Being a brass player myself (mostly trumpet) I agree that one way to
view the instrument is as an impedance matching device between the lips
and the world. As such, Leigh Palmer is correct that the impedance
matching allows one to play more loudly. And if we view the impedance
matching as frequency dependent (which it is) then we can also say that
impedance matching is also responsible for intonation and timbre. I am
writing just to make sure that we don't view impedance matching as
primarily enabling us to play more loudly, and I don't lose sight of
the original "resonant vibration" aspects that started this discussion.
When ranking the importance a various aspects of what a brass
instrument does for us, in first place, in my opinion, would be playing
in tune, especially being able to switch from one note to another
rapidly. The length of the tubing pretty much locks the playable
frequencies into the correct ballpark such than even students in 4th
and 5th grade bands can play a tune their parents can recognize. On
the contrary, go to a 5th grade strings concert where placement of the
fingers on the fingerboard is important to obtain the correct
frequency. My wife is a 5th-grade teacher so we often go to the
5th-grade music concerts as a "show of support." When the strings
play, it's a good thing the director tell us the names of the tunes,
otherwise we might not know.
Yes, I am aware that good brass players can play the Star Spangled
Banner with their lips alone... I can do a recognizable job of that
myself. But the intonation (in-tune playing) is so much better with
the instrument in place. Of course the poor trumpet player can still
blow the wrong harmonic, or the poor player can blow the correct
harmonic slightly out of tune. But the interaction between the
standing wave and lips to "lock-in" nearly the correct frequency has
got to be the number one thing the instrument does.
Second, but only slightly less important, the instrument determines
most of the timbre. Even when "the correct frequency" is being played,
harmonic frequencies are also present, and their ratios determine the
timbre. I've never met anyone who could create a good trumpet sound
(timbre) using his lips alone or even using a mouthpiece. Good players
can produce a more acceptable timbre than poor players, but if you hear
a young player blowing a trumpet, you can usually identify it as a
trumpet; no need to see it.
There are sufficient interesting things about the physics of
instruments that they can (and do) fill books. Since we've discussed
impedance matching, I find it interesting how important the flare is
for that (as well as for some degree of timbre), yet the flare works
against intonation aspects. For example, get a straight non-flared
tube the same diameter and same length as a trumpet. Put the trumpet
mouthpiece in one end of the tube and try to play a bugle tune such as
Taps or Revelry. This is easy to do; in fact, there is less leeway in
intonation. That is, I cannot sharp or flat the frequency nearly as
much as with an actual trumpet. The location of end of the non-flared
tube is much better defined. That means the length of the tube is well
defined, and that means the acceptable standing wave(s) is much better
defined.
In terms of timbre, the straight non-flared tube sounds much more like
a trumpet than the mouthpiece alone, but it definitely sounds muted.
Much of the muting effect is caused by the loss of impedance matching
which is provided by the bell on the actual instrument. I simply
cannot play the straight non-flared tube very loudly. But as we flare
the end and get better impedance matching, the end of the tube becomes
more vague. A wider frequency range for a given harmonic becomes
possible and more responsibility is placed on the player to attain the
exact frequency desired. I guess that goes with the territory: if you
want to want to be heard, you had better be talented.
Perhaps the brass instrument that requires the most talented lips is
the French horn. Compared to the diameter of the bulk of the tubing,
the bell is extremely flared. The thin tubing and wide flare force us
into a situation such that the standing waves have a high harmonic
number (there are many wavelengths contained in the length of the horn)
and the end of the tubing is poorly defined. The instrument barely
"locks-in" any frequencies at all. The player must coordinate the hand
and lips, especially lips, to play in tune. Although my bias and
experience makes me love the trumpet and similar instruments (read this
as: I don't care very much for French horn), I have to admit that I
have tremendous respect for good French horn players.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817