In the last section we discussed a simplified model of speech production which used a single tube of constant cross section to model the vocal tract. As was mentioned their, a slightly more realistic model includes a constriction in the tube to represent the position of the tongue during articulation. Fairly detailed models of articulation can be developed by using a small number of tubes to model the vocal tract -- a common model uses one tube for the area behind the tongue, one for the constriction created by the tongue, one for the area front of the tongue and a final tube for the lip apperture. The lengths and cross sectional areas of these tubes can be adjusted to account for a number of speech sounds. This model is very useful in predicting the gross changes of formant positions caused as the tongue is raised or lowered and moved from the back to the front of the mouth.

As discussed in Chapter 3 of Harrington and Cassidy, the effects of different vocal tract configurations can be explored via a nomogram which is a plot of the predicted resonant frequencies in a four tube model as the constriction tube is moved from along the vocal tract. The tube configuration is illustrated in Figure 7.2 while Figure 7.3 shows an example nomogram.

You can explore tube models in the exercises for this lecture. These models illustrates one approach to generating synthetic speech, namely articulatory synthesis. Models with a larger number of tubes can be used to produce more accurate reproduction of various speech sounds. It is also possible to derive a tube model for a given speech sound via LPC analysis -- this won't be covered in this unit but is discussed in Harrington and Cassidy, Chapter 8. Such a derived tube model can be used to re-synthesise speech by applying a suitable source to the model.