For my final project/presentation, I wanted to try and take some of the concepts we had
learned in class, particularly dealing with resonance and timbre of different musical instruments,
and apply them to a medium I’m familiar with and interested in. Specifically, I decided to look
into the impact of different design features in saxophone mouthpieces on the tonal elements and
projection of sound. From a musician’s standpoint, these design differences have a great impact
on the tone quality, projection, and ease of play, and it is very common for musicians to change
mouthpieces when performing multiple genres, or searching for a different sound.
The sound production of the saxophone begins with the mouthpiece and reed. Through
combined lip pressure underneath the reed and air pressure into the mouthpiece, the reed vibrates
rapidly over an opening into the mouthpiece, closing entirely over the mouthpiece about 50% of
the time, being completely about open 25% of the time, and being in motion about 25% of the
time. This process displaces air inside the mouthpiece and thus causes a vibration of the air
column throughout the instrument, with the frequency determined by the length of the tube.
However, while this describes the general mechanism for producing a sound, even the
most casual of listeners can discern the difference between a beginner and experienced
saxophonists, and more applicably, between a classical and jazz tone. While much of the
difference is in the ability and stylistic preferences of the musician, subtle, nuanced design
differences have a profound impact on tonal quality as well. These design differences are
particularly relevant in the mouthpiece, as the initial source of sound that carries through the rest
of the instrument. While, admittedly, the mathematical and acoustical grounding for these
observed phenomena is extremely complex and under-researched, it’s worth noting a few of the
general concepts that underlie design choices. As discussed on the UNSW page on saxophone
acoustics, the vibrations of the reed itself emit a high natural frequency (the source of “squeaks”
in beginner players). Though the lower lip of the player absorbs some of this vibration, the
natural frequency produces higher harmonics that resonate in the mouthpiece cavity, and the
prominence of the different harmonics are thus impacted by the size of the cavity and the amount
of the chamber that the reed is in contact with (window length). Dalmont’s article also discusses
another important factor, which has to do with the compliance of the reed, which is interrelated
with the volume of the mouthpiece cavity. As observed, these differences impact the amount of
air displaced and the velocity of the airflow in the mouthpiece, with implications for tuning,
particularly in the higher register, and projection.
Another important concept to mention, which is discussed at length on the UNSW
website and in Fletcher’s book, is acoustical impedance, which is the relationship between the
acoustic pressure (related to the oscillating reed and pressure differences in the mouthpiece) and
acoustic volume flow (related to the natural frequency series of the tube). This is particularly
relevant in the mouthpiece, as the source of the sound, and the different shape and sizes of the
resonating cavity, as a result of acoustical impedance, have an impact on the strength of the
resonance of different partials. This is also particularly relevant to the mouthpiece because,
though most mathematical modeling operates under the assumption that a saxophone is a perfect
conical resonator, it is in fact a truncated cone with a resonating cavity (mouthpiece) attached.
As a result, as Nederven discusses in his book, slight changes in the shape of the mouthpiece and
size of the bore can impact the relative strength of resonance at different partials, thus impacting
the tone quality produced. Finally, as discussed in Fletcher’s book, different levels of lip pressure
have the impact of diminishing the tip opening and acoustical pressure, as a result impacting
acoustical impedance and timbre. These same principles are applicable when discussing design
differences in the size of the tip opening and shape of the mouthpiece interior at the opening
(baffle), rather than variation in human manipulation of the reed itself.
Given all of these acoustical principles impacting mouthpiece design and the timbre, it’s
worth quickly outlining the primary elements of tonal quality and their relationship to
quantifiable data. Within the overarching concept of timbre, or the relationships between
different overtones that allow us to distinguish between different instruments, intensity can be
approximated as the overall acoustical energy produced. Resonance, as it relates to timbre, can
be approximated as the efficiency with which the initial source of power (the human body) is
translated into sound by the generating mech