THE SOUNDS OF REEDS
By: Dan Lavry

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 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.

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