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Differences of Sound Spectra in Violins by Stradivari andGuarneri del GesirAnders Buen

Brekke & Strand akustikk asHovfaret 17, NO-0275 Osfo, Norway

[email protected]

ABSTRACTThir ty f ine Cremonese viol ins made in the shops of AntonioStradivari and Gu arneri del Ges6 are compared based o n long-timeaverage spectra. One-third octave band spectra were obtained froma commercially available recording where the same music piecesa r e p la yed und e r s im i la r c ond i t ions o n e a c h o f t he v io l in s .Generally the spectra conform to a 10 dB band from 250 to 4,000Hz. T he average Stradivari is stronger in the 200 Hz and 250 H zbands and above 1.6 kHz. Del Gesus are on average stronger from315 Hz up to 1.25 Hz. These differences are perceived as a morebrilliant sound and stronger fundamentals of the lowest notes ofthe Stradivari, versus a more dark sound in the del Ges6.INTRODUCTIONViolins and other musical instruments are often studied based onadmittance or radiation curves [1,2,3] . Such curves are rapidlyrecorded and are invaluable for judging and analyzing details ininstru men t character istics and acou stical qualities [4] . How ever,few good instruments are available for such measurements. Makersand players prefer to play instruments to judge the quality ratherthan using analytical measurement methods, and musicians usuallyjudge an instrument within seconds of playing. A trained listenershould be able to do the same, even if the sounds come from arecording. Imp orta nt information for judging the quality shouldbe found in the sound spectra from the played violin. Th us itshould be feasible to analyze recordings for the study of soundspectra from violins. Thi s article investigates the soun d spectraf rom f ine Cremones e viol ins m ade by Anto nio S tradivar i andGiuseppe Guarneri del Ges6. A more general aim is to present asimple method that may be applied to available recordings, mayberight from your own CD archive.METHODSignals from a commercially available recording (The MiracleMakers, by Bein and Fushi [4]) were plugged into a spectruma n a l y z e r c a p a b l e o f p e r f o r m i n g o n e - t h i r d o c t a v e b a n dmeasu remen ts. Com pact disks were played using a portable C Dplayer (Sony SL-S320; bass boosting network turned oft), and the

signal was sent to a Norsonic N ll O unit. One -third octave baanalysis yielded equivalent sound pressure levels ( t ime averasound p ressure levels) from 6 3 Hz to 20 kHz. C- weighed equivalsums of the spectra were calculated simultaneously. This standaacoust ics ins t rumenta t ion is commerc ia l ly ava i lable for aboUS$5000. It may also be done using a personal com puter with a CROM, a sound card, and a spectrum analyzing program capable perform ing one-third octave (or finer) band analysis. Matrices data from the N ll O analyzer were copied to a spreadsheet for furthanalysis.This method is in pr inc iple the same used by Gabr ie lsson aJansson [5]. They did their recordings in a reverberation chambthus reducing the effect of directivity from the instrum ents. Similathe recordings studied here were made in a recording studio wacoustical wall elements probably making the sound quite diffuin the frequency region of interest for violin (above about 200 HGabrielsson and Jansson instructed the player to play each note a complete scale as loudly as possible, whereas here the "excitationis normal playing of musical pieces. It is importan t that th e recordiconditions of the Bein and Fushi C D are very similar, if no t identicfor all instrum ents. One -third octave band analysis o f recordinby solois ts p laying the same piece has a lso been done by WLottermoser [6].SOME PHILOSOPHY ON THE METHODResearchers in acoustics use specific instruments and methods s im pl i f y the c om ple x spe c t r a o f m us ic . F o r e xa m ple , souninsulation and impact levels of building elements and reverberatitimes in auditoria are often measured in one-third octave bands."gives good frequency resolution for the experienced sound fieland this octave band encom passes much of the "crit ical bands he ar ing", t he na tu ra l spe c t r a l ba nds o f ou r e a r s . Ho we v emeasuring time-average spectra has its limitations. Information highly harmonic str ing sounds, temporal changes l ike str ing boattack and decay, vibrato, and dynamic changes in the music aaveraged out. Also, the changing timbre from playi 'ng differestrings and positions is smeared out and thus buried in the avera

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Anders Buen - Differences of Sound Spectra in Violins by Stradivari and Guarneri del spectrum. All of these are at tr ibutes we would need to hear torecognize the sound as coming from a violin. T a b l e 1. Violins studied using sound spectra analysis (fromThe strength of the method is, however, simplification reflectingthe ear's sensitivity to loudness in different frequency bands. Th eba nds a r e su f f i c i e n t ly de t a i l e d t o g ive im por t a n t g r oss sc a l einformation on the vibrating and radiating structure of the source.A trained acoustician will be able to tell much, but not all, fromseeing time-averaged one-third octave band spectra and combiningit with knowledge ab out the source. We may therefore expect todescribe the overall timbre and loudness of the violin by measuringthe played sound from the violin by using time-averaged one-thirdoctave band so und sp ectru m levels. A calibration signal on therecordings (usually 94 d B @ 1 kHz) , i s however miss ing. Thepresented sound pressure levels are therefore some 15-20 dB lowerthan what is expected to be normal at the microphone position.ON THE VIOLINS AND THE RECORDINGSThir ty famous Cremonese ins t ruments (Table 1) are played byElmar Oliveira, a well known soloist. Oliveira plays two of theinstruments (no. 5 an d 26) on a regular basis.Two music sequences are used:

1. Jean Sibelius, excerpt from Movement 1, Violin C oncerto inD Minor, Opus 47, is played on each of the 30 instruments(duration: 1 minute).

2. Fifteen different pieces are each played on a Stradivari and adel Gesh. Eight of the pieces are with accompanying piano(duration: 1-10 minutes). T he comp osers are Bach, Kreisler,Bloch, Martinon, Paganini, Ysaye, Brahms, and Vitali.

RESULTSWeighed Equivalent Sound Pressure LevelsThe simplest f i l ter ing of the recorded data is the t ime-averageweighed sound levels (L,,J from each instrument (Figure 1). T h evalues are weighted using a C-filter, which represents the ear's highersensitivity for low-frequency sound when levels are higher thanabout 85 dB. Figure 1 shows the overall loudness o f each instrument.L e ve l s va r y f r om a bou t 62 t o 68.7 dBC. Suc h a va r i a t i on i se xpe r i e nc e d a s a l i t t l e unde r a doub l ing o f t he sub je c t i ve lyexperienced so und level, which is a quite significant. How ever,both groups of instruments (Stradivari and del Gesu) give a meansound level of 66 dBC. More detailed information of the soundspectra is required to analyze the timbre.

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M a k e rAntonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del GesuAntonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del GesuAntonio StradivariGuarneri del GesuAntonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del Ges6Anton io S radivariGuarneri del Ges6Antonio StradivariGuarneri del Ges6Antonio StradivariGuarneri del Ges6Antonio Stradivari

D a t e167917421690174216921737170117351707172017081737171017401709173417151735172217441723173417271739173417261736

N a m eHel l ierWieniawskiA u e rSloanOliveiraKing Jostp hDushkinSennhauserL a CatbidraliK a r t ma nR u b yStern, l'anetteVieuxtemps, HauserYsayeKing MaximilianLe Violon du Dzable'Baron KnoopPlowdenJupiterOle BullKiesewetterHaddockDu p o n tKortschakWi N emo t t eStrettonM u n t x

28 Guarneri del Gesu 1738 K e m p29 Omobono St radivar i 1737 Rawl ings30 Guarneri del Ges6 1735 D'Egville

F i g u r e 1. C-weighed 1 minute equivalent sound pressure lfrom same music piece played on each of 30 Cremonese instrum[4]. C- we igh ing r e pr e se n t a bou t t he e a r ' s l oudne ss spe csensitivity at high sound pressure levels (> 85 dB).

One-third Octave Band Specfra 3 6saFigure 2 shows spectra from the same musical piece on all 30 3 "instruments. Only the bands that are expected to be interesting for v 63a violin are shown; fro m 200 Hz to 10 kHz. We see that the width of 1 24the loudness is about 7 dB at the 250 an d 315 Hz bands and about 10 8,dB over the restof the spectrum. The curves also show some global

80similarities, which are difficult to attribute t o either the m usic piece -mmr.m=.-l$I.g&gj~R~or the instruments.

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Anders Buen - Differences of Sound Spectra in Violins by Stradivari and Guarneri del Gesu

Figure 3 shows th e spectrum from th e 1 5 different pieces each playedon a s t r a d iva r i a nd a del ~ ~ ~ 6 ,e see a wide r ba nd a t low F igu r e 2. One-third octave band spectra of 1 min excerpt of Sibeliufrequencies, the 200 Hz and 250Hz bands. The higher levels here D Minor concert played On 30 Cremonese instruments f41.are from pieces with piano accompaniment. We also see similaritieswith the curves in Figure 2. Th e falloff starts at 4 kHz; there is a ~-.. . -peak at 2.5 kHz, a valley at the 1.6 kHz band, a peak around 1 kHz,and finally a peak at 315 Hz. 60Average Spectra of the One-third Oc tav e Band Levels E 55e,T o smo oth o ut the picture we may look at the average responses of -Ieach ins t rument group (F igure 4) . We see the s imi la r i t ie s as 2 5mentioned above more clearly. We also see a difference between 0

~ 4 0the two series around 500 Hz where the one-piece series show avalley while the 15-piece series show a peak. We expect the 500 Hz $ 35band, which h as its -3 dB levels at 440 Hz and 565 H z respectively,to contain the important C3 resonance, typically found around 550 A sHz. This resonance is usually high in good instruments [1,2], but 25there is also typically a de ep valley between the T 1 (around 430-480Hz) and the C3 resonance (around 520-560 Hz) often found around500 H z [I 2].

113octave bands@tz]

When we look closer at the musical tones that are played in theSibelius violin concert excerpt, there are only a few fundamentals F igu r e 3. One-third octave band spectra of 1 5 musical pieces eachor harmonics played in that band (A#4, B4, C5 or C#5). The first ~IaYedon a violin by Stradivari 2nd Charneri del Gesu [41.harmonic in the string signal gives a 6 dB reduction in force level -compared to the fundamental [I]. Also, the musical tones there areprobably played quite weakly. This explains why there is a valleyat the 500 Hz one-third octave band from the Sibelius excerpt inFigure 4.The average curves for the Strads and del Gesus look quite similar,although there seems to be a systematic difference. The microphoneis probably closer in the one-piece run, giving higher recorded levelsfor that series. Anyhow, black lines tend to lie at the same side of -. . - -- - . . . . . . .the gray line in each band as seen in Figure 4.Differences Between the Ave rag e Sp ectraFigure 5 shows the difference between the average curves shown inFigure 4. The curves show similar it ies indicating that there is acontr ibution from the frequency response of the instruments inspite of different played music pieces. Th e average Stradivari islikely to have higher sound levels in the bands 200 Hz, 250 Hz andabove 1.6 kHz. The average del Ges6 is likely to have higher soundlevels in the bands from 315 H z to 1.25 kHz. The likelihood of thebands 800 Hz, 2 kH z, 2.5 kHz and 4 kH z being different is somewhatless than the others as one o f the curves a re crossing the OdB line inthese bands. The differences are still quite small. Two imaginaryinstruments with the average responses as shown in figure 4 wouldsound very similar, and differences of about half a decibel shouldbe barely audible.Figures 2 and 3 show that the widths of levels are about 7-10 dB,indicating the level of differences between individual instruments.

Th e d i f f e r e nc e be twe e n ou r im a g inar y a ve r a ge S t r a d ivar i a ndaverage del Ges6 is less than + 2 dB. I t is thus not unlikely thatdistinct Strads and del Gesus may have larger differences betweenthem than the difference response curve in Figure 5.

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A representation of the natural variation may be seen in Figure 6where the standard deviation for each band is shown as error barso n the curve. All these variation bars cu t the 0 dB level. Statisticallyabout 63% of the differences between these instruments will havetheir difference curve lying within the error bars. Using 2 standarddeviations would include about 95% of all instruments. Then thewidth of the error bars would be from 4 dB at the 250 Hz band toabout 1 2 dB at the 1.25 Hz band.

-1 - ,.'-;.113 octave band&] - ,

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Anders Buen - Differen ces of S ou nd Sp ec tra in Violins by Stradivari and Guarneri del Ge

i g u r e 4. Average responses of the violins. Thin lines are from Fi g u re 6 . Difference between mean levels of violins by Stradivaecordings o f the same m usic piece, thick lines from 15 musical and Guarneri del Gesli (error bars show 5- 1 standard deviation fieces each played on a violin by Stradivari and Guarneri del Gesli each band; 63% of spectra differences between instruments is like[4]. Black lines are m ean values o f Stradivari and grey lines are to be found within these error bars . Increasing to -t 2 standamean values of Guarneri del Gesus. deviations for each band would include 95% of all instruments).

- A 3 Strads same pieceA y delGeshs same piece

- - - A 3 S h d s 15 different pieces - .----- A 4 del GesOs 15 diferent pieces. - - .

IMoctave bandMI6.0 113octave bawlsplz]

Fi g u re 5. Difference between mean levels of violins by Stradivari F i g u re 7. Difference between mean levels of violins by Stradivaand Guarneri del Gesu [4]. and Guarneri del Gesli (error bars show + 1 standard deviation f

each band; 63% of spectra differences between instruments is like3 0 ---I - ame music piece to be found within these error bars. From series with same piece o. - - 5 different all instruments).2.0 f --+ ,f8.0 -- --same music piece6.0 .....................................................

7 T -

Figure 7. They are a bit wider than tho se sho wn in figure 6, probablybecause the series with 15 different musical pieces are longer in exceptions, look quite similar in shape, indicating similar timbrtime thus increasing the measurement precision. Figure 7 conf irms O n a record ing the loudness o f the ins trument does no t mat tthe analysis as made for Figure 6. Comparing a Stradivari and a del because we may turn u p the volume if we like more sound. HoweveGes6 may give a different result than comparing the average of all for a player and a listener in a concert hall, 7-10 dB represen ts a hug

tradivaris and del Gesus. B ut th e average curve will still be the be st difference. If this variation is representative fo r such g ood old violinfor a difference between these instrument groups. we may ask, "what are the causes for such variations?' And is th

result representative for the violin in general?DISCUSSION It is puzzling to see that the curves are not higher in the so calle

iation between the 30 instruments is about 7-10 dB. Such a "body hill region" arou nd 2.5-3.15 kH z than for the oth er m ois clearly audible al thoug h the curves and , with few resonant regions [I]. These instruments may sound more pleasa

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