Linear scaling of vowel-formant ensembles (VFEs) in consonantal contexts

Abstract

There are familiar terms such as “contour” and “trajectory” to refer to a vowel formant frequency as a function defined on the time axis, but there is no readily understood term for the analogous idea of how a formant behaves on the “vowel axis”. For this we introduce the concept of a vowel-formant ensemble (VFE) as the set of values realized for a given formant (e.g., F 2) in going from vowel to vowel among a speaker's vowel phonemes for a fixed time frame in a fixed CVC context. The VFE affords a simple description of our development: we observe that D.J. Broad and F. Clermont's [J. Acoust. Soc. Am. 81 (1987) 155] formant-contour model is a linear function of its vowel target and that as a consequence all its VFEs for a given speaker and formant number are linearly scaled copies of one another. Are VFEs in actual speech also linearly scaled? To show how this question can be addressed, we use F 1 and F 2 data on one male speaker's productions of 7 Australian English vowels in 7 CVd contexts, with each CVd repeated 5 times. Our hypothesized scaling relation gives a remarkably good fit to these data, with a residual rms error of only about 14 Hz for either formant after discounting random variations among repetitions. The linear scaling implies a type of normalization for context which shrinks the intra-vowel scatter in the F 1F 2 plane. VFE scaling is also a new tool which should be useful for showing how contextual effects vary over the duration of the syllable's vocalic nucleus.