saunders the mechanical action of instruments of the violin family jasa 1946

8/8/2019 Saunders the Mechanical Action of Instruments of the Violin Family JASA 1946

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THE JOURNALACOUSTICAL Volume7 Number

OF THESOCIETY OF AMERICA

JANUARY- 1946

The Mechanical Action of Instruments of the Violha FamilyF. A. SAU,OEaS

Professor meritus,Hanrd University*. . (ReceivedAugust17, 1945)

INTRODUCTION

EARLYen earsgo groupn thearvard laboratories began to study themechanicalbehavior of violins, in the hope offinding out how the best ones differ in theirvibration from those which are recognizedasinferior. It was hoped that the results mightlead to improvementsn new violins. Since thiswork has spreadover severalyears,and notesonit have appeared n various places,we shouldbegin with a brief summary of it.The first publication includedan accountofan analyzer developed for this work; the em-barrassing ariety of harmonic patterns disclosedin violin tones; the response (or frequency)curves obtained by means of the analyzer frommany new and old violins; the curves of totalintensity against frequency; he mechanicaleffi-ciency of violins; the effects of variations ofbowing,and of moisture,string tension,etc.; thefriction betweenbow and strings;etc. This articleraisedmany unanswered uestions.It was followed by a papers in which the

* Now Visiting Lecturer, Mount Holyoke College,SouthHadley, Massachusetts. J. Actus. Soc. Am. 9, 81 (1937); referred to as A below. J. Frank. Inst. (Jan., 1940); hereafter referred to as B.

responsecurves of several famous violins werecomparedamong themselves nd with those ofnew violins; the filtering action of the bridgewas discussed; suggestionwas made in regardto the meaning of the term "carrying power" sooften used by violinists; and an account wasgiven of the results of a test of the ability of anaudience o pick out the tone of a Stradivarius,when it and two new violins were played insuccession behind a screen.

The next publicationwasa shortone n whichthe excellent old instruments of the CurtisString Quartet were shown to have responsecurves very like those produced by copies re-cently made of them by a skilled craftsman inPhiladelphia. An account was included of testsconducted by the Quartet on the judgment ofeight audiences n trying to discover which setof instruments was being played on, behind ascreen.A brief discussion f the psychologicaleffects involved was added in the attempt toexplain why these udgmentsdependedmainlyon the order in which the two sets of instrumentswere played.A note in the Year Book of the American

a In Overtones (April 1940), the journal published bythe Curtis Institute of Music in Philadelphia.169


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170 F. A. SAUNDERSPhilosophical Society (1940) mentioned someexperiments in which Jamha Heifetz took part,which were designed to measure and compare,from high speed records of actual playing, theperiodsof growth and of decay,when an excellentand a bad violin were used in succession; henceto secure n indication of the value of the damp-ing in the wood of theseviolins.The resultsofthese experimentsare given later on in thisarticle.

The last publicationwasby Watson, Cunning-ham, and Saunders and gave an account of anew and superior method of obtaining responsecurves directly, without tone analyses, by ex-citing the violin electromagneticallywith a forceoscillatingwith a single frequency, which couldbe varied over the whole rangeof the instrument.All response urves recently obtained have beendoneby this method,but this part of the experi-mental work came to an end in 1941. The newmethod included direct measurements of thedecay of pure tones, from which the dampingat a few selected requenciescould be obtained.One of these frequencieswas chosen o coincidewith that of the main vibration of the air insidethe body; the others coincided usually withnatural vibrations of the body, which were un-affected by the insideair.A preliminary report of the latest work wasmade at the meeting of the AcousticalSocieWin May, 1943. The presentarticle covers thiswork to date.RESULTS FROM RESPONSE CURVES OF STRAD$

BY THE NEW METHODThe responsecurves obtained by the old and

new methodsdiffer in certain respects.The oldcurves are based on observations taken a semi-tone apart, while the new curvesare continuous,and includeall frequencies. hus a narrow peakof responsewhich might be missed by the firstmethod is caught by the second. This is im-portant in the high frequency region, where theovertones of the violin body are so crowded thattwo or three may occur inside the interval of asemitone.

In the old method, the intensitiesobtained fortwo or three of the lowest tones were made4 R. B. X, atson, W. J. Cunningham,and F. A. Saunders,J. Acous. Soc. Am. 12, 399 (1941); referred to as D.

somewhatuncertainby experimentaldifficulties,which tended to raise the values. This errorcould have been removed by increasing theduration of each record, but this might haveintroducedother errorsdue to unevenbowing.In the new method the violin body is excited atall frequencies hrough the foot of the bridgewhich is under the G string, through forcesactingon a wire which takes he placeof the Gstring. f the responsen thismethod s ntegratedby semitones, curve is obtainedwhich agreeswell with the curve of the first method in themiddle ranges but is lower at both extremesoffrequency. These differencesare not very im-portant, since the object of the experiments wasto comparegood violins with bad, and this canbe done well enough f both are measuredbythe same method. It is still possible o comparethe response urve of a violin measuredby thesecondmethod with one measured by the first,by making allowances for the differencesdis-covered by measuring several violins by bothmethods.

All the response urves have been integratedby planimeter to find the average intensiW ofresponsen decibels db) abovean arbitrary levelin different regionsof frequency. f one choosessmall ranges of frequency the results vary somuch as not to be useful; if one uses a largerange one may misssome mportant peculiarityof the violin. A fair compromisewould be tochoose ctave intervals. This procedurehas beenadopted exceptat the two extremesof frequency.In the region from 200 to 350 c.p.s. the emissionof sound in all good violins is largely due to thevibrations of the included air. It seemed wise totreat this interval of somewhat less than anoctave separately. The interval next above wasmade a little more than an octave, to make thefirst two equal to two octaves. Above 4000 c.p.s.the emissionusually drops sharply. In order totrace this drop more in detail it seemedxvise osplit the upper octave into two shorter ranges.The ranges used in the violin tables to followare denoted by I, II, etc.; I covers from 196 to349 c.p.s.; II from 349 to 784; Ill from 784 to1568; IV from 1568 to 3136; V from 3136 to4186; VI from 4186 to 6272. The intensity above6300 is relatively negligible in good violins.


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 171TABLE I. Stradivarius violins. Average intensities (indb) in different frequencyranges measuredby the newmethod.

Violin I I1 Ill IV V VIStrad B"Halir" (1694) 15.2 25.0 24.6 26.5 20.8 7.1Strad D"Darnley" (1712) 16.0 23.9 23.8 24.2 26.3 9.0Strad E (Joachim,Kneisel, 1715) 15.2 25.1 24.6 26.2 21.7 6.5Strad G "TomTaylor"(1732) 11.6 23.0 26.9 25.9 23.7 10.6Strad ",M,rquiseRiviere (1718) 11.9 22.3 24.7 25.3 24.5 16.4Strad S "Spanish"(1723) 14.3 23.3 30.1 28.6 25.5 14.0Strad W "Titian"(1715) 14.5 23.2 25.0 24.6 22.7 12.7Averages 14.1 23.1 25.7 25.9 23.6 10.9Different ranges are used below in consideringviolas and cellos.

Many violins, including two or three of theseven Strads for which we have curves by thenew method, showa weakness n the range 1300to 1800 or 2000 c.p.s., amounting to a drop of4 to 8 db. This.appearsnot to have beennoticedby violin experts, and to have no importanteffect on the reputation of the violins concerned.Our range ending at 1568 almost bisects this"hole," and this accident hides it from view inour tables. In such a violin there is a weaknessin the fundamental of the tone in the first fewsemitonesof the secondoctave on the E string;but the upper overtonesmay be so strongas tomake up the deficiency to the ear. On thisaccount t has not been thought worth while tochoose ny differentranges n this region.Table I shows the average intensity emittedin the chosen requency ranges by seven well-known Stradivarius violins. The values wereobtainedwith somewhatdifferent amplifications.The distance of the violin from the microphonewas about 40 cm but it could not be kept quiteconstant.For these,or perhapsother reasons, tis not possible o compare the total intensityemitted by one violin with that from another.Instead, all records were reduced to the sametotal area, first by integrating the audiographcurves with a planimeter, then reducing thefrequency scale to a uniform logarithmic one,and then adjusting the base level from whichthe areas were measured until the total area for

eachviolin was the same.This is approximatelythe same as reducing each violin to the sameloudness. Most of the sounds measured wereloud enoughso that the loudnesswas approxi-mately proportionalo the intensity n db. Thepurpose of the measurementswas to comparethe distribution of loudness in one violin withthat in another. The errors of our methods arenot likely to affect this comparisonseriously.Table I discloses considerable variations instrength in different ranges,especiallyat theextremes. Some of these variations may be dueto differencesn the spatial emission attern for.differentwave-lengths. he values are given totenths of one decibel, but the error (due to allcauses)may amount to as much as 2 db; therelative accuracyof the values for one violin isprobablyhigher.The table shows hat all Stradsdo not sound alike, as experts already know,Probably this was true evenwhen they were new.but somedifferencesmay have arisen from thechanges incemade n theseviolins.Someplayersprefer a "full" or "round" tone, with morestrength n low frequencieshan in high; othersprefer a more biting tone, with the strengthsreversed. Table I cannot settle which Strad isbest, or which should have the highest price.These data apply to steady onesonly, and thequality of a tone (meaningby this the distribu-tion of strength among its partials) is not theonly item of importanceabout a violin. In factit is so variable from one tone to another that itmay be rather unimportant omparedwith othereffects, uchas thoseoccurring ear the beginningand end of each tone. All these Strads must beconsidered s excellentsince hey commandhighprices,and sincea large number (if not all) ofthe experts have agreed upon them. We haveassumed hat the averagedistributionof strengthin our chosen ranges furnished by these sevenStrads representsthe closest approach to astandard of excellence that we cad attain.

It shouldbe noted that the completehistoryof these and of mostother) Strads s not known.Some are in Hill's great book on Stradivarius,but even these historiesusually begin a centuryor so after the date of birth of the violin. Dataabout alterations made in famous violins are notusually made public. None of these instrumentscan be in their original condition.The standard


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172 F. A. SAUNDERS

of pitch has risen, equiring ncreasedension nthe strings of old violins; hence longer bass-barshave been put into them to increase theirstrength. These changes serve to satisfy thedemand for louder violins to fit our concert halls.If the changeshave beenwell made they may notlower the value of the violins. The longer bass-bars may be valuable; and the changes n thewood itself that have come with age or longplaying have probably mproved the quality. Itis not surprising hat Strads are found to differamong themselves, ven if they were made onthe model of the "golden age."

THE HEIFETZ TESTIn April, 19,0 an interesting test was con-ducted by Jascha Heifetz, with the help ofSaschaJacobson.American violin makers hadbeen invited to send n samplesof their work forcomparison, and nearly 100 violins had beenreceived. The first tests eliminated a largenumber of these. The final tests on the 'four best

violins should be described. Two violins to becompared,A and B, were played by each ofthe artists, H and J. With his back turned, Jlistened at one end of a large room, while H atthe other end played a certain passage rom aconcerto on one string of violin A and thenchanged to violin B, repeating the same passageon the same string of B. The one acting asjudge did not know which of the two violinswasbeing played, but decided which one soundedbetter on this string. The same process wasrepeated on the other strings of violins A and Bin turn. Then J becameplayer and H judge withthe same violins. In case the judgments did notagree (which was unusual) more testswere madeuntil agreement was reached. The differencesbetween two violins on the same string weresometimes very small, but usually quite definite;TABLE II. Modern violins in the Heifetz test. Averageintensities in different frequency ranges.

RangesViolin I II III IV V VI

Yurkevitch 12.7 24.4 27.1 25.3 22.0 8.6Phillips 13.1 23.5 25.2 26.8 22.9 10.0SangsterNo. 35 12.4 23.5 23.8 25.6 28.9 11.0Average 12.9 23.8 25.4 25.9 24.6 9.9Strad average 14.1 23.7 25.7 25.9 23.6 10.9

even the author, who was permitted to bepresent, was soon able to detect them. But sodelicate were these differences that a change inthe music played, or any conversationbetweenthe tests of A and B, tended to destroy theaccuracyof judgment. When the relative meritsof violins A and B were settled on all four strings,violins A and C were treated in the same way,then A and D, B and C, etc., taking all possiblecombinations.Thus the relative positionsof thefour violins were settled. If A represents thewinner, B the one in second place, and so on,it is interesting o note that when A and D werecompared t was agreed that D had the best Estring of the four, and nearly as gooda G stringas A. This showshow closewere the qualitiesofthese four instruments.

This test can be criticized on the ground thatthe violinswereplaled stheyhadbeen djustedby their makers. Their order might have beendifferent if they had all been adjusted by thesame person,or if they had been supplied withdifferent strings, or bridges, or bass-bars. t wasnot practicable to do any of these things. Inspite of this possibledefect, the test had aparticular value in connectionwith our research.Mr. Heifetz had the idea from the beginningthat the winners should be tested in the HarvardLaboratories, and later on this was done withthree of the four at the top. But we profired inother ways than by securing he opportunity ofmeasuringomenterestingiolins.Aftera fewjudgments had been made durihg the test, itseemned bvious, if one was at all accustomed tomaking tone analysesby ear, that the artistswanted two qualities in a violin; first, greatpower; second,an even distribution of strengthamong all rangesof frequency, the lowest octavebeing of special importance. It was said afterthe test that the winner gave the impressionthat the limit of its power was never reached.One should add that even a poor violin can bemade to emit a great deal of sound, such as it is.The power referred to here is limited by thecondition that the tone must remain good; withmostviolinsa very. oud tone becomes npleasant.Since the power output could not readily bemeasured,and probably depends somewhat onthe player, we put the winning violins throughthe same tests as already outlined for the seven


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIX; F,\MII. Y 173

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I I , l20O0 4000FREQUENCY20O0 400O 200 5O0FREQUENCYFla. 1. Response urvesby new method of three Strads, and three new violins which led in the Heifetz test.


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174 F. A. SAUNDERSStrads. The violins tested were (A) by M. V.Yurkevitch (1938) of New York City; (B) byB. F. Phillips of Pittsburgh, Pennsylvania; D)by E. H. Sangster, now of Worcester, Massa-chusetts. Table II shows the results. The distri-bution of strength in different ranges s unusuallyuniform (the rangeswere the sameas in Table I),and its average is the same as the Strad average,within the allowable experimental error.The responsecurves of these three violins(particularly the Yurkevitch) showan evennessof response hich s unusual.They still danceupand down in a way that no proper loudspeakercurve does,but the general evel is steady,moreso than is usual even among famousold violins.Figure 1 showsa seriesof response urves,alltaken by our new method. Three Strads areshown, and the three violins of the Heifetz test.There is a "hole" in the middle of the curve forStrad D (and others), amounting to a drop of8 or 10 db in the region from 1300 to 2000 c.p.s.The only effect of this hole seems o be to pro-ducedifferencesn tone qualityof which heplayer is not aware, or which he may even enjoyfor their variety.We can find no evidence in such responsecurves or the existenceof any special"formant,"or region of strong response,which is supposedto give the characteristic uality to the soundofa violin. In fact, it seems ikely that we recognizea violin tone as different from that of an oboe,for instance, y the way the tonestartsand stops.There is no marked difference in the toneanalyses of the two instruments. It would notbe difficult to test this by experiment, permittingthe listener to hear the tones only after theyhad started, and not allowing him to hear theirnatural endings.

TABLE III. Average values of intensity in the samefrequency anges,by old and new methods.

I II III IV V VI9 violins, averages, old method 37.0 42.4 38.0 38.6 37.5 27.3Same by new method 13.7 23.3 25.3 26.3 23.8 11.6Difference due to method 23.3 19.1 12.7 12.3 13.7 15.77 Strads, new method only 14,.1 23.7 25.7 25.9 23.6 10.95 Strads, old method only, butcorrected to new 14.6 24,.4, 24.0 25.4 23.1 11.710 Strads, both methods 14.2 23.8 24.7 25.7 23.9 10.7

RESPONSE CURVES BY BOTH METHODSThe intensity distribution for a number ofother newviollns, measuredby the new method,is given in Table IV, along with the results

obtained y the old method,whichwe mustnext consider.In our article (D) on the new method it wasstated that the results differed from those bythe old method at both ends of the frequencyrange. n the old methodordinary human bowingis used,and ordinary strings. n the new methodonly one "string" (a phosphor-bronzewire) isused, and only from the G-string position. Itstension s equal to that of the ordinary G string,

but its linear density is less. It could not beexpected o shake he whole violin exactly as theG string does; the loudness s appreciably less,though this may be mainly due to the absenceofovertones.The observed eduction in the highestfrequenciesby the new method may be due tothe fact that the excitation is from the G-stringposition.Some writers state that if the E and Gstrings are interchanged, the high notes areweakened. These differences aise a difficulty incomparing he resultsof the two methods.A method of reducing the values obtained byone method to those by the other was found bystudying the violins which were measured byboth. These were five Strads and four new violinsThe average value in each of the six frequencyrangeswas obtained for each of these nine violinsby both methods. The averages for the ninewere then obtained (Table III). If the new-method values are subtracted from the corre-spondingold-methodones, hesedifferencesmaybe used to convert any old-method results tonew, or vice versa. This assumes that the violinswere in the same condition in both tests, andthat no other variations occurred, such, forinstance, as might come from diffraction effects.With nine violins to work with it seems reason-able to hope that the averagesare .not seriouslyaffected by any such variations.In all, 73 violins were studied. Response urveswere taken for 60 of these, 48 by the old method,22 by the new, 10 by both. We have the responsecurves of 38 violins by the old method only.This massof observationalmaterial is of value byitself, but it is better to be able to compare he


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 175TnBtE V. Intensities n different frequency anges.

RangesViolins Method I II III IV V VI

Strad K (1684)Strad A (1691)Strad B (1694)Strad M (1698)Strad J (17097)Strad D (1712)Strad E (1715)Strad W (1715)Strad S (1723)Strad H (1731)Strad G (1732)Strad N (1737)Strad average

Strads, by both methodsold 15.9 22.9 22.3 24.5 24.7 11.4old 15.5 23.7 24.1 21.9 25.7 15.7old 17.3 19.9 28.1 25.9 25.7 7.3new 15.2 25.0 24.6 26.5 20.8 7.1old 11.7 24.5 25.3 26.7 24.1 10.5old 15.1 24.9 25.1 26.1 22.9 6.9new 11.9 22.3 24.7 25.3 24.5 16.4new 16.0 23.9 23.8 24.2 26.3 9.0old 15.3 24.1 25.7 24.3 24.7 9.1new 15.2 25.l 24.6 26.2 21.7 6.5old 12.5 23,3 23.9 27.3 24.5 12.9new 14.5 23.2 25,0 24.6 22.7 12.5old 13.1 25.9 24.6 26.3 25.3 12.3new 14.3 23.3 30.1 28.6 25.5 14.0old 14.9 25.1 23.7 26.5 19.7 10.0new 11.6 23.0 26.9 25.9 23.7 10.6old 10.1 25.7 24.7 27.3 21.5 11.3

14.1 23.8 25.1 25.8 23.8 10.8Guarnerius d. Gesu violins; old methodGuarnerius R (1743) old 10.3 25.7 24.5 26.3 25.9 10.3Guarnerius H (1742) old 13.6 24.9 27.6 25.5 21.9 5.9Guarnerius B (1728) old 12.9 23.7 25.1 27.9 24.1 10.1Guarnerius F (1738) old 11.9 22.3 27.9 25.3 22.1 13.5

Guarnerius average 12.2 24.1 26,3 26.2 23.5 10,0Old Italian violins; makers probably as indicatedMaggini old 15.7 23.7 26.3 23.3 22.5 12.3P. Guarnerius (Cremona) old 14.6 19.4 22.8 28.7 27.6 15.7

Stainer old 14.5 21.3 24.1 27.5 24.5 14.5A. Guarnerius old 13.5 24.5 25.7 25.1 20.5 11.O$tradivarius old 12.7 22.7 24.9 25.7 23.5 15.1Guarnerius, J old 18.1 23.3 24.7 24.1 22.9 11.3Gagllano old 18.1 27.1 28.3 22.5 14.7 5.7Guadagnini old 15.1 23.5 24.1 25.l 21.1 14.1Pressenda old 12.5 22.3 24.3 27.1 22.l 16.7These old violins, average 15.0 23.1 25.0 25.5 22.2 13.0

Violins Method I II III IV V VI

J. A. Gould (1882)W. S. Goss (1912)Sangster's No. 30Sangster's No. 33Sangster's No. 34Sangster's No. 35Sangster's No. 37Sangster's No. 38

New violinsold 13.5 22.9 27.3 25.7 25.5 9.7old 10.1 24.1 27.7 24.3 21.5 15.1old 10.3 26.1 23.5 27.7 23.7 11.3new 13.4 22.1 24.6 26.2 24.6 13.3old 12.9 26.1 26.1 25.3 21.3 9.0new 13.0 23.2 21.0 27.4 27.1 13.9new 12.4 23.5 23.8 25.6 28.9 I 1.0new 11.7 24.9 23.3 25.8 26.2 11.9new 12.6 22.5 24.4 26.6 23.2 13.8

Moennig,opyof tradB old 12.1 24.0 24.3 24.7 28.3 15.3new 11.3 21.3 27.8 26.2 23.2 13.4Moennig, copy of $trad J old 11.1 24.5 26.3 23.l 21.9 16.9Moennig, copyofaStrad old 14.5 21.3 22.6 23.6 28.8 17.8Moennig, copy of aGuadagniniurkevitchB. F. PhillipsKoch

StanleyMoglie (1930)

old 15.2 20.8 26.4 22.7 22.3 17.9new 12.7 24.4 27.1 25.3 22.0 8.6new 13.1 23.5 25.2 26.8 22.9 10.0old 15.3 21.9 25.9 26.7 18.9 14.1new 14.0 23.8 23.2 26.2 24.9 11.5old 12.5 20.9 26.5 28.1 20.7 15.5new 13.5 23.6 23.1 26.9 25.9 10.7new 11.5 23.3 29.3 26.2 22.6 6.9

Averages of good new violins 12.7 23.3 25.1 25.8 24.0 12.7Two bad violins

Violin X ($5.00) new 13.9 18.5 29.5 23.4 22.6 17.6Violin new 2.6 20.5 '20.9 42.2 17.0 16.4

results f the two methods,s we can by the "long"model, ndone K) is of thehighmodelabove rocedure.able II includesheaverage (1684). he results onotagreewitha commonvaluesor 7 Strads y the newmethod,or 10 belief hat the differencesn shape ffect heStradsby bothold and newmethodsreduced distribution f strengthhroughouthe range.to new),and or 5 StradswhichweremeasuredThe two long-modeliolinsdo not agreewithby the old methodonly. Theseresultsshowonly each other. There is a rather uncertain trend insmalldifferences,ndicatinghat the processf thedirection f diminishingow requencymis-comparisons successful. sionwith ncreasen ageof themaster raftsman,We nextconsiderhe results f measurements ut thesedifferencesre usually ess han theon the most nteresting f the violinsmeasured possiblerrorof the measurements.by the new method, and also those by the old In Table IV thereare four famousviolinsmademethodranslatedo thenew-methodcale. he by J. Guarneriusdel Gesu)whose verages12 Strads ncludedn Table IV are all pedigreed fairly close o that of the Strads.There seemsothoroughbredsf unquestionedtanding,hough be slightly essemissionn the lowest requencyone naturally does not know just how their range, though this differences too small to bepresent condition differs from that of their sureof; there are alsosome ndividual variations.infancy.Two of these A and B) are of the The secondn the ist s the "David,"played y


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176 F. A. SAUNDERSTABLE. Intensity istributionn violinschosenby one artist.

RangesViolins I II III IV V VI

Strad H 14.9 25.1 23.7 26.5 19.7 10.0Guarnerius H 13.6 24.9 27.6 25.5 21.9 5.9Yurkevitch 12.7 24.4 27.1 25.3 22.0 8.6

Heifetz; the third the "Verviers," played byZ. Balokovic; he fourth the "Fontaine," playedby .Miss Thelma Given.A group of Italian violins follows, arrangedapproximately in the order of their ages, whichrun from 370 to 100 years. While these instru-ments are all valuable and undoubtedly oldItalian, someof them lack the highestcertificates,so that one can say only that the makersareprobably as indicated. This group again showsmarked individual variations, with an averagenot far from that of the Strads, though theemission at both ends of the scale is a littlehigher. Note how the Gagllano emphasizes helower tones,while the highly arched P. Guarneriusputs more strength into the higher ones.

The group of new violins in Table IV showsthe same variations as the other groups. If onewere certain that any particular Strad was idealin its distribution, and should be copied by allmakers, then one could find in this table at leastone modern violin which approximately dupli-cates it. This matching can be done for highmodel violins, or for low. One cannot say thatone model is good and another bad. Artists whoare much in the public eye use different models,and are presumably pleased with what theyhave. It happens that we are in a position togauge the preferencesof Mr. Heifetz. We havemeasureda Strad and a Guarnerius, both chosenfor his own use, and we have the winner of thenew-violin test, which also represents. what heprefers.Table V presents he distribution in thesethree violins; the consistencyof judgment shownin their selection is indicated by the valuespresented here. The Heifetz type is evidentlyone in which the two upper ranges which o-gether cover the octave from 3136 to 6300 c.p.s.)are relativelyweakcompared ith the middleo.ne.s. d the lowest ange s fairly .st.rong.Sinc fro artist 'can flou?ishf his listeners re

not pleased,and since Mr. Heifetz has a greatmany listeners,we might assume hat his typeis generally preferred; but it is to be rememberedthat a great violinist can play a rather ordinaryviolin in sucha way that the average istener squite content, and thinks that he is hearing afamous instrument.The data in Table IV on Sangster's violinsenable us to test the variability of the productof one modern maker, using the same modelthroughout.Actually,as the resultssho{v,hisviolins vary less than the Strads do, though thedifferencesare uncertain on account of experi-mental error. This table also includes an inter-

esting violin made by Moennig in Philadelphia,a handsomecopy of Strad B. Comparing thevalues for this copy with those of the original,we see that the Strad is stronger in the low fre-quenciesand weaker in the high than its copy,though the differencesare not greater than thosethat occur among Strads. Smaller differencesarefound between Strad J and its copy by Moennig.The Koch violin is of some interest since twolecture audiences thought it was more surelyItalian (and old) than a Strad with which it wasbeing compared (behind a screen). Its distribu-tion of strengthwith frequency ollows he Stradpattern rather closely. The Stanley (Boston) isnot very different from the Koch.There are some unpleasant irregularities inTable IV. For instance, the values taken by oldand new methods for Strad B differ unreasonably.In this case the violin had been treated to a newbass-bar in the interval between tests, and thechangewas probably real. The very large differ-.ence n the upper range for Strad J may again bedoe to a change n the instrument. Similarly, inthe Koch and Stanley violins (range V) there aredifferenceswhich are larger than the experi-mental error. In all these cases there was a gapof a year or two between the two tests, and inthis time all the instruments had been played agooddeal, and their bridgesand stringshad beenchanged. Unfortunately, we took no tests byboth methods on the same instrument at thesame ime, so hat we cannot say positively,whendifferencesare found, whether these are due tothe peculiaritiesof the methodsor to changesnthe violins. Unpublishedtestswhich we havemade nbridgesndons{ringsave hownhat


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 177a violin is sensitive o changes n these items;even the change rom a thin string to a thickerone affects the distribution of strength over thefrequency ranges. Hence we believe that theabove irregularities are probably real.At the bottom of Table IV two violins areentered. Violin X is one of the cheapest type,made n Czechoslovakia;t could be bought withcase,bow, and a set of directions or playing it,for less than $15.00. It had, however, been some-what "doctored" by a new bridge arranged tofilter out someof the excessive igh frequencies,and by new strings to give more strength in thelow ranges. It sounded well when Mr. Heifetzplayed it, but not otherwise.The figuresgivenfor it make it appear better than it was since thad strong emissionabove 6300 c.p.s., which ourtablesdo not include.Violin Y was a flat-toppedmodel made out of common lumber by an un-skilledworkman or hisown pleasure. t possessedto his ear a beautiful tone, though its lowfrequencyemissionwas almost absent, and itshigh frequency trengthextended ar beyond heproper range.

RESPONSE CURVES OF VIOLAS AND CELLOS

Nine violas were measured, six old and threenew. No. 1 was the "McDonald" Stradivarius(1701) in the Warburg collection; No. 2 theAmati (1677) used by M. Aronoff of the CurtisQuartet; No. 3 a Gaspar da Salo (about 1570)owned by Miss Eunice Wheeler, an especiallylargeand responsivenstrument; No. 4 a Storionibelonging to Marcel Dick; No. 5 a probableGaspar da Salo; No. 6 possiblya Klotz (madeabout 1770); No. 7 a new viola made by Haenelof Toronto; No. 8 a copy of No. 2 made byMoennig; No. 9 by Dieudonn (1939). Therangesof frequencyusedwith violas were seven,four octaves and three shorter intervals; I from131 to 262 c.p.s.; II from 262 to 523; III from523 to 1046; IV from 1046 to 2093; V from 2093to 3136; VI from 3136 to 4186; VII from 4186to 6272.

Table VI was obtained by a proceduresimilarto that used for violins. Viola 6 was the only oneof the nine which was measured by bot]q old andnew methods. Violas 4, 5, and 9 were measuredby the new method only; violas 1, 2, 3, 7, and 8by the old method only. The differencesn values

by the two methodswere found from data onviola 6, and were used (lacking a more accurateway) to convert from one method to the other.The values given are in terms of the old method,because more of the violas were measured thisway. The total areas of the response urveswereequalized, as with violins, to make the resultscomparable.The first (lowest) frequencyrange staken as an octave and includes the regionaffected by the air resonance. he second ange(another octave) is relatively strong in mostviolas and includes the first body resonance,which s the sourceof the "wolf" tone. This bodyresonance s stronger in the larger instruments,and has the effect of strengthening the tones inits region. It must on this account be regardedas actually beneficial, and it is of course un-avoidable. The actual wolf is found only at theexact point of maximum resonance but thebeneficialeffectsof this resonance preadover aconsiderable ange on either side. The wolf canbe reducedby any device which tends to checkthe productionof the particular pattern of sub-divisionof the top plate of the instrumentwhich'is responsibleor the excessiveesonance.heother (higher) body-resonancesre well scatteredand numerous. The values for the three shortfrequency ranges at the top of the scale varysomewhat erratically in instruments of equalmerit. If a strong resonancehappens o fall inthe middle of one of these ranges ts effect isfully evident in the measurement or this range;if, however, it falls at a boundary, its effect isspread between two ranges,and is then partlyhidden in our numerical values.

Figure 2 shows the response curves (oldmethod) for four of the most interestingviolas inthis group.

Ta.nLEVI. Intensities n different requencyranges or violas.Rallge8

Violas I II III IV V VI VIIViola I 26.3 37.7 35.3 29.9 29.1 24.3 18.1Viola 2 29.0 38.0 33.2 32.8 29.0 19.6 15.2Viola 3 27.3 35.9 33.1 31.7 32.1 23.7 17.5Viola 4 28.2 38.2 28.8 35.0 35.3 23.8 18.8Viola 5 27.3 38.9 31.1 34.6 36.9 22.0 16.0Viola 6 28.2 39.6 30.6 35.6 30.8 22.0 18.6Viola 7 24.0 35.8 29.2 33.8 37.0 26.2 19.4Viola 8 27.8 36.8 33.2 28.2 30.4 28.0 19.0Viola 9 27.8 37.1 30.2 33.6 33.7 26.0 23.1


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178 F. A. SAUNDERS

FIG.2. Responseurvesf our iolasNos. ,2,3,and8)taken y theoldmethod.hescale elows ikea pianokeyboard,2divisionso theoctave;requenciesf C'sgiven. heverticalcalehowshe ogarithmf the n-tensity,n decibels.he numberedcaleeferso theStrad; heother urvesreshifted ach 0 db upwardnsuccession,o save onfusion.hus, he inemarked 0 sthe zero for the Gaspar.Four celloswerestudied s; he old method.The resultsare shown n Table VII.Cello 1 is a Pressenda, layed by MauriceStad;No. 2 isa Montagnanalayed y OrlandoColeof the CurtisQuartet;No. 3 is a Strad, he"Vaslin," layed y GeraldWarburg; o.4 isacopy yNloennigfNo.2.Table II showshatthese ourdiffer emarkablyittle among hem-selvesn their intensitydistribution. hey allshow large missionn themainbody-resonantregionII), and gainn range I. Theone ewinstrumentn the grouphas high emissionnthe owestange, ndrelativelyow n thehigh

ranges;n otherwords,t showshe' missioncharacteristicshichwe havecome o associatewith the best old instruments. s before, ntreatinghemeasuredesultsncellos,heareasof thecurves ereequalized.hus he relativestrengthn differentangessgiven, utnot heactual intensities.It is unfortunatehat no cellos ouldbemeasuredy the new method.Our apparatuswasnot arge nough,nd t wasnotthoughtlikely hatresultsf anynew -pe would eobtainedroma larger ne.Figure showsheresponseurvesoldmethod)f Cellos, 3,

and 4. They resemble ne another n the lowerfrequencies.he data at high requenciesufferfrom the fact that the observations were takenonlyat semitonentervals,herebymissing uchinterestingdetail. The two oldestcellosshowsharppeaks t the two lower esonances,hilethe new one showswider peaks. Sharpnessnresonance ay be a signof very free vibration,and maywell ncrease ith age;but a widepeakspreadsts helpfulnfluenceverseveral elni-tones,which is distinctly better.CONCLUSIONS FROM RESPONSE CURVES OFVIOLINS, VIOLAS, AND CELLOSTwo positive onclusionsanbe drawn ronlthispart of thework.These re hat there s no

correlationbetween the price of an instrumentand its distribution of strengthwith frequency;and that, whatever s the bestdistribution,t isnot exclusivelyhe propertyof old instrmnents.There is about the samevariation in distributionamonghe old as alnong oodnewones, ndwhateverype heplayerprefers, emayfind teither in old or new instruments. his beingso,we must examine other properties of theseinstruments o seek the reason or the very highregardn which ld talian nstrumentsreheld.While it is true that the response urvesofviolas and cellos strongly resemble hose ofviolins, here s an interesting ifferencen thepositionf themain ir resonanceoint, swellas in the strengthof the main body resonance.Countingy semitonesrom he owestoneofthe instrument, he air resonancesuallyoccursin violinsnearNo. 6, in violasnearNo. 9, and ncellos near 7 or 8. The main body resonancecomessomewhere ear 17 in all these instru-ments,with variations f two semitonesitherway. There s a region f weaknessear hebottomof the scaleand anotherbetween he twomain resonances.he positionof the air reso-

TABLEVII. Cellos. ntensitiesn different requencyranges,ach n octaveower han orviolas.RangeaCelloa I II III IV V VI VII

Cello 35.2 46.5 35.9 32.1 29.9 36.3 27.3Cello2 35.0 44.4 36.8 32.8 27.4 37.4 29.2Cello 36.8 45.2 35.4 31.2 28.8 35.6 30.2Cello4 39.1 45.9 36.5 31.3 27.7 31.9 26.9


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MECHANICAL ACTION.OF INSTRUMENTS OF THE VIOLIN FAMILY 179nance can be lowered permanently only bymaking the volume of the body greater, orby making the total area of the openingsofthe f-holes smaller;but it may be loweredex-perimentally by filling the body with carbondioxidegas througha small rubber tube, or bycovering a considerablepart of the f-holeopenings vith "Scotch"tape (which peelsoffagainwithout injury to the varnish).The greatmastersof the craft placed t about lnidway be-tween the bottom and the first body resonance,where t woulddo the mostgood n strengtheningthe otherwiseweak lower toues. Why does t notoccurat the sameposition n all instrumentsofthe violin family?The ansxvero this question s not certain, buttwo suggestionsan be made.Onewhichappliesparticularly o violas s that, as Professor urtSachshas pointedout, violas were made longerand deeperbefore1700 han they are now.Thismightwell havebrought he air resonanceownto where it is in violins, but such instrumentswere so deepas to be clumsy o play, and theyhavebeensupersededy smallerones.Many oldones were then altered to be less deep, thusraising heir air resonant oints.This has madethe tones on the lowest string in many smallviolas rather weak, and sometimes mean inquality;but thereare many ongviolasof recentmake which seem satisfactory, even with ratherhigh air resonances.his anomalycan be ex-plained y a suggestionade n thenextsection.

CURVES OF INTENSITY (OR LOUDNESS)We must now consider other types o[ testswhich throw light on the peculiaritiesust men-tioned. The simplestof theseare curvesgiving

the total intensity (or approximately he loud-ness) of tones over the whole range o[ theinstrument.Thesemay be obtainedby meanso[a sound-meter. The player keeps a constantdistance from the sound-meter in a deadenedroom, and first plays as softly as he can on onetone while the loudness s read on the meter. Thisis repeatedor each one by semitones)ver herangeof the instrument. hen the wholeexperi-ment is repeated,but this time to measure hemaximum loudness hat can be produced.Eachset of observations ields a curve in which themainresonantrequencieshow speaks, nd the

Fro. 3. Response urvesof three cellos 'qos. 2, 3, and 4).The scales re as iu Fig. 2. The note C has a frequency131 c.p.s.two curves run approximately parallel. Thedifference between the loud and soft values ateach tone is nearly constant, though there aresmall erratic errors due probably to the player.These differencesgive the range of loudnessofthe instrument, which for a violin varies littlefrom 30 (lb. This number is of no special nterestbecause t is nearly the same or old and new, andfor goodand bad violins. lf, however,we averagethe two values at each tone, we get a set ofnumbers yielding an average loudness curve,which is significant. t differs from the responsecurves already considered.The latter show theresponseof the violin for one frequency at atime, dealing with only one partial tone (e.g., thefundamental). Loudness curves show the re-sponseproducedby the bow for one tone at atime, but each tone contains all its partials. Theloudness curve does not discriminate between atone which has a strong fundamental and weakpartials, and one having a weak fundamental andstrongpartials. Every peak on the response urveappearson the lcu(lnessurve, but the latter mayshow additional peaks not present n the former.The most important case is that in which thefundamental is not strong, but the secondpartialis so loud that it more than makes up for theweaknessof the fundamental. This happens oneoctave below each of the most important bodyresonances.Thus a violin may have its air reso-nance at the open D (294 c.p.s.) and a body peaknear B flat on the A string (466 c.p.s.). Theresult is that the loudness urve showsa peak at


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18(I

FiG.4. Curves f averagentensitiesor a viola No. 6),two old violinsand a new one. The horizontal cale sthesame s that n Fig.2 for theviola,but for theviolinsthe lowest one s G. The verticalscales re as before.233,aswellas those t 294and466.Since heresonancesre not very narrow,snchan arrange-ment ields fairlysatisfactoryoudnessver helower ange f the violin. f, however,he airresonances at C sharp (277) and the bodyresonances aboutan octavehigher, he loudnessnear277 s needlesslynhanced y the strengthof the second artial, and there s nothing ostrengthenheweak ones elow 77,or in theintervalbetween 77and 554.The lower onesofsncha violinare weak,as well as thosecenteringaround 10,midwaybetweenhe two peaks.Weknow of one famous violin in which strongresonances ccur near all the C's in-four octaves,to the detriment of the strengthof many othertones in its range.Figure4 showshreeaverageoudnessurvesfor violins,and one for a viola. The top curveshows body esonancet A (440)which n-creaseshe loudnesst 220.This makes muchbetterarrangement,speciallyor the G string,than that shown n the curve below or an oldItalian violin, probablyAmati, where hereareweak hollows because he two main resonancesare aboutan octave p.art. he nextviolinshowsthebody esonancet B flat (466)helpingo fillout the tone n the region f 233.Viola 6 at thebottomhasa strong odypeakbetween and Fsharpabout 60)which xertsnexcellentffectan octavebelow.Of the twelveStrads isted n

SAUNDERS

Table IV, fivehavea good rrangement trength-ening he owestones,hreedefinitelyack hisadvantage, nd four are intermediateor onereason or another. New bass-barswhich havebeenput into all theseviolinshave probablyshifted the body resonances, o that we cannotsay hat this ecord ims hehaloover heheadof Stradivarius.In iolas, f the ones ested re representative,there is some variability. Many have weak Cstrings, ut more ave heir ower ones trength-ened by the help of body resonancesn octavehigher. inceheair resonanceieshigherhan tdoes n violins relatively), he chance hat theair andbody esonancesillbeanoctave part ssmaller. Moreover, the body resonances arensuallystrong.Here may be the reason orplacingheairresonanceearheninth emitone,rather than at the sixth, as n violins.This appliesto cellosalso. If there is no wolf tone there is nostrong ody esonance,ndhenceheC stringslikely o beweak; n such ases relativelyowair resonancewonld be of some advantage.In all the four cellos tested the main bodyresonances about an octave above the air reso-nance. he curvesn Fig. 3 show his. t is likelythat the G stringsof thesecelloswouldbe ap-preciably mproved f the air resonance eremovedupward,say by enlarginghe f-holes(scandalouss such suggestionaybe).Themainbodyresonances strong nougho giveampleoudnessnoctave elow,nd herewouldbe a moreevenresponsever the low tones.

EASE AND QUICKNESSOF RESPONSEWe mustnowconsider therqualities f violinsto which players reqnently efer. These arevaguelyncludedn their dea f the one ualityof the instrument. heseattributesare referredto as the easeof playing, r the quicknessfresponse,r "facilearticulation,"r by manyother hrases.ome f these ave odowith hegrowth f thesotrodt thebeginningfa tone, ritsdecay t theend.Playersssumehat f thetoneseasily roducedt must tartquickly ndcontinue n for a long time after the bow ceasesto act on thestring, ut physicistsnow hat fa vibration s slow o decay t mustalsobe slow

in starting.his s rue f theconditionsfvibra-tionare hesamen bothcases, hich s notquite


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 181the case with bowed violins, since the bow is incontact with the string during the growth, butnot during he decay.Theseeffects eserve omestudy. Violinsalso differ in efficiency, hat is inthe amountof powerwhich must be exertedbythe player to make them sing.This may be con-nectedwith the quickness f growthof the tones,but it is not the same thing. Two lines of in-vestigation are suggested y these thoughts:(1) to measure he powerneeded o makevariousviolinssing; (2) to measure he rate of growth oftheir tones, or the rate of decay. The decay isperhapsmorecharacteristic f the violin than thegrowth,and lessof the player; the decay s alsomuch easier to measure.

RAMAN CURVESThe measurement f power s done by meansof a type of apparatus evisedby Raman (seearticle A). We call the resulting urve he Ramancurve of the violin. This yields the samedistribu-tion of resonanceshat is given by the loudnesscurve, and it is more difficult to measure accu-rately;but it alsoyieldsnumerical alues or thepower nee(led o make the instrumentspeak,which are not obtainable otherwise. We have

restricted these measurements to the tones in thefirst octave on each of the two loweststrings,andwill save space here by presentingonly theaverage alues or the thirteen onesmeasured neachstring.Theseaverage umbers re found odepend reatlyon the typeof stringused, hat is,on its tensionand linear density. Since an artistcannot be asked to change the stringson hisviolin, we have had to contentourselveswithwhat we found there, trusting that his selectionwas the best possible. he numbersgiven inTable VIII are in gramsof forcewith whichourrotatingwheelbowpressedn thestringwhile tscircumference as goingby at a speedof 38 cmper sec.,a speedkept approximately onstant.The distanceof the bow from the bridge was heldat 4 cm; the resultswould be altered if either ofthese numbers were changed.Accordingo these umbersheeasiestiolinto play n this ist is the Balistrieri 1776,ownedby W. Wolfinsohn).he next"best" s oneof theMoennigs,which was perhaps wo years oldx0henmeasured. he Sangsters veragea trifleeasier'lhafi"the' trad, hnd the latter are' easier

than those by J. Guarnerius. The $5.00 fiddlecomesout very near one Guarnerius!This showsrather conclusively hat the easeof playing haslittle to do with the merits of a violin. Evidentlythese orces,varying from eight to twenty gramsor so, are so small that no violinist notices hem,or cares about them. These data refer to theproductionof soft sounds piano on the musicalgradation); n fortissimopassages ne can easilyexerta forceof 150gramswith the part of the bownearest to the hand, but even this (one-third of apound) is too small to fatigue the player, and itis small comparedwith the force which he mustexert to raise his own arm. The differences in easeof playing may not be detectableby the playerwhen they are small, but it seems ikely that thedifference could be felt when it amounts to 20gramsor more, even though t doesnot botherhim. Certainly if the player wants a violin thatis easy to play he can find one without troubleamong either old or new instruments. t is alsopossible hat the violin that is hardest to playmay be the loudest,and may on this accountbepreferredby the player.

DAMPINGWe now turn to the study of the rate ofdamping of the vibration of a violin. Manyexperts onsiderhat the sound f the bestviolinsrings on for a relatively long time after theexcitation has ceased to act. One can give theback of a violin a sharp rap with a knuckle andhear a brief sound thereafter, and the duration ofthis soundmay be an indicationof the quality ofthe instrument. To make this test properly onemustprevent he strings nd the tail-piece rom

TABLEVIII. Average orce n gramsneeded o press owagainst tring o makeviolin speak.Old violins New violinsG D G Dstring string string string

Strad BStrad JStrad SStrad WStrad GStrad DStrad averageGuarnerius RGuarnerius HBalistrieriStainerP. Guarnerius

13 11 X.urkevitch 14 1412 13 Phillips 13 1112 13 $angster's No. 30 12 1014 11 Sangster's No. 33 12 1013 11 Sangster's No. 34 13 914 15 Sangster's No. 35 1 t 912.9 12.4 Sangster's No. 37 11 917 12 $angster's No. 38 13 915 10 Stanley 11 99 g Koch 12 1020 14 Moennig, copy of16 17 Strad J, first It 8Strad $. second 13 11Strad B 13 -11Violin X ($5.00) 16 12


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182 F. A. SAUNDERS

vibrating, in order to be sure that what one hearscomesonly from the body, or the included air.A gifted violinist may have only to hold theviolin resting on his extended hand and feel itsvibration while he talks to it. Such effectsdependon the lightnessof the violin, and on the rate ofgrowth or decay of vibrations in it.The growth of sound when a bow touches astring is a complex affair, and takes place at adifferent rate from the decay of the sound afterthe bow leaves the string. Our first experimentson growth and decay were carried out with thehelp of Mr. Heifetz, who played his Guarnerius,and then the $5.00 fiddle, in front of a micro-phone.With a speciallyquick-actingcircuit anda high speedmoving-filmcamerawe were able torecord the motions of the spot of a cathode-rayoscilloscope,hus getting the wave-formsof thevibrations in great detail. The film moved at arate from 200 to 500 cm/sec. A repeatingpatternof eight toneswas played spiccatowith extraor-dinary speedand cleanness, t the rate of about14 tones per second.An interval of silence wasfound between each pair of tones except in thecaseof one of them (A 880) which resonatedwitha harmonic of an idle string. The tone of theGuarnerius was louder than that of the cheapfiddle, and took longer to grow or to decay bysome 25 percent. But the form of the complexwaves which were produced altered so muchduring a change n loudnesshat measurementsof ratesof growth or of decaywere very uncertain(see Fig. 5). This alteration was due to the factthat the rate of growth or decay changeswithfrequency.Some details of a single typical record areworth giving. The tone had a frequency of 569c.p.s.; the film speed was 370 cm/sec., and therecord of this tone covered 26 cm of film. Inspiccato bowing the bow bouncesclear of thestring between one tone and the next. The initialcontact of the bow with the string showsclearlyand can be measured to about 0.0001 sec. Forabout 0.005 sec. the contact was being made,more and more of the bow-hairscoming o gripswith the string. During this interval an irregularmotion occurredwith one or more strong highfrequencycomponents 5000 to 7000 c.p.s.), butthis soundwas both short and relatively weak, sothat it probably did not contributemuch to the

total effect. After the bow made full contact, thetone grew in volume for about 0.012 sec., thenlasted at full volume for 0.014 sec. Then the bowleft the string, taking about 0.004 sec. to do so,and an irregular motion occurred in this timewhile the string was taking on its free type ofvibration. The decay then followed, asting about0.018 sec. Finally there was an interval of 0.02sec. of almost complete silence.The period ofgrowth of the tone was less than that of decay,and the form of the vibration was different, asone might expect since n the first case he bowwas driving the string, while .in the second hestringwas free. These igureswere obtained roma record of the cheap fiddle, which was the onewhich reacted more quickly. With a good nstru-ment the times of growth and of decay are bothlonger, as was shown from the records of theGuarnerius. In fact the decay was so slow thatthere was no longer complete silence betweensuccessiveones, though this differencewas notnoticed by the listener.Figure 5 gives a reproductionof part of therecordof Heifetz playing the rapid fingerexercisealready mentioned on his Guarnerius. The end ofthe decay of a tone of frequency 880 c.p.s. isshownand the beginningof a tone of frequency740 c.p.s. The open A string resonatedwith itssecond partial tone in the interval between,though this is mixed with other tones from theviolin, whosevibrationswere dying out slowly.The film speedwas 240 cm/sec. Here the maxi-mum amplitude goes off the film. The figuresgiven in the previous paragraph apply to thisrecord also, approximately, as they are charac-teristic of the player rather than the instrument.The beginningof bow contact for the second oneis very definitely shown n the figure, and thehigh-frequency omponent n the irregular mo-tion at that stage has now a frequency near10,000 c.p.s.Since he experimentsust described ouldnotyield accuratemeasurements f the rate of decayof a vibrating violin, we turned to the method ofpure-tone excitation (article D). By this methodof shakinga violin at one frequencyat a time, itwas easy to choose particular frequencies atwhichto take high speedrecords f decay.Thiswas done for a considerable number of violins,both old and new. Records were also taken of


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 183O. Ol sec.

> ?Decay, Contact DriveFIG. 5. A high speed ecordof the vibrations produce(by Heifetz on his Guarnerius near the interval betweentwo short tones.

knuckle knockings, in which case the vibrationsdisclosedwere made up of the main air resonance,which persisted onger than any others, togetherwith two or three body-resonant vibrations. Theduration of the main air vibration could bemeasuredalmost equally well by both methodsofexcitation.

The logarithmicdecrement ) of the amplitudeon the records s found from the equation= (2.303 n) log]0 At/A),

where n is the number of vibrations between thetwo whose amplitudes were measured,A0 is theinitial amplitude, and A the final amplitudeselected or measurement. f the decay is expo-nential, /i should be the same at all frequenciesproduced by the same type of vibration. Thedamping of the air resonancemay possibly bedifferent from that of the body resonances, inceit may be caused largely by radiation of soundthrough the/-holes, and lessby viscosit3' n thewood. Of course, the body resonant vibrationsalso lose energy by radiation, but the process slikely to be lessefficient than in the caseof the airresonance.

Thereare many ndicationshat the energyputinto a violin is largely dissipatedas heat in thewood tself,so hat only a smallpart of it escapesas sound.The latest work on this was by Rohloffwho measured tile motion of the wood in differentplacesover the violin when it was made to vibrateover a considerable ange of frequenciesboth inordinary air and in a partial vacuum of about1.7 cm of mercury pressure. In the best violinsthe energy at the air-resonant frequency wasahnostentirelyabsentat the ow pressure,hough

E. Rohloff, Ann. d. Physik 8, 177 (1940); Zeits. f.Physik 177, 64 0940).

with the body resonancest was often as high asusual. Assuming a low efficiency for the violin,the damping must be due mainly to viscosity nthe wood,with onepossible xception, amelyatthe main air-resonance requency.The frequencieswhich we choseas points atwhich to take readings were almost all resonantpeaks, and they are recorded n Table IX as airor body resonances, ith their approximate fre-quencies.The values of/i are given in this tablefor various violins and for a few violas. Thedamping coefficients ere given may be in errorby as much as ten percent. The knocking timesmeasure the duration of the air resonance, sincethis is the most persistentsoundafter the knock.The amount of energygiven to the violin by theknock varies somewhat rom one trial to another,but that given by the electromagneticexcitationis much more uniform. The variation in time ofdecay from the knocking is not large, as theinitial decay is very rapid. Unfortunately, thistable s not complete n all items,as the necessaryobservationscould not always be made.When the electromagneticexcitation is cut off,there is a redistribution of energy among thenatural modes of vibration of the violin, and thisgives rise to beats. The beats have frequencieswhich are the differences of frequency of thestrongest adjacent natural modes. Such beatswere first observed by Knudsen in a small roomin which pure tones of low frequency and con-siderable energy were being started and thenstopped. In our case this redistribution accountsfor the fact that the first part of the decay is notexponential. Observations taken of the decay ofthe first few vibrations led to higher values of thedamping; the listed values were derived frommeasurements of some 15 to 20 vibrations, aftermost of the initial disturbance had subsided.The conclusions that can be drawn from astudy of thesedamping cocfficients re again asconfusingas before. The average knocking timeof the old instruments s slightly longer than forthe new, but the damping coefficientsaverageabout the same. Individual new instruments (e.g.,the Yurkevitch and one by Moennig) have as lmvdamping as tile lowest of the Strads (B and J).The values for Strad S (a famousand beautifulviolin) would, of themselves,place it among theleast promisingof the new instrmnents.On the


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 183

Fro. 5. A high speedrecord of the vibrations producedby Heifetz on his Guarnerius near the interval betweentwo short tones.knuckle knockings, n which case the vibrationsdisclosedwere made up of the main air resonance,which persisted onger than any others, togetherwith two or three body-resonant ibrations. Theduration of the main air vibration could bemeasured lmostequallywell by both methodsofexcitation.

The logarithmicdecrement (i) of the amplitudeon the records s found from the equation/J= (2.303/n) Iog0 Ao/A),

where n is the number of vibrations between thetwo whose amplitudes were measured,A0 is theinitial amplitude, and .4 the final amplitudeselected or measurement. f the decay is expo-nential, shouldbe the same at all frequenciesproduced by the same type of vibration. Thedamping of the air resonancemay possiblybedifferent from that of the body resonances, inceit may be caused argely by radiation of soundthrough the f-holes, and lessby viseosiW in thewood. Of course, the body resonant vibrationsalso loseenergy by radiation, but the process slikely to be lessefficient than in the caseof the airresonance.

Thereare many ndicationshat theenergyputinto a violin is largely dissipatedas heat in thewood tself, so that only a small part of it escapesas sound.The latest work on this was by Rohloffwho measured the motion of the wood in differentplacesover the violin when it was made to vibrateover a considerable ange of frequenciesboth inordinary air and in a partial vacuum of about1.7 cm of mercury pressure. In the best violinsthe energy at the air-resonant frequency wasalmostentirelyabsent t the owpressure,houghE. Rohioff, Ann. d. Physik /18, 177 (1940); Zeits. f.Physik 177, 64 (1940).

with the body resonancest was often as high asusual. Assuminga low efficiency for the violin,the damping must be due mainly to viseosiW nthe wood, with one possibleexception,namely atthe main air-resonance frequency.The frequencieswhich we chose as points atwhich to take readingswere almost all resonantpeaks,and they are recordedn Table IX as airor body resonances, ith their approximate fre-quencies.The values of i are given in this tablefor various violins and for a few violas. The

dampingcoefficients ere given may be in errorby as much as ten percent. The knocking timesmeasure the duration of the air resonance, sincethis is the most persistentsoundafter the knock.The amount of energygiven to the violin by theknock varies somewhat from one trial to another,but that givenby the electromagheticxcitationis much more uniform. The variation in time ofdecay from the knocking is not large, as theinitial decay is very rapid. Unfortunately, thistable is not complete n all items, as the necessaryobservations could not always be made.When the electromagnetic xcitation s cut off,there is a redistribution of energy among thenatural modesof vibration of the violin, and thisgives rise to beats. The beats have frequencieswhich are the differencesof frequency of thestrongestadjacent natural modes. Such beatswere first observedby Knudsen n a small roomin which pure tones of low frequencyand con-siderable energy were being started and thenstopped. n our case his redistributionaccountsfor the fact that the first part of the decay is notexponential.Observations aken of the decay ofthe first few vibrations ed to highervaluesof thedamping; the listed values were derived frommeasurements of some 15 to 20 vibrations, aftermost of the initial disturbance had subsided.

The conclusions that can be drawn from astudy of these damping coefficientsare again asconfusing s before.The averageknocking imeof the old instruments s slightly longer han forthe new, but the damping coefficientsaverageabout the sane. ndividual new nstruments (e.g.,the Yurkevitch and one by Mocnnig) have as lowdamping as the lowestof the Strads (B and J).The values for Strad S (a famous and beautifulviolin) would, of themselves, lace t among heleast promising f the new instruments.On the


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MECHANICAL ACTION OF INSTRUMENTS OF THE VIOLIN FAMILY 185have led to the same result. We know of oneconductedby Mr. Stokowskion the membersofan orchestra,and another by the famousviolinistIsaye on a group of professionalmusicians; hereare several others recorded.

We have not made accurate measurements onthe maximum volume of tone that an artist canproduce on violins of different sorts, nor on theefficiencyof these nstrumentsas producers fsound energy; these may be important to theartist, but we are sure that they are not to thelistener, who neither knows nor cares how hardthe player is working, and whose impressionofloudnessdependsas much on the acousticsof theconcert hall as on anything else. The crucialquality which we seek does not lie in this field.

The extraneous oises roduced y the scrapingof the bow, especially t momentsof contactwiththe string, or releaseof the string, are so small asnot to enter into the listener's udgment. Theyare not noticedat any considerable istance,andthey are so weak in the caseof steady tones hatour analyses o not show hem; that is, they areat least 30 db down from the maximum of thecomponent partials. The "scratchy" tone of thecheapestviolins is almost certainly due to thepresencen their steady tonesof an excess mountof very high frequencyenergy.There is one experiment on violins which isvery difficult to carry to completion; this is tofind the effect of centuries of time on them. Itseems o be a general belief that a good violinimproves with age; whether a bad one also im-proves no onh seems to know. There are twoeffects hat might be included in the processofageing; 1) chemicaland physicalchangesn thewood, or in the varnish, due to the passage ftime, with its inevitableaccompanyingluctua-tions of temperature,atmosphericmoisture, m-purities n the air, etc.; and (2) effectsdue to theplaying process.The latter consist mainly ofeffects due to continued vibration, but theinfluence f the heatand moisture ontributed ythe player may greatly accelerate the chemicaland physical changesmentioned above. The airnear a player's body in warm weather is almostsaturated with water vapor, and a considerableamount of this will be absorbed by the violinduring a long playing session. his will make thewood expand across the grain, and thereby

change he forces n the violin body somewhat.Daily playing or yearsmight thusdo somethingto a violin which would not happen o one whichis resting in its case.Our measurements indicate that old violinsweigh lesson the average than new ones.SevenStradsvaried from 373 to 394 grams with chin-rests emoved);average383 grams.Six other oldviolins varied from 354 (Stainer) to 389 grams;average 374. Thirteen new violins varied from381 to 435 grams;average410 grams. The threeviolins in the Heifetz test weighed rom 391 to413 grams; average 410 grams. The new violinsare 7 percent heavier than the Strads. Naturally,the lighter a violin is, the easier it is to shake. Itought to be as light as is safe, considering hestrong forces which the tension of the stringsimposes n the instrument. Modern makershavesaid that one cannotsafely make a violin top asthin as thoseof Stradivariuswithout danger ofcollapse. his can hardly be due to any change n200 years in the nature of the wood availablefrom the tree whosewood is almost universallypreferred, the Norway spruce,Picea excelsa. t istrue that the tension of violin strings is nowgreater than it was 200 years ago, becauseof therise of musical pitch; but the Strads, fitted withstrongerbass-bars, re capableof withstandingthis. So we conclude hat the wood has gainedstrength with age, or that it was treated by theearly makers in such a way as to increase thestrength at the time, or at least to make an in-crease n strength more likely through age. It hasbeen stated that the few Strads that have sur-vived without having been played very much arenot as good as those which have been in activeuse. t is also true that Strads have grown greatlyin reputation, and probably in merit, since heywere new. These facts point to an aging processacceleratedby playing, which is responsible orthe present strength of the wood in Strads.We have already mentioned (article A) thatwith age and long playing a certain amount ofcracking of the glue is found in the purfling, andperhaps elsewhere,so that the top of the violinhas become ess ightly bound, and is better ableto vibrate. This may be an important part of theageing process, though it does not satisfy therequirement of an increase n the strength of thewood.


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186 F. A. SAUNDERS

More research s neededon the effectsof age,and of continued vibration, on wood, and this ismost convenientlydone on small strips of wood,rather than on wholeviolins,where he propertiesof the wood (Young's coefficient of elasticity,density,velocityof sound n the Wood,dampingcoefficient, etc.), can conveniently be measured.At the same time the effects of various varnishtreatments (or of the first "filler") can bestudied, and a searchbegun for a substancewithwhich to impregnate the wood so as to add to itsstrength, protect it from moisture, decrease tsdamping, etc. One might also search or betterwoods, now that wood from all over the world canbe obtained. Some of these studies have beenstarted, conducted y various nterestedpeople,and methods of treatment involving heat orchanges n pressureare being tried. As far as weknow none of these methods have as yet led toany very striking results. Future work mustincludea longprogramon treatedstrips ncludingfurther studiesof their damping.

Our sincere hanks are due to many artists andcollectorsfor permission to test their preciousinstruments, and in some cases for active as-sistance n the tests. The list includes JaschaHeifetz, Wolfe Wolfinsohn, JacquesGordon, LeoReisman, Z. Balokovic, the members of theCurtis Quartet (MessrsBrodsky, Jaffe, Aronoff,and Cole), Marcel Dick, Gerald Warburg,Bernard Robbins, William Lincer, Miss ThelmaGiven, Maurice Stad, Mrs. W. E. Ellcry, Mrs.Olga Petzoff, Mrs. E. Ginn, Miss Lillian Shattuck,Miss Sally Dodge, Henry Guerlac, Kerr Atkinson,H. S. Shaw, A. P. Saunders, Malcolm Holmes,F. C. Keyes, and many others, both amateurmusiciansand violin makers. We are especiallyindebted to ProfessorCurt Sachs for advice, andto E. H. Sangster, Wm. Moennig and Son, andJ. A. Gould and Sons for loans of instruments,adjustments, etc. Finally, the credit for theoperationndadjustm.nt of the apparatus,ndfor the construction of much of it, goes to Dr.Robert B. Watson without whose skillful helpthis research could not have been done.

saunders the mechanical action of instruments of the violin family jasa 1946

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