Target–locus scaling methods for modeling families of formant transitions

An approach is proposed for modeling families of vowel-formant transitions in terms of linear-scaling relationships which tie the transitions into a structured system. The model incorporates the hypotheses that (1) transitions are scaled copies of consonant-specific shapes, and (2) the scale factors are the differences between the vowel targets and consonant loci. The terms “target” and “locus” are adopted for their historical roots in acoustic phonetics, but are used here as relational elements. The model is first evaluated with second-formant transitions from VC syllables (the vowels /ɪ, ε, æ, a, ɔ, u, ʌ, ɝ/ combined with the consonants /b, d, ɡ/), repeated 3 times by one adult-male speaker of American English. The model fits these data to within the level of variation among the speaker's repetitions and, within a comparable level, its linear-scaling structure is validated as an approximate feature of the family of transitions. The model's wider capability is then explored by (1) splitting /ɡ/ into its palatal and velar allophones, (2) representing transition shapes with exponentials, and (3) connecting its parameters and properties to those of locus equations. These results illustrate the model's workability and coherency, and argue for its potential to uncover further systematicity in coarticulation.