# Find A Formula For 1 2 3 2 5 2 Euphonium Valves – Three, Four, and Compensating Set Ups and Making Sense of Them All!

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## Euphonium Valves – Three, Four, and Compensating Set Ups and Making Sense of Them All!

Brass instruments, in their simplest form, are just tubes. On one side, a musician blows his lips to create a sound, which releases the instrument on the opposite side. Any tube (even demonstrated on YouTube for gardening) can produce wide intervals. These intervals are dictated by harmonic series, commonly called partial series by brass players. In order to play notes between partial series, the performer must have a way to change the length of the tubing on the instrument. Some instruments, such as trombones, have a movable slide, while euphoniums, baritones, trumpets, and French horns have valves to change the amount of tubing through which air flows.

A valve is a device in many devices that redirects airflow to a separate section of tubing before returning to the main tubing. When depressed, this “extra” tubing is in use, therefore increasing the working tubing length and reducing the pitch. In almost all modern horns, the valves work the same way: the second valve lowers the pitch by one half step, the first valve lowers the pitch by one whole step (two half steps), and the third valve lowers the pitch by one. and 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 the valves though. A valve combination of 2-3 will be slightly sharp, a 1-3 combination will always be quite sharp, and a 1-2-3 combination will always be very, very sharp. Let’s explore why this happens.

Now you’re probably wondering how instrument manufacturers know how much tubing to add so that the pitch is lowered by half a step. And if you’re not, I’m still going to explain it! Due to acoustic principles, to lower the pitch by half a step, the working length of the instrument must increase by about 1/15, or 6.67% of the working length. For illustration purposes I will use an instrument 100 inches in length (which is actually close to the length of a euphonium). This means the length of the second valve must be 100/15 or 6.67″ to lower the pitch by one half step. Now, to lower it by a half step you need to add 106.67/15 or 7.11″ so the length of the first valve is 6.67″+7.11″ or 13.77 inches. Now let me explain that last statement because it may have thrown some of you off. The reason the first valve isn’t just 2(6.67) is because to lower the pitch a full step, there must be enough tubing to lower the pitch a half step (6.67″) and then enough tubing to lower the pitch a half step (7.11″). This same principle goes for the third valve, and gives a length of 21.36 inches.

The formula for the theoretical length of tubing, TL, required to reduce the set number of half steps, x, for a device of length, L, is TL = L (16/15) ^ x. Example: 100″ instrument decrements 3 half steps: TL = 100(16/15)^3. TL = 21.36.

So the valve instruments are set up so that each valve is individually tuned. Problems arise when performers must use valve combinations to adjust pitch by more than three half steps. As you can see from the previous calculation, each time you add another half step, the task length must increase by more than the previous increment. Using the example of a 100″ instrument, the third valve extends the length to 121.36″ to produce an in-tune note three half steps below the original pitch. To lower the pitch after a half step of this note, 8.09″ tubing is required. However, since the second valve is only 6.67″ long, this combination will be slightly sharper. This problem resolves itself and in the 1-3 and 1-2-3 combinations, the loss 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 fourth-step sharp!

A fourth valve solves some problems and adds to others. The fourth valve adds 38.08 inches of tubing in the case of our 100″ instrument. This is an alternative to the 1-3 combination because the fourth valve has the correct amount of tubing in-tune. Similarly, the 4-2 combination produces a more in-tune pitch than the 1-2-3. does because it only lacks about 2.54 inches of tubing from the theoretical length. So that’s cool, now we have seven relatively common combinations in tune? It’s true, though, that this fourth valve provides access to a range that three valve devices can’t reach. Combining with a fourth valve When used, euphoniums can reach notes such as D below the staff, a note that is not possible using three valves. Now we get the curse of the fourth valve. Using the fourth valve in combination with other valves to reach these low notes, the problem described above in itself becomes even more compounds. After depressing the 4th valve the pitch should be 19.02″, to reduce the pitch a full step. A fourth valve was added in addition to its length. Normally, the first valve will lower the pitch by a full step, but remember the length of the first valve tubing? 13.77 inches. Again, this problem compounds as more valves are depressed. Using a 1-2-3-4 combination that uses the valve’s half-step definitions, the pedal should provide a B natural half a step above Bb. However, the tubing length for the Low B Natural is 203.38 inches! The combined length of all four valves is only 173.22 inches… that’s just enough for a slightly sharper C! That’s right, that means B natural is not possible (without lips from the performer) on a non-compensated 4 valve euphonium.

Four valve compensation system

So how do we account for all this shortage of tubing when more and more valves are depressed? The answer is compensatory euphonium. Compensating euphoniums wind through a “double loop” when the fourth valve is depressed. What this means is that when the air leaves the fourth valve slide, it actually re-enters the valve block. In this second pass, there are small compensating loops through which air flows, if the 1st, 2nd, or 3rd valve is depressed in conjunction with the 4th valve.

The beauty of this system is that, while the compensating loops depend on the fourth valve being depressed, the first 5 fingers (2, 1, 3, 2-3, 4) remain unchanged because their intonation is satisfactory. However, as you go further down (2-4, 1-4, 3-4, 2-3-4, 1-3-4, 1-2-3-4) an additional compensation loop is added to each valve. This brings the pitch of these fingerings to a satisfactory level.

The compensation system also has another, additional advantage: when playing under the staff, musicians can use traditional fingers in addition to the 4th valve. For example, on a non-compensated euphonium, a musician should play D down the staff with 2-3-4 fingers. AD in the middle register is pointed to 3. By adding compensating loops, a performer on a compensating euphonium plays the D down the staff by adding the 4th valve to the 3rd.

Why does it seem so confusing?

At this point, your mind is probably spinning. That’s okay because, as an artist, you don’t know why the compensation system works. You don’t need to know the mathematical and acoustic theory behind what happens when you press the 1st 3rd and 4th valves. A compensated euphonium does all the work for you. This solves the intonation problems that valves create. For compensating euphonium, playing down the staff doesn’t require you to change from traditional fingering.

Look at a professional tuba for example. These tubas can have five, six, seven valves to play a low chromatic range! I don’t believe it? Watch a video of Mnozil Brass on YouTube and pause it for a close-up of the tubist. His device has seven valves! The fact is that compensating euphoniums offer a chromatic range with only four valves, while non-compensating instruments can achieve that feat by adding only one or two valves.

Location of the fourth valve

Look at the Yamaha YEP-321S, then look at the YEP-842. Aside from the gold accents on the 842, the most obvious difference is the placement of the 4th valve. 321S has fourth valve next to third valve; This arrangement is called in-line arrangement. On the other hand, the 842 has a fourth valve on its right side, at about the midpoint; This arrangement is called 3+1 arrangement. In the case of in-line valves, the 4th valve is operated with the right pink. For instruments using a 3+1 arrangement, the 4th valve is operated by the left index or middle finger. Adding combinations like 2-4 can be problematic due to the lack of strength in your pinky when using the 4th valve with your right pinky. So from a physical point of view, the 3+1 system is generally easier to operate, especially on fast routes.

All compensated euphoniums are 3+1 (although, not all 3+1 euphoniums are compensated) which provides an additional benefit. Euphoniums are conical bore instruments, meaning that the bore increases until it reaches the end of the bell. The exception to this is on valve slides (1-2-3 on all horns and 1-2-3-4 on non-compensating four valve devices) where the bore remains constant. By moving the fourth valve below the horn, the bore may be enlarged as the fourth valve approaches. This extra expansion allows for a more overall 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 light, free-flowing, and doesn’t overcomplicate the horn. A three-valve euphonium is the best choice for beginners, but they should be upgraded as the musician develops. Most high schools will purchase four valve “inline” non-compensated euphoniums for their students. A compensated euphonium costs much more and produces no difference in anything except intonation in the lower register. When purchasing a personal euphonium, there is no need to pay extra if you know you don’t need a compensation register. However, I recommend getting a compensation horn if for no other reason than it’s better to have it and not need it than to need it and not have it. As for valve placement, I’ve found that most people prefer a 3 + 1 arrangement over an inline. The 3+1 arrangement is simply much easier and more comfortable to operate.

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