The Human Instrument

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PHYSIOLOGY The Human Instru me nt When judged by its si ze, ou r voca l system fa i ls to i mpress as a musica l inst ru ment. How t hen can singers produce a ll t hose remarkable sounds? By In go R. Titz e

he human vocal system would not to describe how great singers produce those receive much acclaim if instrument amazing sounds. KEY CONCEPTS T makers placed it in a lineup of tradi- ■ Although the human vocal tional orchestral instruments. Arranged by size, Music-Making Keys system is small, it manages to for example, the voice box (larynx)—and the Structural and operational shortcomings in the create sounds as varied and airway it sits in—would be grouped with the human vocal apparatus are apparent in all its beautiful as those produced piccolo, among the smallest of mechanical parts. To make music, an instrument needs by a variety of musical music makers. And yet experienced singers three basic components: a sound source that instruments. compete well with all man-made instruments, vibrates in the air to generate a frequency that

■ All instruments have a sound one on one and even paired with full orchestras. we perceive as pitch, together with higher fre- source, a resonator that Recent investigations of how our singing voice quencies that deﬁne the timbre (sound color); reinforces the basic sound and generates a remarkable range of sounds have one or more resonators that reinforce the fun- a radiator that transmits the revealed surprising complexity in the behavior damental frequency by increasing its vibration sound to listeners. of the vocal system’s elements and in the ways strength; and a radiating surface or oriﬁce that

■ A human’ s sound source is the they interact. transfers the sounds to free air space and, even- vibrating vocal folds of the For more than half a century, scientists ex- tually, to a listener’s ear. larynx; the resonator is the plained the voice’s ability to create song by invok- In the case of, say, a trumpet, a player’s lips sound-boosting airway above ing a so-called linear theory of speech acoustics, vibrate as lung-pumped air rushes between them the larynx; and the radiator is whereby the source of sound and the resonator into a cup-shaped mouthpiece to create a funda- the opening at the mouth. of sound (or ampliﬁer) work independently [see mental frequency and several higher frequencies ■ The human voice can create “The Acoustics of the Singing Voice,” by Johan that are called overtones. The instrument’s met- such an impressive array of Sundberg; Scientific American, March al tubes serve as the resonators, and the expand- sounds because it relies on 1977]. Researchers have now learned, however, ing aperture of the horn radiates the sound. nonlinear effects, in which that nonlinear interactions—those in which Trumpeters alter fundamental frequency by small inputs yield surprisingly source and resonator feed off each other—play modifying the lip tension and by pressing the large outputs. an unexpectedly crucial role in generating hu- valves to change the effective length of the tubes. —The Editors man sound. Such insights now make it possible Or take a violin: the strings vibrate to create

AARONGOODMAN much smaller equipment.

© 2007 SCIENTIFIC AMERICAN, INC. [THE BASICS] pitches, the central air cavity and wooden top supply resonance, and the f holes in the top plate HOW INSTRUMENTS MAKE MUSIC help to send the sound into the surrounding air. Nearly all musical instruments, both man-made A singer, on the other hand, relies on vibrat- and biological, share three basic elements: ing vocal folds, blowing air across them to gen- VIOLIN ●1 a sound source that vibrates in air to create a erate the sound frequencies. Vocal folds are two certain fundamental frequency (which is perceived small bundles of specialized tissue, sometimes Tuning pegs as pitch) and its related harmonic frequencies called “vocal cords,” that protrude pouchlike (integral multiples of the basic frequency), which from the walls of the larynx. They generate a define the timbre, or sound color; ●2 a resonator fundamental frequency by rapidly oscillating as that reinforces or amplifies the fundamental they contact each other, separate and come in frequency and its harmonics; and ●3 a sound contact again. The glottis (the space between the radiator that transfers the sound to free air space folds) opens and closes. The laryngeal vestibule, and on to a listener’s ear. an airway passage just above the larynx, acts Fingerboard like the mouthpiece of the trumpet to couple the sound to the remaining part of the resonator known as the vocal tract. The lips radiate the sound outward like the bell of the trumpet. Instrument manufacturers examining the vo- ●1 SOUND SOURCE (string) cal folds, which are collectively the size of your thumbnail, would not find their potential for making orchestral musical sounds impressive. ●2 SOUND RESONATOR (top plate) Beyond their small size, one immediate objec- tion would be that they would seem too soft and spongy to sustain vibration and create a variety of pitches. Bridge Nature, biology’s instrument maker, might ●3 SOUND RADIATOR (f hole) respond that although the folds are certainly undersized, the airways can produce enough resonance to reinforce the sound of the larynx substantially. But here, too, the musical instrument maker would probably still fail to be per- suaded: the typical air tube extends just 15 to 20 centimeters above the larynx and 12 to 15 centimeters below it, no more than the length of a piccolo. The rest of the body contributes little or nothing. Wind instruments that approximate the pitches created by the human voice (trom- frequencies via a square root relation. Thus, to bones, trumpets, bassoons) typically contain make a steel string of a given length double its much longer tubes; the bell and valves of a trum- LINEAR VS. frequency (raise the pitch by an octave), one must pet, for instance, uncoil to about two meters NONLINEAR quadruple the string tension. This rather strin- and those of a trombone to about three meters. Voice scientists used to gent requirement may limit the range of frequen- explain the performance of cies that can reasonably be obtained by altering Source Design the human vocal system in a source’s stiffness or tension. To understand how nature the instrument maker terms of linear effects, ones Fortunately, a player can also change the fre- has developed the vocal folds that perform in which the outputs of a quency of a sound source’s vibration by effec- beyond expectations, first consider some stan- function are proportional to tively lengthening or shrinking the oscillating dard requirements for sound sources. For a reed the inputs (and so can be rep- element. Within a vibrating string, for instance, resented as a line, for exam- or string to sustain its vibration, it needs to be frequencies are inversely proportional to the ple). More recently, research- made of an appropriately elastic material so it length of the vibrating segment. By pinning the ers have concluded that the can snap back when deformed. Elasticity is mea- human vocal system behaves string on one end with the finger, a player selects sured by its stiffness (or, conversely, flexibility) different frequencies. If a string’s vibrating length nonlinearly. In a nonlinear iStockPhoto E or its tension: a reed has a bending stiffness; a feedback system, small is cut in half without changing the tension, for string vibrates under tension. Generally, a sound changes can result in dispro- example, the vibration frequency doubles. To

source’s stiffness or tension determines the sound portionately large effects. produce a wider range of frequencies, a single STEVEDIBBLE

HUMAN VOCAL SYSTEM

Ingo R. Titze, a world leader in the scientiﬁc study of the human voice, has published more than 500 articles on the topic. He currently serves as the University of Iowa Foundation Distinguished Professor in that institution’s department of speech pathology and audiology, and he directs the 3 SOUND RADIATOR ● National Center for Voice and (mouth) Speech (www.ncvs.org) at the Oral cavity Denver Center for the Performing Arts. Titze, who received his Ph.D. Pharynx (throat) in physics from Brigham Young University in 1972, teaches singing and sings in multiple styles, includ- ●2 SOUND RESONATOR ing opera, Broadway and pop. Larynx (airway)

●1 SOUND SOURCE (vocal folds of larynx)

Trachea

musical instrument often uses multiple strings. cles to shift its end points. But should we length- String instruments, then, have three distinct en or shorten the vocal folds to raise frequency? mechanisms for changing frequency: altering An argument could be made for either adjust- the length of a string, modifying its tension, or ment. Longer vocal folds would vibrate at lower skipping to another string. Players of stringed frequency, but tenser folds would vibrate at instruments typically set the tensions by turn- higher frequency.

) ing pegs around which the strings are wrapped; The physics formula describing the frequen-

the strings retain this same tension between end cy of a string ﬁxed at both ends under tension

illustration points. Players almost never can manipulate says that to get the maximum increase in fre- both the length and tension simultaneously. quency, one should increase the tension (actu- ally the tensile stress, or tension per cross-sec-

);GEORGE PIMENTEL The Little Source That Could tional area) while decreasing the length. Such a );ADAM QUESTELL (

Titze SHRIEK ROCKER Steven Tyler is In playing the human vocal folds, in contrast, response requires an unusual material, because Tyler (

celebrated for his ability to singers must do what no other string instrument most materials can increase tension (stress) only scream tunefully. Aerosmith’s can do: vary the length and tension of the vibrat- when they are elongated. Think of a rubber lead singer creates that ex- ing material simultaneously to change frequency. band; pull on it, and it tightens up. Thus, length treme sound by using a large Rather than pinning down a vocal fold with a and tension are in competition for changing amount of nonlinear effects in WireImage/GettyImages COURTESYOF INGO R. TITZE ( ﬁnger to shorten its effective length, we use mus- frequency. his vocalizations.

www.SciAm.com SCIENTIFIC AMERICAN 97 © 2007 SCIENTIFIC AMERICAN, INC. [HUMAN SOUND SOURCE] HOW OUR VOCAL FOLDS WORK Unlike violin strings, the human sound source—the vocal folds (or vocal cords) in the larynx—has a complex, three-part structure that allows us to generate several octaves of frequencies. At the core of each fold is a stringlike ligament (cross section). Internal to the ligament are contractile muscles. And covering it all is a highly ﬂexible mucous membrane. Each component brings a special capability to the whole. The ligament’s tensile stress rises rapidly with elongation (by muscles that move the cartilages attached to the folds), which helps to produce higher frequencies. The vocal-fold muscle can increase tensile stress as it contracts. In doing so, it generates an even larger frequency range. The soft, pliable surface of the outer membrane, which oscillates like a ﬂag in the wind as air from the lungs passes over it, exchanges vibrational energy with the airstream to create sound waves.

LARYNX VIEWED FROM MOUTH

Airﬂow Vocal folds

LARYNX

Ligament Vocal folds Muscle Mucous membrane

VOCAL-FOLD Glottis CROSS SECTION

Nature has addressed these problems by con- Complex Cords structing the vocal folds out of a three-part mate- Biology has also found a second way to expand rial that displays properties not found in standard the pitch range of the vocal folds, including a instrument strings. One component is a ligament material that can increase in tension as it short- that looks somewhat stringlike, which is why ens, namely, muscle tissue. The internal con- the folds came to be called “cords” popularly. traction of muscle ﬁbers can raise the stress Scientists have shown in biomechanical tests that between a vocal fold’s end points, even when the stress in this ligament rises nonlinearly when the fold itself shortens. About 90 percent of the it is stretched just a little; it can be virtually limp volume of the vocal fold is muscle tissue. In when short but impressively tense when elongat- essence, nature has solved the pitch problem

ed. Stretching its length from 1.0 to just 1.6 cen- largely by growing a group of strings side by ) timeters, for example, can raise its internal stress side as a laminate, with some layers having con-

BROADWAY STAR Ethel Merman by a factor of 30, which would yield a frequency tractile properties and others not. But how can illustration belted out songs with precise change ratio of more than 5 to 1 (recall the this complex tissue be kept in vibration when it enunciation and pitch so the square root relation mentioned earlier). But the cannot be bowed or repeatedly plucked inside audience could hear her even fact that the length increases by 60 percent low- the larynx? The only source of energy available

without amplification. The );ADAM QUESTELL ( ers the vibration rate, bringing the true frequency to deform the folds and thereby induce vibra- female “belt” voice gains resonance from vocal-tract inertive ratio back to around 3 to 1, about one and a half tion—the way that wind passing across a flag Merman reactance [see box on opposite octaves in musical terms. Most of us speak and makes it flap—is air flowing from the lungs. A page], which boosts the sec- sing in this frequency range, but some singers can muscle and a ligament alone would be too stiff ond harmonic frequency (dou- produce as much as four to five octaves, which to develop such vibrations as air passes over

ble the fundamental). is still considered extraordinary by scientists. their surfaces. For the needed air-driven oscil- BETTMANN/CORBIS(

98 SCIENTIFIC AMERICAN Januar y 20 0 8 © 2007 SCIENTIFIC AMERICAN, INC. lation to occur, a soft, pliable surface tissue is natural (freely vibrating) frequencies compete in DID YOU KNOW? required, one that can respond to the airstream these tissues for dominance. This competition by generating waves akin to those the wind may result in unexpected pitch jumps or rough- Humans tend to think of the forms at the surface of the ocean [see “The ness in the sound [see “The Throat Singers of entire body as the human Human Voice,” by Robert T. Sataloff; Scien- Tuva,” by Levin Edgerton; Scientific Ameri- instrument, which would make it comparable in size tific American, December 1992]. can, September 1999]. to a double bass. But most And indeed, the folds have a third layer, a For low pitches and moderate-to-loud sound of the human body contrib- mucous membrane that stretches over the mus- volumes, the singer activates the vocal fold mus- utes nothing to the sound— cle-ligament combination to provide this ener- cle and sets all the layers into vibration. The vo- neither the chest, the back, gy-transfer function. This mucosa, which con- cal folds are short, and the muscle stress largely the belly, the buttocks nor sists of a very thin skin (epithelium) with a flu- determines the pitch. In this case, the mucosa the legs. All the sound comes idlike substance underneath, is easily deformed and the ligament are both relaxed and serve from the voice box (larynx) and can support a so-called surface wave. My mainly to propagate the desired surface waves and the air passages. colleagues and I have shown mathematically for self-sustained oscillation. For the sound vol- that this airstream-driven wave sustains vibra- ume to be reduced at these pitches, the muscle tion. The buckling, ribbonlike motion often does not vibrate and is used only to adjust the makes the tissue look like it is folding bottom to vocal-fold length. It is the combined elasticity of top, which is how the name “vocal fold” arose. the mucosa and ligament that determines the frequency. To create high pitches, the singer Playing the Vocal Folds elongates the vocal fold; ligament stress alone How can this triple-decker system be played then dictates the frequency while the mucosa over several octaves so as to produce a single carries the surface wave. frequency? Only with much experience and It is not hard to imagine the complicated con- dexterity. Chaotic effects always lurk in the trol system and innervation of the laryngeal background during vocalizations as multiple muscles needed to finely regulate these tensions

[HUMAN SOUND RESONATOR] HOW THE VOCAL AIRWAYS AMPLIFY SOUND Singers use a nonlinear energy-feedback process in the laryngeal vesti- presses against the motionless air column in the vestibule. The inertia bule (the airway above the larynx) to resonate, or amplify, sounds cre- of the stationary air column raises the air pressure in the glottis, which ated by the vocal folds. This process, called inertive reactance, occurs drives the folds even farther apart (2). Then the lungs begin to accel- when singers create special conditions in the vestibule to provide an erate the air mass upward. As the air column moves, the elastic recoil extra, precisely timed “kick” to each cyclic opening and closing of the of the folds begins to send them back together to close the glottis, folds that reinforces their vibration to create stronger sound waves. cutting off the airﬂow from the lungs (3). Those responses leave a The kick comes in when the motion of the air column in the vesti- partial vacuum in the glottis that acts to slam the folds together bule lags with respect to the movement of the vocal folds. When the strongly (4). Thus, like a well-timed push on a kid’s swing, the inertive vocal folds start to separate at the beginning of an oscillation (1), reactance—the push-pull action—of the air in the laryngeal vestibule lung-driven air ﬂows into the glottal space between the folds and augments each swing of the vocal folds, creating resonance.

GLOTTIS OPENING GLOTTIS CLOSING

Mobile air column Stationary air column

Laryngeal Rising pressure Falling pressure vestibule

1 2 ●3 4 ● ● Folds closing ● Larynx Vocal fold Folds opening Glottis Decreasing Increasing airﬂow airﬂow High pressure ADAMQUESTELL

www.SciAm.com SCIENTIFIC AMERICAN 99 © 2007 SCIENTIFIC AMERICAN, INC. [HUMAN SOUND RADIATOR] BIG MOUTHS AND SMALL MOUTHS Acting as a tube resonator, the vocal tract adopts certain shapes to better project certain pitches and resonant overtones. To produce powerful high notes, belters often open their mouths as wide as possible. This so-called MEGAPHONE megaphone conﬁguration resembles a trumpet (top), Vocal fold with the vocal folds and vestibule serving as the “lips and mouthpiece” and the mouth as the “horn.” Other Vestibule Mouth singing styles are better produced when the vocal tract Trachea of larynx takes on an inverted megaphone shape—that is, with the mouth narrowed (bottom).

INVERTED MEGAPHONE

Vocal fold

Vestibule Trachea of larynx Mouth

to produce a desired frequency and volume lev- many brass and woodwind instruments, the el. Laryngeal muscles outside the vocal folds horn (with its valves) is designed to match many precisely coordinate length changes in the vocal of the source frequencies at whatever pitch is fold. During these complicated manipulations, played. voice quality may suddenly change, a phenom- Because physical law dictates that all steady enon known as registration. It is caused to a (continuous) sounds are composed of source large extent by overusing or underusing the vo- frequencies that are harmonically spaced— cal-fold muscle to regulate tension. Singers use meaning that all source frequencies are integer registration artistically to present two contrast- multiples (2:1, 3:1, 4:1, ...) of the fundamen- ing sounds to the listener, as in yodeling. If a tal—the resonator must often be quite large to singer involuntarily or accidentally changes reg- accommodate these wide frequency spacings. ister, however, it can cause embarrassment, be- This physical law dictates that trumpet horns cause such a slip suggests a lack of control of the are 1.2 to two meters long, trombone horns singer’s instrument. stretch three to nine meters, and French horn tubing uncoils from 3.7 to 5.2 meters. Resonating Airways Nature is stingy with the size of the singer’s In musical instruments, the resonator for the resonator. The total size of the human airway most part determines the instrument size, but above the vocal folds is only about 17 centime- singers have to make do with a pint-size resona- ters long. The lowest frequency that can be res- tor. The human resonator, however, performs onated is around 500 hertz (cycles per second)— ) effectively despite its overt limitations. and half that when certain vowels are sung, In a musical instrument, boards, plates, ket- such as /u/ or /i/ (as in “pool” or “feel”). Be- illustration tles, horns or tubes typically act to reinforce cause the vocal tract is a resonant tube that is DAME Joan Sutherland knew and amplify the frequencies that the sound nearly closed at one end, its resonant frequen- instinctively that some vowels source produces. In the violin, for instance, the cies include only the odd-integer multiples (1, 3, cannot be used when singing strings pass over a bridge support that connects 5, ...) of the lowest resonance frequency. There- );ADAM QUESTELL ( certain pitches. The Australian to the top plate, which has been carefully fash- fore, this short tube can resonate simultaneous- soprano changed some of the Sutherland vowels in her opera lyrics ioned to vibrate sympathetically at many of the ly only the odd harmonics of a 500-Hz source (

same natural frequencies that the strings can frequency (500 Hz, 1,500 Hz, 3,500 Hz, ...). orbis (even to the point of mispro- C nouncing the words) to best produce, thereby boosting them. The air mass And because the vocal tract cannot change tube match them with the between the top and bottom plates can also os- length with valves or slides (other than a few

desired pitches. cillate at the strings’ natural frequencies. In centimeters by protruding a lip or lowering the IRANOWINSKI

100 SCIENTIFIC AMERICAN Januar y 20 0 8 © 2007 SCIENTIFIC AMERICAN, INC. larynx), our resonator seems as if it should be Megaphone Mouth hopelessly restricted in what it can do. Different singing styles rely on different vocal tract shapes to make optimal use of inertive Resonating a Short Tube reactance. In producing an /æ/ vowel (as in Here again recent studies indicate that nonlinear “mad”), the vocal tract approximates a mega- effects come to the rescue. This time it is a non- phone shape. A small cross section at the glottis linear interaction among the system’s elements. is paired with a large opening at the mouth [see Rather than reinforcing each harmonic with a box on opposite page]. Singers can find inertive specific tube resonance (as occurs, for example, reactance as high as 800 or 900 Hz for males in organ pipes of different sizes, each of which and 20 percent higher for females. At least two resonates certain harmonics), our short vocal harmonic source frequencies can achieve tract reinforces a cluster of harmonics simulta- inertive reactance for fairly high pitches, and neously by using an energy-feedback process. several more can for low pitches. This fact The vocal tract can store acoustic energy in one means that one strategy for obtaining powerful part of the vibration cycle and feed it back to the high notes is for the singer to open the mouth as source at another, more advantageous time. In ITALIAN TENOR Luciano Pavarotti, wide as possible, as in belting or calling. When effect, the vocal tract gives a “kick” to each cycle famed for the brilliance and the vocal tract adopts this megaphone configu- beauty of his tone, produced of oscillation of the vocal folds so as to increase ration, it approximates the shape of an ampu- the rich resonance in his voice the amplitude of vibratory motions. In analogy tated trumpet (with no coiling tube or valves, by fine-tuning nonlinear to pushing someone on a playground swing, this inertive reactance in his throat. but with a bell, or horn). cyclic kick resembles a carefully timed push to An alternative approach to reinforcing vocal- boost the amplitude (travel distance) of the fold vibration with inertive reactance is to adopt swing’s oscillations. the so-called inverted-megaphone shape, in The ideal timing of the kick comes when the which the laryngeal vestibule, the “mouthpiece,” movement of the air column in the tube is de- is kept narrow, the pharynx (the part of the layed with respect to the movement of the vocal throat situated immediately behind the mouth folds. Scientists say that the air column then has and nasal cavity) is expanded as widely as pos- inertive reactance (slow or sluggish response to sible and the mouth is narrowed somewhat. This an applied pressure). Inertive reactance helps to configuration is approximated to verbalize the sustain the flow-induced oscillation of the vocal /u/ vowel (as in “took”). The inverted-mega- folds in a profound way [see box on page 99]. phone technique is ideal for female classical When the vocal folds begin moving apart at ➥ MORE TO singers who wish to sing in the middle of their the inception of a vibratory cycle, air from the EXPLORE pitch range and male classical singers who wish lungs starts to flow into the glottal space between The Physics of Small-Amplitude to sing in the high part of their pitch range. Clas- them and begins pushing on the stationary air Oscillation of the Vocal Folds. sical training involves finding more regions of column located just above in the laryngeal vesti- I. R. Titze in Journal of the Acoustical the singing range where the vocal tract provides bule. Air pressure in and above the glottis rises Society of America, Vol. 83, No. 4, inertive reactance for the source frequencies, at pages 1536–1552; 1988. as the air column accelerates upward to allow all pitches and for many different vowels. The new air to fill in behind it. This pressure increase Acoustic Systems in Biology. training also involves getting a “ring” into the pushes the folds even farther apart. When elastic Neville H. Fletcher. Oxford Universi- voice, which is accomplished by the combination recoil springs the folds back from the walls to ty Press, 1992. of the narrow vestibule and the wide pharynx. close the glottis, the flow of air through the glot- Singing teachers use terms such as “covering” tis subsides. Because of inertia, though, the air Vocal Tract Area Functions from the voice or “turning it over” to describe the Magnetic Resonance Imaging. column continues to move up, leaving a partial B. Story, I. Titze and E. Hoffman in process of choosing just the right vowel for the vacuum in and above the glottis that acts to slam Journal of the Acoustical Society of given pitch so that most of the source frequen- the folds more strongly together. Thus, like a America, Vol. 100, No. 1, pages cies experience inertive reactance. well-timed push on a kid’s swing, the inertive re- 537–554; 1996. Singing styles are based on what human bi- actance of the air in the vocal tract augments each ology can offer to produce an acoustically effi- Principles of Voice Production. swing of the vocal folds with a push-pull action. Reprint. I. R. Titze. National Center cient instrument. Researchers who study the el- Still, the vocal tract does not automatically for Voice and Speech, 2000. ements of the human vocal system, and the un- behave in this inertive way for all vocal shapes. www.ncvs.org expected ways in which it functions, are A singer’s task is to adjust the shape of the vocal garnering an ever greater understanding of how Corbis tract (by carefully selecting favorable “singing” The Physics of Musical Instru- accomplished singers ply their art. Both scien- ments. Second edition (corrected vowels) so that inertive reactance is experienced fifth printing). N. H. Fletcher and tists and singers will benefit substantially from g ETHANMILLER over most of the pitch range—no easy task. T. D. Rossing. Springer, 2005. continued close cooperation and study.