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How do we manage with
only three valves?
We
have occasionally been asked how a brass player can produce all
those notes with only three valves. It seems almost intuitive that
an instrument such as a clarinet can play many different notes, festooned
as it is with lots of complicated metalwork. But how is it done on
a brass instrument with only three valves? Here is an explanation
for non-musicians.
 A
length of brass tubing can be made to produce a series of quite
distinctly separated notes by ‘buzzing’ into it at one end using
various lip pressures. The more we tighten the lips, the higher the
note. It is not at all easy to do with a simple tube, but if we put
a mouthpiece at one end and a tapered bell on the other it gets
easier - and if we choose the right dimensions and apply some
plating to smarten things up, we would have one form of post-horn,
those "yard-of-ale" instruments which are sometimes produced for
specialist performances. You can see one being played on the left
(click on the photograph to see a larger version).
A little essential background
The notes we can fairly readily produce with our post-horn - those
notes which "speak" easily - are the notes for which one or more
wavelengths[1] of the associated sound waves exactly fit along
the effective length of the instrument.
We get the lowest note, called the fundamental[2], in the
one-wavelength case, with the lips relatively relaxed. The higher
notes, called harmonics[2], are those for which 2, 3, 4, etc
wavelengths fit along the effective length of the instrument. So we
have the series: fundamental, 2nd harmonic, 3rd harmonic, 4th
.....etc.
This phenomenon is called resonance and the post-horn is said to
resonate at the fundamental and the harmonics. The resonance is
weakest for the fundamental and for that reason, the fundamental is
not as easy for the player to sound or to control as are the
harmonics and is therefore little used.
In terms of the notes of the equitempered musical scale on which
virtually all our music is based, there are eleven notes between
fundamental and 2nd harmonic, six notes between 2nd and 3rd
harmonics, four between 3rd and 4th and increasingly fewer notes
between higher adjacent harmonics. The post-horn cannot play these
"in-between" notes - only the harmonics.
If we increase the length of our post-horn, all the wavelengths
increase proportionally and in consequence the corresponding
fundamental and harmonic notes become lower. Musicians would say
that we lower the pitch of the notes.
If we choose the post-horn's length (musicians would say tune the
post-horn) so that the 2nd
harmonic is the same as one of the notes of the musical scale, we
find that the 3rd, 4th,
5th, 6th
and 8th harmonics (but not the
7th) lie very close to (other)
notes of the same musical scale - so close that for most practical
purposes we can ignore what small differences there are.
The
outcome
the outcome of all this is that we can use our basic post-horn to
play a small but useful series of notes, all of which are notes from the
musical scale We can therefore play simple musical sequences - such
as bugle calls and the famous "post-horn gallop" - using lip
pressure only to select the harmonics required.
We can also tune the instrument by the simple expedient of adjusting
the instrument's overall length, in order to be able to play in tune
with other instruments.
However, in a brass band we want to be able to play all the
notes of the scale, not just some of them. To do this we need to
find a way of playing the 'missing' notes - those notes which lie
between the harmonics.
Filling in
Luckily, if we ignore the fundamental and consider only the
harmonics, there are never more than six of these missing notes
between adjacent harmonics. So we could fill in the gaps if we had
a range of six extension tubes to increase the length of our
post-horn and thus tune it to each of the missing notes. We would
have six sets of harmonics available to us, one for each extension
tube, and somewhere in those six sets we would find any note we
want.
In case this seems a jump too far, the reasoning is expanded at [3]
below.
The final stages
We wouldn't need six separate tubes though. We could make up
the three longest tube lengths by adding together various
combinations of the three shortest ones. Interestingly enough, if
you look at the photograph of the post-horn again you will see two
such extension tubes at the mouthpiece end of the instrument. They
are there for overall tuning purposes, but they illustrate the idea.
But of course we couldn't play music this way. Even with only three
tubes to worry about, it would be impossibly inconvenient and slow.
However - we could transform the situation if we were to connect the
three extension tubes permanently and use a valve to connect each
one into the air stream as required. Using the three valves we
could then change tube lengths as quickly as we could move our fingers.
Wrapping
it up
 And,
of course that is just what is done in a real three-valve brass
instrument. With the
three valves we can play all the notes we want, as quickly as our
fingers will allow. For each note, we use the valves to select the
required tube length and our lip pressure to select the
required harmonics.
All that remains is to bend our much-modified post-horn with its
extra tubing and valves into a convenient shape (sound waves
don’t mind going round bends) until we have a cornet, like the one
shown here.
In the photograph (click on it to get a larger image) you can
clearly see the main tube running from the mouthpiece, through the
valves and on to the bell. The three extension tubes can also be
seen: we are looking end-on at the shortest extension tube which is
controlled by the middle valve. The next-longest tube is controlled
by the left-hand valve and runs out to the left and back again to
the valve. The longest tube is controlled similarly by the
right-hand valve and runs out to the right and back.
The larger instruments, which play the lower notes in the band, use
the same basic idea. The tubing, valves and mouthpieces are larger
but the principle remains the same.
Three valves aren't quite the whole story. Recall that we started
with the 2nd harmonic because
from there on upwards we only need three valves to be able to play
every note of the scale. Well, some instruments, the Basses
(Tubas) in particular, are asked to play notes down to that more
difficult lowest note, the fundamental (which musicians call a pedal
note). To be able to play all the notes between second
harmonic and fundamental (there are eleven of them) requires a
fourth length of tubing, and a fourth valve to control it. So
all tubas, and some euphoniums, have four valves. The fourth
valve may not be obvious (it is operated by the player's left-hand
index finger), but if you look carefully at the euphoniums and tubas
the next time you got to a brass concert, you will spot it.
As usual there are in practice more angles to the story. These
mainly concern the things which are done to attain good intonation -
correcting those inherent differences, albeit small, between the
harmonics and the true notes of the musical scale. That fourth
valve that tubas have, for instance, has a part to play in achieving
good intonation as well as in playing notes down to the fundamental. But
such details will have to wait for a future article.
The other way of doing it
 There
is, of course, another way, a much more obvious way perhaps,
of approaching the problem. We could have bent our post-horn
into a suitable shape and then added a slide which is moved in and
out to achieve the six lengths of tubing we need. Well -
that way of doing things was also adopted, and led to that
well-known instrument (photo at right) which is usually to be found
on the right-hand side of the band during concerts.
[1] The wavelength of a wave is
the distance from one wave crest to the next. See the "Sound
Waves" page for further information.
[2] Fundamental and harmonic are scientific
terms. Musicians often call the fundamental a "pedal note" and
they use the terms "partials" and "overtones" for the harmonics. But
then, musicians always like to be different. The scientific terms
are more precise and are to be preferred.
[3] To illustrate how it would work, the following example may
help. If, say, we were to start at the 3rd
harmonic of our post-horn and were then to fit our six extension
tubes in sequence starting at the shortest, we would find that we
could lower the pitch of the 3rd
harmonic in steps of one note (in this context, musicians call this
step a semitone) until we were one note (one semitone) above the 2nd
harmonic of the original post-horn. At that point, we could remove
the final extension tube and play the (original) post-horn's 2nd
harmonic to complete the series of adjacent scale notes. In this
way we would, using our six extension tubes, be able to play all the
notes of the scale between the 2nd and
3rd harmonics of our
original post-horn. In a similar way could play the all the missing
notes between any other adjacent harmonics - and so, we could play
all the notes there are to be played.
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