First and second valves vs third valve

Question

On B♭ trumpet to play notes E or A is prefered to use 1 and 2 valves, but there is possible to use third valve (most used in our brass band).

1 (valve 1) + 0.5 (valve 2) = 1.5

1.5 (valve 3)               = 1.5

So both makes same length.

I read 1 + 2 combination has better tune, but why ? What is different ?

I think is simplier to use only one valve.

Answer 1

The answer here is that you have a misconception about the "value" of each valve. The science of making a length of tube with three independent binary variances ("valves") fully chromatic across multiple octaves is an exercise in compromise.

Each individual valve is slightly out of tune from what it "says on the label", such that the various combinations it can play with other notes are more in tune. Even with only two valves, the distance between G and F# is ever so slightly different than the distance between F and E, and so the 2nd valve has to be somewhere in between. (And that's not the logarithmic distance that we hear in, but the linear distance that causes the physics required to produce those notes.)

Long story short, your third valve is not exactly the same as your 1+2 combination, but for certain notes it may be more appropriate to have that tuning (when playing the 3rd of the chord, for example). If you're interested in more detail, the answers to the related question linked above have a lot more information.

Answer 2

To spin off from NReilingh's answer, the half-tone between G and F# requires less extra tubing to be in tune, than the half-tone between E and Eb.

I believe that the third valve's length often is determined to have Eb in tune, and is therefore a little too long the have an in-tune E.

Let the tubing required to get from G to Gb be a reference, let's say value 1.

Gb -- 1 -- G

The subsequent half-tones downward grow larger the lower you go. Say for example that the required extra tubing to get from Gb to F is of length 1.01 instead of 1 (probably a wrong value, but the principle remains).

F -- 1.01 -- Gb -- 1 -- G

And the lower the half-tones, the more extra tubing is required.

Db -- 1.05 -- D -- 1.04 -- Eb -- 1.03 -- E -- 1.02 -- F -- 1.01 -- Gb -- 1 -- G

Perfect tuning in order to go from:

• G to F is 1 + 1.01 = 2.01
• G to E is 1 + 1.01 + 1.02 = 3.03
• G to Eb is 1 + 1.01 + 1.02 + 1.03 = 4.06

Say that your first and second valves were made in tune. Valve 2 (G to Gb) would have a length of 1. Valve 1 (G to F) would have a length of 2.01.

Now to get from G to E, you can combine 1 and 2, and get tubing for 1 + 2.01 = 3.01. It is a little short since in-tune tubing requires 3.03.

To get from G to Eb, you can combine 2 and 3. The third valve length is not determined yet, you can build it so that 2+3 has in-tune length of 4.06. The 3rd valve has then length 4.06 - 1 = 3.06.

So here you are, with valves set for in-tune Gb, F, and Eb, the tubing length for E is:

• in-tune -> 3.03
• 1+2 -> 3.01
• 3 -> 3.06

1+2 is closer to being in-tune. It is also at a higher pitch, and it is much easier to compensate with your lips downwards than upwards.

In real cases, I suppose that none of the valves really are in tune, there are many compromises.

All this letting alone the dexterity issue: pressing the third valve alone is often more difficult than 1+2. This is not always the case of course.

Answer 3

Actually you're right. In fact, if you tune 1 and tune 2 correctly individually, 1 and 2 together will always be sharp, as is the case for any finger combination. See

For 12 you can use 3 instead, which will be better in tune.