A mathematical model of the vowel space

TL;DR

This paper introduces a simplified mathematical model linking vowel formant frequencies to vocal tract parameters, enabling better analysis of speech production through a bijective relationship.

Contribution

It proposes a novel bijective model between vowel space and vocal tract parameters using a mixture of cosines, improving upon existing articulatory-acoustic models.

Findings

The model generates main vowels with two formulas.

The coordination function behaves similarly to Fant's model.

The approach simplifies the study of speech production.

Abstract

The articulatory-acoustic relationship is many-to-one and non linear and this is a great limitation for studying speech production. A simplification is proposed to set a bijection between the vowel space (f1, f2) and the parametric space of different vocal tract models. The generic area function model is based on mixtures of cosines allowing the generation of main vowels with two formulas. Then the mixture function is transformed into a coordination function able to deal with articulatory parameters. This is shown that the coordination function acts similarly with the Fant's model and with the 4-Tube DRM derived from the generic model.