An Investigation of the Timbre of My Violin
Shiqi Xu
UIUC Physics 193
Fall Semester, 2013
Introduction
Why did Satan choose the fiddle to make his music? He was a former angel, and as such a
trumpet might have suited him better and surely wouldn’t burn so easily. If not blow the
trumpet, then why not at least beat the drum, as other angels drawn by these great Italian
artists.
The answer is simple enough. With most of us Satan requires a little preparation: he must
allure us, lead us down the garden path. These are not moments in which to sound trumpets
or loud cadences of drums. Here,
these dubious melodies are that a
flute or a fiddle might convey. But
even the flute is limited largely to
life’s peaceful moments. However,
the violin was just the thing. It can
let you towards the flame, into the
heat. It has the magic to work on a
love song as well as begin the great
betrayal into incendiary brilliance.
Fig.1 the structure of a violin
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That was what the fiddle could do, as long as those who played upon it could summon up its
fabulous potential.
So, what is the violin? The violin is a four-string instrument tuned in perfect fifths. It is the
smallest, highest-pitched member of the violin family. The violinist produces sound by
drawing a bow across one or more strings or by plucking the strings. The body of the violin is
a large hollow chamber that functions as both speaker and amplifier for vibration. The strings
are suspended above the body of the instrument by a bridge and a small maple piece of wood
called bridge secured to the top of the instrument by the tension of the strings. The vibration
from the strings is transferred through the bridge to the body of the instrument where the
sound is then amplified.
It’s a great experience to listen to these extraordinary recordings of violin masters. Usually
their performances are so exquisite owing to musicians’ sophisticated skills, meticulous hold
changing, accurate finger position and detailed emotion. All these soloists reproduce the
thought of the composer written on the score; nevertheless, you can easily recognize the
violinist even you never heard his recording of this piece before. I can tell you this piece is
played by Jascha Heifetz while the other is played by David Oistrakh. That’s not only
because they used different Stradivari violin, played in different tempo, but also they use
different rate of vibrato and prefer different kind of glissando. As you can see, violin is
flaring instrument with a number of skills.
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Project
I played violin for a couple years, so I set up my project in this field. In my project, I want to
have a look at the timbre of some notes of my violin. Professor Errede help me set the
experiment and record these notes using a 24 bit recorder, which allow me to analysis the
harmonics of different E5 and A5 notes.
E5 on different strings
At first, I try E5 (around 659.3Hz) on each of four string in order to find out why different
tone quality present by different stings. Since we know that the quality of a tone does not
depend significantly on the relative phases of its harmonics, and the software I use does not
work so well on calculating and present the relative phases (it give me some obviously wrong
data), I put more attention on the relative amplitude, which mainly affect the tone quality of
the note. Owing to the fact that the frequency separation becomes relatively small for
high-frequency harmonics, the details of their frequency seems rather unimportant, so I only
pick the 1st to 8th harmonics. As an example, the spectra of 1st -8th harmonics of E5 on
different strings of the violin are shown below.
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(a)
(b)
4
(c)
(d)
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Fig. 2. (a)amplitude of 1st to 8th harmonics of E5 on E string(open E); (b)amplitude of 1st to 8th harmonics
of E5 on A string; (c)amplitude of 1st to 8th harmonics of E5 on D string; (d)amplitude of 1st to 8th
harmonics of E5 on G string.
Fig.2 a) shows the open E whose amplitude of fundamental, 2nd and 4th harmonic are almost
same. A little bit lower come the rest of harmonics except 8th. 8th harmonic is much weaker.
Fig.2 b) shows harmonics of E5 on A string in which the amplitude of 4th harmonic exceeds
3rd while the 8th is still the weakest. Fig.3 b) is responsible for E5 on D string. It’s interesting
that the amplitude of 4th harmonic exceed fundamental harmonic for a while and 1st to 4th
harmonic have close loudness that stronger than the rest. Fig. 2 d) gives the spectra of E5 on
G string with obviously louder fundamental harmonic.
The relation of harmonics tells us
why the same note of same
frequency sounds different on
different strings. The E5 sounds
warmer and brighter on E string
and A string because of amplitude
of higher-frequency harmonic are
larger than those on D string and G
Fig. 3. Spectra for E5 on A string.
string; the notes on D string sounds soft and occasionally sad.
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Besides the amplitude, I also notice the effect of the tone structure. Figure 3 is responsible
for E5 on A string. The 6th and 5th harmonics of E5 on A string are not so constant probably
owing to the resonance. These sharpness leads to a brighter tone quality on A string. That’s
why composers wrote notes on A string to express delight themes.
Mute
Secondly, I tried same notes but
with a mute. The violin mute is a
small rubber device that can be
affixed to the top of the violin
bridge. After I placing the mute on
(a)
the violin, the notes not only sounds
quieter but also softer and more
peaceful.
Placing
the
mute
in
position
increases the mass of the bridge
causes the sidewise forces of the
(b)
vibrating strings to produce smaller Fig. 3. (a) is the harmonic amplitudes for E5 on E string with mute;
(b) is the harmonic amplitudes for E5 on D string with mute.
accelerations hence smaller vibrations of the bridge. According to the textbook, the amount of
reduction is greater for the higher the frequencies of the harmonics. However, figure 3 tells
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me that the effect of mute goes farther than reducing the amplitude; it also significantly
reduces the amplitude of odd harmonics except the fundamental. Unfortunately, I am not able
to figure out how this happens yet. I do not find an article talking of the effect of the deficient
of odd harmonics either. For me, the sound of notes with mute is just more nostalgic. Maybe
this is why a mute is required while playing the third part of zigeunerweisen composed by
famous Spanish composer Sarasate.
Overtones
According to the definition in acoustic physics
field, an overtone is any frequency higher than
the
fundamental
frequency.
However,
the
definition of overtone for string instruments like
(a)
violin or viola is a little bit different which
includes both “natural” and “artificial” overtones.
The natural overtones are notes produced by the
vibration of string when the player put his finger
in some specific position slightly. Actually, this
is not overtone. The sound of this kind of notes
sounds misty and mystical.
(b)
Fig.4 (a). amplitude for A5 “nature”, (b) amplitude
for A5 “artificial”.
I think this is
because of the lack of high harmonics as well as
the relatively weak fundamental.
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On the other side, the “artificial” overtones(shown in fig. 5(b)) are real overtones. It is usually
provided by a “fifth”. For instance, the G5 (784.0Hz, which is about 3 times of the original C4,
261.6 Hz) I played is produced by the G3 as well as C4. I press the position of G3 normally
with my index and put my pinky slightly on the position of C4 and then magically G5 comes
out. The amplitudes of harmonics start to reduce significantly from the third one. This kind of
overtones may have close formant with whistles since they sounds similar with each other; I
need more data to prove it.
Formants
Rumor has it that violins made by the great Italian violin maker Antonio Stradivari exhibit
formant frequencies resembling vowels produced by females, and Fritz Kreisler is famous of
using his violin imitating sopranos.
Although it’s very sad that I am not able to find the formant of my violin yet, I still do some
research on this part.
Fig. 6 formant analysis for violin
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Fig. 7 comparison for formants of different music instruments.
Fig. 6 shows the first and second formant frequency of the violin. F1 is at 592Hz, and F2 is at
1766Hz. This is fairly close to the tenor saxophone. Maybe that’s why both of them are good
at depicting romantic theme.
However, the data I found (fig. 8)
formant tracks for female speakers
does not prove my assumption.
Obviously
there
are
significant
differences between the timbers of
Figure 8
different violins, so I think that’s why
most of violin doesn’t sounds like female voice and are not worth 2 million dollars.
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Works cited
John McCarty “TimbralAnalysis” 2003< https://ccrma.stanford.edu/~jmccarty/formant.htm>
Summerhays,
summerhaysmusic.com
“how
does
a
violin
sound
<
http://www.summerhaysmusic.com/sound%20string.html >”
John Backus,1977,1969 by W.W. Norton &Company, Inc. “the acoustical foundations of
music”
Sidney Wood “Praat for beginners” 27 Dec 2003
David Lawrence “Dance macabre, or the devil made me do it” 2000 Deutsche Grammophon
Gmbh, Hamburger.
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