comparing the sound of golden age and modern violins

8/12/2019 COMPARING THE SOUND OF GOLDEN AGE AND MODERN VIOLINS

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C OM P AR IN G T H E S O U N D O F G O L D E NAGE A ND M OD ERN VIOLINS:

LONG TIME AVERAGE SPECTRAAnders Buen

Vallegata 2B NO-0454 Oslo Norwayan-buen@online no

bstractRecordings of the sound spectra produced by violins made by AntonioStradivari 15), Giuseppe Guameri del Gesu 15), and 18 contemporarymakers were analyzed and compared In general, the sound produced bythe 30 violins crafted by the two great Italian masters is very strong in theregion from about C q to G4 (274 to 41 0 Hz) and signij7cantly stronger inthe highrfiequency regionfrom to G7 (2901 to 3073 Hz) and from B, toG 8 (3868 to 6494 Hz). The particular group of modem violins we ana-lyzed had relatively equal or stronger fundamentals at very low notesbelow q (6.5 H z ) . Overall, the sound produced bythe violins of Stradivari and Guameri was darker, less nasal, somewhatstronger in the high-brightness region, nd possibly less sharp than wastypical of the modem violins.

M st violinmakers and violinists are keenly interested inthe similarities and differences in the tonal qualities pro-duced by the finest old and modern instruments. Domodem violins compare to the old master instruments in tone?Are there similarities between the sounds of violins made by themost famous old makers? We seek to answer these questions byanalyzing the sound spectra obtained from commercial record-ings made by two prominent violin soloists one playing on repre-sentative examples of the greatest of the old Italian violins andthe other performing on a selection of fine modem violins madeby highly respected contemporary makers.For the first set of recordings The M ir ac le M a k e r s , producedby Bein Fushi Inc. [ I ] Elmar Oliveira played an excerpt fromthe opening of the Sibelius Violin Concerto on fifteen violinsmade by Antonio Stradivari and fifteen by Giuseppe Guarneri d e lGesiL, which are listed in Table 1. In the second set of recordings

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The egacy of Cremona, produced by Dynamic Srl. Italy 21,Ruggiero Ricci played an excerpt from the second-movementcadenza of the Beethoven Violin Concerto on eighteen violinsmade by well-known contemporary makers which are listed nTable 2. A booklet with pictures and a short biography of the vio-lin and/or the makers accompanied both sets of recordings.Some of the modem makers are highly profiled and have donewell in violinmaking competitions; some also have a cted a sjudges in various competitions.

Table 1 The analyzed old Italian violinsFrom The Miracle Makers 11)

No.12345678910111213141516171819202 1222324252627282930

MakerA. StradivariG. Guam eri del GesuA StradivariG. Guarne ri del GesuA StradivariG. Guarneri del GesuA StradivariG. Guarner i del GesuA. StradivariG. Guarneri del GesuA StradivariG. Guarneri del GesuA StradivariG. Guarner i del GesuA StradivariG. Guarner i del GesuA. StradivariG. Guarneri del GesuA StradivariG. Guarneri del GesuA. StradivariG. Guarneri del GesuA StradivariG. Guameri del GesuA StradivariG. Guarner i del GesuA. StradivariG. Gua rner i del GesuOmobono StradivariG. Guarneri del Gesu

Date167917421690174216921737170117351707172017081737171017401709173417151735172217441723173417271739173417261736173817371735

NameHellierWieniawskiAuerSloanOliveiraKing JosephDushkinSennhauserLa Cathedrali.KartrnanRubyStem, PanetteVieuxtemps, HauserYsayeKing MaximilianLe Violon du Diablci.Baron KnoopPlowdenJupiterOle BullKiesewetteraddockDupontKortschak

WillrnotteStrettonMuntzK e wRawlingsD Egville


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No.12356789101112131415161718

Table 2 The analyzed modem violins(From The egacy of Cremona [2])

MakerGregg lfSam uel ZygmuntowiczPeter GreinerPrimo PistoniWilliam MiillerJohn DilworthPatrick RobinAlberto GiordanoDavid Bague i SolerRoger HargraveChristoph GottingLuiz Bellinikederic-Hugues ChaudiereDomenico FantinJoseph CurtinRoberto RegazziGiancarlo GuicciardiRenato Scrollavezza

Origin and dateAnn Arbor, MI, USA, 1997Brooklyn, New York, USABonn, GermanyCremona, Italy, 1997Croton-on-Hudson, NY USALondon, UK 1998Angers, FranceGenoa, Italy, 1999Barcelona, SpainMeyenburg, GermanyMichelmersch, Hampshire, UKNew York, USAMontpellier, FranceVarese, ItalyAnn Arbor, MI, USA 1998Bologna, ItalyS. Damaso di Modena, ItalyCanneto Parma, Italy

Previous WorkIn an earlier paper 31,we analyzed the spectra from the BeinFushi recording in -octavebands. These bands are nearly equiv-alent to (slightly wider than) the bandwidth of our listening sys-tem and are a much-used standard of resolution in commercialacoustics instrumentation. Each -octave band spa ns the fre-quencies of three or four musical halftones. In the present work,we have extended the analysis to higher-frequency resolution inH octaves, which is equivalent to analyzing a half note per band.Earlier investigators (Bazant, StepanCk, and Melka) [4] found ahigh correlation between HZ-octaveband spectra, obtained from aswept sine signal fed to the bridge, and the subjective soundquality of violins.

ethod and the usicSince the musical compositions used for the tonal comparisonson the two CDs were different, we had to find the connectionbetween the time-average spectra from each of the musicalpieces. Therefore, we had the same professional violinist (GunnarIhlen of the Norwegian National Opera Orchestra) play both theSibelius and the Beethoven excerpts on five different violins inthe same room. The sequence was recorded on a DAT tape forlater analysis on a Norsonic 840 unit capable of Hz-octave band


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analysis. We also recorded scales on each of the ins trum ents forcomparison and made time-average %-octaveband analysis usinga light Norsonic 118 unit during the session. By subtracting theaverage spectra from the Beethoven from the Sibelius pieces, itwas possible to significantly reduce the effect of the room and theplayer on the spe ctra . We refer the inter ested reader to theAppendix for basic information about the sound meters and fil-ters and our normalization of the audio spectral measurements.

ResultsFirst we compare the summed equivalent sound pressure levels ofeach played violin, as shown in Fig. 1. The sound pressure levelshave been corrected so that the average level over the old and thecontemporary violins is equal. We see from Fig. l a (old Italian vio-lins) and Fig. l b (modem violins) that the levels varied from 83 to91 dB. For the old Italian violins, the difference between the mostand least powerful recordings was 6.8 dB; for the modem violins itwas 7.5 dB. This level span is quite considerable. We illustratedthis difference by playing four of the weakest recordings simulta-neously to get almost the same sound level as the most powerfulof them. Doubling the number of equally strong sources by a fac-tor of two resulted in a 6 dB increase in the total sound level.However, the subjective perception of a 7 dB increase is a littleunder a doubling of the per eived sound level, which may soundless dramatic than the example illustrates.Some of the variation was related to how similarly the twoviolinists played the pieces. From studies under controlled condi-tions by Gabrielsson and Jan sson [5], he variance introduced bythe violinist playing scales in a reverberant room was less than 1dB, so we assumed that it would be about the same for our con-ditions. A 1dB difference in sound level is just about noticeable.

Several studies of vibration levels and sound radiation from anumber of violins have shown a natural variation of -8-10 dBover the frequency bands 16-81. Miiller attributed this variation todifferences in the wood quality from bad to very good [71. Wewould, however, be surprised if bad wood had been used in theconstruction of any of the fine violins included in this study.Most of the variation should come from the physical instruments,the se t up, properties of the wood, plate thicknesses, and maybeother (unknown) factors influencing the sound power from theseinstruments.

If we count inst ruments within each 1 dB and scale by divid-ing each count by the total number of violins in each group, weget a p icture of how the variance is d istributed. Tha t the oldinstruments were more evenly distributed in sound level thanwere the modem is revealed in Fig. 2.


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P Old35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Iodern- - - - -

Figure 2 Distribution of sound levels among the 3 old Italian violins andthe 18 modem violins


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We would expect a clock curve, i-e., a normal distribution.Our group of modem violins had relatively more instruments inthe center bar from 86-87 dB, while there is a rather flat non-clock distribution around it. This indicates tha t the building phi-losophy and wood may have been more uniform among thecenter-bar makers. The more uneven distribution was moreexpected for the eighteen different modem makers than for theCremonese makers of the 17th- 18th centuries.When we look closer at the old instruments by dividing theminto two groups, we get a flat clock among the Strads and twosmaller clocks among the Guarneri, as shown in Fig. 3 The num-ber of instruments (fifteen) in each group was, however, a bitsmall to draw conclusions, e.g., about the seeming two groupsamong the Guarneri violins. But we see that the curves in Figs. 3are smoother than for the contemporary violins shown in the rightside of Fig. 2. Even i one could be tempted to read ou t of Fig. 3that the Guarneri were slightly stronger, their average levels werenot significantly different. Both averages were close to 86 dB. Acomparison between the average sound levels among the old andthe modem violins can't be done as their averages were adjustedto be the same. This was our best guess because we had no com-mon reference signal on the recordings. Such reference sound sig-nals are not pleasant sounds to have on a musical recording.The average sound level of -86 dB is that typically found nearto a violin. At the player's ears the sound may be 10- 15 dB high-er, depending on the music and how strongly the player choosesto play. For the musician concerned about his/her ears, it isworth considering using earplugs. A weaker sounding violin whilenot being on stage will also pose less risk of damage to the ears.The single number for a measured sound power level by itselfdoes not tell much about the tim re of the tone. We see from Fig.that the difference between the linear equivalent level (not cor-rected pressure level, Leg) and the A-filtered SPL, LASeq,rom theviolins is typically -1 dB. I t will be larger when there is more basssound from the instrument, or smaller if there is less bass. Forexample, we would expect the violin by D Bagui: i Soler to have arich bass spectrum since the LAqeqnd Leg for this violin differ by-2 dB.The linear (uncorrected) levels are likely to give a better ideaof how loudly the instruments sound under the player's ears. Theviolins will sound brighter to a listener at a distance than to theplayer. This is due to our listening systems' lower sensitivity tobass sounds and slightly higher sensitivity to higher frequenciesa t lower sound levels. More th an two single nu mbe rs will, ofcourse, better describe the perceived timbre of the sound. Weneed to look a t the detailed spectra to learn something moreabout the timbre.


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Figure 3 Distributions ofsound levels among the 15 Stradivari violins andthe 15 Guarneri del Gesu violins


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Comparisons of the Sound SpectraThe main aim here was to compare the modem violins with thoseof the old 1talian masters, but we also show the average curvesfor the Stradivari and Guarneri del Gesu violins for comparison.In Fig. 4 we see that the Strads and the Guarneri have quite sim-ilar average spectra. To better see the difference between them,we subtracted one spectrum from the other, as presented in Fig.5. We have also performed a statistical test (t-test) to determine ithe differences we see are significant, just interesting, or notdifferent. Our definitions were somewhat inspired by Bissingerand Gregorian [9]: 1) 'There s a d~fference significance levels(p-values) 5%, 2) ' Therem y be a d~perence significance lev-els between 32 and 5%, and 3) 'There s no d~zerence signifi-cance levels 32%.We see that the six to seven first-half notes played on the Gstring, G3-C4 (196-260 Hz), have stronger fundamentals for theStrads. The next two half notes, D4 and D#4 (290-307 Hz), arestronger for the Guarneri violins, possibly due to their main airresonance being somewhat higher. There is also a region fromA#, to C5 (460-516 Hz) an d the note D5 (579 Hz) where theGuarneri violins appear to be stronger than the Strads. The toneB, is close to the minimum found between th e first, B-, and sec-ond baseball resonance, B', in violins, and the D5 is slightlyhigher than the region we normally find the B+. This might indi-cate that the B+ s located slightly higher in frequency (or tone)for the Guarneri than for the average Stradivari violin.Around C#6 and D6 (1090-1155 Hz) the Guarneri violins seemto be stronger, but from F6 to B6 (1372-1939 Hz) and C7-C#,(2054-2175 Hz) the Stradivari violins are relatively more power-ful. The same seems to be true for the G7-G#, (3073-3255 Hz)and G8-G#* (6131-6494 Hz) half notes tha t are the overtones.

Correlating Spectra w ith AveragesSimilarities and DifferencesWe have shown comparisons between two spectra in one figure a ta time and observed the similarities and differences. To analyze alarge set of data we need a measure of equality. This is also use-ful for later comparisons of spectra from new or other inst ru-ments to the average curves, or for evaluating any individualinstrument from this work.We can compare two violins (or one violin versus the average)by making a graph of the band levels of one violin a s x-valuesand the corresponding band levels for another violin (or the aver-age curve) a s y-values. If the spectra of the two are very similar,the points would be close to a straight line; i not, they would


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1 , , 1 1 , , 1 1 , , 1 1 1 1 , 1 , 1 1 , 1 , , , 1 7 1 , 1 , 1 1 1 1 , , , , 1 , , 1 1 IMusical ton

Figure 4. Long-time-average sound spectra of the Sibelius excerpt playedon 15 violins made by Stradivari and 15 violins made by Guarneri delGesii.

Figure 5. The dtfference between the average sound spectra from theStradivari and Guameri del Gesii violins. The Signijkance numbers 1indicate there s a d~fference, 0.5 indicate there be a d~fference,and 0 indicates nodtxerence.


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tend to spread across the line. The statistical measure for thatspread, called the correlation coefficient, gives a precise descrip-tion of how close the points are to a best-fit straight line. Manyspreadsheets have this function implemented. One simply choos-es the two spectra to be compared, and the function gives theresult a s a number between 0 and 1, with 0 indicating no corre-lation, and 1 indicating very high correlation.By comparing the spectrum for each violin with the averagecurve and looking at each correlation coefficient, we find that thespectrum for the a Cathedral6 is closest to the average spectrumof the Strads; the Oliveira is least similar. The best method tojudge the validity of this result is, of course, to listen to the musi-

cal selections. The Oliveira sounded brighter than any of theother Strads.e Violon de Diable Guarneri del Gesii produces a frequencyspectrum that is closest to the average Guarneri, while the

Stretton is least similar. It is interesting to note that the thick-nesses of the top plates of these two instruments are similar.However, the thicknesses of their backs differ more than for anyof the other Guarneri violins tha t were both recorded in the BeinFushi production l ]and included with plate thicknesses(Comparisons by correlation of the thickness datafor each plate) inthe Biddulph publication, Giuseppe Guarneri de l Gesic [lo] TheStretton has a thinner back and a somewhat different thicknessdistribution. (See the graduation maps in Schleske's article inCASJ May 2002 [I11.) This indicates that the back plate thick-ness must have a significant influence on violin timbre.Among the Stradivari violins, the spectrum of the KingMaxirnilian was closest to the average of the Guarneri del Gesuviolins tested, while that of the Kieswetter Strad was the leastsimilar to the average Guameri. The Sennhauser del Gesic sound-ed least like the average Strad, while the Kartman d el Gesusounded most similar to the average Strad. This might be plausi-ble a s it is said that earlier violins of Guarneri del GeSu weremore similar to those of Stradivari.This analysis may be understood as an aid when listening tothe recordings. Listening indicates that the observations seemreasonably correct, although much information is lost when thespectra are averaged over the entire musical composition. A sum-mary of the results is presented in Table 3


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Table 3. Spectra with highest and lowest correlation coefficients with the average spectrumfor the instrument groups: Stradivari, Guarneri, old (Strads G Guarneri), and modem violins.

(Comparlsons were made using time-average K2-octave bands.)Similarity to mong the Strads mong the Guarneri mong the modemsHighest Lowest Highest Lowest Highest LowestAverage Stradivari L a C a t W O li ve ir a K ar tm an Sennhauser G Alf J . CurtinAverage Guarneridel Gesu King Kieswetter e V b l o ndu Stretton G Alf J . Curtin

Maximilian uDiabEAverage old Italianviolin (Guar. Strad) La Ca tW dra E Oliveira Kartman Sennhauser G Alf J . CurtinAverage modemviolin uby Rawlings Sloan Sennhauser P. Robin D . Bague i Solerand R Hargrave


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Now, how do the modem violins compare with the old Italianviolins? We show their average spectra in Fig. 6 where we repre-sent the old ones with their average spectrum. We see that thedifference between the old and the modem is somewhat largerth an between the two groups of old violins. We see a difference inthe low mid-frequency register. To magnify the differences wesubtrac t the two curves from each other and present them in Fig.7. We have also performed a statistical significance test (t-test)between the old and the modern violin spectra with resultsshown a t the right scale in Fig. 7The differences are clearer in Fig. 7 than in Fig. 5. Larger dif-ferences may have been introduced by the added variation due tothree players and rooms and two musical pieces involved,although we have tried to reduce the differences to a minimum.The players were assumed to have played each piece very sirnilar-ly. We also assumed that the recordings were made under con-trolled conditions by top sound producers who were aware ofsimple acoustical factors. Since we have adjusted the average lev-els of the old and modem violins to the same level, the compari-son was therefore between their relative spectra.

In Fig. 7 we examine four broad frequency regions. The con-temporary violins had relatively stronger tone in the mid and lowfrequencies, while the tone of the older violins was stronger in thelow mid-frequency an d high-frequency (brilliant) regions. Thecomparisons are shown in more detail in Tables 4a and b.From Table 4a we see that basically the fundamentals onthe D-string are stronger in the old violins, while the modernhave stronger fundamentals very low on the G-string, all over theA-string, and much of the lower E-string. From Table 4b we seethat the low brilliance region from 1.5 to 2.5 kHz is dominating inthe modem violins, while the old master violins are stronger inthe high brilliance region from 3 to 6.5 kHz. The latter observa-tion seems to be in line with the findings by Pickering [12].At still higher pitch the output power of the modem violinswas comparable to or stronger than the old violins, and a t veryhigh frequencies the modem violins did seem to be stronger. Thefrequency region > 5 kHz is important for the perception of sharp-ness, the opposite of darkness [13].Thus, the old violins soundedconsiderably stronger in the low mid-frequency region (275-410Hz), less nasal (650 Hz- 1.3 kHz), and somewhat brighter andclearer in the high notes (3-6 kHz).

We may compare the differences between the old and modemviolins with the Strad-del Gesic differences to see if there mighthave been a common strategy of using either Stradivari's orGuameri's methods for building violins. We observe a n apparentcorrelation for the lowest tones from G3 (196 Hz) to F , (365 Hz)and weakly even to G 4 (410 HZ).Here we may say that the mod-


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Figure 6. Average sound spectrafrom the old nd the modem violins. hespectrumfrom the modem violins have been corrected by adding the dg-ference between spectra from the Sibelius and the Beethoven excerptsplayed n the same room by the same player usingjue d~fferent iolins.

Figure 7. The dlfference between the average sound spectra of the old andmodem violins. The Sign~@ance umbers 2 indicates 'there is a dfler-ence, k0.5 indicate there be a dlfference, and ndicates no dif-ference.


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Table 4a Comp arisons of tone regions with average differences indB between the average spectra from the old and mo dem violinsTone G ,-A3, C C ,-G , A,-C ,, D ,-F,, G,-A , D,, Fg5 D,-D , E6-F6%2-oct. and [Hz] 205-230 259 274-410 434-546 613-688 772-917 579 729 1.15-1.22k 1.3-1.37kOld-ModemAvg. difference [dB ] 4.4Which is stronger? M M MString fundamentalor harmonic G (GI r ( G & D ) A & E

Table 4b Comp arisons of up per tone regions with average differences indB between the average spectrafrom the old and modem violins(H Harmonics , HH Higher ha rmonics . )

Tone F ,-A , C7-D, F 7-G, A7 f8 F , G , k E 9H2 oct. band [Hz] 1.45k-1.83k. 2.lk -2.4k 2.9k-3. k 3.4k 3.9k-5.2k 5.8k 6.5k 6.8k-10.2kOld - ModemAvg. difference [dB] -2.0Which is stronger? M 0 M MString fundamentalor harmonic E H E H E H H H H H H HH

an


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e m violins are more of the Strad-type, probably with lower mainair resonance than the average del Gesic. t might also imply thatthe plates of the modem violins were somewhat less stiff thanthose of the Guarneri violins. Also, their top plates might havehad thinner edges than (at least) the average del Gesic.Other than the very low frequency region, no clear correla-tions could be seen. (A test gave the correlation coefficient 0 3with the significant p-value of 3 for the curves in Fig. 8Comparing the spectra beyond 440 Hz gave no significant corre-lation.) There was a slightly higher correlation between the spec-tra of the average Strad and the average modem violin. Of theGuameri violins, the Sloan was similar to the largest number ofthe modem violins. We are unable to conclude that there was anycommon preference in spectra for either of the old mastersamong the contemporary makers.Such correlation also may be done between each modem vio-lin and their average, and with the average Strad or del GesG.This is an aid when listening to the recordings doing comparisonsof the extremes. The modem violins that were most similar to theaverage were the violins by Robin and Hargrave, while the spec-trum of the violin by Bagui: i Soler exhibited the least similarityto the average spectrum of the modern violins. The moderninstrument having the highest correlation with the average Stradand Guarneri del Gesii curves was the violin by Alf. The instru-ment whose sound spectrum showed the least similarity to thoseof the old Italian makers, both averages, was the violin by Curtin.f we perform the correlation in %-octave bands (a less precisereso lution ), the violins by four m akers (Alf, Zygmuntowicz,Miiller, and Dilworth) had about the same correlation. The least

similar to the average old violins in one-third bands was the vio-lin by Chaudikre.To illustrate the similarities and differences, we have plotted

the average curves along with the more-or-less similar violinspectra in Figs. 9 to 12. The spectrum of the violin with leastsimilarity to the average of modem violins is presented in Fig. 11.By comparing each of the old Italian violins with th e averagecurve for the modem violins, we see that the Sloan Guarneri del

Gesii and the Ruby Strad are the most similar to this set of mod-e m violins. The similarity is, of course, less than with the averageStrad and del Gesh curve, bu t the correlation coefficient is aboutthe same as tha t between each of the modem and the old averagecurves. The Sennhauser Guarneri and the Rawlings Strad pro-duced sound spectra least similar to the average of the modemviolins. These correlations are summarized in Table 3.

In Figs. 9 and 12 we still see tha t the old instruments have ahigher response in the upper low-frequency region. Since theBague i Soler violin seemed to have substantial power in that


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Figure 8. Dflerence curves: old-modem and del Gesu --Strad. Note thed5fferent scales on the two axes to the right and ley?

vg S G

Figw-e 9. Average of the old Italian violins by Stradivari and Guarneri delGesii)and the modem violin with the highest correlation with the old vio-lins.


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Figure 10. Average of the old Italian violins by Stradiuari and Guameridel Gesii) and the modem violin with th lowest correlation with th oldviolins.

Figure 1 1 Re sound spectrum of the modem violin least similar to theaverage spectrum of the 18 modem violins had a strong lowzfrequencyresponse in the octavefrom C 4 to C 5.


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Figure 12 The sound spectrum of the Sloan Guarneri del esli had theclosest correlation to the average spectrum of the 18 modem violins

Figure 13 The sound spectrum of the modem violin made b y D Baguk iSoler and the average spectrum of the 30 old talian violins by Stradivariand Guarneri del Gesii


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region, we plotted its spectrum in Fig. 13 together with the aver-aged spectrum for the old Italian violins. We see that it had acomparable or even stronger response in this region, especiallyaround A,-A , (440-460 Hz), which indicates a strong B- (T,) res-onance. It might be strong here a t an expense of a weaker B+ (C3)around the C 15-D5(550-580 Hz).

Conclusions and QuestionsWe have shown that there are small, but characteristic, differ-ences between the sound spectra of the average Stradivari andGuarneri el eshviolins. The Strads have stronger low notes onthe G-string and higher levels of the higher overtones, makingthem sound a bit more brilliant. The average Guarneri el eshs equal or somewhat stronger in the mid-frequency region fromthe higher notes on the G-string, D to about G6.The differences between the average modern violin and theaverage Strad/Guarneri violin were greater than the differencesbetween violins by these Italian masters, again on average. Forthe first six half notes, the contemporary violins exhibited Strad-like characteristics, being equal or relatively stronger than theaverage old master Italian violin. The next eight half notes (C ,-

G ,) were, however, relatively much weaker. From A4 and up toab ou t D,, the contemporary violins were possibly equ al orstronger. (Exceptions were D5, F 5. E6, and F6 where the old wererelatively stronger, o n average.) The old i ns tr um en ts werestronger in the high-frequency regions F ,-G, and B,-G ,. Themodern violins seem to have stronger fundamentals on the A-and E-strings, while the old have a particularly strong D- a sopposed to the A-string. They also have stronger higher harmon-ics affecting practically all played notes.Why do we see and hear these differences? This s certainlynot a simple question to answer, but acoustically, plate thick-nesses are very important [14-161. Thickness and the bass bar,most likely, will also influence the radiation efficiency of the vio-lin. s there a way to predict it in a simple manner? 117, 181Details of the geometry of the f-holes seem to affect high frequen-cy response [16, 191. s there something to learn from the presentknowledge and methods used in guitar acoustics, such as report-ed by Richardson [20], Chaigne [21], and their collaborators?We need to collect more data, not only thickness, but alsowood parameters, weights, and tap tones, arching heights, bridgedetails, details about the position of the sound post (how do weknow that a violin s properly se t up?), and sound speeds in crossand length directions of the violin plates. (Regarding tap tones,why not collect more than only the fifth mode frequency? We canhear a t least six to seven of the plate modes; what we hear we


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may expect the old master did as well.) All these are parametersth at may be registered in most violin shops today. Of coursethere remains the question of how to perform the data collectionin a standardized way to permit valid comparisons.Other questions concern the players: Have the preferences ofmodern violinists regarding the timbre of violin tone changedfrom those of violinists of the past? Do we agree upon what isgood timbre? Do psychoacoustic tests on violin recordings mea-su re the quality of the violins being evaluated or the preferencesof the particular group of listeners involved? Would the results (ifany) apply to violins in general?

SummaryWe have presented a simple method of analyzing long-time-aver-age sound spectra from short music pieces obtained from record-ings with the same pieces played on a significant number ofviolins. By simple statistical methods we have found the record-ings with the closest similarity to the averages for the Strads , theGuarneri el Gesli and the modem violins. The results may beused as an aid for listening to the tracks with most and leastsimilarities with either group of instruments [ l 21. The methodshould be feasible for comparing new instruments to the averagespectra obtained from this work by playing the Sibelius or theBeethoven excerpts and analyzing either in - or %-octave bandspectra. (Finer resolution may also be used, but the amount ofda ta becomes very large to process.) To reduce the risk for singleroom resonances a t >200 Hz a room with a reverberation time of-1 second should have a volume larger than 100 m3. For adeader (living) room with -0.5-second reverberation time, aroom volume 250 m3 should be sufficient.Finally, the author concedes that correlation of long-time-average spectra is, of course, a simplification. Numbers can'tcany the total subtle information connected to music and musi-cal instruments. The author invites the reader to listen to the twocomparison CDs [I , 21 and compare your evaluations to what hasbeen noted in this article.

ACKNOWLEDGMENTSThe author gives thanks to Gunnar Ihlen, violinist in the NorwegianNational Opera Orchestra, for playing the Sibelius and Beethovenexcerpts and for useful discussions regarding acoustics in general andth at of violins in particular. Thanks to Dr. Reidar SkjelkvAle for inspiringdiscussions and for bringing The egacy of remonarecording [2] withRuggiero Ricci to my attention. The author acknowledges the assistanceof his employer, Brekke Strand Akustik A.S., for providing the mea-


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surement equipment used for this project. Also, many thanks to the edi-tor. The author is alone responsible for the content in the article.

REFEREN ES111 R. Bein and G. Fushi, The Miracle Makers - Stradivari GuameriOliveira (Bein Fushi, Chicago, 1998). Book and 3 CDs.121 R. Ricci an d N. Shiozaki, The Legacy of Crernona. Ruggiero Ricciplays 18 contemporary violins, Book CD (Dynamic Srl., Genoa,

2001).[3]A. Buen, Differences of sound spectra in violins by Stradivari and

Guarneri del Gesh, Catgut Acoustical Soc. J. Vol. 4, No. 8 (Series 11).pp. 14-18 (Nov. 2003)[4] P. Bazant, J . StepanCk, and A. Melka, Predicting sound quality of vio-lin from it s frequency response, in Proc. of Stockholm Music AcousticsConf. (SMAC20031, Stockholm, pp. 351-354 (1993).151 A. Gabrielsson and E.V. Ja nsson, Long-time-average spectra andrated qualities of twenty-two violins, Acustica, Vol. 42, No. 1, pp. 47-55 (1979). (Repr. in Res. Papers in Violin Acoustics 1975-1993, Vol. 1,C.M. Hutchins and V. Benade, Eds. (Acoustical Soc. Amer.,Woodbury, NY 1997).161 A. Buen and O .J . Lakberg, Operating deflection modesin five conven-tional and two unconventional violins, in Proc. of Stockholm MusicAcoustics Con- (SMAC2003). Stockholm, pp. 43-46 (2003).[7] H.A. Miiller, How violin makers choose wood and what the proce-du res me ans from a physical point of view, presented a t CatgutAcoustical Soc. Intl. Symp. on Musical Acoustics (ISMA1986). Hartford,CT 1986. Repr. in Res. Papers in Acoustics 1975-1 993, Vol. 2, pp.879-883; op. cit.

181J . Woodhouse, Body vibration of the violin-What can a maker expectto control? Catgut Acoustical Soc. J. Vol. 4, No. 5 (Series 11 . pp. 43-49 (May 2002).[9] G. Bissinger and A. Gregorian, Relating normal mode properties ofviolins to overall quality: Part I: Signature modes, Catgut AcousticalSoc. J. Vol. 4, No. 8 (Series 11 . pp. 37-45 (Nov. 2003).

1101 C. Chiesa, J . Dilworth, R. Hargrave, P. Klein, S. Pollens, D.Rosengard, and E. Wen, Giuseppe Guameri del Gesk (P. Biddulph,London, 1998).[ l l ] M. Schleske, Empirical tools in violin making: Part I: Analysis ofdesign, materials, varnish and normal modes, Catgut Acoustical Soc.J. Vol. 4, No 5 (Series II , pp. 50-54 (May 2002).1121 N. Pickering, A holistic view of violin acoustics, J. Violin Soc. Arner.,Vol. XVII, NO. 1, pp. 29-53 (2000).

1131 J . StepanCk and 2 Otcenasek, Interpretation of violin spectrumusing psychoacoustic experiments, in Proc. Intl. Syrnp. on MusicalAcoustics &%442004), Nara, Japan, pp. 324-327 (2004).

(141J . Loen, Thickness graduation mapping: Surprises and discoveries,J.Violin Soc. Arner., Vol. XIX No. 2, pp. 41-66 (2004).

1151J . Woodhouse, On the bridge hill of the violin, Acta Acustica Unitedwith Acustica, Vol. 91, pp. 155-165 (2005).1161 A. Buen, On correlations between physical measures and timbre ofgolden age violins. Submitted for publ. in VSA Papers (1 Feb. 2005).
http://www.akutek.info/Papers/AB_Violin_spectra_2003.pdfhttp://www.akutek.info/Papers/AB_Deflection_modes.pdfhttp://www.akutek.info/Papers/AB_Deflection_modes.pdfhttp://www.akutek.info/Papers/AB_Violin_spectra_2003.pdf


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[17] A. Buen, Two models for prediction of violin timbre from materialproperties. Submitted for publ. in Catgut Acoustical Soc. J. in August2004. (Results from these models followed the first draft of paper [3]in July 2003.)

[18] G. Bissinger, Contemporary generalized normal mode violin acous-tics, Acta Acustica United withAcustica Vol. 90, pp. 590-599 (2004).[19] F. Durup and E.V. Jans son, The quest of the violin bridge-hill, Acta

Acustica United with Acustica Vol. 9 1, pp. 206-2 13 (2005).[20] B.E. Richardson, The acoustical development of the guitar, Catgut

Acoustical Soc. J. Vol. 2 No. 5 (Series II , pp. 1-10 (May 1994).[21] A.J. Chaigne and M. Rosen, Analysis of gui ta r ton es , CatgutAcoustical Soc. J. Vol. 3 No. 8 (Series 11), pp. 24-31 (Nov. 1999).[22] A. J.M. Houtsma, T.D. Rossing, and W.M. Wagenaars, Auditorydemonstrations: A series of audio demonstrations about hearing oncompact disc. Demonstr. 6: Frequency response of the ear. Prepareda t the Inst. for Perception Res. (IPO), Eindhoven, The Netherlands,Sept. 1987. CD and booklet, 9 3 p. (Available from the Acoustical Soc.Arner.)

Appen dix: Sound Pressure Level Meters Filtersand Normalization of Measured Spectra

The sound pressure level (SPL) meters used for these tests were off-the-shelf ins truments commonly used for measurements in building-, room-,working health- and environmental acoustics applications. The mostusual reading they may give is the time-averaged sound pressure levelduring the measurement period, the so-called equivalent sound pressurewritten as Leq. This is a single number, and the sim-only display such digits for the whole period of mea-sured sound.

Our ears are less sensitive to bass sounds and slightly more sensi-tive to sounds in the range of 2 to 4 kHz (C, C8). We may say that ourlistening system does not have a flat frequency response [22]. And tomake things even more complicated, this frequency response changesslightly with the loudness of the sound to which we are listening. At highloudness we hear the bass a little better. (This is the reason why some ofus use the loudness button on the stereo to boost the bass when weare playing [pop or rock] music at low volume. If we turn the volume up,we may hear that the music played at a higher loudness does not needmuch of a bass boost).

As an early attempt to simulate the frequency response of our ears,SPL meters were equipped with filters given the names A, B, C, etc. TheA filter, in a somewhat simplified manner, was supposed to emulate ourear's frequency response at a sound pressure level, L of -55 dB, theB filter for sounds from -55 to 85 dB and the C fil%::for L P v q igherth an 85 dB. Only the A and C filters have survived in practical use. Inthe present paper the A-filtered sound pressure level is denoted as LA,eq.The difference between the digits for A- and C-filtered time-averagedsound pressure levels, (LcSeq LA,eq), ives valuable information about


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the amount of bass the sound may contain, a useful number when wehave no ability to see the whole sound spectrum. It is also useful forcompression of information into ju st a single number . For musicalsounds from a violin, for example, the C-filtered sound pressure level,LC and the unfiltered level Leq are practically identical. The latter isuseA in this paper.The SPL meters also have choices for different speeds of response,technically termed the time constants. This is also an artifact from his-torical SPL meters where the loudness was displayed by a needle (likemost other early measurement equipment). The needle could be reactingslow or fast to the recorded sound. slow response made it easier toread off the average sound pressure level by sight. The measurements inthese tests were made with a fast time constant, which had a reactiontime of -125 milliseconds. This is the most commonly used time con-stant, e.g., as used in present-day architectural acoustics measure-ments.

By subtracting the average SPL spectra from the played Beethovenfrom the played Sibelius piece we substantially reduced the effect of theroom and the player on the spectra. The connection between the twomusical pieces was found by the following operation for each Xz-octaveband:Leg (Sibelius played by Ihlen) Leg (Beethoven played by Ihlen)Leg (Beethoven played by Ricci) Le (Sibelius played by Ricci)

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