VIBRATION The vibration of the vocal folds is a very

complex movement. Generally speaking, the vocal folds open up from bottom to top and from back to front. The closing of the vocal folds also proceeds from bottom to top, but along the horizontal axis it starts from the middle, closing forwards and backwards at the same time. The closure of the vocal folds is often incomplete, especially for women, since a small triangle next to the arytenoids, at the posterior (back) end of the vocal folds, remains open.

THEORIES A number of different theories have been proposed to

explain the vibration of the vocal folds during speech. While many are no longer supported by recent evidence, we present these arguments in some detail to show how the present theory about vocal fold vibration has developed. Various researchers have assumed that voicing is the result of one of the following:

1 Vibrating string theory: the vocal folds oscillate (move backward and forward) in the airstream just like strings.

2 Neurochronaxic theory: neural impulses of the central nervous system directly control the vocal folds.

3 Aerodynamic theory: a sucking pressure drop of the streaming air.

4 Myoelastic theory: the elasticity of the vocal folds.

THE VIBRATING STRING THEORY The vibrating string theory (Ferrein1741) assumes

that the vocal folds vibrate just like the strings of a violin, and that the vibrating vocal folds produce a tone. This assumption is not plausible, for an oscillating string needs a resonance body in order to be clearly audible. For example, the string of an electric guitar, which does not have a resonance body, can hardly be heard without amplification. On an acoustic guitar an oscillating string can be clearly perceived because it does have a resonance body. As the vocal tract has resonating qualities, but it is a rather poor resonator and it needs the large energy of the air puffs going through the vocal folds to make this quality audible. The vibrating vocal folds alone (without air flowing through them) are inaudible.

THE NEUROCHRONAXIC THEORY

The neurochronaxic theory (Husson 1950) assumes that the vibration of the vocal folds is realized by rapidly contracting and relaxing muscles. But this theory is not plausible either, since no muscle group in the human body is able to execute movements as fast as the vocal folds, which open and close during speech between 100 and 400 times per second. During singing, this may happen even faster, while the vocal folds of a crying baby may oscillate up to 2,000 times per second. No muscle can be actively moved fast enough to attain such high oscillation rates. In addition, even the nerves which activate muscles can only generate up to 1,000 impulses per second. The fast vibration of the vocal folds during the production of voiced sounds thus requires still another explanation.

THE NEUROCHRONAXIC THEORY We now know that the vocal folds do not

oscillate by contracting and relaxing of muscles requiring a resonance body, but rather act more as the mouthpiece of a Woodwind instrument, for example, like an oboe: a stream of air is periodically interrupted, and the resulting impulses of air are perceived as a tone. It is not the vibration of the vocal folds themselves which leads to a sound, but the effect on the air that passes through, as in the case of an oboe, where the interruptions of the airflow make the vibration audible.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY

Imagine the vocal folds as two swinging doors in a drafty corridor. They can be locked shut (adducted), permanently wide open by being hooked to the wall (abducted), or move freely in the draft. The stronger the draft, the further the doors open. We reported that the air pressure in the lungs is kept at a relatively constant level. This implies that the airflow through the trachea and the larynx is relatively steady as well. If the airstream is constant, swinging doors (the vocal folds) could be expected to open to a certain degree, but there is no reason for them to start swinging back and forth. For this reason, it has long been unclear why the steady stream of air should make the vocal folds oscillate between opening and closing, instead of simply keeping them slightly open. This question was answered by van den Berg and his colleagues (1957), who suggested an explanation based on the Bernoulli effect.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY When a liquid or a gas (for instance, air)

flows steadily and without turbulence through a tube, all the molecules move along at approximately the same speed in the direction of the stream. This is known as laminar flow. To be precise, the molecules still execute a number of movements back and forth, but the steady forward movement in one direction predominates. This is comparable to a carnival procession in which the participants are continuously dancing and moving in all directions but, on the average, move along with the parade.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY What happens if the tube is narrowed

(see Figure 5.6)? This is comparable to the situation between the vocal folds in the larynx. The flow entering and exiting the tube remains constant. Since the air molecules have the same speed before and after the narrow passage, the molecules must move faster while they are passing through the narrow passage.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY

This is represented more accurately in Figure 5.7. In this "snapshot," four molecules (represented by four black footprints) are moving along in a single row of four, both before and after the narrow passage. Within the passage, there are also four molecules, but this time grouped into two rows of two because the passage is only half as wide in this part. Now consider the situation a moment later, as represented by the white footprints. The two rows of four molecules before and after the narrow passage have advanced by one step. Within the passage, the four molecules must have advanced as well, since there is no congestion in the steady stream. This means that the molecules within the passage, which are grouped into rows of two, must have advanced by two steps. In other words, a steady forward movement requires that the same number of molecules advance both before and after the narrow passage. But within the passage, the molecules must move faster. The speed of the air is therefore higher when it flows through a narrow passage than before or after it.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY This phenomenon is relatively straightforward to explain and

understand. It may seem a bit of a paradox, however, that the pressure is lower within the narrow passage than before or after. This is counterintuitive, for everybody knows from traffic congestion that the jam (and therefore the pressure) seems to be the highest within the narrow passage.

But this comparison does not hold. When observing the congestion in traffic going from, for example, two lanes to one lane and back again to two lanes, the congestion arises before the narrowing, and the jam is at its maximum before the narrow passage. Within the passage the traffic does move along, although the cars move slowly and are close together. After the narrow passage, the traffic is more spread out and moves fast. The situation is different in a laminar stream, since the density before, within, and after the narrow passage is the same, and the speed is higher within the passage than before or after. Thus, the experience that congestion arises in a narrow passage, and therefore the pressure within the passage must be at its highest, does not correspond to the behavior of air flowing through the narrow part of a tube. How can this be explained?

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY We already mentioned that the molecules move on

average with a certain speed in one direction, although their movements are actually rather disordered. They move back and forth, left and right, up and down. Their speed and direction is only given by the sum of these movements. We compared this to a carnival procession moving through the streets: the individual participants walk freely about, they may even jump in the air, and still continue to move together in one direction. Some participants at the edges of the parade may accidentally bump into spectators; this is the pressure which they exert upon the borders of their path. In the same way, the air molecules bump against the walls of the tube, thus exerting a pressure on the inside of the tube. When the carnival procession moves faster, the individual participants have less time to move to the left or to the right, and therefore bump less often into spectators at the edges of the parade.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY Exactly the same happens to the airstream going

through a narrow passage: the individual molecules move faster in one direction, and less often up and down or left and right. They therefore bump less often against the walls of the tube and the resulting force that they exert on the walls is lower. The air pressure is therefore lower within the narrow passage, where the molecules move faster forward, than before or behind it {or below and above the vocal folds). In other words, instead of increasing the pressure, the narrow passage actually decreases the pressure of the air flowing through. This phenomenon is known as the Bernoulli effect. Since it is a characteristic of flowing air, it is called an aerodynamic effect. As a result of this relatively lower pressure in the passage between the vocal folds, the folds are sucked together instead of being forced apart.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY A simple demonstration of the

aerodynamic Bernoulli effect can be seen in Figure 5.8, where two sheets of paper are attached loosely to pencils and hang next to each other. If one blows in between, the two sheets of paper approach each other. This shows that the air pressure in the passage decreases as a result of the air flowing through at greater speed. The sheets are not forced apart, as is the case when the air pressure increases.

THE BERNOULLI EFFECT AND THEAERODYNAMIC THEORY

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION

Using the aerodynamic Bernoulli effect to explain the behavior of the vibrating vocal folds was an important breakthrough toward understanding the mechanism responsible for vocal fold vibration. The application of the Bernoulli effect made it possible to explain why the vocal folds close so quickly, even though the air pressure from the lungs should push them apart. An aerodynamic account of vocal fold vibration thus involves the following: the vocal folds are initially closed; they are then blown apart by the subglottal air pressure, and, finally, sucked together because of the Bernoulli effect. Once they are closed, the cycle starts all over again. This account nevertheless has at least one shortcoming: under this view, the rate of vocal fold vibration depends on the speed of the flowing air - in other words, it depends on the relation between subglottal and supralaryngeal air pressure. Since the subglottal air pressure is relatively constant, the rate of vocal fold vibration should remain constant as well. However, this rate continuously changes during speech production. Additional mechanisms are therefore required to explain all aspects of vocal fold vibration.

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION A first, important, factor influencing the rate of

vocal fold vibration is the length of the vocal folds: long vocal folds oscillate at a slower rate than short ones. This is comparable to string instruments: a cello, having longer strings than a violin, produces lower tones. And since the vocal folds of men are usually longer than those of women, male voices are usually lower than female voices. An example of the influence of the length of the vocal folds can be observed during puberty, when the length (and thickness, see below) of the vocal folds of boys change rather quickly. This leads to the so-called "voice mutation" during which the speaker has not yet learned to correctly control the changed anatomical structure.

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION A second factor determining the rate of vocal

fold vibration is the elasticity of the vocal folds. Even without the Bernoulli effect, the vocal folds, after being opened, are pulled back together by their own elastic recoil force. This is comparable to a guitar string that swings by plucking it: once the string is moved away from its rest position, it returns to it due to the elastic recoil force and overshoots it to the other side - and so forth. This type of oscillation (without Bernoulli effect) occurs during vocal fold vibration when the folds are very tense and a speaker Uses a very high-pitched falsetto voice.

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION In addition, the rate of vocal fold vibration depends on

their elastic tension: tense folds oscillate faster than slack folds, because they are pulled back to the rest position with more force. The same is true of a guitar string: if the tension is increased, the string oscillates faster (that is, more often per time unit), thus producing a higher tone- this effect is actually used to tune a guitar. Vocal fold tension may be changed by a movement of the cricoid and the thyroid relative to each other caused by the cricothyroid muscles. The vocal folds become slightly longer (since the distance between the notch on the thyroid plates and the arytenoids increases), which causes a drop in frequency. However, the increase in tension predominates, so that the net result of this rotating movement of the two cartilages is a higher rate of oscillation. The fine adjustment of the oscillation rate during speech is essentially achieved by means of this mechanism.

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION A fourth factor influencing the rate of vocal

fold vibration is their mass, which is linked to their "thickness." This too can be related to string instruments: keeping length and tension equal, a thick guitar string produces a lower tone than a thin string. In the same way, thick vocal folds oscillate at a lower rate than thin vocal folds. The thickness of that part of the vocal folds which participates in the vibration is to a certain extent determined by anatomical factors, but can additionally be adjusted by the muscular tissue of the vocal folds themselves.

They can change their form from fleshy lips to thin bands, thus changing the rate at which they vibrate.

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION These four effects, relating the vibration of the muscular vocal folds

to their length, elasticity, tension, and mass, are called myoelastic effects. Our account of vocal fold vibration so far includes the following four factors:

1 The Bernoulli effect enables the vocal folds to close during normal oscillation. This aerodynamic effect depends on the speed of the airstream. As this speed increases, the pressure in the direction perpendicular to the airflow decreases. Since this speed in turn depends on the air pressure difference between the subglottal and supralaryngeal systems, the rate of vocal fold vibration is influenced by this difference in air pressure across the vocal folds.

2 Long vocal folds vibrate at a lower rate than short ones. Length differences between vocal folds are mostly determined by anatomical factors.

3 Vocal folds oscillate faster when they are tense than when they are relaxed. The tension of the vocal folds is determined primarily by the rotating, swing like movement executed by the thyroid and the cricoid. This factor is used to fine-tune the rate of vibration in normal speech production.

4 Vocal folds with a large mass oscillate slower than thin vocal folds. The thickness of the vocal folds is partly determined by anatomical factors, but can additionally be adjusted by the muscles themselves.

THE MYOELASTIC THEORY OF VOCAL FOLD VIBRATION Treating the vocal folds as an aerodynamic and myoelastic

system provides a reasonable explication for the oscillation of the vocal folds and the changes in their oscillation rate. However, no fewer than three additional principles are needed in order to fully explain the actual oscillation characteristics (Broad 1973 ). Imagining the vocal folds as an elastic system submitted to the aerodynamic forces of the Bernoulli effect, they are comparable to a pair of swinging doors in a drafty corridor, as mentioned before: the draft causes them to swing back and forth, and the tension in the hinges as well as the mass and size of the doors determine the rate of their vibration. Such swinging doors in a drafty corridor could only close entirely if the tension of the springs in the hinges is very high; instead, both panels of the door move back and forth periodically, without ever fully closing the passage. But this is not the behavior of the vocal folds: when they are vibrating, the left and right vocal folds do touch each other for a relatively long time and over a relatively long distance. Swinging doors never do so. The next sections introduce additional effects to explain this difference.

TWO-MASS THEORY OF VOCAL FOLD VIBRATION More recent research has shown that the vocal folds

can only oscillate because they do not constitute an indivisible unit, unlike swinging doors; instead, the upper and lower parts of the vocal folds may execute separate, but related, movements. This can be seen in Figure 5.9: first, the lower parts of the vocal folds are forced open by the pressure from the lungs, but the upper parts still remain closed (Figure 5.9b). Only at a later stage are the upper parts opened as well (Figure 5.9d) - partly as a result of the air pressure, partly because they are pulled along by the tissue of the lower parts. As a result of the acceleration of their mass, the upper parts continue to move apart, but at the same time the lower parts are already starting to close again (Figure 5.9e).

TWO-MASS THEORY OF VOCAL FOLD VIBRATION

Somewhat later, the lower parts of the vocal folds are already entirely closed, but the upper parts are still in their closing stage (Figure 5.9g). Both the upper and lower parts of the vocal folds thus execute an opening and closing movement, but they are not in the same phase: the upper parts of the vocal folds follow behind the lower parts. It is precisely this lag between the movement of the upper and lower parts of the vocal folds that enables them to form a complete closure of the trachea. This principle is called the two-mass theory of vocal fold vibration (Ishizaka and Flanagan 1972). This does not mean that only two masses are involved; it can be any number, but two masses are the minimum to explain this behavior.

MUCO-VISCOSE, COVER BODY, ANDFLOW-SEPARATION THEORY The different mechanisms that have already been

described explain the vocal fold vibration to a considerable extent. However, mathematical modeling has led to the insight that the aerodynamic and myoelastic effects occurring at the vocal folds, combined with the phase difference between two masses, cannot explain all the details of the vibration. Two additional characteristics have been identified. First, the outer edges of the vocal folds consist of many layers of different kinds of tissue, which together form viscous(thick and sticky) surfaces (see Figure 5.10). As a result, the surface reacts differently to the airstream than the deeper muscle body and the surface "flutters" when the vocal folds vibrate in the airstream. Just like sheets, fluttering on a clothesline in the wind, this movement of the outer edges causes a pulling force, which stretches the vocal folds somewhat. This effect is called 111uco-viscose by Broad (1979), and is described by the cover body theory of Hirano (1974).

MUCO-VISCOSE, COVER BODY, ANDFLOW-SEPARATION THEORY Second, the flow-separation theory (lshizaka

and Matsudaira 1968) states that the abrupt change of the airstream that occurs at the edges of the vocal folds leads to a certain amount of turbulence (so-called eddies). They are comparable to the eddies that can sometimes be observed in the fall at corners of a house, where fallen leaves start moving around in circles. These small whirlwinds influence the movements of the vocal folds by forcing the tips of the vocal folds apart (see Figure 5.10). Without these additional forces, the vocal folds would not be able to vibrate as they do.

ONE CYCLE OF VOCAL FOLD VIBRATION To summarize, the following factors provide a

complete account of vocal fold vibration: 1 The aerodynamic effect explains why the vocal

folds are able to close as quickly during normal oscillation.

2 The myoelastic effect explains why the vocal folds can be forced open in the first place, and why they are able to oscillate even when the Bernoulli effect does not apply.

3 The two-mass theory explains why the vocal folds are able to achieve complete closure.

4 The muco-viscose and flow-separation theories explain the details of the oscillation characteristics of the vocal folds.

ONE CYCLE OF VOCAL FOLD VIBRATION

In sum, one cycle of vocal fold vibration can be described as follows (see Figure 5.9): initially, the vocal folds are fully closed by adducted arytenoids (a). The vocal folds are slightly tensioned by their own muscular force and the position of the cricoid relative to the thyroid. The pulmonic air pressure pushes the lower parts the vocal folds apart while their upper parts are still together (b). When the folds are forced to open at their upper end (c), air starts passing through them. This initiates the Bernoulli effect that pulls the folds together but the inertia mass of the folds continues to open the upper parts (d). The Bernoulli effect together with the elastic recoil forces of the folds causes the lower parts to mov together, while the upper parts are still moving apart as a result of the inertia of the mass and their muco-viscose structure that pulls the peripheral parts of the folds apart supported by the eddies of the flow-separation (e). The lower parts of the folds finally are almost together (f), which means that the Bernoulli force is particularly strong, pulling them firmly together. The upper parts are moving 'together as a result of the elastic recoil forces and the pulling forces of the lower (g). (Note that this cannot be the result of the Bernoulli effect, since the airflow has stopped.) Eventually, the upper parts close as well and the next cycle begins(h).