length of the vocal tract (Fant 1960; Lieberman and Blumstein 1988; Fitch
1997). In particular, a lengthening of the vocal tract tube will lead to a
decrease in the average spacing between successive formants, or “formant
dispersion” (Fitch 1997; Riede and Fitch 1999). Thus, if vocal tract length is
correlated with body size, there will be an inverse correlation between
formant dispersion and body size, and formants will provide honest cues to
body size. Such formant cues are completely independent of voice fundamental frequency or perceived pitch.
Formant dispersion is simply the average spacing between successive
formants and provides one simple metric for estimating vocal tract length.
However, no single number can accurately capture all of the information
in a complete list of formant frequencies and bandwidths, and in some cases
other statistics that rely only on higher formants, or on the most reliably
excited formants, may be preferable. It may appear that the first formant
would provide an equally good estimate of vocal tract length. There are two
reasons why this is not the case. The first concerns the boundary (end) conditions of an air column contained in a simple tube, which have a drastic
effect on the lowest formant but no effect on formant spacing. For example,
a 17.5-cm tube that is open at both ends has formant frequencies at 1,000,
2,000, and 3,000 Hz, and so on, while the same tube with one end closed has
formants at 500, 1,500, and 2,500 Hz, and so on. The spacing is 1 kHz in both
cases, but f 1 varies between 500 and 1,000 Hz. Although the human vocal
tract during speaking is often idealized as being closed at the glottal end,
this approximation is only strictly correct for a portion of the glottal cycle
and may never be true in certain phonatory modes (e.g., the glottis may
never close during breathy phonation). The use of formant dispersion
avoids the need for any assumptions about glottal state and phonatory
mode and is thus preferable to f 1 as a measure of vocal tract length. A
second reason that f 1 provides a poor correlate of vocal tract length is the
increased role of the yielding walls of the vocal tract at low frequencies. In
much the same way as described for the anuran vocal air sac, the soft parts
of the vocal tract begin to absorb significant energy from the acoustic signal
at lower frequencies. This effect of the vocal tract walls at low frequencies
will place a lower limit on f 1 , irrespective of total vocal tract length
(Fujimura and Lindqvist 1970). This effect will be most pronounced for long
vocal tracts, such as in large mammals, or in animals with vocal sacs.
Is there any reason to expect vocal tract length (which determines
formant spacing) to be more closely tied to body size than vocal fold length
(which determines fundamental frequency)? For mammals, the answer is
clearly yes. The mammalian vocal tract is made up of the pharyngeal, oral,
and nasal cavities, which are firmly bounded by the bones of the skull, and
skull size is closely tied to overall body size (Morita and Ohtsuki 1973;
Dechow 1983; Alcantara et al. 1991; Fitch 2000c). Because the facial region
of the vertebrate skull is involved in so many other life-critical functions (it
houses the sense organs, provides the passageway for water and air, must
3. Unpacking “Honesty”
103
1997). In particular, a lengthening of the vocal tract tube will lead to a
decrease in the average spacing between successive formants, or “formant
dispersion” (Fitch 1997; Riede and Fitch 1999). Thus, if vocal tract length is
correlated with body size, there will be an inverse correlation between
formant dispersion and body size, and formants will provide honest cues to
body size. Such formant cues are completely independent of voice fundamental frequency or perceived pitch.
Formant dispersion is simply the average spacing between successive
formants and provides one simple metric for estimating vocal tract length.
However, no single number can accurately capture all of the information
in a complete list of formant frequencies and bandwidths, and in some cases
other statistics that rely only on higher formants, or on the most reliably
excited formants, may be preferable. It may appear that the first formant
would provide an equally good estimate of vocal tract length. There are two
reasons why this is not the case. The first concerns the boundary (end) conditions of an air column contained in a simple tube, which have a drastic
effect on the lowest formant but no effect on formant spacing. For example,
a 17.5-cm tube that is open at both ends has formant frequencies at 1,000,
2,000, and 3,000 Hz, and so on, while the same tube with one end closed has
formants at 500, 1,500, and 2,500 Hz, and so on. The spacing is 1 kHz in both
cases, but f 1 varies between 500 and 1,000 Hz. Although the human vocal
tract during speaking is often idealized as being closed at the glottal end,
this approximation is only strictly correct for a portion of the glottal cycle
and may never be true in certain phonatory modes (e.g., the glottis may
never close during breathy phonation). The use of formant dispersion
avoids the need for any assumptions about glottal state and phonatory
mode and is thus preferable to f 1 as a measure of vocal tract length. A
second reason that f 1 provides a poor correlate of vocal tract length is the
increased role of the yielding walls of the vocal tract at low frequencies. In
much the same way as described for the anuran vocal air sac, the soft parts
of the vocal tract begin to absorb significant energy from the acoustic signal
at lower frequencies. This effect of the vocal tract walls at low frequencies
will place a lower limit on f 1 , irrespective of total vocal tract length
(Fujimura and Lindqvist 1970). This effect will be most pronounced for long
vocal tracts, such as in large mammals, or in animals with vocal sacs.
Is there any reason to expect vocal tract length (which determines
formant spacing) to be more closely tied to body size than vocal fold length
(which determines fundamental frequency)? For mammals, the answer is
clearly yes. The mammalian vocal tract is made up of the pharyngeal, oral,
and nasal cavities, which are firmly bounded by the bones of the skull, and
skull size is closely tied to overall body size (Morita and Ohtsuki 1973;
Dechow 1983; Alcantara et al. 1991; Fitch 2000c). Because the facial region
of the vertebrate skull is involved in so many other life-critical functions (it
houses the sense organs, provides the passageway for water and air, must
3. Unpacking “Honesty”
103