I think you got it basically correct in your extrapolation from brass
to reeds. The only thing I would criticize is the last phrase in your
statement: "The tube _forces_ the reed to vibrate at the selected
frequency -- selected by musician key press -- and the mouth does
little more than supply air.
The lips and mouth of the player (brass or reed) do interact with the
instrument... that is, the mouth is doing more than supplying air (at
least for a player who knows what to do). I suppose we could say that
beginning students provide little more than air with their mouths. But
eventually they learn (well... some learn) to adjust their lips, mouth,
teeth, etc. to compliment (and sometimes correct) what the instrument
is naturally doing. Otherwise several bad things happen (1) a battle
is taking place between the lips and the horn, and this makes the
player tire quickly, (2) the tone quality isn't as good (i.e. doesn't
conform to the accepted sound the instrument is supposed to produce,
(3) the frequency is likely to be slightly off (out of tune).
As Mel Bartels points out, all instruments need the frequency "bent" a
bit, or the intonation on each note won't be exactly correct. This
means the player in fact has to "fight the instrument" a little bit in
order to play exactly in tune. One reason for this is because the
equal-tempered scale is approximately based upon harmonics, but not
exactly. For example, the fifth note (G in the scale of C) is based
upon the third harmonic frequency. But in the equal tempered scale the
frequency of G (above middle C) is a few hertz higher (sharp) than a
true harmonic G. In the first approximation, the instrument is
performing harmonically, and the player is trying to play equal
tempered. Actually, some players (especially solo, where they don't
clash with other instruments) might be playing harmonically. But
that's a different subject.
My son and daughter each play trumpet. When they ask for my help
(which they've learned not to do any more than absolutely necessary) I
often say, "Okay, let's sing this rather than play it." The typical
response it, "But I can't sing it." To which I reply, "If you can't
sing it, or at least if you can't hear it in your mind, then there is
no way you're going to be able to play it well." Two points: (1)
You'll fight the instrument too much if you depress the proper valves,
but you haven't adjusted you lips properly... and this could cause you
to play the wrong harmonic. (2) Even if you get the correct harmonic,
you won't be in tune if you're not trying to "blow" the proper
frequency.
Speaking of the fine details of playing each note in tune: On my old
trumpet (an inexpensive Conn) the D an octave above concert-middle-C is
quite flat and I have to lip it up quite a bit. The C# (right near
middle-C) is quite sharp and I have to lip it down. In fact the low C#
is so sharp that I cannot lip it down sufficiently. Either my lips
aren't talented enough, or the horn just fights me too much. But the
third-valve slide on essentially all trumpets is supposed to move
easily, and has a finger-ring on it. If I have to play C# (and hold it
long enough that the poor intonation will be noticeable) I can extend
the third-valve slide a bit and fix the problem. My new trumpet (a
professional quality Yamaha) still has the C# problem (which is common
in trumpets) but the D problem is fixed. But then that means I might
have to extend the first-valve slide for some other notes, and a finger
ring is provided for that.
We now have four trumpets in the family, two professional Yamaha's, one
professional Bach, and my old inexpensive Conn. Each of these is
different to play, although the two Yamaha's are almost identical (a
feature I've heard about Yamaha that speaks well about quality
control). The point here is that (to an experienced player) it is
incredible how much difference there is between the Conn, Bach, and
Yamaha even though they are basically the same thing: a flared length
of tubing with a mouthpiece.
This might be more detail than anyone wants, but it's here to make the
point that it takes considerably more talent to play (or build) a wind
instrument with good timbre and intonation than what the non-wind
player realizes, even though it is true that the physics, in the first
approximation, forces the notes to come out close to what they're
supposed to be.
I also play piano, so I know it's myopic to extend this "more talent
than realized" virtue just to wind players. This statement has to be
true of any instrument. In fact, it takes more talent than often
realized just to tune a piano properly. I tune my own Yamaha grand
piano because I am better than most piano tuners around here. That's
not so much a statement about me as much as it describes the paucity of
good tuners in my area. And, of course, when it comes to tuning my own
piano, my fee is pretty low.
Although there's a lot of physics behind any musical instrument, it's
too bad the physics can't be exploited to make every instrument more
easy to play. I would love to play more instruments, and guitar is one
of them. But I'm no good at it and I'm now at the age where it is not
likely I'll ever learn it.
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