Fundamental Facts About the Relation of Formants to Articulation

The main facts about formant frequency variation can be thought of as having to do with vowels on the one hand, and consonants on the other. Vowel height is inversely related to F1 frequency. That is, F1 for high vowels is relatively low in frequency, while F1 for low vowels is relatively high in frequency. Vowel frontness is related to F2 frequency: front vowels have higher-frequency F2, back vowels have lower-frequency F2. Consonantal constriction and closure also has effects on the formant frequencies. Closure at the lips results in falling F1, F2, F3 frequencies; coronal closure shows a ``locus'' effect, where F2 rises into coronal closure if it starts low, and falls into coronal closure if it starts high; fronted allophones of velar consonants (henceforth ``front velars'', likewise ``back velars'') closure results in an F2-F3 ``pinch'', where F3 falls and F2 rises, not so for back velars; rhotic /r/ results in an especially low F3.

These fundamental, empirical observations of the acoustics of speech call out for explanation: Why do these relationships hold between articulation and acoustic structure? One traditional answer has been to point to a transmission-line model: the vocal tract is conceptually sliced into a fairly large number (on the order of 40) of short tubes of particular cross-sections and lengths. Equations for deriving the resonance frequencies from this detailed model of the shapes of the many short tubes are computed, and the resonance structure falls out rather magically. Such ``explanations'' are intellectually dissatisfying; it is impossible, certainly for me, to comprehend the relations of 3 or more frequencies relative to a model of 40 cross-sectional areas and 40 tube-lengths. A computer can certainly understand it -- or calculate its transfer function -- but for a human being, the model is a black box and the relations between articulatory configurations and acoustic structure are opaque. We are unable to reason simply about the most basic aspects of our field: the effects of vocal-tract shape on sound. We need a model for the relations between articulation and acoustics, which is both quantitatively accurate and qualitatively interpretable -- i.e., where the mapping is intuitively predictable from one level to the other. No such model has been applied to explaining all these relations. We will define, justify, and apply such a model in this chapter, explaining the fundamental facts of acoustic phonetics in an understandable way.