This chapter may be read independently of the other chapters as a contribution to general2.1 phonetics. It presents a theory of the mapping from articulation to formant2.2 structure, and applies that theory to explain the main observed facts about that relationship. Within the perspective of this thesis, the purpose of this chapter is to lay the physical groundwork for the phonetic studies of English vowels that form the body of the thesis. The need here is to justify the use of measurements of the first two formant frequencies (F1 and F2) as representations of phonetic vowel quality. These measurements are in many ways superior to (more consistent, precise, and objective than) impressionistic characterizations, but are sometimes considered phonetically uninterpretable. This chapter shows, within a theory of the mapping from articulation to formant structure, how F1 and F2 are direct measures of the fundamental articulatory (and auditory, and phonological) dimensions of vowel quality: height and backness/roundness.
First, I outline the main observed facts about formant structure under various articulatory configurations. Then in the remainder of the chapter I describe an idealized model of the resonating vocal tract, as a lossless, uniform acoustic tube containing standing waves; I present results consistent with the hypothesis that the average vowel (for the speakers studied) is fairly well modelled in this way. Next, I describe and explain a theory of the variation in the frequency of these standing waves, derived from Fant (1960, 1968:216-217), Chiba (1941: Chapter 11), and originally Rayleigh (1894). The physical explanation is qualitative and includes no mathematics;2.3 it should be understandable to anyone who wishes to work through it. Finally, I apply that theory to explain the effects on formant frequencies of mouth opening, tongue-body frontness, and constrictions at bilabial, dental, velar, and retroflex places of articulation. I also apply the theory to predict the results of an investigation of acoustic correlates of voiced stops at three coronal places of articulation. The theory makes its most unusual predictions for sounds with multiple constrictions; these are found to be true. Finally, some consequences of the model for phonetic theory and for theories of phonological structure are explored.