The article shows plots of the sounds made by
two accordion reeds, a clarinet reed and an oboe reed. The instrument used
was an Excelsior, Symphony Grand model; manufactured in the US around 1948
(this time estimate is reasonably accurate). The reeds are hand made.
The sounds were picked up by a Sanken high quality microphone,
plugged directly into an analog to digital converter (made by my company
dB Technologies) with built
in internal gain (thus no coloration due to a microphone pre-amplifier).
The data (accurate to 21 bits) was sent to an audio analysis system (made
by Audio Precision). All the equipment used for the tests is the state
of the art gear, thus yielding more then an order of magnitude of precision
above the CD format. The plots are imported into Microsoft Word for this
presentation.
The first plot titled oboe time plot, shows the
sound generation of a single oboe reed during about one-thousandth of a
second. During that short time period, starting at 0 and moving along the
horizontal axis to 1000, the air pressure generated by the vibrating reed
moves up and down, with the up motion expressing increase in air pressure
(above the 0 line - atmospheric pressure) and the downward motion shows
negative pressure.
The specific shape of that curve is what gives the reed
its timbre a unique sound quality, in this case the oboe reed. Notice
that the pattern is repeated about two times during the measurement (about
2 cycles in one thousands of a second), indicating that the pitch is around
500Hz.
The same time period was used for clarinet reed. The clarinet
time plot, shows that the pattern repeats itself about three times,
thus generating more then three cycles during the same time that the oboe
generated only two. Thus the clarinet reed made a higher pitch sound. Comparing
the clarinet pattern usually referred to as "wave shape" to that of the
oboe shows a lot more up and down motion during a single cycle. The timber
quality is obviously different. Generally speaking, the sound quality changes
rather drastically even with slight alterations in the shape of the wave.
The above patterns (time plots) are not easy to interpret
in terms of sonic quality. While some general wave shape characteristics
go hand in hand with certain families of instruments, interpreting each
and every "wiggle" in the wave is a difficult task. The French mathematician
Fourier found a way to simplify the analysis by "breaking the wave" into
its fundamental component called harmonics. Each harmonic by itself would
sound like a pure whistle, yet the presence of many harmonics simultaneously
yields the given timbre. The harmonics (fundamental components of the sound)
are related in terms of their frequency of vibration. The slowest vibration
defines the pitch. The faster vibrations are synchronized to the fundamental
pitch (twice as fast for the second harmonic, three times as fast for the
third harmonics and so on). The timbre is uniquely define by the relative
amplitude between the harmonics: lower the vibration energy of the second
harmonic or increase the energy of the fifth harmonic and you end up with
a very different sound.
The next plot, oboe frequency plot, shows the
concentration of energy at given frequencies. Note: the numbers on the
horizontal axis are not the actual frequencies. The frequency range marked
as 0 is at 200Hz (to eliminate electric fan and power line noise). The
point marked as 9000 corresponds to 15000Hz.
Shown are the first ten harmonics (the lowest frequency
one is called the fundamental). Most of the harmonics are very pronounced
(nearly the same strength) which is not typical of many other instruments.
The clarinet frequency plot shows a different
harmonic structure. The number of harmonics is lower, because with a higher
fundamental pitch, the sixth harmonic goes beyond the hearing range. Again,
the harmonic energy is very high compared to many acoustic instruments.
The plots shown are for a single reed. Analysis of multiple
reeds yields interesting results, yet the case of the single reed single
reed is the foundation of a free reed instrument, thus it tells much of
the story. While the time analysis provides some intuitive understanding,
the frequency analysis shows the particular tonal signature of the reed.
While many musicians and tuners are preoccupied with the
basic pitch, such signature (the timbre) is of great importance. Contrary
to common belief, reed vibration is a lot more complex the simple "pendulum
like" up and down motion". The article was aimed at familiarizing the reader
with basic timbre theory.
Short bio on Dan Lavry:
Dan Lavry is the President and founder of dB
Technologies, Inc. (The other founder is Bruce Hemingway). His company
is the leading edge manufacturer of high-end audio conversion and processing
equipment, with a client base encompassing the major recording, mastering,
broadcasting and film industries worldwide.
Much of his time is dedicated to his company. His areas
of expertise are analog design, hardware, and applied mathematics. The
bulk of his duties range from management, to research and development,
to design of new equipment, to customer interface.
Dan is married to Priscilla, lives in Washington, U.S.
and has one son, Marc - 18 years old. Dan who was born in Israel
is the son of Marc Lavry, the prominent Israeli composer. Dan got early
exposure and training in various aspects of music, ranging from piano to
music recording and editing. At 53 years old he is still working at improving
his music skills.
Dan's renewed interest in the accordion is only two years
old, yet it consists of the same degree of passion he dedicated to his
family, his business and the piano.