Accordion musette sound is an integral part of folk music.
How does it work? The following article presents a signal theory view of
musette tuning.
Fundamentals of sound:
Any tone starts with an attack and ends with decay. Attack,
the buildup of energy at the beginning of a note, plays a major role in
defining the sound of a drum. Decay, the ending of a note, is an important
element for instruments such as piano and guitar.
While important, attack and decay play a lesser role in
defining many instruments. The bulk of the energy resides in the time period
between the attack and decay. This article examines tone behavior during
a note (ignoring attack and decay times).
A tone can be viewed as a sum of basic components (analogous
to complex molecules made up of simple atoms). Each of the components is
a sinosoidal vibration. The slowest vibration is called the fundamental
frequency and it defines the pitch. The other components in the mix, called
harmonics, give the tone its unique quality, called timbre. The harmonics
vibration frequencies are not arbitrary. For a given pitch, harmonic vibrations
occur at exact multiple rates of the fundamental frequency. A 500Hz pitch
may be coupled with a second harmonic 2 x 500 = 1000Hz (vibrations per
second), a third harmonic, 3 x 500 = 1500Hz , and so on. A 1200Hz vibration
is not a part of the tone since it is not an integer (whole number) multiple
of the 500Hz pitch.
The following pair of plots shows both time and frequency
domain representations of a flute. The left plot marked as Flute shows
variation of air pressure against time. The ear picks up sound by reacting
to air pressure variations created by the string vibration motion. The
particular wave shape is recognized as flute sound. The Plot on the right,
marked as FLUTE shows the fundamental frequency (1KHz in this example)
and the harmonics - 2,3,4,5 and 6KHz (higher harmonics with lower energy
are not show in the example).
Let us compare the flute sound to that of a violin (both
producing the same 1000Hz pitch). Note the existence of high energy harmonics
and lack of 2nd and 3rd harmonics (2Khz and 4KHz).
Two reed musette:
Not surprisingly, when combining (adding) two identical
tones, each containing an identical harmonic structure, will increase loudness.
The sound – variation in air vibration pressure simply doubles. The following
plots demonstrates this phenomena. Note: for the sake of simplicity, the
rest of the presentation is based on a "fixed generic tone structure" containing
1000Hz pitch and 3 harmonics.
Single reed shown in red, two reeds shown in blue:
The harmonic structure of the single reed (left) and two
reeds (right) is the same, with increased energy level being the exception:
We have shown both time and frequency plots of single
and double "generic" reed tone. The time domain plot illustrates almost
three compete vibration cycles. While useful for viewing the fine details
of waveform intricacies, understanding of musette requires display of a
lot more cycles:
The above plot shows many cycles, all identical in amplitude
and shape. Next we will tune the reeds to slightly different pitch to view
the musette action:
The addition of waves generated by slightly off tune pair
of reed produces an amplitude envelop – a slow periodic increase and decrease
in overall volume. The larger the pitch differences between the two reeds,
the faster the "tremolo effect". Reducing the musette tuning by a
factor of two slows down the envelope.
The modulation envelope changes over time in a periodic
manner. The timbre (tonal quality) changes as well, at the same rate. Such
volume and timbre changes, may occur many times per second, giving the
sound its unique quality. Let us expand two regions in order to view the
varying waveform:
The ear is extremely capable of reacting to all the details.
Various modulation envelopes sound very different. Let us plot the focus
on modulation envelope (volume changes).
Three reeds musette:
The addition of a third reed alters the sound further.
Various tuning combinations may make numerous modulation envelopes. Let
us first examine the case where one reed frequency falls exactly between
the other two. Note the sawtooth shape of the envelope:
Next we move the higher pitch reed higher in frequency.
The envelope pattern looks like two large saw teeth, followed by two small
saw teeth and back to two large, two small and so on.
The shapes and rate of repetition of the envelopes, and
the harmonic interactions greatly depend on each individual reed, and the
amount of frequency deviation between reeds. Clearly, a three reed musette
offers more generation of more complex waveforms.
Musette tuning is an art, requiring a good ear and much
experience. This article was written to shed some light on the fundamental
various mechanisms of such art.
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.
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