The Three- and Four-Valve Compensating System
by
David Werden
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All brass instruments
share some common characteristics.
They are all essentially tubes, at
one end of which is found a musician
vibrating his lips in order to produce
a tone. Played in this way, any tube
(even a length of garden hose) will
produce a series of widely spaced
notes, known as the "partial
series." With no other means
of pitch adjustment, the musician
could play only melodies as simple
as bugle calls (a standard bugle is,
in fact, just that simple an instrument).
In
order to fill in between these notes,
brass instruments employ either a
series of valves or a fully movable
slide (as on the trombone). This discussion
deals with valve systems.
The
valve is a device which, when depressed,
detours the sound waves through an
extra length of tubing. This action
(which has the same effect as extending
a trombone's slide) causes the working
length of the instrument to become
longer, thereby lowering the pitch.
The valves of virtually all instruments
in use today are set up in the same
way: the 2nd valve lowers the pitch
1/2 step, the 1st valve lowers the
pitch 1 step (2 half steps), and the
3rd valve lowers the pitch 1-1/2 steps
(3 half steps). If there is a 4th
valve it will lower the pitch by 2-1/2
steps (5 half steps).
Usually
unnoticed by the musician, a great
deal of mathematics is going on under
his fingertips. Based on acoustical
theory, each time the player wishes
to lower the pitch by 1/2 step, he
must increase the working length of
the instrument by approximately 6%.
For the sake of mathematical convenience,
imagine an instrument with a basic
length of 100" when no valves
are depressed (this is only slightly
longer than a Bb euphonium). If the
2nd valve is to lower the pitch by
1/2 step, its tubing would then have
to be 6" long (6% x 100").
The total working length is now 106".
To lower the pitch another 1/2 step
below this level, the instrument needs
an additional 6.36" of tubing
(6% x 106" = 6.36"). Therefore,
in order for the 1st valve to be capable
of lowering the pitch of the basic
instrument by 1 step, its tubing should
be 12.36" long (6" + 6.36").
With just the 1st valve depressed,
the total working length is now 112.36".
For another 1/2 step below this level,
an additional 6.74" of tubing
(6% x 112.36") is necessary.
Therefore, the 3rd valve's tubing
should be 19.1 " long (12.36
+ 6.74) in order to produce the desired
1-1/2 step change.
As
seen in the preceding paragraph, changes
of 1/2 step, 1 whole step, and 1-1/2
steps, require adding 6%, 12.36%,
and 19.1% respectively to the working
length of the instrument. While each
of the 3 valves can be designed to
provide exactly the length needed
when it is used alone, a conflict
arises when 2 or 3 valves are used
at the same time. Using the example
of a 100" instrument, the working
length with the 3rd valve depressed
would be 119.1". To lower the
pitch by 1 step from this point, 12.36%
must be added to its length, which
in this case would be 14.7" (12.36%
x 119.1 " = 14.7"). Since
the 1st valve's tubing is only 12.36"
long, the 1 & 3 combination will
be quite sharp. Because of similar
discrepancies, 2 & 3 will be slightly
sharp and 1, 2 & 3 will be a full
1/4 step sharp.
The
problem becomes more severe with 4-valve
instruments. The 4th valve alone is
used in place of 1 & 3, and can
be designed to provide the 33.8"
(in the case of a 100" instrument)
necessary to lower the pitch a perfect
fourth (5 half steps). Also, the 2nd
and 4th valves can be used together
as a satisfactory substitute for the
troublesome 1, 2 & 3 combination.
However, below this pitch level the
problems become severe. For example,
with the 4th valve depressed the instrument's
working length is 133.8". To
lower the pitch another whole step,
an additional 16.5" (12.36% x
133.8") would have to be added,
but the 1st valve can provide only
12.36", leaving the pitch quite
sharp. However, 1 & 2 together
would add 18.36", making the
pitch somewhat flat. With just the
4th valve depressed, lowering the
pitch by a diminished fifth (6 half
steps) would require the addition
of 55.9" (41.8% x 133.8").
Unfortunately, the 1st, 2nd &
3rd valves together only add up to
37.46", and can produce slightly
less than 5 half steps of pitch change
below the 4th valve alone. On a Bb
instrument such as the euphonium,
all 4 valves together produce a slightly
sharp C, leaving a low B unavailable.
Consequently, a full chromatic scale
between the 1st and 2nd partials is
not possible.
While
mechanical devices (such as lever-operated
tuning slides) may be used on smaller
instruments as a means of adjusting
intonation, such cures are not practical
for instruments the size of euphoniums
or tubas.
The Four-Valve Compensating System
If a euphonium or tuba
player wishes to be able to play a
full chromatic scale in the lower
register, a 4valve compensating system
is the best answer. The 4th valve
tubing routes back through the first
3 valves so that when the 4th valve
is used in combination with any other(s),
air can automatically be detoured
through extra compensating loops.
Progressing
downward from the open horn, the first
five fingerings (2, 1, 3, 23, and
4) don't involve the compensating
system as their intonation is satisfactory.
However, the compensating loops are
used for the next six fingerings (24,
14, 34, 234, 134, and 1234), since
their pitch would otherwise vary from
uncomfortable to unusable. Diagrams
1 through 4 (linked below) show some
of these situations, in which the
detours have provided for bringing
down the pitch of these sharp fingerings.
The
compensating system makes it possible
to play a full chromatic scale between
the 1st and 2nd partials. All four
valves together will produce a usable
B, l/2 step above the first partial.
On a non-compensating instrument,
this same fingering would only produce
a sharp C, leaving the B unavailable.
The
compensated instrument has the further
advantage of being able to play in
the lower octaves using conventional
fingerings. For example, a euphonium
player would use 23 for a middle-range
Db. To play an octave lower he would
simply add the 4th valve. On a non-compensating
euphonium, he would have to use 134
to approximate the lower Db.
While
the compensating system may seem complicated,
remember that the player needn't be
aware of all the mathematical theory
behind it. He need only play the instrument
and let tubing design resolve the
inherent conflicts. In fact, simplicity
is one of the benefits of the compensating
system. As an illustration of this,
consider the professional-grade non-compensating
tubas on the market. Many of these
employ 5 or 6 valves whose purpose
is to allow for enough alternate fingerings
to be able to play a full chromatic
scale.
One
of the most respected of modern texts
dealing with the euphonium and tuba
is The Tuba Family by Clifford Bevan.
He begins his discussion of the compensating
system by saying, " By the 1870's
it was obvious that the most satisfactory
method of compensation would be completely
automatic (probably the player's lack
of enthusiasm for extra valves, levers
and keys was striking home). In fact
the first completely automatic system
turned out to be the best.'' (Clifford
Bevan, The Tuba Family (New York:
Charles Scribner's Sons, 1978); p.
82)
4th-Valve Placement: a "Side Issue"
While many manufacturers
place the 4th valve immediately next
to the 3rd, Hirsbrunner and Sterling-Perantucci
place the 4th valve halfway down the
right side of the instrument, intended
to be played with the left hand. While
this can be justified by simply noting
the relative weakness of the 4th finger
of the right hand, there is also a
consideration relating to the compensating
system.
A graduate of The University of Iowa, Mr. Werden was the euphonium soloist with
The United
States Coast Guard Band for 26 years. He has performed throughout
the United States, as well as in Canada, England, Japan, and the former Soviet
Union. Mr. Werden has performed under the baton of
Zubin Mehta,
Osmo Vänskä,
Frederic, Fennell,
H. Robert Reynolds,
Leonard Falcone,
Laurence Rosenthal and many others. He performed on soundtracks for NBC Television and Hollywood movies,
and in live concerts with the New York Philharmonic and the Minnesota Orchestra.
Watch Dave's latest videos here... Through FM and TV broadcasts, his solos have been heard in dozens of countries
around the world. He is a recitalist and clinician, and has performed at local,
national, and international symposiums. He was a member of The USCG Band Euphonium/Tuba
Quartet, the Atlantic Tuba Quartet, the Saints Brass Quintet, and the Classic
Brass Band (now named Charter Oak Brass Band). He has taught at the University of Connecticut and the University
of Minnesota, and he is
listed in Marquis' Who's Who in American Education.
His efforts to expand the role and recognition of the euphonium led the British
magazine Sounding Brass in conjunction with the American publication Euphonia
to name him the international "Euphonium Player of the Year" in 1980. He is the first
American awarded this honor. In 1981 he was elected to the post of Euphonium
Coordinator for the International
Tuba-Euphonium Association (formerly called Tubists Universal Brotherhood
Association: T.U.B.A). In 1987 he was appointed to the Honory Board of Advisors of
ITEA. His many solo performances and his efforts to expand the role of the euphonium
in music earned him the prestigious Coast Guard Commendation Medal. He has also
been awarded two Coast Guard Achievement Medals, the Coast Guard Special Operations
ribbon, two Coast Guard Unit Commendations, and three Coast Guard Meritorious
Unit Commendations. In 1993 he was inducted into the Pi Kappa Lambda honors society. And in June of 2012 he was awarded the highest honor of the International Tuba-Euphonium Association, the Lifetime Achievement Award.
David Werden is currently living in Minnesota, working as a computer consultant
and teaching tuba and euphonium. Since moving to Minnesota he has performed with Symphonia (America's Premier Large Tuba-Euphonium Ensemble), the Minnesota
Orchestra, the Sheldon
Theater Brass Band, was a special guest artist at the International Euphonium Institute, performed for the International Trumpet Guild, and has been heard on live national broadcasts of A
Prairie Home Companion. In 2012 David Werden began working with Adams Custom Brass as an Adams Euphonium Artist to help them enhance their already best-in-class professional euphonium.
Euphoniums
are essentially conical-bore instruments.
That is, their tubing is almost constantly
expanding from the mouthpiece to the
bell. The most notable exception to
this is found within the 1st, 2nd
& 3rd valves, where the bore size
is constant. However, the separation
between the 3rd and 4th valves allows
the connecting tubing to expand gradually
as it approaches and passes through
the 4th valve's tubing, maintaining
a more constant taper. For example,
in the case of the Sterling-Perantucci
euphonium the main bore (measured
at the 2nd valve) is.592". At
the compensating loops it has expanded
to .630", and it expands to .670"
within the remainder of the 4th valve
tubing. By preserving a more conical
bore through this area, freedom of
response and consistency of tone are
enhanced.
Diagrams
of Compensating Action
Diagram
1: the sound passes
through the 1st valve tuning slide and
no others
Diagram
2:
the sound passes
through the 4th valve tuning slide and
no others
Diagram
3:
the air passes
through the 1st valve tuning slide, the
4th valve tuning slide, and the 1st valve
compensating loop
Diagram
4:
the air passes
through all valves and all compensating
loops
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David
Werden
He has published articles in BAND Magazine, Euphonia magazine, The
Instrumentalist magazine and
the T.U.B.A. Journal.
He is the author of The Blaikley Compensating
System, Scoring for Euphonium,
co-author with Denis Winter of the Euphonium
Music Guide, co-author with Barbara Payne and Brian Bowman of Euphonium Excerpts from the Standard Band and Orchestral Library, and a co-author of the Brass Player's Cookbook. He compiled and edited a series of papers by Arthur Lehman
into the book The Brass Musician. He has also published over 150
arrangements for a variety of solo instruments and ensembles, and published a popular and authoritative article on the world wide web explaining the difference between baritone
and euphonium.
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