On vocal tract asymmetry/symmetry

To obtain the maximal formant frequency variations for minimal area function deformations, the deformations of the acoustic tube must be anti-symmetrical in case of a closed-open tube (anti-symmetrical structure) and symmetrical in case of a closed-closed tube (symmetrical structure). It means that, in the first case, a front constriction is associated with a back cavity and vice-versa, in the second case, a central constriction is associated with 2 lateral cavities. Thus, in the first case, the optimal solutions are obtained when the length of the pharynx cavity is equal to the length of the mouth cavity. The vowel triangle, the main places of articulation for vowels and consonants are automatically derived from this deductive approach. Nevertheless, several questions are arisen: 1) Which strategy can be used to pass from the anti-symmetrical to the symmetrical configuration and vice-versa? 2) The optimal acoustic solutions correspond to the male speaker production. Thus, how to explain the configurations with small pharynx cavity such as female or child vocal tract? 3) How to simulate vowel production with advance tongue root (ATR) ? Results of simulation for these situations show how to deform an uniform tube to produce different formant variations. The linearity and orthogonality of the relation between the area function deformation and the resulting acoustic F-pattern are pointed out.