Euphonium Valves – Three, Four, and Compensating Set Ups and Making Sense of Them All!
Brass instruments, in their simplest form are simply tubes. At one end, a musician buzzes their lips to create sound, which leaves the instrument at the opposite end. Any tube (even ones for gardening as demonstrated on YouTube) can produce wide intervals. These intervals are dictated by the harmonic series, brass players generally call this the partial series. In order to sound the notes in-between the partial series, the performer must have a way to change the length of the tubing in the instrument. Some instruments, such as the trombone have a moveable slide, while others including euphoniums, baritones, trumpets, and french horns have valves to change the amount of tubing the air flows through.
A valve is a device on many instruments which redirects the airflow into a separate section of tubing before returning to the main tubing. While depressed, this “extra” tubing is in use, therefore increasing the length of working tubing and lowering the pitch. On almost all modern horns, the valves work in the same way: the 2nd valve lowers the pitch by one half step, the 1st valve lowers the pitch by one whole step (two half steps), and the 3rd valve lowers the pitch by one and a half steps (three half steps). If there is a fourth valve, it will lower the pitch by two and a half steps (5 half steps).
There is a slight flaw with valves though. The valve combination of 2-3 will be slightly sharp, the 1-3 combination will always be quite sharp, and the 1-2-3 combination will always be very, very sharp. Lets explore why this phenomenon happens.
Now you’re probably wondering how instrument makers know how much tubing to add so that the pitch is lowered by half step. And if you’re not, I’m still going to explain it! Because of acoustical theory, to lower the pitch by a half step, the working length of the instrument must increase by about 1/15, or 6.67% of the working length. For explanation purposes I will be using an instrument which is 100 inches in length (which is actually close to length of a euphonium). This means the second valve should have a length of 100/15 or 6.67″ in order to lower the pitch by one half step. Now, to lower it a half step past that you must add 106.67/15 or 7.11″ so the first valve must have a length of 6.67″+7.11″ or 13.77 inches. Now let me explain that last statement as it may have thrown some of you off. The reason the first valve would not be simply 2(6.67) is that in order to lower the pitch by a whole step, there must be enough tubing to lower the pitch by a half step (6.67″) and then enough tubing to lower that pitch a half step (7.11″). This same theory goes for the third valve, and yields a length of 21.36 inches.
The formula for the theoretical length of tubing, TL, needed to lower a set number of half steps, x, for an instrument of length, L, is TL = L (16/15) ^ x. Example: 100″ instrument lowering 3 half steps: TL = 100(16/15)^3. TL = 21.36.
So valved instruments are set up so that each valve, individually is in tune. Problems occur when performers must use valve combinations to adjust the pitch by more than three half steps. As you can see from the previous calculations, each time you add another half step, the working length must increase by more than the previous increase. Using the example of a 100″ instrument, the third valve increases the length to 121.36″ to produce an in-tune note three half steps below the original pitch. To lower the pitch a half step past this note, 8.09″ of tubing is required. However, because the 2nd valve’s length is only 6.67″ this combination will be slightly sharp. This problem only compounds itself and in the 1-3 and 1-2-3 combinations, the deficit between the actual length and the “in-tune” length is 2.94″ and 5.04″ respectively. As you can tell, this creates a big problem, in fact, the 1-2-3 combination is about a fourth-step sharp!
The 4th valve solves some problems and adds others. The 4th valve adds 38.08 inches of tubing in the case of our 100″ instrument. This is a substitute for the 1-3 combination as the 4th valve has the correct amount of tubing to be in-tune. Likewise, the 4-2 combination produces a pitch more in-tune than 1-2-3 as it only lacks about 2.54 inches of tubing from the theoretical length. So this is great, now we have all of the seven common combinations relatively in tune right? This is true, however, this 4th valve grants access to a range which three valve instruments cannot reach. When using combinations with the 4th valve, euphoniums can reach notes such as D below the staff, a note which is not possible using three valves. Now we get to the curse of the 4th valve. When using the 4th valve in combination with other valves to reach these low notes, the problem described above compounds on itself even further. To lower the pitch a whole step after depressing the 4th valve, 19.02″ must be added in addition to the length of the 4th valve. Generally, the first valve would lower the pitch by a whole step, but remember the length of the first valve tubing? 13.77 inches. Again, this problem compounds as more valves are depressed. Using the 1-2-3-4 combination, which using the half-step definitions of the valves, should provide a B natural a half step above pedal Bb. However, the length of tubing for a low B natural is a whopping 203.38 inches! The combined length of all four valves only equates to 173.22 inches… Thats only enough for a slightly sharp C! Thats right, that means that B natural is not possible (without lipping from the performer) on a non-compensating 4 valve euphonium.
Four Valve Compensating System
So how do we account for all this lack of tubing when more and more valves are depressed? The answer is the compensating euphonium. Compensating euphoniums run air through a “double loop” when the 4th valve is depressed. What that means is that when air leaves the fourth valve slide, it actually re-enters the valve block. On this second pass, there are smaller compensating loops which the air runs through, if the 1st, 2nd, or 3rd valve is depressed in combination with the 4th valve.
The beauty of this system is that, because the compensating loops depend on the fourth valve being depressed, the first 5 fingerings (2, 1, 3, 2-3, 4) remain unchanged since their intonation is satisfactory. However, as you descend further (2-4, 1-4, 3-4, 2-3-4, 1-3-4, 1-2-3-4) an extra compensating loop is added to each valve. This brings the pitch of these fingering down to satisfactory levels.
The compensating system also has another, added benefit: when playing below the staff, musicians can use conventional fingerings in addition to the 4th valve. For example, on a non-compensating euphonium, a musician would have to play a D below the staff with the fingering 2-3-4. A D in the middle register however is fingered with 3. With the addition of the compensating loops, a performer on a compensating euphonium plays a D below the staff by simply adding the 4th valve to 3.
Why Does This Seem So Confusing?
At this point, your brain is probably spinning. That’s OK because, as a performer, you don’t have to know why the compensating system works. You don’t have to know the mathematical and acoustical theory behind what happens when you press down the 1st 3rd and 4th valves. A compensating euphonium does all the work for you. It resolves the intonation problems which valves create. For a compensating euphonium, you do not need to change from conventional fingerings when playing below the staff.
Look at a professional tuba for instance. These tubas can have five, six, even seven valves in order to play a low chromatic range! Don’t believe me? Look up a video of Mnozil Brass on YouTube and pause it on a close up of the tubist. There are seven valves on his instrument! The fact is that compensating euphoniums provide a chromatic range with only four valves, whereas non-compensating instruments could only achieve that feat with the addition of an extra valve or two.
Placement of the Fourth Valve
Take a look at a Yamaha YEP-321S, then look at a YEP-842. Besides the gold accents on the 842, the most obvious difference is the placement of the 4th valve. The 321S has it’s 4th valve beside the 3rd valve; this arrangement is called an in-line arrangement. On the other hand, the 842 has it’s 4th valve on the right side, at about the midpoint; this arrangement is called a 3+1 arrangement. In the case of in-line valves, the 4th valve is operated with the right pinky. For instruments utilizing a 3+1 arrangement, the 4th valve is operated by the left index or middle finger. Using the 4th valve with your right pinky can be troublesome when you add combinations such as 2-4 due to the lack of strength in your pinky. Therefore from a physiological standpoint, a 3+1 system is usually easier to operate, especially in fast passages.
All compensating euphoniums are 3+1 (however, not all 3+1 euphoniums are compensating) which provides one extra benefit. Euphoniums are conical bore instruments, meaning that the bore is ever increasing until it reaches the end of the bell. The exception to this is in the valve slides (1-2-3 on all horns and 1-2-3-4 on non-compensating four valve instruments) where the bore stays constant. By moving the 4th valve further down the horn, the bore can expand while approaching the 4th valve. This extra expansion allows for a more overal conical design and provides a more characteristic euphonium sound.
So Which Euphonium is Right for Me?
Most students will start on a standard three valve system. This makes the horn lightweight, free-blowing, and doesn’t over complicate the horn. For beginners the three valve euphonium is the best option, however as the musician develops they must upgrade. Most high schools will buy four valve “inline” non-compensating euphoniums for their students. A compensating euphonium costs much more and doesn’t yield any difference in anything except intonation in low register. When buying a personal euphonium, if you know that you’ll never need the compensating register, then there is no need to pay the extra money for it. However, I would suggest getting a compensating horn if for no other reason than because its better to have it and not need it than to need it and not have it. As for the placement of the valve placement, I have found that most people prefer the 3+1 arrangement over inline. The 3+1 arrangement is simply much easier and more comfortable to operate.
