On Formants is intended for phoneticians and others interested in speech production. We present ways of thinking of the relationship between vocal tract shape and formants that have never been presented before to researchers in phonetics.
The approach taken here is to treat the distributions of pressure, air velocity, as well as energy densities throughout the tube as primary. First, we examine the particular phenomenon that a short constriction tends to limit formant frequency increase or greatly decrease formant frequency as constriction degree increases. Short refers to the dimension in the direction of the vocal tract axis.
To approach more general situations, we approximate the vocal tract using straight sub-tubes. To calculate formant frequency we essentially count the number of wavelengths of standing waves in each sub-tube, sum over the sub-tubes, and use the reciprocal relation between wavelength and frequency. We generalize the method of counting wavelengths with something called spatial phase. Finally, we examine the possibility of deriving vocal tract shape from formant frequencies. This is a key step in putting vowel and other sonorant production onto an articulatory footing because acoustic data are abundant and relatively easy to collect.
There are a few mathematical sections, but these are clearly marked, may be omitted on a first reading, and the main points understood without reading these sections. Otherwise, there is a minimum of elementary mathematics that can be understood without calculus.
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