8. Cremona Revisited - The Science of Violin Making, A. Hs

7/29/2019 8. Cremona Revisited - The Science of Violin Making, A. Hs

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28 E N G I N E E R I N G & S C I E N C E N O . 4

Photo by Akira Kinoshit


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29E N G I N E E R I N G & S C I E N C E N O . 4

e lights dim, and a hush falls over the concerthall. e concertmaster rises, and as the orchestratunes, the faint rustling of programs is heard inthe background. Tonights concert features oneof the greatest living soloists performing with theorchestra, and the anticipation is palpable. econductor appears and is duly acknowledged bythe crowd; but he is not the one they are waiting tosee. Finally, the soloist emerges, leaning on a pairof walking sticks, and takes his seat at center stageto thunderous applause.

It is the distinguished violinist Itzhak Perlman,and the instrument in his hands is one of the fineststring instruments ever made: the Soil Stradivar-ius, crafted in 1714 by the Italian master AntonioStradivari. Even before the first notes have beenplayed, members of the audience are transfixed by

the sight of the violin, its brilliant red varnish andthe stunning flame pattern of its back catchingthe eye as they reflect the bright stage lights. econductor raises his baton, and as the first notesreverberate through the hall, they complete theimage of the renowned virtuoso and his legendaryinstrument.

Each violin, viola, cello, and bass is a master-piece, simple lumber converted into a sublimelyexpressive musical instrument. Most were madelong before the musicians playing them were born.Musicians and violin makers claim that a violinssound improves with age, and therefore it is notentirely surprising that most musicians prefer older

instruments.e best-known string instruments, with onlya few exceptions, are the work of either AntonioStradivari or Giuseppe Guarneri, both active inCremona, Italy, in the first half of the 18th cen-tury. eir violins were often passed down fromvirtuoso to virtuoso and sometimes named afterfamous past owners. Both Stradivari and Guarnerigenerated a sort of mystique about themselvesby selling their instruments only to virtuosi or toextremely wealthy customers, and the quality of

instruments such as those played by great soloistspast and present has served to not only perpetuatebut to increase the Cremona mystique. e twomen maintained an extraordinary level of secrecythroughout their lives, suggesting that they mightnever have revealed some of their techniques to theworld. e possibility of such secret techniquesexisting continues to provoke vigorous debate andexperimentation, even after hundreds of years.

A BRIEF HISTORY

e violin family first appeared in northernItaly in the first half of the 16th century, and haschanged little since the 1550s. Instruments madeas early as 1560 are still in regular use today and

are in most respects identical to their more recentcounterparts.e years from 1650 to 1750 were a golden age

of violin making. Nicolo Amati (15961684), thelast and greatest of the Amati line of violin mak-ers, was almost single-handedly responsible for theemergence of the many famous masters of the era;his students included Antonio Stradivari (16441737) as well as Andrea Guarneri (ca. 16261698),grandfather of the better-known BartolomeoGiuseppe Guarneri (16981744).

Antonio Stradivari and Giuseppe Guarnerideparted significantly from previous designs, whichhad very highly-arched front and back plates, by

building instruments with relatively flat bodies.ese were better able to withstand high stringtensions and had greater carrying power in largeconcert halls. Stradivaris violins were known fortheir brilliant tone color; Guarneris for their full,dark character.

With the deaths of Stradivari in 1737 andGuarneri in 1744, the Cremonese school of violinmaking came to an abrupt end. Since then, theirviolins have been frequently copied. Some makerseven built reputations for producing high-quality

by Andrew Hsieh

Cremona Revis ited:The Science of Viol in Making

Itzhak Perlman in

concert.


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replicas by painstakingly measuring every aspect ofthe old instruments. However, while the copyistscould duplicate the appearance of the Cremoneseviolins, they could never duplicate the sound.

BUILDINGAVIOLIN

e violin appears simple at first glance, but it isone of the most complex musical instruments, builtfrom more than 70 separate pieces of wood that areshaped and assembled by hand. No two violins areexactly alike; a trained ear can distinguish betweenindividual violins. Whether it is a centuries-oldmasterpiece or a mass-produced fiddle, each violin

has its own unique voice.Many of the features of the violin that appearmerely ornamental are highly functional. e lowvaulting of the front and back plates is essential forstrength and for amplification of sound. e nar-row middle bout, or waist, allows the player moreroom to bow on the highest and lowest strings.e purflingthe decorative trim around theedges of the instrumentprotects the body fromcracking, but also changes the dynamics of vibra-tion considerably. Cutting the groove in which thepurfling is inlaid allows the plates to vibrate as ifthey were hinged rather than clamped at the edge.

e process of making a violin begins with the

selection of materials. Choosing wood is an artin itself: it must be strong, flexible, and as dry aspossible. Wood for violins is always cut during thecold dormant months, when the amount of sap init is at a minimum, and seasoned for years undervery dry conditions. e wood used in the best in-struments is aged at least ten years, and sometimesas long as fifty years.

Equally important is the process of shaping thefront and back plates. e front plate is made froma softwood, typically spruce, while the back plate

Right: X-ray cross sec-

tions of a 1654 Amati

violin (top) and a 1698

Stradivari violin (bottom),

showing the more gentle

slope of the front and

back plates in Stradivaris

instrument.

Below: The parts of a violin.

From David Boyden et al., Te Violin Family(New York: W. W. Norton & Co., 1989) p. 4.


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IMAGE NOT LICENSED FOR WEB USE

is normally maple. e arched outer surfaces arecarved rather than formed by bending. e arch-ing gives the thin front plate increased resistanceto the lateral force exerted by vibrating strings,and subtly alters the modes in which both platesvibrate. e violin maker carefully tunes thefront and back plates, tapping the plates with theknuckles, listening for the characteristic tap tones.e pitches of different harmonics are adjusted byscraping away material as necessary. Tuning thefront and back plates is easily the most demandingpart of making a violin, and takes years to master.

VIOLINSAND SOUND

A vibrating string alone produces almost nosound, as it is too thin to sufficiently disturb theair. erefore, it is not the string itself, but thebody of the violin, that actually generates its soundWhen a string vibrates, the bridge rocks back andforth at the same frequency. e soundpost im-mobilizes the front plate directly beneath the rightfoot of the bridge, so that the right foot remainsstationary, and the front plate is driven rapidly upand down by the left foots pumping motion.e bass bar, mounted lengthwise under the leftfoot of the bridge, reinforces the front plate andcouples the upper and lower bouts so that theymove together.

e body of the violin has a number of resonantfrequencies, or natural vibrational frequencies, atwhich a weak stimulus can cause large vibrations.Forced vibration of the top plate produces someamplification at any frequency, but the amountof amplification at a given frequency depends onhow well it corresponds to one or more of these

resonant frequencies. e bridge transmits a wholeset of harmonics from a vibrating string to thefront plate, and each harmonic is amplified accord-ing to the resonance generated at that frequency.e violins relative response levels to differentfrequencies create the instruments unique timbreby preferentially amplifying some harmonics anddamping others.

e resonant frequencies of the violin body as awhole depend most strongly on the resonant modeof the front and back plates. e plates themselvescan be modeled most simply as two-dimensionalpanels, free to move at all points out to the edges.Just as a string vibrates in harmonics corresponding

to standing waves on the string, a two-dimensionalpanel vibrates in specific resonant modes; thegraphic above left shows the calculated resonantmodes of a simulated square panel.

In violins, there is a further complication:wood has very different mechanical propertiesalong different axes. Its mechanical properties aredetermined entirely by its cell structure. Wood ismade up of long, thin cells with walls composed ofthe polymers cellulose, hemicellulose, and lignin.Cellulose, a carbohydrate that forms long straight

Above: The resonant

modes of a square plate

with free edges. The X

mode and the ring mode

are the second and third

ones, respectively, in the

top row. The numbers

below each mode are fre-

quencies corresponding to

the modes, relative to that

of the first mode. Lines

represent nodes, or places

that remain stationary

as the plate vibrates at a

given frequency.

From David Boyden et al., Te Violin Family(New York: W. W. Norton & Co., 1989) p. 6.

From Neville H. Fletcher and omas D. Rossing, Te Physics of Musical Instruments, figure 3.13, p. 79.Copyright 1991, Springer-Verlag.

Below: Quarter-cut (left) and slab-cut (right) sections of a

log, with the look of a violin back made from each. These

are the only cuts of wood used in violins; the softwood

front plate is traditionally quarter-cut while the hardwood

back plate may be quarter-cut or slab-cut. In either case,

the longitudinal axis is in the plane of the plate.


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chains, is the main structural component of wood.Cellulose chains usually form microfibrils, fibersconsisting of groups of parallel chains held firmlytogether by hydrogen bonding. In wood, cellulosemicrofibrils lie parallel to one another in four lay-ers, and spiral around the cell in its long direction,with different angles of spiraling in each layer.Lignin and hemicellulose, which form highly cross-linked structures, act as a glue that holds togetherthe cellulose components and binds adjacent cellstogether. e longest dimension of each cell runsparallel to the growth of the tree trunk, in the

longitudinal axis, and therefore wood has its great-est tensile strength in the longitudinal direction.As a result, wood plates must be elongated alongthe grain of the wood, in the direction of greatesttensile strength, in order to achieve the same typesof resonant modes that are observed in an idealsquare plate.

Many modern-day violin makers use visualiza-tions of resonant modes to aid in tuning a violinsfront and back plates. During construction, modalpatterns in a plate can be seen by covering thesurface of the plate with a fine sand and inducingmechanical vibrations at various frequencies. Asthe plate resonates, the sand moves about, except

at the nodes, which remain stationary. e sandcollects at the nodes or is bounced away, creatingmuch the same patterns as shown above.

Two particularly strong modes are the secondand fifth harmonics of the plate, often referredto as the X mode and the ring mode for theshapes of their nodal patterns. ese harmon-ics are the main components of a plates tap tone.Recently, a number of violin makers have recom-mended tuning each plate such that the ring modesounds exactly an octave above the X mode, in

order to mimic the efforts of early violin makers,who would have tuned the most prominent modesto exact musical intervals. While the theory isdifficult to test, it seems highly plausible becausetuning tap tones to musical intervals requires nospecialized equipment and therefore could havebeen done by even the earliest violin makers. Inaddition, the idea parallels Renaissance ideals ofmathematical perfection, which may well haveguided the Italian violin makers of centuries past.

LUMBER

REDUX

: ANOTHER

LOOK

AT

WOOD

Do violins actually improve with age? eacoustical properties of the wood used in their con-struction certainly change with the passage of years

Moisture in wood absorbs vibrational energy,converting it to heat energy by evaporation.Although the wood used in violins is already dry,minute changes in water content can have dramaticeffects on violin acoustics: a 1 percent decrease inmoisture content reduces damping by up to 3.5percent. e long-term improvement of acousti-cal response depends mainly on the degradation ofhemicellulose, the component of wood that adsorbs

water most readily and degrades most dramaticallyover time. As hemicellulose degrades, the woodsmaximum water content decreases. Even over veryshort periods, the sound of a frequently playedviolin may noticeably improve as small amounts ofwater evaporate from the wood.

ANALYZING CREMONA

Age, however, does nothing to explain the

The vibrational modes

of the front plate (top)

and back plate (bottom)

of an unassembled violin

made by a modern master

craftsman are revealed

by laser interferometry.

Nodal areas appear white.

The X modes and ring

modes of both plates are

highlighted in red. The

numbers are the frequen-

cies at which the reso-

nances occur.


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difference between Cremonese violins and theircontemporaries. e recognized superiority of theCremonese instruments must still be a result ofunique acoustical properties.

One way to examine these properties is byperforming a mathematical technique called a FastFourier Transform (FFT) on the waveforms that aregenerated when the violins are played. e soundwaves produced by a musical instrument are thesum of the fundamental frequency of the note andall of its harmonics; the FFT breaks down a soundinto its component harmonics and allows us tochart their relative strengths in what is known as anFFT spectrum.

It is difficult to generate a steady waveform froma bowed string instrument, as the act of bowing thestrings brings many unpredictable factors into play.

erefore, FFT spectra are never perfectly con-sistent; large variations can occur even in spectraproduced by a single instrument. Such variationsmight be worked around by mechanically vibratingthe bridge to simulate constant, perfectly consistentbowing. e resulting FFT spectrum is steady andcan be used to create a response curve that repre-sents the amount of amplification generated bythe body at any given frequency, as shown at right.Peaks on the response curve indicate resonant fre-quencies of the violins body, at which amplificationis particularly high.

ere are also easier ways to generate a responsecurve. Instead of simulating the full set of harmon-

ics generated by the bowed string, one can producethe same results by vibrating the bridge at a rangeof pure frequencies, and measuring the resultingsound output in decibels. Ultimately, becausebody resonances are the main factor determiningthe tone quality of a violin, it is the response curvesthat provide the most insight into a violins acousti-cal properties.

In 1985, German violin maker Heinrich Dn-nwald compared the response curves of a group ofCremonese violins to two control groups, one of

violins built by master violin makers and one offactory-made violins. e most striking contrastwas seen at high frequencies. e Cremoneseinstruments showed a broad, strong maximumaround 2500 Hertz (Hz), or vibrations per second,which is in the region of greatest human auditorysensitivity. ere was a large reduction of responseabove 3000 Hz. Modern master-crafted instru-ments showed an overly strong response in thesame range, which explains modern violins widely-held reputation for shrillness; factory-made violinshad a consistently dull response above 2000 Hz.

In a second experiment conducted the sameyear, Dnnwald found another characteristic traitof Cremonese violins: two of their response peaksare particularly strong. One peak, covering a fairlywide band located between 1300 Hz and 2500Hz, was sufficiently strong that virtually any noteplayed on the instrument had its strongest har-monic within that range. e other peak occurredat the air resonance frequency, the natural reso-nant frequency of the air inside the violin ratherthan of the violin body itself. Nearly every testedCremonese violin showed a strong response at thatfrequency, as shown on the next page. In the vastmajority of the other tested violins, both peakswere much weaker.

e Dnnwald experiments demonstrated con-clusively that there is a clear acoustical differencebetween violins made by Stradivari and Guarneri,

Above: The FFT spectra

of the open (unfingered)

A string on two violins,

the 1725 Stradivari DaVinci and a 2002 Joseph

Nagyvary violin. (The A

above middle C is tuned

to 440 Hertz, a standard

frequency also known as

international pitch.)

How a response curve corresponds to FFT measurements.

The FFT of a vibrating string (top) decreases smoothly with

increasing frequency. The violins body (middle) amplifies

harmonics that correspond to its resonant modes, while

other harmonics are amplified very little. The sound we

hear (bottom) thus has a very different FFT spectrum than

does the string in isolation.

Courtesy of Joseph Nagyvary, www.nagyviolins.com.


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and contemporary violins. e characteristicCremona sound appears to be the result of strongselective amplification of several key harmonics.e cause of this amplification remains an openquestion.

VARNISHAND SALT

For many years it was fashionable to study thevarnish used by both Stradivari and Guarnerithebrilliant, reddish hue of their instruments suggestedthat their varnish was unique. e claim mostcommonly made by violin makers was that a secretrecipe for varnish was the most important factorin tone quality. However, varnish is unlikely toimprove the sound of a violin. Its only acoustical

effect is to damp vibrations, and because its mainfunction is to form a hard protective layer over theexterior of the instrument, it is highly implausiblethat any varnish could selectively damp very highfrequencies. Furthermore, ultraviolet photographyhas revealed that most of Stradivaris and Guarnerisviolins have lost much of their original varnish,and have been recoated in the last 150 years withmodern varnishes. Since many modern violinmakers believe that their violins sound better inthe white than varnished, the best thing to dowith varnish may simply be to use less of it.

e process of stewing, or gently heating woodin a salt solution before drying, was also identi-

fied as a likely difference between the Cremoneseschool and the modern day. Analysis of woodshavings provides strong circumstantial evidencethat Guarneri stewed his wood. e main effect ofstewing is to substantially accelerate the degrada-tion of hemicellulose, so the hemicellulose contentof stewed wood should be far lower than is normalfor its age. From comparison of growth rings toknown climate data, we know that the wood inGuarneris instruments cannot have been cut morethan two decades before the instruments were

made, yet the hemicellulose levels in the wood arewhat would be expected for wood three or fourdecades older.

But stewing was hardly a secret; on the con-trary, it was a familiar process long before the 18thcentury. Evidence for it exists as early as 1580,when French chemist Bernard Palissy wrote: Saltimproves the voice of all sorts of musical instru-ments. e purposes usually stated for stewingwere to prevent rot, to repel woodworm, and tostabilize water content. e last does not enhanceacoustic response, but guards against cracking bypreventing rapid changes in water content. Saltactually does this by hydrogen-bonding to wateritself, slightly increasing the woods water contentand partially offsetting the effect of hemicellulosedegradation.

e stewing theory has another flaw: there isno evidence that Stradivari stewed his wood. Bythe early 18th century the process was graduallypassing out of standard practice. It has seen aresurgence in recent years, but still only a few violinmakers practice it routinely.

THE SECOND COMINGOF STRADIVARI?

If varnish and salt are not the answers, thenJoseph Nagyvary, a biochemistry professor atTexas A&M University who moonlights as a violinmaker, claims to be closer to knowing the secrets

of the Cremonese masters. Recently he has gainednotoriety in musical circles for making violins thatshow an amazing similarity to those of Stradivarihimself. As a violin maker, Nagyvary was familiarwith the extant literature on Cremonese violins;as a chemist, he gradually became convinced thatphysical characteristics alone could not adequatelyexplain the Cremonese sound. He therefore hy-pothesized that Stradivari and Guarneri used someform of wood treatment that substantially alteredthe composition or structure of the wood itself. To

Left: Dnnwalds second experiment. Lis the relative

strength of the air resonance frequency in decibels, and N

is the percentage of possible notes for which the strongest

harmonic is between 1300 Hz and 2500 Hz. Violins made

by the old Cremonese masters are indicated by squares,

and other violins are indicated by dots.

From H. Dnnwald, Ein Verfahren zur objektiven Bestimmung der Klangqualitt vonViolinen,Acustica, Vol. 58, (1985) pp. 162-169.


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From J. Meyer, e Tonal Quality of Violins, Te Journal of the Catgut Acoustical SocietyMay 1984. Reprinted with permission of the Violin Society of America.

test this hypothesis, he acquired and analyzed woodshavings from Stradivari instruments.

Nagyvary discovered that these instruments weremade with wood containing extremely large quan-tities of embedded minerals, suggesting immersionin some mineral salt solution. However, he wasunable to develop a wood treatment method thatwould cause sufficient penetration of minerals intothe wood.

Eventually Nagyvary stumbled upon an un-expected answer to this problem. He currentlyconstructs violins with timber salvaged from thebottom of Lake Superior. For over three centurieslogs were floated to lumber mills across the lakechained together in large rafts, and some becamesufficiently waterlogged to break away and sinkto the bottom. Decades of soaking have left thewood heavily impregnated with a variety of mineralresidues which, as Nagyvary discovered, closelymatched the mineral content of wood shavingsfrom one Stradivari cello.

Nagyvarys revised theory is that Stradivari andGuarneri stored their wood in mineral-rich brack-ish water for years before beginning to dry it out.is storage allowed minerals to seep in and fillthe empty space left as microbes digested hemicel-lulose in the wood. Nagyvary even suggests that18th-century treatises calling for dry storage withno additional treatment may have been a deliber-ate deception aimed at obscuring the practices ofthe masters. e acoustical effect of embeddedminerals is not yet well understood, but Nagyvarysexperiments suggest that microscopic mineral crys-tals may modify resonant modes by stiffening woodin some directions and adding flexibility in others.

BAROQUE TUNING

In addition to treating wood differently frommodern practice, the Cremonese masters designedtheir instruments to fit specifications that distin-guish them from their modern counterparts.

Most significantly, the tap tones of all early Ital-ian violins are tuned distinctly lower than those ofother violins. is in turn produces response peaksat lower frequencies. e difference is on the orderof a half-step or a whole-step, which makes sensewhen one notes that Baroque orchestras commonlytuned to pitches that were approximately that farbelow modern standards. Violin makers may have

begun to tune their tap tones to higher frequenciesto match a late 18th-century rise in orchestral tun-ing pitch, affecting the violins timbre in ways thatthey could not have predicted.

CODA

Although much has been discovered about theacoustics of violins in recent years, whether wehave truly unlocked the secrets of Stradivari and

Guarneri remains in question. Craftsmanship anddesign are likely as important to achieving high-quality sound as any purported secret recipe ortechnique, and there may be no substitute for threehundred years of graceful aging.

e present is an exciting time for violin makersand researchers alike. Acoustical analysis of Cre-monese violins has, by revealing the specific pat-terns that define the Cremona sound itself, givenviolin makers a target to aim for. e exact way inwhich these patterns were achieved is still unclear,

but new ways of looking at old instruments havegenerated plausible scientific explanations for manyaspects of the art of violin making, as well as theo-ries and avenues of research that could lead to fur-ther breakthroughs. Regardless of whether all thesecrets of Stradivari and Guarneri are ever found,such technical advancements help contemporaryviolin makers fulfill every violin makers ambition:to produce instruments that violinists might beproud to play three centuries from now.

The distribution of the most prominent tap tones of

100 violins. f0is the air resonance; f

1is the first body

resonance. 17th- and 18th-century Italian instruments

are marked with numbered circles; black circles indicate

Stradivari violins.

Joseph Nagyvary applies

varnish to a violin in his

workshop in College Sta-

tion, Texas.

Pho

tobyKathleenPhillips,TexasA&MA

gNews,August2003.

Andrew Hsieh (BS 04, biology) wrote this paperfor the Core 1 science writing class. Hsieh plays both

violin and viola, and is also active as a composer. Heperformed in both the Caltech chamber music pro-gram and the Occidental-Caltech Symphony Orches-tra as an undergraduate. He is currently a member ofthe Division of Biology research staff and plans to goto medical school. Hsiehs faculty mentor for the paperwas Jed Buchwald, the Dreyfuss Professor of History.

In the spring of 2004, the faculty modified the Core1 requirement to emphasize technical writing for jour-nals. A new course on science writing for the public,En 84, is now offered at the Hixon Writing Center.

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8. Cremona Revisited - The Science of Violin Making, A. Hs