On The Bridge-Hill of The Violin
On The Bridge-Hill of The Violin
On The Bridge-Hill of The Violin
Mahmood Movassagh
MUMT 618 Final Project
McGill University
Fall 2009
Introduction
Many excellent violins show a broad pick of response in the vicinity of 2.5 KHz, a
feature which has been called the bridge hill. This arises from a combination of
resonance of the bridge and response of the violin body at the bridge foot positions
[1]. Figure 1 shows a typical violin bridge and its rocking motion which is the
main motion in a bridge resulting from its stiffness and its feets motion.
Figure1Atypicalviolinbridgeanditsrockingmotion[1]
Figure2Atypicalviolinresponse(orbridgeadmittance)[1]
Figure3Massspringmodelforviolinbridge[1]
A rotational admittance is defined for the contact between torsion spring and
bridge base (from that contact downward) which was shown can be obtained using
following equation [1]:
In which Yij is velocity response of the violin body at the position bridge foot j to a
force of unit amplitude applied at bridge foot i. Using the obtained R and
following relation violin response or bridge mobility can be obtained [1]:
He finally concluded that if we consider two infinite plates for a violin and use the
following relation to obtain Yij s for infinite plates:
Figure 4 and 5 respectively show typical rotational and violin response with
skeleton (dashed line) obtained from Woodhouse model.
Figure4RotationaladmittanceanditscorrespondingSkeltonobtainedfromwoodlouses
model[1]
Figure5TypicalbridgeadmittanceanditscorrespondingSkeltonobtainedfromWoodlouses
model[1]
Table 1 shows different violin bridge and body parameters and considered in
Woodhouse model and their typical values:
Table1Standardparametervaluesfortheviolinandbridgemodels[1]
Figure6Anormalandasolidplatebridge[2]
Figure7Bridgemobility(violinresponse)forthenormalandplatebridgesused[2]
In the second experiment they used a single normal bridge for two different
violins: a very good old Italian violin (Stradivarius 1709) and a new violin (Stefan
Niewczyk). The bridge mobility for both of them is shown in figure 8. It can be
seen that even though the same bridge was used they show very different bridgehills. These two experiments showed that bridge-hill cannot be due to bridge alone
[2].
In contrast, another question is: Does bridge-hill depend only on violin body
characteristics? Another experiment was done by Jansson the result of which gives
a negative answer to this question and is consistent with what Woodhouse model
predicts. In this experiment Jansson considered four plate bridges with different
shapes. The first one was a bridge with just one foot and the other ones had two
feet but different widths (see figure 8).
Figure9Differentbridgeswithdifferentshapes[2]
Figure 9 shows mobility of a normal bridge (a) and the different plate bridges used
(b-e for bridges D1-D4). It can be seen that for bridge D1 there is no bridge-hill
and for the other ones by increasing the width bridge-hill center frequency is
increased but its level is decreased.
Figure10Frequencyresponses(bridgemobility)oftheLBviolin.Ineachpair,theupperframe
showsthelevelresponsethelowerframeshowsthephaseresponseoftheLBviolinwith:(a)
originalbridge,(b)platebridgeD1(c)platebridgeD2,(d)platebridgeD3,and(e)plate
bridgeD4.TheP1peak,theP2peakandtheBHhillaremarked.Smallcircles,markselected
frequencies,levelsandphasesoftheBHhill[2].
The individual results for different violins and the averaged data was shown again
in Tables 2 (bridge-hill center frequency) and Table 3 (bridge-hill level). This
experiment shows that bridge-hill as its name comes from bridge cant be due to
violin body alone and is very sensitive to bridge shape.
Table2FrequenciesfortheBHhillpeak(kHz)fororiginalbridgesanddifferentplatebridges
D1D4[2]
Table3LevelsfortheBHhillpeakfororiginalbridgesanddifferentplatebridgesD1D4[2]
Figure11(a):Fholemodels,typicalfholeinblackandexperimentalfholewithstraight
lines(b):dimensionsofthemodelinmm[3]
In the first experiment they considered two steps: In first step f-hole had just its
lower and upper sections and in the second step straight section was added (see
figure 12).
Figure12Rectangularplateandfholecuttingsteps[3]
The results for this experiment were shown in figure 13. It is seen that there is no
considerable bridge-hill for the case there is no f-hole and there is no straight
section. But when the straight section is added bridge-hill appears in mobility
response.
Figure13Bridgemobility,levelandphase,ofcuttingstepsinFigure12andmarkedabove[3]
In the next experiment, they first created just the straight section and in the next
step added the two other sections. As can be seen in figure 14 when there is just
straight section bridge-hill is much weaker than when the two other sections are
added.
Figure14Bridgemobility,levelandphase,ofsteps1and2markedabove[3]
In fact what they finally concluded was the bridge-hill depends on f-hole wings
area. The wings are shown in figure 15 and f-holes with different wing area are
shown in figure-16.
Figure15theWingsatthefholes[3]
Figure16Basicplateandfholecuttingsteps[3]
The result for the case that the wing area is zero is compared with that of the case
with typical area in figure 17 and as it can be seen when the wing area is zero there
is actually no bridge-hill.
Figure17Bridgemobility,levelandphase,ofbasicplateandstep1and3inFigure16and
markedabove[3]
Figure18Bridgemobility,levelandphase,ofstepsmarkedabove[3]
They also performed another experiment to see effect of changing the relative
position of bridge and f-holes on bridge-hill (see figure 19). Their results showed
that bridge-hill is stronger when it is closer to wing mass center.
Figure19Bridgemobility,levelandphase,ofsteps1and3markedabove[3]
Figure20Leftpanel:Radiativityforagood(filledcircle)andbad(opensquare)violinRight
Panel:goodbadradiativityratioforthetwoviolinsinviolinsoundcharacterizationscheme
originallyproposedbyDunnwald[4]
Another cue for the above conclusion comes from another experiment in which
effect of bridge waist trimming (to change its stiffness) on violin radiativity was
evaluated. Left panel of figure 21 shows individual radiation change range resulted
from trimming for Guarneri violin and a modern violin from Alf, 2003. Open
symbols show results for least trimming and closed symbols for most trimming.
Right panel in this figure shows three steps of trimming for Guarneri violin. As it
can be seen in that figure radiation change for bridge-hill area is much less than the
frequency range 3-5KHz and hearing tests showed that by going from least
trimming (shaded curve) to most trimming (thick line) the very good violin
Guarneri sounds like a very bad violin. This huge change in violin quality cannot
Figure21Effectoftrimmingongoodandbadviolinradiativity.Leftpanel:individualresults
Rightpanel:Effectoftrimmingin3stepsongood(Guarneri1660)violin[4]
Indeed Bissinger claims overall radiation curve is a much better criterion for
judging about violin quality and in another experiment he compares radiation curve
of the good violin (Guarneri 1660) having a standard bridge with 20 other Alf
bridge trims (Alf violin bridge modification by trimming). His results showed that
the trimming profile leading to highest violin quality is one with radiation curve
(see figure 22) closest to Guarneri violin curve (thick line).
Figure22Acousticprofilesfor20Alfviolinbridgetrims,comparedtotargetA.Guarneri
profile(thicklinewithopensquares)[4]
References
[1] J. Woodhouse, On the Bridge Hill of the Violin, J. Acta Acustica United With Acustica,
Vol. 91, 2005.
[2] E.V. Jansson, Violin Frequency Response Bridge Mobility And Bridge Feet Distance ,
Elsevier Applied Acoustics, 2004.
[3] F. Durup E. V. Jansson, The Quest of the Violin Bridge-Hill, F. Acta Acustica United With
Acustica, Vol. 91, 2005.
[4] G.Bissinger, The Violin Bridge As Filter, J. Acoust. Soc. Am., July 2006.
[5] H. Dunnwald, Deduction of objective quality parameters on old and new violins, Catgut
Acoust. Soc J. 1, 1-5, 1991.