears modulated in amplitude ~see
below!, but do not produce the physical phenomenon of am-
plitude modulation nor the new heterodyne sideband compo-
nents. Thus, the presence of a modulated-amplitude wave-
form may indicate, but is not conclusive evidence of, an
amplitude modulation process. That verification requires de-
tailed analysis of the frequency composition of the Fourier
spectrum.
FIG. 2. Amplitude waveforms generated electronically using SIGNAL sound-
analysis software ~Beeman, 1996!. ~A! The harmonic signal generated by
adding four sinusoidal signals ~183, 366, 549, and 732 Hz!, each with a
0.1-mV dc component ~Bradbury and Vehrencamp, 1998! and an initial
amplitude of 1.0 V. ~B! The amplitude-modulated signal generated by mul-
tiplying two sinusoidal signals ~183 and 2017 Hz!, each with a 0.1-mV dc
component and an initial amplitude of 1.0 V. ~C! The amplitude-modulated
signal generated by multiplying two multi-frequency harmonic signals ~183
Hz with 4 harmonics and 2017 Hz with 3 harmonics!, each with a 0.1-mV
dc component and an initial amplitude of 1.0 V. ~D! The beat signal gener-
ated by adding together two sinusoidal signals ~1822 and 2005 Hz!, each
with a 0.1-mV dc component and an initial amplitude of 1.0 V.
FIG. 3. Schematic Fourier power spectra for signals illustrated in Fig. 2. ~A!
Power spectrum of the multi-frequency harmonic signal of Fig. 2~A!. The
fundamental repeating unit, or fundamental frequency, is designated by the
f
1
component at 183 Hz. Spacing between each component in the spectrum
is also 183 Hz, and each component is found at an integral multiple of 183
Hz ~e.g., 366, 549, and 732 Hz!. ~B! Power spectrum of the amplitude-
modulated signal of Fig. 2~B!. dc components in both original signals are
signified by component frequencies in the spectrum that represent the fun-
damental frequencies of both input signals, f
1
and f
2
~183 and 2017 Hz,
respectively!. Sidebands occur at f
2
2 f
1
and f
2
1 f
1
. ~C! Power spectrum of
the amplitude-modulated signal of Fig. 2~C!. dc components in both original
signals are signified by component frequencies in the spectrum at f
1
and f
2
~183 and 2017 Hz, respectively!. The multi-frequency harmonic nature of
both input signals is illustrated by the presence of numerous component
frequencies at integral multiples of the modulating frequency, f
1
, and mul-
tiple sidebands above and below the carrier frequency, f
2
. A second har-
monic of the carrier frequency is at 2f
2
~4034 Hz!, with numerous sidebands
above and below it. A third harmonic of the carrier frequency would be at
3f
2
~6051 Hz!, with its full complement of sidebands, but is omitted for
clarity. ~D! Power spectrum of the beat signal of Fig. 1~D!. This spectrum
shows that the beat signal is generated from the linear interaction ~addition!
of two input signals: The only two components in the spectrum are those of
the original input signals, f
1
and f
2
~1822 and 2005 Hz, respectively!.
493 493J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

Mathematically, frequencies that result from the nonlin-
ear process of amplitude modulation can be predicted by
multiplying the two original input signals. The exact spectral
composition of the final output signal depends on two critical
features: ~1! whether the carrier and/or modulating signals
are single frequency ~i.e., pure tone! or multi-frequency har-
monic signals; and ~2! whether a direct current ~dc! compo-
nent exists in either signal. ~Note: dc components are typi-
cally generated by a unidirectional air flow past a sound-
generating organ. All voiced vocalizations, such as the vowel
sounds and contact calls discussed here, thus have a dc com-
ponent manifest in the spectrum as an energy component at
zero Hz; Bradbury and Vehrencamp, 1998.! Consider a
sound constructed from single-frequency harmonic carrier
and modulating signals, each with a dc component, described
by two sine waves with the formulas
Modulating Signal5signal 1:
v
1
~
t
!
5 A1 B cos2
p
f
1
t,
Carrier Signal5signal 2:
v
2
~
t
!
5 C1 D cos2
p
f
2
t,
where f
2
and f
1
are the carrier and modulating signals, re-
spectively, and f
2
> f
1
; A and C represent the dc components
of each signal, and B and D the amplitudes. For simplicity, I
omit the 2
p
symbol from subsequent equations. Multiplica-
tion of these two formulas yields
v
1
~
t
!
3
v
2
~
t
!
5 AC1BCcos f
1
t1 AD cos f
2
t
1 BDcos f
1
t cos f
2
t. ~1!
From simple geometric identity, two cosine terms may
be represented as
cosx
*
cos y5 1/2 cos
~
x1 y
!
1 1/2cos
~
x2 y
!
, ~2!
so that the above equation is expressed as
v
1
~
t
!
3
v
2
~
t
!
5 AC1BCcos f
1
t1 AD cos f
2
t
1 1/2BDcos
~
f
2
1 f
1
!
t
1 1/2BDcos
~
f
2
2 f
1
!
t. ~3!
Equation ~3! provides terms for the features defining an
amplitude-modulated process: First, both the carrier (f
2
) and
the modulating (f
1
) signals are present in the output signal,
albeit with altered amplitudes, and are thus identifiable by
their distinct component frequencies in the spectrum. Sec-
ond, two sum and difference frequencies are generated that
were not present in either input signal, and are found in the
spectrum equidistant above and below the carrier signal, at
f
2
1 f
1
and f
2
2 f
1
. These frequencies, or sidebands, create a
spectrum characteristic of amplitude-modulated signals with
energy distributed symmetrically on either side of the carrier
signal ~Nowicki and Capranica, 1986a, b; Bradbury and Ve-
hrencamp, 1998!. The presence of the original input signals,
f
1
and f
2
, in the output signal depends upon the existence of
dc components associated with each input signal. If neither
input signal has a dc component ~if A5 C5 0!, then only the
sum and difference frequencies (f
2
1 f
1
and f
2
2 f
1
! are pro-
duced. If f
1
but not f
2
has a dc component, only f
2
will be in
the output signal, etc. Determining amplitudes of each output
component is theoretically possible from the mathematical
equations; practically, the exact amplitude of each indepen-
dent input signal is difficult to determine for a biological
signal ~unless measured just above the source@s#!. I thus do
not further discuss amplitude values for spectral components.
Figure 2~B! shows an amplitude waveform, and Fig.
3~B! the spectral frequencies generated by multiplying two
single-frequency harmonic signals, one at 2017 Hz and one
at 183 Hz, each with a dc component. Both signals are rep-
resented in the output signal waveform, and direct measure
of the waveform yields components that correspond to the
fundamental frequencies of the carrier and modulating sig-
nals: In Fig. 2~B!, the 2017-Hz frequency is clearly identifi-
able, and is modulated in amplitude at a rate of 183 Hz,
producing the characteristic amplitude-modulated waveform
envelope. In Fig. 3~B!, the 2017-Hz frequency is represented
by a centrally located component surrounded on either side
by components at 183-Hz intervals; note the four spectral
components at the mathematically predicted frequencies: f
1
,
f
2
, f
2
2 f
1
, and f
2
1 f
1
.
Consider now two multi-frequency harmonic signals,
each with a dc component:
Modulating Signal5 signal 1:
v
1
~
t
!
5 A1 B
1
cos f
1
t1 B
2
cos2f
1
t1 •••,
1B
m
cosmf
1
t,
Carrier Signal5signal 2:
v
2
~
t
!
5 C1 D
1
cos f
2
t1 D
2
cos2f
2
t1 •••,
1D
n
cosnf
2
t,
where f
2
> f
1
, m and n are integers ~1,2,3,...! representing
the harmonics of each multifrequency signal, A and C are the
dc components, and B and D the amplitudes.
Multiplication of these two signals yields
v
1
~
t
!
3
v
2
~
t
!
5 AC1B
1
Ccos f
1
t1 AD
1
cos f
2
t
1 1/2B
1
D
1
cos
~
f
2
1 f
1
!
t1 1/2B
1
D
1
cos
~
f
2
2 f
1
!
t1 CB
2
cos2f
1
t1 1/2B
2
D
1
cos
~
f
2
1 2f
1
!
t1 1/2B
2
D
1
cos
~
f
2
2 2f
1
!
t
1 AD
2
cos2f
2
t1 1/2B
1
D
2
cos
~
2f
2
1 f
1
!
t
1 1/2B
1
D
2
cos
~
2f
2
2 f
1
!
t1 ••• . ~4!
Equation ~4! provides terms for three defining features
of this type of amplitude modulated signal: First, because
each input signal has a dc component, components that cor-
respond to the fundamental frequencies of both the carrier
(f
2
) and modulating (f
1
) signals are present in the output
signal, and are represented by components at these frequen-
cies in Fig. 3~C!. Second, output signal components at fre-
quencies corresponding to harmonics of each input signal
occur at integer multiples of the input signals ~i.e.,
CB
m
cosmf
1
t, AD
n
cosnf
2
t!. Third, sum and difference fre-
quencies corresponding to each cross-product,
1/2B
m
D
n
cos(nf
2
1mf
1
)t and 1/2B
m
D
n
cos(nf
2
2mf
1
)t, pro-
duce multiple sidebands, spaced mf
1
Hz above and below
each integer multiple of the carrier signal. These sideband
frequencies are again products of the nonlinear multiplica-
494 494J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

tion process of amplitude modulation, and are not in the
original input signals.
Figures 2~C! and 3~C! show the complex amplitude
waveforms and spectral frequencies generated by multiply-
ing two multifrequency harmonic signals with fundamental
frequencies of 2017 Hz ~with 3 harmonics! and 183 Hz ~with
4 harmonics!, respectively, each with a dc component @using
Eq. ~4!#. In Fig. 3~C!, note the components that correspond
to fundamental frequencies and harmonics of the original
input signals (f
1
and f
2
, mf
1
and nf
2
, respectively!, and the
multiple sidebands above and below each harmonic of f
2
.
When discussing amplitude-modulated signals, terms
such as ‘‘fundamental frequency’’ and ‘‘harmonic~s!’’ are
neither appropriate nor correct. An amplitude-modulated sig-
nal is not a harmonic signal: It has no fundamental frequency
nor harmonics of that fundamental. Although the terms fun-
damental frequency and harmonic may be appropriate, and
even helpful, for describing the separate carrier and modu-
lating signals, they are not appropriate for describing the
resultant amplitude-modulated signal. In the above explana-
tions, I have used these terms only to describe how specific
components of an amplitude-modulated spectrum arise.
3. Beating
Beating occurs when two signals sum ~a linear interac-
tion!. Beating ~e.g., between signals of 2005 and 1822 Hz!,
produces a waveform that waxes and wanes in amplitude
periodically, thus resembling an amplitude-modulated signal
@compare Fig. 2~B! and ~D!#. The rate at which the envelope
of this amplitude waveform ‘‘beats’’ ~or waxes and wanes!
equals the difference between the two signals ~here, 183 Hz!.
Fourier spectra of signals produced by beating and amplitude
modulation, however, are very different @compare Fig. 3~B!
and ~D!#. The Fourier spectrum of a beat signal contains
components at, and only at, the exact frequencies of the two
original signals, in contrast to the sum and difference fre-
quencies produced by amplitude modulation. Although beat-
ing can also create what are known as difference or combi-
nation tones ~i.e., perception of a 183-Hz signal!, these tones
are perceptual illusions produced solely by nonlinearities in
auditory or neural systems of the receiver. These tones are
not part of the output waveform ~Roederer, 1995!, and thus
not represented in the Fourier spectrum.
C. The current study
Acoustic evidence for the presence of amplitude modu-
lation in both budgerigar contact calls and English vowel
productions is presented below. In the discussion that fol-
lows, implications of the presence of amplitude modulation
are considered, specifically with respect to the ontogeny of
budgerigar vocalizations, and the neural and mechanical
bases of vocal production in budgerigars.
I. METHODS
A. Subjects
I present vocalizations from four male budgerigars.
Three birds, Buddy, Forest, and Frans, were removed from a
breeding aviary at fledging ~4–5 weeks! and subsequently
trained to produce human vocalizations. Buddy and Forest
were housed alone in cages, but in auditory and visual con-
tact with humans and other birds. Frans was housed in a
soundproof isolation box, with little auditory or visual con-
tact with other birds. Frans had at least1hofhuman inter-
action 5–6 days/week, and was exposed to auditory tapes ~of
either a human reading or soft classical and easy-listening
music! for 6–8 h/day. A fourth male, M03, neither hand-
raised nor trained on English vocalizations, was obtained
from a commercial breeding flock and subsequently caged
with 11 other budgerigars in various combinations ~two–five
birds at a time!. All birds received food and water ad libitum.
M03’s conspecific vocalizations allowed comparisons be-
tween flock-reared and human-reared birds ~i.e., Buddy, For-
est, and Frans!.
B. Training of English vocalizations
Buddy, Forest, and Frans were exposed to and trained to
produce English words and phrases via the Model/Rival
~M/R! technique ~Todt, 1975; Pepperberg, 1981!, or a modi-
fied version ~using only one trainer; Banta and Pepperberg,
1995; Banta, 1998!. Each bird was trained for ;1 h/day, 5–6
days/week, from about 6 weeks of age. Buddy, Frans, and
Forest were recorded in the laboratory during training and
while vocalizing freely on a perch or in their cage when they
were fully adult ~at least 6 months old!, and when the target
vocalization was produced in a clear and stable manner. Tar-
get vocalizations were single words and phrases, e.g., ‘‘pa-
per,’’ ‘‘cork,’’ ‘‘wood,’’ ‘‘bear,’’ and ‘‘truck.’’ Birds also
acquired vocalizations used during training and social inter-
actions, e.g., ‘‘kiss,’’ ‘‘climb,’’ ‘‘tickle,’’ ‘‘you’re right,’’
‘‘good boy,’’ ‘‘okay,’’ and ‘‘come here.’’ The primary tutors
for Buddy, Forest, and Frans were humans, but all three birds
were at times in auditory contact with other birds ~both bud-
gerigars and Gray parrots!; thus, they may have also learned
some vocalizations from other birds. M03 received no formal
human tutoring.
C. Audio recordings
Vocalizations were recorded on Maxell XLII audio tapes
with a Sony TCM 5000 tape recorder and AKG C541 EB,
Sennheiser ME 66, or Sennheiser ME 67 microphones. M03
was recorded while isolated in his cage. M03’s and human
~PB’s! vocalizations were recorded with Fuji DR-II audio
tapes on a Marantz PMD221 portable cassette recorder, and
with an Audio-Technica AT835b condenser microphone.
D. Acoustic analyses
Acoustic analysis methods were as follows: Frans’ and
Forest’s vocalizations were filtered at ,400 Hz and at
.10000 Hz with a Hewlett-Packard bandpass filter ~model
8056A!. Buddy’s vocalizations were produced at a greater
amplitude, and contained less background noise than those of
the other birds ~he often sat closer to the microphone and
preferred to vocalize when it was quiet!, and thus did not
require filtering. Frans’ and Forest’s recordings were digi-
tized with a Kay Elemetrics 5500 DSP sona-graph ~20 480
495 495J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

Hz sampling rate, 8-kHz frequency range!. Buddy’s, M03’s,
and PB’s recordings were digitized with
SIGNAL ~Beeman,
1996! sound-analysis software ~25 000-Hz sampling rate,
8-kHz frequency range!. M03’s and PB’s vocalizations were
first alias filtered above 10 000 Hz. Spectra and amplitude
waveforms were analyzed on the Kay and with
SIGNAL. For
English words, 40-ms sections of vowels were isolated and
analyzed; for contact calls, entire vocalizations and sections
of various lengths ~see Sec. II! were analyzed. Power spectra
were calculated with a 1024-point transform length that re-
sulted in 20-Hz resolution for the vocalizations of Frans and
Forest, and 24.4-Hz resolution for the vocalizations of
Buddy, M03, and PB ~differences in frequency resolution are
due to differences in sampling rate!. Spectrograms were cal-
culated with various transform lengths ~see Sec. II!.
II. RESULTS
A. Budgerigar contact calls exhibit amplitude
modulation
Figure 4~A!–~D! show wide- and narrow-band spectro-
grams, a power spectrum, and an amplitude waveform, re-
spectively, from flock-reared M03’s contact call. Note the
harmonic-like stack of component frequencies in the spectro-
grams in the region demarcated by the time cursors @Fig.
4~A!,~B!#. A 1024-point power spectrum of the last 10 ms of
this region @82–92 ms, where the stack occurs; Fig. 4~C!#
also reveals a harmonic-like spectrum, with energy compo-
nents at apparently regular intervals from 723–6973 Hz. In
the spectrum, however, the maximal energy occurs at 3106,
not 723, Hz. Moreover, although the first and second com-
ponent frequencies at 723 and 1484 Hz are integer or near-
integer multiples of 742 Hz ~0.97 and 2.0, respectively!,
none of the other spectral components is an integer multiple
of 742 Hz ~e.g., 3106/74254.186!, a pattern inconsistent
with a harmonic signal. Instead, energy components are
evenly spaced at 742 Hz on either side of 3106 Hz, a pattern
consistent with an amplitude-modulated signal having a
dominant ~i.e., component with greatest energy! or carrier
signal of 3106 Hz. Also, an integer multiple of this dominant
component ~corresponding to the second harmonic of the
carrier frequency! can be identified at 6211 Hz ~6211/3106
52.000!, as a local energy peak with components located
nearly symmetrically 723 Hz below and 762 Hz above this
integer multiple component. If this vocalization were a har-
monic series with a fundamental frequency of 3106 Hz, no
other frequency components of significant energy would be
found below the fundamental frequency or between the fun-
damental frequency and its second harmonic. At this point in
M03’s call, however, numerous components lie below this
dominant component, and between the dominant component
and its second harmonic, a pattern inconsistent with a har-
monic signal.
Direct inspection of the amplitude waveform @Fig.
4~D!#, reveals a high-frequency signal modulated in ampli-
tude at a much slower rate. The 20 ms of signal that precedes
the stack of frequencies ~only the last 10 ms shown! is char-
acterized by a waveform of relatively constant frequency
~;3850 Hz!.At;78 ms, amplitude of the oscillation de-
creases rapidly, but the waveform frequency remains con-
stant. At ;83 ms, the waveform frequency drops slightly to
3349 ~694! Hz, and its amplitude begins to increase and
decrease periodically, at a frequency of 717 ~667! Hz. Both
the dominant frequency and rate of modulation in the wave-
form correspond well to the dominant frequency component
~3106 Hz! and the intervals between components ~742 Hz! in
the spectrum, respectively, corroborating that the spectrum
corresponds to an amplitude-modulated signal.
Of particular interest in this vocalization is the upper
sideband at 3848 Hz @Fig. 4~C!#, which is nearly identical to
the dominant frequency of the portion of the signal immedi-
ately preceding this amplitude-modulated segment ~at
FIG. 4. M03’s contact call. ~A! Wideband spectrogram ~500-Hz analysis
filter!. Time cursors demarcate the 20-ms section displayed in the amplitude
waveform @~D!#. ~B! Narrow-band spectrogram ~150-Hz analysis filter!.
Time cursors demarcate the same region as in ~A!. ~C! 1024-point power
spectrum of the last 10-ms region of the waveform with periodic modulation
in amplitude @~D!,82–92ms#. The dominant component is at 3106 Hz, with
components evenly spaced 742 Hz above and below. Components at 723
and 1484 Hz are at integral multiples of the modulating signal. ~D! Ampli-
tude waveform of the 20-ms period demarcated by cursors in ~A! and ~B!,
from which the 10-ms period for the power spectrum in ~C! was taken. The
dominant ~carrier! signal measured directly from the last 10 ms of this
waveform is 3349 ~694! Hz; the modulating signal is 717 ~667! Hz.
496 496J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

;3850 Hz!. Indeed, in the narrow-band spectrogram @Fig.
4~B!# the two segments appear almost continuous. This ex-
ample demonstrates how an incorrect inference regarding the
activity of the source ~e.g., the frequencies produced! can
arise when only the Fourier spectrum is analyzed.
Forest’s contact calls ~as well as those of seven of nine
other budgerigars analyzed for nonlinear amplitude modula-
tion to date! exhibit amplitude-modulation patterns similar to
those of M03. Figure 1~A! shows the entire amplitude enve-
lope of one of Forest’s calls, and 1~B! an expanded section of
time from that call. Note the extensive amplitude fluctuations
throughout. Figure 5~A!–~D!, respectively, show wide- and
narrow-band spectrograms, the power spectrum, and another
portion of the amplitude waveform from the call in Fig. 1.
From 147–166 ms, the amplitude of the waveform @Fig.
5~D!# is modulated in a regular or periodic manner. Inspec-
tion of the wideband spectrogram at this point @Fig. 5~A!,
between the time cursors# reveals an apparent drop in fre-
quency of the dominant component, accompanied by a smear
of energy that extends across a large span of frequencies
~from ;500–5500 Hz!. Inspection of the narrow-band spec-
trogram @Fig. 5~B!# reveals several closely apposed compo-
nent frequencies at apparently evenly spaced frequency in-
tervals. A 1024-point power spectrum ~of the 20 ms between
the vertical lines! identifies the spectrum’s dominant compo-
nent at 2600 Hz, with components evenly distributed 480 Hz
above and below this frequency, a pattern consistent with
that of an amplitude-modulated signal. Components also ex-
ist at 480 and 960 Hz, but the dominant frequency, 2600 Hz,
is not an integer multiple of 480 Hz ~2600/48055.4167!;
thus, this component is not simply a harmonic of a 480-Hz
fundamental whose energy has been enhanced by suprasy-
ringeal filtering. Energy at 480 and 960 Hz is consistent with
components that correspond to the fundamental frequency of
the modulating signal and its first integer multiple. Note the
many spectral components between the carrier signal and its
second harmonic ~at 5220 Hz!, a pattern inconsistent with
that of a harmonic vocalization.
Inspection of the amplitude waveform of this section of
the call @Fig. 5~D!# confirms that the spectrum is generated
by an amplitude-modulated signal. Direct measure of the
waveform reveals a 473 ~649!-Hz modulation superimposed
upon the dominant 2798 ~640!-Hz signal. Both the dominant
frequency and rate of modulation in the waveform corre-
spond well with the dominant frequency component ~2600
Hz! and the intervals between components ~480 Hz! in the
spectrum.
B. Human and budgerigar vowel spectra differ in
their properties
When subject to Fourier analysis, most human vowels
produce a quasi-harmonic spectrum consisting of a funda-
mental frequency and a stack of harmonic components, with
each component located at an integer or near-integer mul-
tiple of the fundamental frequency ~the fundamental of a
human vowel is the frequency at which the vocal folds, or
larynx, vibrate open and closed!. Figure 6~A! and ~B! show
wide- and narrow-band spectrograms of a typical harmonic
human vocalization, PB’s ‘‘bear’’ ~produced with the same
intonation as used when training budgerigars!. A power
spectrum @Fig. 6~C!# of the /|./ sound reveals a fundamental
frequency of 220 Hz, and harmonics at integer or near-
integer multiples of the fundamental ~i.e., 440, 659 Hz, etc.!.
Direct measure of the amplitude waveform @Fig. 6~D!# yields
a fundamental frequency of 221 ~62! Hz ~i.e., the waveform
repeats every 4.5–4.6 ms!.
Budgerigar vowel spectra ~Figs. 7–9!, in contrast, pos-
sess features of amplitude-modulated rather than harmonic
signals. When represented via Fourier analysis, budgerigar
vowel sounds possess a complex array of frequency compo-
nents. The greatest spectral energy occurs in the middle of a
group of components with significant energy distributed
symmetrically on either side of this local maximum.
A 1024-point power spectrum @Fig. 7~C!# of a 40-ms
section ~155 to 195 ms! of Frans’ /|./ in ‘‘bear’’ revealed
that the maximal energy was at 1840 Hz, with component
frequencies 100 Hz below and 40 Hz above the 1840-Hz
FIG. 5. Forest’s contact call. ~A! Wideband spectrogram ~300-Hz analysis
filter! of the call in Fig. 3. Time cursors demarcate the 20-ms section dis-
played in the amplitude waveform and analyzed in the power spectrum. ~B!
Narrow-band spectrogram ~150-Hz analysis filter!. Time cursors demarcate
the same region as in ~A!. ~C! 1024-point power spectrum of the 20-ms
region demarcated by cursors in ~A! and ~B!. Note the dominant component
at 2600 Hz, and components evenly spaced 480 Hz above and below, and
integral multiples of the modulating frequency at 480 and 960 Hz ~D! Am-
plitude waveform for the 20-ms period demarcated by cursors in ~A! and
~B!, on which the power spectrum was performed. The dominant ~carrier!
signal measured directly from this waveform is 2798 ~640! Hz; the modu-
lating signal is 473 ~649! Hz.
497 497J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

frequency. Direct measure of frequencies in the amplitude
waveform @in Fig. 7~D!, from the peak of one high-frequency
period to the next, or from the first peak of one slow-
frequency period to the first peak of the next# yielded a
dominant frequency of 1866 ~612! Hz, and a modulating
frequency of 100 ~62! Hz. Returning to the spectrum, the
lower 1740-Hz sideband occurs exactly where predicted ~100
Hz below 1840 Hz!, but the upper sideband at 1880 Hz is not
100 Hz above the carrier frequency. Note, however, the sig-
nificant energy at 1940 Hz @e.g., 100 Hz above 1840 Hz; Fig.
7~C!#, possibly reflecting the presence of an upper sideband
at 1940 Hz that is obscured by another energy component at
1880 Hz. This possibility is discussed in greater detail below.
Thus, evidence from signal analyses suggest that Frans’
/|./ vowel sound is produced by amplitude modulation. The
dominant frequency identified in the waveform @Fig. 7~D!#
contains the greatest energy of all components in the spec-
trum @Fig. 7~C!#, and is surrounded on either side by energy
components @Fig. 7~C!#, two defining characteristics of an
amplitude-modulated signal. The 1840–1866-Hz signal is
the carrier; the 100-Hz signal is the modulating signal. Note
the second and third integral multiples of the carrier signal
near 3680 and 5520 Hz, indicating that the carrier is a mul-
tifrequency harmonic signal. The presence of the carrier sig-
nal in the spectrum indicates that the modulating signal has a
dc component.
Frans’ /er/ amplitude waveform envelope @Fig. 7~D!# re-
sembles that of a classically amplitude-modulated signal.
Such appearance suggests but is not definitive evidence for
amplitude modulation. As described above, beating can pro-
duce a similar amplitude envelope, but a very different Fou-
rier spectrum. For budgerigar vowel spectra, component fre-
quencies occur symmetrically around the frequency with the
greatest energy, an attribute consistent with a spectrum gen-
erated by an amplitude-modulated signal, not by beating
@compare Fig. 3~B! and ~C! with Fig. 3~D!#.
Buddy’s /|./ in ‘‘bear’’ ~Fig. 8! produces a similar spec-
trum. A 1024-point power spectrum @Fig. 8~C!# identifies the
component with maximal energy as 2656 Hz. Direct measure
of the amplitude waveform yields a carrier signal of 2676
~621! Hz and a modulating signal of 255 ~69! Hz. Fre-
quency differences between adjacent components vary from
78–352 Hz, but numerous components are separated by 254
or 273 Hz, values close to that of the modulating signal
FIG. 6. A human’s ~PB’s! production of ‘‘bear.’’ ~A! Wideband spectro-
gram ~300-Hz analysis filter!. Time cursors demarcate a 40-ms section
~450–490 ms!. ~B! Narrow-band spectrogram ~45-Hz analysis filter!. Time
cursors demarcate the same region as in ~A!. ~C! 1024-point power spectrum
of the 40-ms section demarcated in ~A! and ~B!. Note the integrally spaced
harmonics. The fundamental frequency determined from the power spec-
trum is 220 Hz. In this vocalization, the component with the greatest energy
is the second harmonic. ~D! Amplitude waveform of a 20-ms portion of the
40-ms section demarcated by cursors in ~A! and ~B!. The fundamental fre-
quency determined from direct measure of the waveform is 222 ~62! Hz.
FIG. 7. Frans’ production of ‘‘bear.’’ ~A! Wideband spectrogram ~300-Hz
analysis filter!. Time cursors demarcate a 40-ms section ~450–490 ms!.
Components are located at integral multiples of the carrier frequency ~3600
and 5220 Hz!. ~B! Narrow-band spectrogram ~45-Hz analysis filter!. Time
cursors demarcate the same region as ~A!. ~C! 1024-point power spectrum
of the 40-ms section demarcated in ~A! and ~B!. The dominant frequency
identified in the power spectrum is 1840 Hz. Component frequencies are
100 Hz below and 40 Hz above the dominant frequency ~at 1740 and 1880
Hz, respectively!, but significant energy is in the spectrum at 1940 Hz ~100
Hz above the carrier signal, where the dashed line and the spectrum inter-
sect!. ~D! Amplitude waveform of the 40-ms section demarcated by cursors
in ~A! and ~B!. Direct measure of the amplitude waveform yielded a carrier
signal of 1866 ~612! Hz, and a modulating frequency of 100 ~62! Hz.
498 498J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

derived from the amplitude waveform. The component two
bands below the 2656-Hz component is separated from it by
273 Hz; the component two bands above the 2656-Hz com-
ponent is separated by 254 Hz. At lower frequencies ~this
vocalization was not filtered!, a harmonic-looking series of
components is separated by either 254 or 273 Hz. These
components appear to be integer multiples of the fundamen-
tal frequency of the modulating signal and thus indicate a dc
component in the carrier, and a multifrequency harmonic
modulating signal. The second integer multiple of the carrier
is visible at 5195 Hz ~5195/265651.96!, indicating its mul-
tifrequency harmonic nature. Note also the sidebands 235 Hz
below and 273 Hz above the 5195-Hz component. Numerous
frequency components exist between the first and second
harmonics of the carrier, a pattern inconsistent with a har-
monic vocalization.
Figure 9 shows Forest’s ‘‘o’’ from ‘‘okay.’’ Spectral
components of this sound are consistent with properties of an
amplitude-modulated signal: ~1! components corresponding
to the fundamental of the carrier signal ~3980 Hz! and integer
multiples of the modulating signal are present ~the funda-
mental of the modulating signal is 260 Hz, but its first visible
component is 520 Hz because of filtering ,400 Hz!; ~2!
numerous integer multiples of the modulating signal indicate
its multifrequency harmonic nature ~Note: the 8000-Hz sam-
pling range eliminates a second integer multiple of the car-
rier signal!; and ~3! numerous energy bands on both sides of
the carrier signal are visible, many of which are separated by
either 260 or 280 Hz.
Measurements of the amplitude waveform concur with
frequencies in the spectrum. The modulating signal, at 279
~621! Hz, corresponds to the 260–280-Hz modulating signal
identified in the spectrum. The carrier signal identified in the
amplitude waveform, at 4617 ~6295! Hz, differs more ~al-
though only by 14%! from the 3980 Hz derived from the
power spectrum than did these estimations in other birds.
When the amplitude waveform is as drastically modulated in
amplitude as in this bird’s vocalization, however, difficulties
arise during wave shape analysis in distinguishing peaks of
FIG. 9. Forest’s production of ‘‘okay.’’ ~A! Wideband spectrogram ~300-Hz
analysis filter!. Time cursors demarcate a 40-ms section ~40–80 ms! of the
/Ç/. Note how low-frequency components extend in time beyond the region
of the sound with the majority of energy ~below arrowheads!. ~B! Narrow-
band spectrogram ~45-Hz analysis filter!. Time cursors demarcate the same
region as in ~A!. ~C! 1024-point power spectrum of the 40-ms section de-
marcated in ~A! and ~B!. The dominant frequency in the power spectrum is
3980 Hz. Numerous components are separated by either 260 or 280 Hz,
including the components that are two below ~at 3700 Hz! and two above ~at
4240 Hz! the carrier signal. ~D! Amplitude waveform of 8 ms of the 40-ms
section demarcated by the cursors in ~A! and ~B!. Direct measure of the
amplitude waveform yielded a carrier signal of 4617 ~6295! Hz, and a
modulating signal of 279 ~621! Hz.
FIG. 8. Buddy’s production of ‘‘bear.’’ ~A! Wideband spectrogram ~300-Hz
analysis filter!. Time cursors demarcate a 40-ms section ~220–260 ms!.
Components are located at integral multiples of the carrier frequency ~5195
and ;8000 Hz!. ~B! Narrow-band spectrogram ~45-Hz analysis filter!. Time
cursors demarcate the same region as in ~A!. ~C! 1024-point power spectrum
of the 40-ms section demarcated in ~A! and ~B!. The dominant frequency
identified in the power spectrum is 2656 Hz. Component frequencies are
273 Hz below and 254 Hz above the dominant frequency ~at 2383 and 2910
Hz, respectively!, but other components exist between those components ~at
2481 and 2754 Hz, respectively!. ~D! Amplitude waveform of 18 ms of the
40-ms section demarcated by cursors in ~A! and ~B!. Direct measure of the
amplitude waveform yielded a carrier frequency of 2676 ~621! Hz, and a
modulating frequency of 254 ~69! Hz.
499 499J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

the carrier signal from what may be small energy peaks gen-
erated by harmonics or vocal-tract resonances of the carrier
or modulating signals, or by spurious background noise.
Two other features are of particular interest in this ‘‘o’’
sound. First, note @Fig. 9~D!# the striking similarity of the
shape and pattern of modulation of the amplitude waveform
of this vocalization and the synthesized amplitude-modulated
signal @Fig. 2~C!#. Second, note how several low-frequency
components in the spectrograms @beneath arrowheads, Fig.
9~A! and ~B!# extend in time beyond the portion of sound
containing the broad spectrum of frequencies. A 1024-point
power spectrum of this region of the vocalization ~200–240
ms! reveals a dominant component at 610 Hz. Direct mea-
sure of the amplitude waveform yields a dominant frequency
of 628 Hz. In this region of the vocalization, the carrier sig-
nal apparently ceases, and only what previously was the
modulating signal continues to be produced. The actual fun-
damental frequency in this region may be 305 Hz, but pre-
analysis filtering ,400 Hz may have removed the energy at
the fundamental. This hypothesis is supported by the pres-
ence of four other apparently harmonic components that ex-
tend up to 2167 Hz, and that are spaced at integer or near-
integer multiples of 305 Hz @i.e., Fig. 9~B!, components at
915, 1267, 1909, and 2165 Hz#. This phenomenon was ob-
served in samples of other budgerigar vocalizations, and pro-
vides further evidence for the presence of two separate and
independent frequencies.
For numerous budgerigar vowel sounds ~and all budgeri-
gar vocalizations described above!, I calculated the carrier-
and modulating-signal periodicity directly from the ampli-
tude waveform. Pitch-synchronous spectrum analyses veri-
fied that the carrier signal is not an integer multiple ~i.e., a
harmonic! of the modulating signal ~i.e., carrier signal/
modulating signal Þ an integer!. These results further sup-
port the conclusion that the carrier and modulating signals
are not harmonically related.
Finally, I analyzed both budgerigar vowels and
amplitude-modulated regions of contact calls for the pres-
ence of frequency modulation. Periodic frequency modula-
tions are also capable of producing discrete sidebands ~Mar-
ler, 1969!. Budgerigar vocalizations clearly exhibit
frequency modulations in the form of both slow and rapid
transitions of the carrier signal frequency ~e.g., from one
frequency to another!. For example, as described above,
M03s contact call exhibits a rapid transition from ;3850 to
;3349 Hz at ;83 ms in the call @Fig. 4~D!#. It is thus pos-
sible that periodic frequency modulations ~e.g., periodic in-
creases and decreases of the dominant signal! within each
modulating period are responsible for the production of side-
band components. My analyses showed, however, that fre-
quency modulations of the carrier signal within single modu-
lated periods are aperiodic modulations rather than periodic
modulations ~data not presented!. The carrier frequencies of
budgerigar vocalizations do not systematically increase, de-
crease, or increase and decrease in frequency within periods
of the modulating envelope, but rather fluctuate around the
carrier signal ‘‘target’’ frequency ~the dominant frequency
that the bird is attempting to produce!. Furthermore, the
period-to-period frequency of the carrier signal is not corre-
lated with the peak-to-trough amplitude of the waveform
~data not shown!. Periodic-frequency modulation is thus not
responsible for producing the discrete sideband components
of budgerigar vocalization spectra.
III. DISCUSSION
A. Budgerigar vocalizations contain amplitude
modulation
Evidence presented here supports the conclusion that
some portions of the acoustic spectra generated by budgeri-
gar vocalizations arise from the nonlinear process of ampli-
tude modulation. Note, however, that not all budgerigar vo-
calizations exhibit the nonlinear phenomenon of amplitude
modulation responsible for creating sideband frequencies
~e.g., budgerigar productions of English consonants and per-
haps some warble-song elements; Note: many warble song
elements are clicks or buzzes which are neither harmonic nor
amplitude-modulated signals!. Furthermore, amplitude
modulation that creates discrete sidebands is not necessarily
present or obvious throughout entire vocalizations ~e.g., re-
gions within contact calls where amplitude remains relatively
constant, or fluctuates aperiodically!. Thus, although entire
budgerigar vocalizations may not exhibit all of the key fea-
tures of amplitude modulation, these features are exhibited in
portions of contact calls and in learned English vowel
sounds. These key features include:
~1! Vocalizations with acoustic spectra that do not conform
to those produced by harmonic vocalizations. These vo-
calizations do not have a dominant component at what
would be the predicted fundamental frequency, and cal-
culations fail to yield either a common or a plausible
fundamental frequency. Furthermore, the frequency
component in the spectrum with greatest energy is not an
integer or near-integer multiple of any plausible funda-
mental.
~2! Acoustic spectra that contain a centrally located domi-
nant component surrounded on each side by relatively
symmetrical sidebands that, collectively, represent most
of the energy in the signal.
~3! Two separate periodic, or almost-periodic, signals that
are identifiable in the amplitude waveform and that ac-
curately reflect frequencies of the carrier and modulating
signals identified in the spectrum. The higher-frequency
carrier signal in the waveform corresponds to the domi-
nant frequency identified in the spectrum, and the lower-
frequency modulating signal in the waveform corre-
sponds to the frequency difference between many
components in the spectrum.
~4! These two separate frequencies are not integrally related
~i.e., the carrier signal is not an integer multiple of the
modulating signal!.
~5! A localized prominent component ~compared to sur-
rounding component amplitudes! occurs at a frequency
twice that of the central dominant component ~i.e., an
integer multiple of the fundamental frequency of the car-
rier signal!. This component is likewise surrounded lo-
500 500J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

cally by a pattern of energy, consistent with sidebands in
an amplitude-modulated signal.
Amplitude modulation is evident in budgerigar produc-
tions of English vowel sounds. As mentioned above, bud-
gerigar vowel spectra contain a centrally located dominant
component and numerous sideband components separated by
a frequency similar to the modulating frequency ~determined
from the waveform!. At times, however, particular sideband
components can be difficult to identify definitively because
they occur at positions not predicted by the modulating fre-
quency @e.g., the 1880-Hz component in Frans’ /|./in
‘‘bear,’’ Fig. 7~C!#. Possible reasons for this inconsistency
are discussed below.
For budgerigar calls, the presence of a gross temporal
envelope @Fig. 1~A!# and an amplitude waveform @Fig. 1~B!#
that fluctuates in amplitude is obvious @this is the case for the
calls of all ~more than 16! budgerigars examined to date#.
However, only isolated regions of calls ~e.g., approximately
10%–20% of the duration! exhibit periodic amplitude modu-
lation @Figs. 4~D!,5~D!#. At these points, the vocalization
spectrum changes drastically, and sideband components are
detectable. Thus, evidence in both the time domain ~in the
amplitude waveform! and in the frequency domain ~in the
Fourier spectrum! provide consistent verification of an un-
derlying amplitude-modulation process in the generation of
these isolated portions of budgerigar contact calls. The
physical and acoustical processes responsible for producing
the remainder of the call are, however, not yet known. Spe-
cifically, are the frequent, obvious fluctuations in the ampli-
tude of the waveform throughout the rest of the call also
produced by nonlinear amplitude modulation, or are they
spurious fluctuations in amplitude?
B. Additional acoustic mechanisms and their
influence on budgerigar vocalizations
1. The complexity of nonlinear amplitude modulation
As mentioned above, budgerigar vowel spectra also de-
viate somewhat from what is predicted by a simple model of
amplitude modulation. One reason for this deviation is that
components arising as integer multiples of the fundamental
frequency of the modulating signal, and those generated as
sidebands ~i.e., components surrounding both the carrier and
integer multiples of the carrier signal! may overlap in the
spectrum. A simple example illustrates this phenomenon.
Consider an amplitude-modulated signal with multi-
frequency harmonic carrier ~2000 Hz! and modulating ~300
Hz! signals. Integer multiples of the 300-Hz modulating sig-
nal would be found at 300, 600, 900, 1200, 1500, 1800, 2100
Hz, etc. The carrier signal produces a component at 2000 Hz,
and sidebands would surround the carrier signal at 300-Hz
intervals below ~at 1700, 1400, 1100, 800, 500, 200 Hz! and
above ~at 2300, 2600, 2900 Hz, etc.! the carrier signal.
Where the modulating and sideband components overlap,
however, energy would occur at 200, 300, 500, 600, 800,
900, 1100, 1200, 1400, 1500, 1700, 1800, 2000, 2100, 2300
Hz, etc. ~This phenomenon also occurs where sidebands of
the carrier signal and its second integer multiple overlap.!
This region in the spectrum would be difficult to interpret, as
it would consist of numerous closely apposed components
separated by 100- and 200-Hz intervals, but not necessarily
by the 300-Hz interval predicted by the modulating signal.
~Note that such an array might be incorrectly interpreted to
be a harmonic stack with a fundamental of 100 Hz, but with
various missing harmonics.! Finally, depending on the win-
dow size of the Fourier transform, very closely apposed
overlapping components may not be distinguishable, but
rather may be represented as one single wideband compo-
nent, further complicating the analysis. The described array
of components resembles that of many budgerigar vowel
spectra. By deriving specific information regarding both the
carrier and modulating frequencies from the Fourier spec-
trum and amplitude waveform, however, the array can be
identified as generated by the nonlinear process of amplitude
modulation.
2. Suprasyringeal filtering
The contribution of suprasyringeal filtering to budgeri-
gar vocalization spectra must also be considered. The present
analyses cannot assess the role that the vocal tract plays to
emphasize or de-emphasize frequencies created by the syrinx
and other sound sources ~if existent!, but such filtering likely
exists ~Westneat et al., 1993; Brittan-Powell et al., 1997b!.
The budgerigar vocal tract likely emphasizes frequencies be-
tween 2000–4000 Hz ~the dominant frequency range of con-
tact calls; Dooling, 1986!, thus emphasizing sidebands that
occur near the carrier signal, but not those at other frequen-
cies. Analyses of other budgerigar vowel productions ~Banta,
personal observation!, suggest that budgerigars may also se-
lectively emphasize components that occur above, while de-
emphasizing or filtering out those that occur below, the car-
rier signal.
3. Aperiodic amplitude modulation
Inspection of the amplitude waveform for the major por-
tion of any budgerigar call ~i.e., in regions that do not exhibit
an amplitude-modulated spectrum with discrete sidebands!
reveals a waveform that appears to be modulated in ampli-
tude aperiodically or chaotically @Fig. 1~B!#. Interestingly,
nonlinear amplitude modulation that results from the interac-
tion between a periodic carrier signal and an aperiodic modu-
lating signal results in a much different spectrum than those
presented in Fig. 3~B! and ~C!. Instead of producing a spec-
trum with discrete sidebands of energy ~i.e., line spectra!,an
amplitude-modulated signal with a periodic carrier signal
and an aperiodic modulating signal will have a large cen-
trally located dominant component surrounded on either side
by diffuse sideband energy that may be incorrectly hypoth-
esized as arising from aperiodic frequency fluctuations or
noise. The distance that this sideband energy extends on ei-
ther side of the carrier signal is determined by the instanta-
neous rate at which the frequency of the modulating signal is
fluctuating. Because the modulating signal can fluctuate in
frequency very rapidly ~e.g., with each period of the carrier
signal for a chaotic modulating signal!, Fourier transforma-
tion results in a ‘‘smearing’’ of the sideband energy with
time, thus giving the spectrum a ‘‘broadband’’ or noisy ap-
501 501J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

pearance. Indeed, inspection of spectrograms from both
M03’s and Forest’s calls @Figs. 4~A! and ~B! and 5~A! and
~B!, respectively#, reveal this broadband or noisy character.
4. Beating
The simple linear summation phenomenon known as
beating cannot explain all of the spectral frequencies present
in portions of budgerigar calls and budgerigar vowel sounds.
Although beating can produce a waveform that is modulated
in amplitude, its Fourier spectrum contains only the two
original input frequencies. Even if beating occurred between
two multi-frequency harmonic signals, the spectrum would
not contain a centrally located dominant component sur-
rounded symmetrically by other components. Such a spec-
trum results only from a nonlinear process such as amplitude
modulation. Thus, the modulated waveform of budgerigar
vowels and calls is not produced by beating.
5. Frequency modulation
Budgerigar vocalizations and their Fourier spectra are
influenced by frequency modulations, but are not the product
of periodic frequency modulation, which can also produce
discrete line sidebands similar to those produced by periodic
amplitude modulation ~Marler, 1969!. My analyses showed
that periodic frequency modulations do not play a role in the
production of discrete sidebands in the production of bud-
gerigar vocalization spectra ~data not presented!. Frequency
modulation, however, may contribute to some of the spectral
smearing observed around regions of contact calls where
aperiodic amplitude modulation is also observed ~i.e., aug-
menting the broadband appearance!. The overall contribution
of each of these mechanisms, aperiodic frequency modula-
tion versus aperiodic amplitude modulation, to the signal
spectrum is difficult to estimate when the two processes oc-
cur simultaneously, but undoubtedly, both mechanisms con-
tribute to the complex spectra of budgerigar vocalizations.
Further acoustical and physiological investigations are
needed to elucidate the roles of these mechanisms in the
production of budgerigar vocalizations.
6. Additional evidence for the presence of aperiodic
amplitude modulation
Insufficient acoustic evidence exists to determine con-
clusively if all the frequent aperiodic fluctuations in ampli-
tude observed in budgerigar calls arise via amplitude modu-
lation, but, given its demonstrated presence in some portions
of calls, and its prominence in English vowel productions, it
is distinctly possible if not probable. Further evidence, how-
ever, comes from the analysis of contact calls produced by
budgerigars with lesions in the vocal control nucleus NLc
~central nucleus of the lateral neostriatum!. NLc lesions af-
fect the amplitude of the regions of budgerigar calls that
fluctuate aperiodically, as well as regions that are clearly
amplitude modulated, suggesting that amplitude throughout
the entire call is regulated by a common mechanism and is
under the control of a neural circuit whose primary target is
the syrinx ~Banta and Pepperberg, 1997; Banta, 1998!. This
result would not be expected if the aperiodic modulations of
amplitude observed in budgerigar calls were simply spurious
fluctuations as observed in all biological signals.
C. Implications of amplitude modulation for
investigations of budgerigar vocalizations
Budgerigars’ ability to produce amplitude modulation
has significant implications for future investigations of their
sound production, and necessitates re-evaluating results and
interpretations of previous studies of ontogenetic, neural, sy-
ringeal, and acoustic mechanisms underlying their vocaliza-
tions. For example, fundamental frequency is an inappropri-
ate concept when considering amplitude-modulated
vocalizations. Analyzing a vocalization containing amplitude
modulation as if it were harmonic may lead to serious acous-
tic and physical misrepresentations of the signal. Future in-
vestigations of budgerigar vocalizations must include acous-
tic analyses appropriate for amplitude-modulated signals
~e.g., ruling out the possibility that the vocalization is har-
monic; ensuring concurrence between the Fourier spectrum
and the amplitude waveform!, and must use appropriate ter-
minology to refer to vocalization components. Specifically,
because the present study raises serious questions as to the
nature of budgerigar contact call production and suggests
amplitude modulation as the underlying mechanism, use of
neutral terms such as ‘‘dominant signal’’ may be preferred to
terms such as fundamental frequency until the issue is re-
solved.
The presence of amplitude modulation in vocal signals
impacts most significantly researchers’ reliance on acoustic
analyses performed solely with Fourier techniques. Such
analyses may lead to incorrect inferences about the signal
source, and the frequencies it produces. Sidebands, for ex-
ample, which account for most of the components in the
Fourier spectrum of a complex amplitude-modulated signal,
are not source-produced frequencies, but rather result from
nonlinear interactions between two other signals originally
produced by the source~s!. This inference is not possible
solely with visual inspection of the Fourier spectrum. Only
after accounting for all frequencies present in the spectrum,
and reconciling the amplitude waveform and Fourier spec-
trum, are the acoustic properties of the source clarified.
1. Mechanical and neural substrates of budgerigar
vocalizations
Analyses relying solely on visual inspection of Fourier
spectra have led to misinterpretations of the physical, struc-
tural, and neural mechanisms underlying production of bud-
gerigar vocalizations. Reports from Heaton et al. ~1995!,
Brauth et al. ~1997!, and Shea et al. ~1997! suggested that
budgerigar contact calls are harmonic vocalizations, and that
the fundamental frequency of these calls is significantly re-
duced in birds that have undergone bilateral denervation of
the syrinx. Brauth et al. ~1997! proposed a model for bud-
gerigar syringeal function based on these findings. However,
this purported decrease in fundamental frequency has not
been reconciled with findings that ~a! calls of syringeal den-
ervated birds are essentially a harmonic stack of frequencies
~Heaton et al., 1995!, and ~b! the dominant frequency of
these harmonic productions shifts when produced in helium,
whereas the dominant frequency of calls of normal, inner-
502 502J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

vated birds does not ~Brittan-Powell et al., 1997b!. This dif-
ferential effect of helium would not be predicted if the source
frequency was the only feature affected by denervation, but
may indicate that the harmonic components of denervated
budgerigar calls are produced in a fundamentally different
manner than a normal bird’s call. Unfortunately, the authors
did not report effects of syringeal denervation on the gross
temporal envelope or amplitude waveform for any calls they
present. Re-evaluation of the results and interpretations from
these studies in the context of amplitude modulation might
greatly increase our understanding of mechanics of the bud-
gerigar vocal apparatus.
Studies have also fallen unexpectedly short in identify-
ing effects of lesions in the vocal control system on the pro-
duction of budgerigar vocalizations. To date, few studies
have documented the post-lesion fate of budgerigar calls.
Hall et al. ~1994! present data from budgerigars lesioned uni-
laterally and bilaterally in and around Field L and nucleus
basalis ~NB!. No effects were found following Field L le-
sions, but NB lesions caused deterioration, loss of individual
distinctiveness, and loss of all frequency modulation ~as
identified by visual inspection of Fourier spectra! of contact
calls. What is not known, however, is how lesions affected
the gross temporal envelope, amplitude waveform, or ampli-
tude modulation present in these vocalizations. Lack of un-
derstanding of the acoustic nature of budgerigar vocaliza-
tions may similarly have hindered analyses of other
unpublished lesion studies. In contrast, preliminary evidence
from recent experiments shows that even small, unilateral
lesions in the central nucleus of the lateral neostriatum ~NLc!
can significantly and specifically affect amplitude modula-
tion found in both budgerigar contact calls and productions
of learned English vowel sounds, although the Fourier spec-
tra may appear relatively unaffected ~Banta and Pepperberg,
1997; Banta, 1998!. Consideration of the acoustic implica-
tions of amplitude modulation will facilitate future investiga-
tions to define more thoroughly and accurately effects of
lesions in vocal control nuclei.
2. Vocal learning
The presence of amplitude modulation in budgerigar vo-
calizations has intriguing implications for studies of vocal
learning. Budgerigars can continue vocal learning throughout
adulthood ~Brown et al., 1988; Farabaugh et al., 1994!, and
juveniles require auditory feedback to develop their calls
~Dooling et al., 1987!. The acoustic or temporal features to
which birds actually attend and learn when they begin to
produce their first contact calls or modify their adult call
repertoire as adults are, however, unknown. Budgerigars’
ability to produce a specific pattern of amplitude modulation
to mimic English vowels strongly suggests that budgerigars
may also ‘‘learn’’ when and how to vary amplitude in their
contact calls, as well as other conspecific vocalizations. As
mentioned previously, a budgerigar call may exhibit 3–5 fre-
quency changes throughout its duration, but 10–15, or more,
amplitude changes. Whether all modulations of amplitude
are due to the nonlinear process of amplitude modulation ~in
contrast to simple amplitude fluctuations of the gross tempo-
ral envelope, discussed above!, is not yet clear but is a dis-
tinct possibility. Perhaps budgerigars learning contact calls
learn not only which dominant frequency to produce, and
how to vary that frequency, but also a pattern of amplitude
modulation. Indeed, perhaps amplitude modulation is the
critical acoustic feature monitored by budgerigars engaged in
vocal learning. Brittan-Powell et al. ~1997a! and Hall et al.
~1997! investigated the ontogeny of call production in bud-
gerigars, but not the development of amplitude modulation.
Such analyses may greatly improve our understanding of
mechanisms underlying vocal learning in this species.
D. Syringeal mechanisms underlying the production
of amplitude modulation
Acoustic characteristics of amplitude-modulated vocal-
izations in songbirds were first described by Nowicki and
Capranica ~1986a, b!. They found that the ‘‘dee’’ syllable of
the black-capped chickadee ~Parus atricapillus! call was not
a simple harmonic vocalization, but rather resulted from the
nonlinear interaction of two harmonic signals. The chicka-
dee, like all songbirds, has two syringeal apertures ~one on
each side of the tracheobronchial junction!, each with a
membrane capable of producing a separate sound. Nowicki
and Capranica proposed that the spectral characteristics of
the ‘‘dee’’ arose because each side of the syrinx produced a
different frequency. In contrast, the budgerigar, like all par-
rots, has a single syringeal aperture with two opposing lateral
tympaniform membranes ~LTMs; Nottebohm, 1976! in the
tracheal portion of the tracheobronchial junction, and these
membranes purportedly cannot produce sound independently
~Nottebohm, 1976; Heaton et al., 1995; Brauth et al., 1997!.
Thus, how do budgerigars produce amplitude-modulated vo-
calizations?
A clue about budgerigar syringeal mechanisms may
come from research on the monk parakeet, Myiopsitta mona-
chus. This bird not only produces amplitude-modulated call-
like vocalizations ~‘‘a rattling squawk’’!, but two intrinsic
muscles of its syrinx, the syringeus and the tracheobronchia-
lis, are temporally correlated with pulsatile elements of this
vocalization ~Gaunt and Gaunt, 1985!. A similar mechanism
may be responsible for budgerigars’ production of
amplitude-modulated signals. For example, the dominant or
carrier frequency may be produced by a flow-induced, self-
sustaining oscillation of the LTMs ~achieved by Bernoulli
action-like forces of air on the LTMs!. The carrier frequency
amplitude may then be modulated by either adducting or
abducting the LTMs ~i.e., moving them, respectively, into or
out of the tracheal lumen, and thus into and out of the air
flow!. Although direct syringeal muscle activity may be re-
sponsible for producing amplitude modulations of this type
in monk parakeet calls ~Gaunt and Gaunt, 1985!, I find
amplitude-modulation rates ranging from 100–742 Hz in the
budgerigar. Because these upper frequencies are far greater
than the rate at which even the fastest skeletal muscle can
contract, direct syringeal muscle activity is not likely respon-
sible for producing the modulating signal in all budgerigar
amplitude-modulated vocalizations.
Nonlinear oscillations of the syringeal membranes may
also be responsible for producing amplitude modulation in
budgerigar vocalizations. Fee et al. ~1998! describe nonlin-
503 503J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

ear dynamics present in the excised syrinx of the zebra finch
~Taeniopygia guttata!. They postulate that these nonlinear
mechanics are responsible for some nonlinear characteristics
observed in zebra finch song, such as period doubling, mode-
locking, and sudden transitions from periodic to aperiodic or
chaotic signals. Tests on a biophysical model of the syrinx
further support their hypotheses and suggest that, at least for
mode-locking, coupling of the Bernoulli force-driven oscil-
lation to a higher vibrational mode in the membranes may be
responsible. Similar mechanisms might produce nonlinear
acoustical features of budgerigar vocalizations: Smooth yet
rapid transitions in amplitude, and between periodic and ape-
riodic or chaotic modulations, are evident in regions of calls
that lack obvious spectral evidence of amplitude modulation
@Fig. 1~B!#. If budgerigars indeed use such mechanisms to
mimic the sounds of human speech, they must have central
control over at least some aspects of the syringeal dynamics
to initiate, terminate, and modulate production of this non-
linear activity. Further experiments are necessary to assess
the roles of both the syrinx and the central vocal-control
system in producing nonlinear acoustical features of budgeri-
gar vocalizations.
IV. CONCLUSIONS
In summary, evidence presented here supports the con-
clusion that the nonlinear process of amplitude modulation
significantly influences the acoustic properties of budgerigar
contact calls and learned English vowel sounds. The mecha-
nisms budgerigars use to produce amplitude modulation are,
however, unknown. Future studies considering the presence
of amplitude modulation should shed further light on the
ontogenetic, physical, and neural bases of budgerigar vocal-
izations, and, in turn, these studies should further our under-
standing of how budgerigars produce amplitude-modulated
vocalizations.
ACKNOWLEDGMENTS
I would like to thank I. M. Pepperberg, R. R. Capranica,
and P. Lavenex for the enormous amounts of help, guidance,
and insight they have given me throughout this study. I thank
numerous undergraduate students at the University of Ari-
zona for endless hours of assistance with training budgeri-
gars, and S. Rubin and L. Freeman for excellent care of the
breeding flock of budgerigars. I thank B. Brittan-Powell, F.
Goller, and R. Suthers for helpful discussions, and C. Clark,
F. Goller, P. Narins, and two anonymous reviewers for criti-
cal comments on previous drafts of this manuscript. I thank
T. Glattke, S. Hopp, and P. Marler for helpful discussions
and access to equipment necessary to complete this study,
and D. Amaral for access to equipment. This project was
supported by funds from the Whitehall Foundation ~No.
AS92-03 to I. M. Pepperberg!, the National Science Founda-
tion ~SGER No. 9237 to I. M. Pepperberg!, and the Univer-
sity of Arizona Program in Neuroscience and Graduate Col-
lege.
Banta, P. A. ~1998!. ‘‘Neuroethology of acquired English and conspecific
vocalizations in the budgerigar ~Melopsittacus undulatus!,’’ Ph.D. Disser-
tation, University of Arizona.
Banta, P. A., and Pepperberg, I. M. ~1995!. ‘‘Learned English vocalizations
as a model for studying budgerigar ~Melopsittacus undulatus! warble
song,’’ Soc. Neurosci. Abs. 21, 958.
Banta, P. A., and Pepperberg, I. M. ~1997!. ‘‘Ibotenic acid lesions in bud-
gerigar NLc affect production, but not memory, of learned English words
and natural vocalizations,’’ Soc. Neurosci. Abs. 23, 797.
Beeman, K. ~1996!.
SIGNAL Technology, V3.0 ~Engineering Design, Bel-
mont, MA!.
Bradbury, J. W., and Vehrencamp, S. L. ~1998!. Principles of Animal Com-
munication ~Sinauer, Sunderland, MA!.
Brauth, S. E., Heaton, J. T., Shea, S. D., Durand, S. E., and Hall, W. S.
~1997!. ‘‘Functional anatomy of forebrain vocal control pathways in the
budgerigar ~Melopsittacus undulatus!,’’ Ann. ~N.Y.! Acad. Sci. 807, 368–
385.
Brittan-Powell, E. F., Dooling, R. J., and Farabaugh, S. M. ~1997a!. ‘‘Vocal
development in budgerigars ~Melopsittacus undulatus!: Contact calls,’’ J.
Comp. Psych. 111, 226–241.
Brittan-Powell, E. F., Dooling, R. J., Larsen, O. N., and Heaton, J. T.
~1997b!. ‘‘Mechanisms of vocal production in budgerigars ~Melopsittacus
undulatus!,’’ J. Acoust. Soc. Am. 101, 578–589.
Brown, S. D., Dooling, R. J., and O’Grady, K. ~1988!. ‘‘Perceptual organi-
zation of acoustic stimuli by budgerigars ~Melopsittacus undulatus!: III.
Contact calls,’’ J. Comp. Psych. 102, 236–247.
Dooling, R. J. ~1986!. ‘‘Perception of vocal signals by budgerigars ~Melop-
sittacus undulatus!,’’ Exp. Biol. 45, 195–218.
Dooling, R. J., Gephart, B. F., Price, P. H., McHale, C., and Brauth, S. E.
~1987!. ‘‘Effects of deafening on the contact call of the budgerigar Melop-
sittacus undulatus,’’ Anim. Behav. 35, 1264–1266.
Dooling, R. J., and Searcy, M. H. ~1981!. ‘‘Amplitude modulation thresh-
olds for the parakeet ~Melopsittacus undulatus!,’’ J. Comp. Physiol. 143,
383–388.
Dooling, R. J., and Searcy, M. H. ~1985!. ‘‘Temporal integration of acoustic
signals by the budgerigar ~Melopsittacus undulatus!,’’ J. Acoust. Soc. Am.
77, 1917–1920.
Evans, H. E. ~1969!. ‘‘Anatomy of the budgerigar,’’ in Diseases of Cage
and Aviary Birds, edited by M. L. Petrak ~Lea and Febiger, Philadelphia!,
pp. 45–112.
Farabaugh, S. M., Linzenbold, A., and Dooling, R. J. ~1994!. ‘‘Vocal plas-
ticity in budgerigars ~Melopsittacus undulatus!: Evidence for social factors
in the learning of contact calls,’’ J. Comp. Psych. 108, 81–92.
Fee, M. S., Shraiman, B., Pesaran, B., and Mitra, P. P. ~1998!. ‘‘The role of
nonlinear dynamics of the syrinx in the vocalizations of a songbird,’’
Nature ~London! 395, 67–71.
Gaunt, A. S., and Gaunt, S. L. L. ~1985!. ‘‘Electromyographic studies of the
syrinx in parrots ~Aves, Psittacidae!,’’ Zoomorph. 105, 1–11.
Greenewalt, C. H. ~1968!. Bird Song: Acoustics and Physiology ~Smithso-
nian Institution, Washington, D.C.!.
Hall, W. S., Brauth, S. E., and Heaton, J. T. ~1994!. ‘‘Comparison of the
effects of lesions in nucleus basalis and Field ‘L’ on vocal learning and
performance in the budgerigar ~Melopsittacus undulatus!,’’ Brain Behav.
Evol. 44, 133–148.
Hall, W. S., Cookson, K. K., Heaton, J. T., Roberts, T., Shea, S. D., and
Brauth, S. E. ~1997!. ‘‘Audio–vocal learning in budgerigars,’’ Ann.
~N.Y.! Acad. Sci. 807, 352–367.
Heaton, J. T., Farabaugh, S. M., and Brauth, S. E. ~1995!. ‘‘Effect of sy-
ringeal denervation in the budgerigar ~Melopsittacus undulatus!: The role
of the syrinx in call production,’’ Neurobiol. Learn. Mem. 64, 68–82.
Marler, P. ~1969!. ‘‘Tonal quality of bird sounds,’’ in Bird Vocalizations,
edited by R. A. Hinde ~Cambridge University Press, Cambridge!, pp.
5–18.
Nottebohm, F. ~1976!. ‘‘Phonation in the orange-winged Amazon parrot,
Amazona amazonica,’’ J. Comp. Physiol. 108, 157–170.
Nowicki, S., and Capranica, R. R. ~1986a!. ‘‘Bilateral syringeal coupling
during phonation of a songbird,’’ J. Neurosci. 6, 3595–3610.
Nowicki, S., and Capranica, R. R. ~1986b!. ‘‘Bilateral syringeal interaction
in vocal production of an oscine bird sound,’’ Science 231, 1297–1299.
Pepperberg, I. M. ~1981!. ‘‘Functional vocalizations by an African grey
parrot ~Psittacus erithacus!,’’ Z. Tierpsychol. 55, 139–160.
Roederer, J. G. ~1995!. The Physics and Psychophysics of Music ~Springer,
New York!.
Shea, S. D., Heaton, K. J., Heaton, J. T., Hall, W. S., and Brauth, S. E.
504 504J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar

~1997!. ‘‘The role of contact calls in the social behavior of the budgerigar
~Melopsittacus undulatus!,’’ Ann. ~N.Y.! Acad. Sci. 807, 571–573.
Silaeva, O. L. ~1998!. ‘‘Comparative analysis of acoustic characteristics of
human speech models: Prototypes and imitones of the budgerigar ~Melop-
sittacus undulatus!,’’ Biol. Bull. 25, 37–43.
Suthers, R. A. ~1997!. ‘‘Peripheral control and lateralization of birdsong,’’ J.
Neurobiol. 33, 632–652.
Titze, I. R. ~1994!. Principles of Voice Production ~Prentice-Hall, Engle-
wood Cliffs, NJ!.
Todt, D. ~1975!. ‘‘Social learning of vocal patterns and models of their
application in Grey parrots,’’ Z. Tierpsychol. 55, 139–160.
Turney, S. M., Banta, P. A., and Pepperberg, I. M. ~1994!. ‘‘Comparative
acoustical analyses of learned English vocalizations of two parrot spe-
cies,’’ Anim. Behav. Soc. Abs. 89.
Westneat, M. W., Long, Jr., J. H., Hoese, W., and Nowicki, S. ~1993!.
‘‘Kinematics of birdsong: Functional correlation of cranial movements
and acoustic features in sparrows,’’ J. Exp. Biol. 182, 147–171.
505 505J. Acoust. Soc. Am., Vol. 106, No. 1, July 1999 P. Banta Lavenex: Vocal production mechanisms in the budgerigar