Natural Science Forum / Physics / Acoustics / December 2008

Perhaps this can help:

Saxophone Harmonics:
http://www.petethomas.co.uk/saxophone-harmonics.html

Saxophone Harmonics: Hearing with the Ears and the Embouchure:
http://www.wku.edu/~john.cipolla/saxharmonicsWKU.pdf

Saxophone acoustics: an introduction
http://www.phys.unsw.edu.au/jw/saxacoustics.html

JazzLab: Harmonics on tenor sax
http://www.youtube.com/watch?v=wAPoAPfsdpc

Saxophone Harmonics
http://video.google.com/videoplay?docid=6604414214026077986&hl=en

Cheers Jens

In article
<3d7a38f1-e93c-46fe-b792-bdae196dc29d@i18g2000prf.googlegroups.com>,

The saxophone uses a tapered bore. You can imagine a variable instrument
starting with a clarinet that has a uniform bore and varying the taper.
At one extreme, it becomes like an oboe with the reed end becoming the
apex of a cone.

As a clarinet, only odd harmonics of the fundamental get excited. As an
oboe, both odd and even harmonics harmonics are excited. These would be
the same as harmonics of a flute of the same length. The fundamental of
a clarinet of that length would be half the frequency of a flute's
fundamental.

The saxophone falls between the clarinet and the oboe as the taper
changes. Thus, two entirely different harmonic patterns form with the
saxophone in the middle. The relatively large diameter at the reed end
for the saxophone means that you do not get the full effect of a closed
cone end. It should not be surprising that the overtones are going to be
off-pitch to some extent. How closely a saxophone's resonances follow a
flute is determined by the ration of the blown and open end diameters.

If you want to get better numbers, to to the AIP Handbook where the
resonant frequencies of tapered open tubes are calculated. Remember that
the holes in a saxophene my be pushed a bit to give good tuning.

Bill

I think here are a couple important things left out of this
discussion.  One is the difference between sustained, forced
vibration, which reaches steady-state (periodic) motion, and transient
motion.  With strings, and with transient motion, as in the action of
a piano string or a plucked guitar string, the overtones experience
significant departure from a harmonic series, due to stiffness and
other effects mentioned in this thread.  Bells, plates and chimes
behave similarly.  With strings in forced motion, however, as in a
bowed instrument, the stick/slip phenomenon that maintains steady
state occurs principally at the frequency of the fundamental, and of
course must be periodic.  This fact alone requires that all overtones
be precisely some integer multiple of the fundamental.  If such were
not the case, the overtones would very quickly become out of step with
the stick/slip process, as well as with the major string motion.
Noise would result.  A very fine adjustment to this statement, for the
real world, is that there can be very small departures from this rule
only because the overtones have a very small effect on the stick/slip
process.  The same is true with reed instruments, which operate in
forced motion, and let's take beating reeds as an example (e.g.
saxophone).  The beating frequency is that of the fundamental, and all
overtones must thus be precisely some integer multiple of that
frequency, otherwise they would be out of step with the vibration of
the reed, and with the periodic vibration of the air column, and here
as well, the same refinement applies.

A second comment is that, although theoretical solutions for air
column vibration in reed instruments predict, for instance, only odd
harmonics in clarinets, in practice, significant contribution to the
musical tone is made by even harmonics, and I think this is due to
nonlinear effects in coupling the air column vibration with reed
vibration.  This contribution of course is not as pronounced as with
the tapered bores, but it can be observed, as for instance in
Benade's, Fundamentals of Musical Acoustics.

Best regards,
Tom

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