Although the production of indistinct sounds and noises by the human vocal apparatus is a relatively simple phenomenon from a strictly physical point of view (see How the voice is produced), the articulation of phonemes and their organization into intelligible sequences is instead a very complex phenomenon, which cannot be described within physics alone.

Of course we do not want to deal with this fascinating subject in detail here, since it requires an understanding of many physiological and perceptual aspects as well as strictly acoustic ones; but we want to show that, at least in some simple cases, a few elementary basic notions of wave physics can provide rather accurate predictions, and greatly clarify some essential aspects of the production of the sound associated with the articulation of vowels.

The sound of vowels

The sound of vowels is the easiest to describe in physical terms, because it is an almost stationary sound, produced without evident noise components, which are instead typical, for example, of consonant sounds. What distinguishes one vowel from another? Vowel sounds have different colours, but this is a component of the timbre that has nothing to do with the timbre of the speaker's voice. The usefulness of this fact is evident: it allows us to tell an A from an I almost independently of the particular quality of the speaker's voice. Looking at the sonograms in the figure, it is evident that the different vowels have different sounds, but how are these differences related to the characteristics of the "instrument" that produced the sound? To find out which factors influence the particular timbre features that allow us to distinguish vowels, it is useful to create a physical model of the human vocal tract.

sonogram Audio VOX_AEEIOOU.mp3 spoken vowels

The simplest possible model consists of a tube of variable diameter, at whose base there is a source of acoustic oscillations (the glottis), and whose other end is open (the mouth).

If the tube had a constant diameter, it would be a cylindrical bore closed at one end (the cross-section at the glottis is very narrow) and open at the other: its resonances would fall at v/4L, 3v/4L, 5v/4L and so on. For a vocal tract 17 cm long this gives about 500, 1500 and 2500 Hz: precisely the formants of the "neutral" vowel, the one pronounced with a relaxed mouth (like the "a" in English "about"). The other vowels arise from narrowing or widening the tube at different points, which shifts these resonances.

Although describing the vocal tract in these terms is a great simplification, it nevertheless provides much useful information, and is in some respects an illuminating model. This model lends itself to being simulated with the same technique we used for the other tubes (see acoustics of wind instruments: model). We will discover below that the simulations turn out to be surprisingly accurate, given the simplicity of the model, and are able to associate correctly some morphological features of the vocal tract with the sound of the different vowels.

Needless to say, the ability to simulate the sound leads directly to the ability to synthesize it (something that many electronic devices, even portable ones, can commonly do today, starting for example from a written text).

Of course many fine features are lost, and some sounds (such as nasalized vowels) that require additional resonant cavities cannot be simulated accurately.

From X-rays to the model

One of the first to practise this approach systematically was the Swedish scholar G. Fant who^[1] had the idea of deducing the diameters of the vocal tract from a set of X-ray images taken while a subject pronounced the six vowels of the Russian language.

In what follows we have used our JPipes app to simulate the response of the vocal tract on the basis of Fant's data.

The drawings on the left show (only schematically) the configuration of tongue, palate and lips while the subject pronounces the corresponding vowel. In the middle is the cross-section of the corresponding vocal tract, simplified so that it has a circular cross-section and a straight axis. The 0 is placed in the larynx at the vocal folds, while the end point corresponds to the mouth. The whole tract for this subject is about 16 cm long. Finally, on the right is the frequency response calculated with the numerical simulation.

Keep in mind that the frequency response does not correspond to the spectrum of the sound of the vowel, but is an intrinsic property of the vocal tract. To obtain the sound, one must add the frequencies produced by the source (the glottis). In any case, the sound of the five Russian vowels shown is quite similar to that of the corresponding Italian ones.

drawing (indicative only)	X-ray measurements	frequency response
The vowels U and O are articulated with very similar shapes of the vocal tract. The most relevant difference lies in the closure of the lips, which form a narrower opening for U than for O. Apart from the shape of the lips, both vowels appear to be associated with a shape made of two truncated-cone sections, one converging and one diverging, of similar length. The constriction is in the rear part of the channel, up to about the middle.		The most evident feature of the response is the presence of two very close peaks below 1000 Hz, followed by a broad region of substantial antiresonance, and then two more close peaks around 4000 Hz.

drawing (indicative only)	X-ray measurements	frequency response
The shape of the vocal tract for A looks like the junction of two channels. The first has a much smaller diameter than the second. Although the shape of the two sub-tracts is somewhat irregular, we will see that the salient feature of the system lies in the presence of two sections with different diameters. A simplified model in which the two sections are assumed to be cylindrical, in fact, gives equally satisfactory, though less accurate, results.		The response of the vocal tract for A resembles that for U and O, but the first two peaks are shifted to higher frequencies (around 1000 Hz). In terms of timbre, this corresponds to a less "dark" sound. Indeed, while the Italian closed O is closer to the sound of U, the open O is much more similar to an A.

drawing (indicative only)	X-ray measurements	frequency response
E and I are both characterized by a situation opposite to that of A: a section of larger diameter precedes one of smaller radius. The constriction is in the front half of the channel. In I the difference between the diameters is much more pronounced.		These two responses resemble each other, while they differ from those of all the other vowels in that the first two peaks are far apart. The second, in particular, always falls in a frequency range that corresponded to an antiresonance for A, O and U. In I the distance between the first two peaks is even more marked.

Conclusions

We said that the vowels shown in the previous section sound quite similar to the corresponding Italian vowels. Can we visualize these similarities from our data? Does a common pattern emerge?

Let us try to compare the formants obtained by simulation for five Russian vowels with the formants of the corresponding Italian vowels, extracted directly from our sound samples (Human voice).

Since it is not easy to compare the spectra directly, let us look at the positions of the first two peaks (specialists call them formants).

Note that the absolute position of the formants cannot be exactly the same in the two cases, because the vocal tract that was X-rayed and simulated is not that of our singer, and therefore has a different morphology. In particular, the tract in the X-rays is longer, and is therefore characterized by lower frequencies overall.

Nevertheless, the comparison clearly brings out a similar structure in both cases and, indeed, vowels placed at equivalent points of the triangles in the figure on the right are recognized as identical (or very similar to each other).

The model, that is, makes it possible to describe accurately the differences between vowels in terms of the position of the first formant and the distance between the first and second formants.

simulated formants	measured formants	Comparison
The light blue arrow marks the position of the first formant. In both the simulated and the real spectra, the frequency of the first formant increases going from I to A, while it decreases going from A to U. The blue arrow marks the distance between the first two formants. It is greatest for the vowel I, slightly smaller for E, and much smaller for the other vowels.		The graph shows the position of the first two formants extracted from our samples of the Italian vowels (in red) and those simulated for the vocal tracts of the Russian language (in green). It is immediately apparent that both series of vowels are arranged to form a triangle with vertices I, A and U. These vowels sound very similar in both languages, and this fact is reproduced very well by our simple model.

For further discussion, and more on extracting formants from the sound spectrum, see the page The vowel A.

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