Veröffentlicheung Fleischer 1999: Deadspots_e

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<H1>Acoustical Society of America <BR>ASA/EAA/DAGA '99 Meeting Lay Language 
Papers </H1>


<P><B>Helmut Fleischer - <A 
<BR><BR>Institute of Mechanics <BR>Faculty of Aerospace Engineering 
<BR>University of the Federal Armed Forces <BR>D-85577 Neubiberg, Germany <BR>
<P>Popular version of paper 5aMUb6 <BR>Presented Friday morning, March 19, 1999 
<BR>ASA/EAA/DAGA '99 Meeting, Berlin, Germany 
<P><I>Why is the "sustain" generally better for an electric guitar or bass than 
for an acoustic one?</I></P>
<P>The musical signal of an electric guitar or bass originates from string 
vibrations. In contrast to comparable acoustic instruments, the electric ones do 
not radiate the sound themselves. Since there is no need to transfer energy from 
the strings via the bridge, the body may be made from solid material. The string 
supports are relatively immobile and the strings vibrations, consequently, do 
not decay as rapidly as for a self-radiating instrument. That means that the 
"sustain", which is considered as a quality attribute, generally lasts longer 
for an electric guitar or bass than for acoustic models.</P>
<P><I>What are "dead spots"?</I></P>
<P>However, this long decay is not observed for each fret at which the player 
fingers a string. There are particular locations on the fingerboard where the 
sustain of a string is considerably shorter than for adjacent frets. This 
irregularity is well-known among players of electric basses and guitars; they 
call it a "dead spot". An electric guitar of the well-known Stratocaster type is 
chosen as an example to illustrate the effect and its diagnosis.</P>
<P><I>How can dead spots be quantified?</I></P>
<P>The sustain is quantified by the decay time (in our investigation: defined by 
a 30 dB level difference) of the total signal at the output socket of the neck 
pick-up. In the normal case, the decay time decreases steadily with increasing 
fret number. As an exception to this rule, the decay proves as uncommonly short 
<I>e.g</I>. at the 4<SUP>th</SUP> fret of the D string of the Stratocaster 
indicating a dead spot. At the same string the contrary ("live spot") holds for 
the 11<SUP>th</SUP> fret. An additional study has revealed that the decay of the 
total signal is ruled by the fundamental tone of the complex string signal.</P>
<P><I>What causes dead spots?</I></P>
<P>Resonances of the instrument are supposed to cause dead spots. The vibrations 
were measured using a Laser Doppler Vibrometer. Since the boundary conditions of 
an object influence the vibrations to a high extent, special care was taken to 
perform the measurements in a normal playing position<I> </I>("<I>in situ</I>"; 
cf. Fig. 1). The guitar was excited by random noise via mini-shaker at the rear 
of the neck. Several resonances were found. An example for 430 Hz is given in 
Fig. 1. Obviously, at particular frequencies the guitar does not at all respond 
rigid but exhibits pronounced resonances.</P>
<CENTER><IMG alt=Fender height=320 src="deadspots/Fender.jpg" 
<P><SMALL>Fig. 1 In-situ measurement of body vibrations by means of a Scanning 
Vibrometer. A vibration pattern of an out-of-plane resonance at 430 Hz is 
<P><I>Which of both, the bridge-end or the neck-end support of a string, is more 
<P>Experiments indicate that, in the normal case and in obvious contrast to an 
acoustic instrument, the bridge of a solid-body electric guitar or bass is much 
less mobile than the neck. The string may induce body vibrations via the neck 
rather than via the bridge. Energy is transferred to the instrument and gets 
lost for the string vibration. The "vibration willingness" of the neck is the 
cause for additional damping of the strings, <I>i.e.</I> for dead spots. Former 
studies have revealed that the motion of the instrument perpendicular to the 
fingerboard dominates this effect.</P>
<P><I>Under which conditions may a string excite a neck resonance?</I></P>
<P>In order to induce a vibration of the neck by an excitation from the string 
two requirements must be fulfilled:</P>
  <LI>The frequency of the string has to be close to the frequency and 
  <LI>the excitation point (string support) must not be located in a node, but 
  closely enough to an antinode</LI></OL>
<P>of a resonance. In that sense the body vibrations are not easily interpreted 
in terms of an excitation by the strings.</P>
<P><I>Which measuring parameter suits to characterize energy losses at the 
string supports?</I></P>
<P>The point admittance (velocity/force), measured at the neck-end of the 
strings, promises to be a more direct parameter. Its real part, the conductance, 
characterizes the transfer of energy via a string support. The conductance was 
measured <I>in situ</I> with a subject holding the instrument in playing 
position. The force and velocity were simultaneously picked up by an impedance 
head which was mounted on a shaker and perpendicularly pressed against the 
fingerboard. The signals were analyzed by a dual-channel FFT analyzer. The 
diagram in Fig. 2 shows a condensed 3-D representation of the normalized neck 
conductance. The curves were measured at the positions of the nut and first 19 
frets as indicated by the numbers and combined to one diagram typical for each 
guitar or bass. A conductance "landscape" is created in which the "mountains" 
reflect the resonances (Fig. 1) of the instrument. The higher the conductance, 
the more energy will the string loose if fingered at the corresponding fret and 
vibrating with the corresponding frequency.</P>
<CENTER><IMG alt="Fig 2" height=309 src="deadspots/fig2.jpg" width=600> 
<P><SMALL>Fig. 2 Conductance as a function of frequency measured along the 
fingerboard between the two mid strings from the nut to 19<SUP>th</SUP> 
<CENTER><IMG alt="Fig 3" height=280 src="deadspots/fig3.jpg" 
<P><SMALL>Fig. 3 Overlay chart featuring the fundamental frequencies of all 
string-fret combinations.</SMALL></P>
<P><I>How to interpret the conductance "landscape"?</I></P>
<P>Since a high conductance corresponds to high damping of the string at the 
corresponding location and frequency, the peaks serve as indicators for possible 
dead spots. Only distinct location-frequency combinations are used on a guitar. 
They are marked in the overlay chart of Fig. 3, which is intended to interpret 
the conductance landscape. The circles indicate the fundamental frequencies 
versus the fret positions (open and fingered up to the 19<SUP>th</SUP> fret) for 
all six strings in standard tuning. For basses a modified chart including the 
four to six strings is used. The magnitude of the conductance (Fig. 2) has to be 
checked for each string-fret combination. Coincidence with a high value 
(mountain) suggests a dead spot, with an extremely low value (valley or plane) a 
life spot. Comparisons between different experimental data for several guitars 
and basses confirm these relations and verify the neck conductance as a key 
parameter for diagnosing dead spots.</P><B>&nbsp; </B>
<P><I>What, in summary, is new?</I></P>
<P>At the first glance, an electric guitar or bass looks rather rigid. At the 
second glance, however, it proves as very flexible at particular frequences. A 
dead spot, defined by an abnormally fast decay of the fundamental tone, is 
caused by damping due to energy transfer from the string to the instrument body. 
For a well-balanced instrument the bridge proves as practically immobile, while 
the neck is flexible and exhibits resonances. Under certain circumstances, the 
string may excite a neck resonance with the result that the string vibration is 
additionally damped. The mechanical conductance is a suitable indicator of the 
frequency-selective damping of the string supports. An <I>in-situ</I> measuring 
approach is suggested to ascertain the out-of-plane conductance on the neck. The 
combination of the curves as obtained at the nut and frets creates some kind of 
a landscape which represents a "fingerprint" of a guitar with respect to dead 
spots. An overlay chart based on the fundamental frequencies makes its 
evaluation easier as the higher the conductance for a string-fret combination is 
the more probable it is to find a dead spot. Thus, the fingerboard conductance 
of an electric guitar or bass can be simply measured and promises to be a key 
parameter for diagnosing and avoiding dead spots.</P>