3 Voiced sounds production by the phonatory system

Transcription

1 3 Voiced sounds production by the phonatory system In this chapter, a description of the physics of the voiced sounds production is given, emphasizing the description of the control parameters which will later be considered uncertain. 3.1 Overview of the anatomy of the phonatory system The phonatory system, illustrated in Fig.3.1, can be divided into three parts: 1. the subglottal subsystem, composed of the lungs and the trachea, is used to regulate the airflow in the phonatory system, by controlling the pressure in the lungs. 2. the vocal folds, when appropriately placed, start to vibrate due to the airflow coming through the trachea. Due to the vibration of the vocal folds, the airflow is transmitted as a series of air pulses, also called glottal flow. 3. The series of air pulses is an acoustic input to the supraglottal subsystem, called vocal tract in this work. The vocal tract is an acoustical resonator, Figure 3.1: Global view of the phonatory system (sagittal plane). From

2 Chapter 3. Voiced sounds production by the phonatory system 24 Figure 3.2: Sagittal cut of the phonatory system(left), view of the abducted vocal folds from above (lower right) and view of a cut of the section of a vocal fold (upper right). (adapted from (Sata07)) consisting of the pharynx, the oral cavity and the nasal cavity. It acts as an acoustic frequency filter, emphasizing some frequencies among others, defining the spoken vowel. 3.2 Vocal folds physiology The focus of this thesis is to infer some parameters linked to a numerical vocal folds model. Physiology of the vocal folds is herein described, so it can be further related to the numerical model. The vocal folds, situated in the larynx, are represented in more details in Fig Representing the section of a vocal fold As shown in the upper right quadrant of Fig.3.2, a vocal fold is composed of various layers, each one with specific mechanical properties. From the surface, the successive layers are: the epithelium (skin), having a thickness of 0.05 to 0.10 mm,

3 Chapter 3. Voiced sounds production by the phonatory system 25 Figure 3.3: Di erent schemes used to represent the vocal folds in mechanical models (adapted from (Titz94)), along with some corresponding references. the lamina propria, which is 1 to 2 mm thick, is made of di erent fibers, some having a rubber like behaviour (superficial layer), while others are almost inextensible (deep layer), the thyroarytenoid muscle, which is 7 to 8 mm thick. When representing the vocal folds by a mechanical model, di erent schemes may be used to represent the section of a vocal fold, as shown in Fig Although a more accurate representation of the vocal folds is desirable, it has some drawbacks. One of them is to be computationally expensive, which makes it prohibitive for stochastic simulations such as the one used in this work. Another one is the fact that there is no consensus on the average mechanical properties for the human vocal folds, nor on each of its subcomponents (Cook09b, Tao07). As the main focus of this thesis is to infer some of the mechanical properties of the vocal folds, the use of a more simple, computationally cheap and yet reasonably accurate model is natural. Before presenting the numerical twomass model to be used, some more physiological and mechanical properties of the vocal folds are described.

4 Chapter 3. Voiced sounds production by the phonatory system Displacements of the vocal folds The vocal folds are attached on the posterior end to the arytenoid cartilage, and, on the anterior end to the thyroid cartilage (commonly known as the Adam s Apple). The mechanical and geometrical properties of the vocal folds depend on various parameters (Sata07, Titz94). The muscles involved in vocal folds positionning are represented in Fig.3.4. Figure 3.4: Larynx skeleton, vocal folds and muscles acting on it (adapted from (Rank53)). Their role is as follows: The crycothyroid muscle, when contracted, applies an extension e ort on the vocal folds. The vocalis and thyroarytenoid muscles, when contracted, apply a compression e ort on the vocal folds. The posterior cricoarytenoid separates the vocal folds (abduction) by approximating the posterior end of the arytenoid cartilages, separating the anterior end.

5 Chapter 3. Voiced sounds production by the phonatory system 27 The lateral cricoarytenoid is contracted to join the anterior parts of the arytenoid cartilages, during adduction. The interarytenoid approximates the arythenoid cartilages one from the other. It is worth noting that those muscles can be contracted without changing length (isometric contraction). While breathing, the vocal folds are separated (abducted) as shown on Fig.3.5. On the other hand, when producing voiced sounds, the vocal folds are approximated (adducted) and the airflow passes through a thin slit (called glottis) between the vocal folds. Figure 3.5: Adducted and abducted vocal folds viewed from above. In the mathematical model herein used to represent the phonatory system, the vocal folds are always considered adducted and parallel. Their length, mechanical properties and position in the vocal tract will be parameters of the model. 3.3 Vocal folds vibration The production of a voiced sound starts by the adduction of the vocal folds, and, the creation of a pressure di erence between the lungs and the ambient pressure. A flow going from the lungs to the lips, passing through the glottis, is then created. Due to this flow, the oscillation of the vocal folds is eventually triggered. The whole process results in the creation of pulses of air at the output of the glottis. The typical vibration pattern of the vocal folds, along with the sketch of a typical glottal flow, is represented in Fig.3.6. The vibration of the vocal folds usually starts at step 3 (this is observed, for example, when pronouncing harp insisting on the h) of Fig.3.6.

6 Chapter 3. Voiced sounds production by the phonatory system 28 Figure 3.6: Vocal folds vibration pattern and glottal flow for modal voice. Due to the Bernoulli e ect induced by the flow passing through the narrow glottis, the vocal folds are sucked together (step 4). It is worth noting that the contact starts from the downstream part of the vocal folds (step 5) to finish by the upstream part (step 1). Finally, the elastic properties of the vocal the vocal folds separates them, starting by the downstream part again (step 2). Due to the elastic properties of the vocal folds, and, to the alternatively positives and negative forces applied to the vocal folds surface and due to the flow, the oscillations of the vocal folds are maintained (Thom05). 3.4 Supraglottal resonators The vocal tract is like an acoustical filter for the glottal signal, such as mu ers for vehicle motor noise or trumpets for lips signal. The vocal folds are seen as a punctual acoustic source by the vocal tract, and, its input signal is the glottal flow shown in Fig.3.6. During the production of a voiced sound, a quasi steady acoustic wave propagates in the vocal tract, and, its output at the lips is a vowel we can discriminate. The produced vowel depends on the shape of the vocal tract which amplifies some frequencies and damps others (Fant60). In order to determine the vocal tract shape during speech, a set of radiographies such as the one shown in Fig.3.7, are usually used. The section area along the vocal tract can be estimated from Figs. 3.8 and 3.9, resulting in Fig Using such imaging technologies, the typical vocal tract transversal section shape and area, along it length have been

7 Chapter 3. Voiced sounds production by the phonatory system 29 Figure 3.7: Vocal tract radiography (sagittal cut). PUC-Rio - Certificação Digital Nº /CA determined (Fant60). Figure 3.8: Variation of the vocal tract height (sagittal cut) (Fant,1960). Figure 3.9: Section variation along the vocal tract of Fig. 3.8 (Fant,1960). The acoustic wave propagated in the vocal tract is of low frequency compared to the vocal tract section. Then, the vocal tract is generally represented by a cylindrical tube which section area along its length is equivalent to the real one. This simplification is justified n the next chapter. Typical value are shown in Fig For a male speaker, depending on the speaker and the spoken vowel, the vocal tract length is around 17 centimetres.

8 Chapter 3. Voiced sounds production by the phonatory system 30 Figure 3.10: Equivalent of the area along the vocal tract for the cylindrical approximation (Fant,1960).