The Stradivarius Challenge
Alex Prokup
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BACKGROUND
Violins are a stringed instrument made up of the body, neck, bridge, and
fingerboard. The bridge is what transfers the vibrations of the strings to the hollow body.
Wood is generally maple or
any other hardwood with metal
strings. Originally strings were
made from gut, which are only
used today to replicate 18th
century performances. Violins
are a vital part of orchestras
and string quartets, and can
stand alone in a solo recital. A
famous composer, Antonio
Vivaldi of the Baroque era, used the violin in many of his compositions. Perhaps the most
known violin maker was Stradivarius, who was born in Italy in 1644. He started a music
business in 1680 to make violins, violas, and cellos. His best violins were made from
1698 until his death in 1737. To try and match the fine sound of the Stradivarius violin,
Dr. Joseph Nagyvary used computer-based signal analyzers to create a violin. Tests were
performed to determine which violin truly had the better sound. Information based on
amplitude of harmonics, frequency, and relative phase was analyzed.
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PROCEDURE
1. Sounds from the Stradivarius Challenge CD were saved to the computer
2. Sound clips were created by separating each note from a scale played by the
performer
3. Using the MatLab program, the sound files were analyzed and graphs were
created based on the properties of the first five harmonics.
Note: Left channel/speaker was selected for all notes
4. The graphs of notes 1, 15, and 22 were selected and analyzed
Figure 1
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Figure 2
Figure 3
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Figure 4
Figure 5
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Figure 6
Figure 7
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Figure 8
Figure 9
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Figure 10
Figure 11
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Figure 12
Figure 13
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Figure 14
Figure 15
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Figure 16
Figure 17
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Figure 18
DISCUSSION
Analysis was performed to determine which violin had the best sound. The
determination was decided based off of qualitative and quantitative factors of notes 1, 15,
and 22 of both violins. These notes were selected due to them being octaves of each
other. Note 8, the second octave, was not used due to an error in graph creation.
One quantitative factor used in determining the best sounding violin was the
harmonics produced by each note. The harmonics present decided how full or rich the
sound was. The more harmonics present, the better sounding a note will be. This decision
was based off of the size of the harmonics present, with special consideration for the
fundamental. If a note is considered strong, the fundamental is large. The fundamental is
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the main harmonic expected to be expressed for a note. The larger the harmonics 2-6 are,
the fuller the sound.
Figure 1 shows the harmonics of note 1 of violin 1. The fundamental is small, but
harmonics 2-5 are quite apparent. This gives a full, but overall weak sound.
Figure 4 shows the harmonics produced for note 15 of violin 1. The fundamental
is quite large, but only half the size of the third harmonic. This sound is stronger than
note 1, but not as full.
Figure 7 shows the harmonics produced for note 22 of violin 1. The fundamental
is large as well as the next harmonics. This is a strong and full note. This note is strongest
and fullest out of all analyzed for violin 1.
Figure 10 shows the harmonics produced for note 1 of violin 2. The fundamental
is very small with harmonics 2 and 5 dominating. This note is weak but full in sound.
Figure 13 shows the harmonics produced for note 15 of violin 2. The fundamental
is large with strong 2nd, 4th, and 5th harmonics. This note is very strong and full.
Figure 16 shows the harmonics produced for note 22 of violin 2. The fundamental
is average sized with strong 2nd, 3rd, 5th, and 6th harmonics. This note is as strong as note
15, but fuller.
The average amplitude for the fundamental harmonic of violin 1 was 4.67
decibels. For violin 2, the average amplitude of the fundamental harmonic was 5.67
decibels. Both violins contained varying sized 2-6 harmonics, but violin 2 had slightly
larger averages of amplitudes for harmonics 2-6. From this data, on the basis of
harmonics, violin 2 is both stronger and fuller in sound. It is interesting that in both
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violins, the fundamental is was usually the smallest in amplitude, which means the main
sound of the note comes from another harmonic.
Frequency of the notes was measured and graphed using MatLab. For the best
sound, the most horizontal a line, the more steady a note is. This is determined
qualitatively from observations of figures 2, 5, 8, 11, 14, and 17.
Figure 2 shows the frequency of the harmonics produced over time for note 1 of
violin 1. The frequencies of all the harmonics are all flat, except harmonic 5. In harmonic
5, there are 9 peaks that occur. Overall, this is a steady note.
Figure 5 shows the frequency of the harmonics produced over time for note 15 of
violin 1. Harmonics 3, 6, and especially 5 have many peaks where the frequency
drastically changes.
Figure 8 shows the frequency of the harmonics produced over time for note 22 of
violin 1. All harmonics except the fundamental contain many peaks. This note would be
the least stable of all on violin 1.
Figure 11 shows the frequency of the harmonics produced over time for note 1 of
violin 2. This note is quite stable with only the fundamental showing significant changes
in frequency. This note is less steady than note 1 on violin 1.
Figure 14 shows the frequency of the harmonics produced over time for note 15
of violin 2. Only harmonics 5 and 6 show a change in frequency over time. Otherwise,
the other harmonics are very steady.
Figure 17 shows the frequency of the harmonics produced over time for note 22
of violin 2. The fundamental is steady, but the other harmonics are increasingly more
unsteady.
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On the basis of observations from figures 2, 5, 8, 11, 14, and 17, violin 2 would
be considered to contain the steadiest notes. This is difficult to conclude due to the
justification being qualitative and not quantitative. However, if figures 5 and 14 are
specifically viewed, one can see that violin 2 contains much steadier lines than violin 1.
Relative phase involves the position of a harmonic’s waveform in relation to the
fundamental. From the relative phase graphs, it can be seen that despite the similar
sounding violins, the harmonics produced for the same note are drastically different in
terms of their relative phase. Matching the relative phase for harmonics produced may be
a key component of replicating sounds. For Dr. Nagyvary to truly replicate the sound of a
Stradivarius violin, special attention should be given to matching the relative phase of the
Stradivarius.
ERROR ANALYSIS
There are many reasons for why a violin may perform better than the other. If the
string was not bowed in the same place for each violin, the harmonics produced would be
different. Since the fingerboard contains no frets, the position of the finger on the string
can have an effect on the harmonics produced for the note. If the violin was made of even
slightly denser wood, the sound can completely change. For this experiment, the left
channel was selected. If the performer played the one violin closer to the left channel then
the other, different harmonics would be heard more distinctly. Also, to truly declare one
violin the best, all possible notes would have to be analyzed on more than one trial. Due
to time constraints, only 3 from each could be analyzed.
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CONCLUSION
In conclusion, violin 2, Dr. Nagyvary’s violin, proved to be the better sounding
violin mathematically. This decision was based on harmonics, which proved to have a
stronger and fuller sound, as well as in frequency, which stayed the steadiest. It was
difficult to conclude what the better violin was, due to the two being so similar. Dr.
Nagyvary definitely created a violin to rival Stradivarius’. I think that the Stradivarius
violin will always be renowned for its awesome sound, but after the analysis of the two
violins, special consideration should be given to the Nagyvary violin.
Despite mathematical reasoning for what violin sounded better, opinion always
has the final say. People are different and unique in their own way; therefore, everyone
will have a natural desire for a certain sound. Also, depending on the shape of a person’s
ear and how well they can hear can cause someone to enjoy the sound of a certain violin.
The Stradivarius has already withstood the test of time and is the most demanded violin
in the world.
SPECIAL THANKS
Special thanks go to Dr. Nagyvary for sending a free copy of his CD, The
Stradivarius Challenge.
REFERENCES
1. [Picture] <http://illumin.usc.edu/_images/pictures/i7_138_violin_anatomy.gif>
Accessed December 13, 2006.
2. “About the Violin” from website <http://www.theviolinsite.com/history.html>
Accessed December 13, 2006
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3. “Stradivarius Violins” from website
<http://www.si.edu/resource/faq/nmah/stradv.htm>
Accessed December 13, 2006
4. Nagyvary Violins from website: <http://www.nagyvaryviolins.com/>
Accessed December 13, 2006
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