Why do Brass Instruments Have at Least Three Valves?
A brass instrument is just a long piece of plumbing (or tubing) coiled up for compactness. In the photo you can see a trumpet, stretched out so that its tubing is mostly straight. You can also see a coiled up flugelhorn. The tubing in both instruments is the same length, but the flugelhorn is lots easier to carry and play. Most brass instruments are coiled for convenience.
The player of a brass instrument buzzes his or her lips into the tube, to start the air column in the tube resonating. That resonance is the note you hear coming out of the bell. Longer tubes play lower notes.
Without Valves You got Yourself a Bugle
So, without valves, a brass instrument is a tube with buzzing lips at one end and the whole world listening at the other. That kind of tube can only play a few notes. If the tube is tuned to Bb, here are the first 9 of those notes (from low to high):
Bb – F – Bb – D – F – Ab* – Bb – C – D
*This note is very flat.
Those notes, known as the harmonic series, cover a little more than two octaves. The harmonic series continues upward, but many of the higher notes are badly out of tune. In the early days of brass instruments, without valves, they could only play those few notes.
Valves Expand the Range of the Horn
The valves let us play the notes in between the notes of the harmonic series. The idea is to make the tubing longer so that the notes will be lower. When you lengthen the tubing, all of the notes in the harmonic series go down by the same amount. So if the low Bb goes down to A when the valve is depressed, then the F goes down to E, the next Bb goes down to A, and so forth. The whole series drops a half-step.
Look again at the flugelhorn picture. Each valve has a loop of tubing. Depressing the valve adds that loop of tubing to the pipe, making the pipe longer and making the notes lower. So every valve allows lower notes, and pressing two or three valves allows even lower notes.
Making Rhyme and Reason out of Valves
How do we fill in the gaps in the harmonic series? In the harmonic series, the biggest interval between adjacent notes is between the low Bb and the low F. That interval is a perfect fifth, which is seven half-steps. So to get all of those notes in between, we need to add tubing that will lower the note by 1, 2, 3, 4, 5, or 6 half-steps. It turns out that we can do this with three valves, but not with any fewer. And if we can get all of the in-between notes in this biggest interval, we can get all of the other in-between notes too.
Looking again at the flugelhorn, you can see that the middle valve has the shortest loop, the first valve a bit longer, and the third valve the longest loop. The middle valve drops the pitch by 1 half-step, the first valve drops it by 2 half-steps (a whole step), and the third valve drops it by about 3 half-steps (a minor third). So starting on the lowest F and going down, we can get the following notes of the chromatic scale:
No valves down, F;
Middle valve down, 1 half step, E;
First valve down, 2 half steps, Eb;
Valves 1 and 2 down, 3 half steps, D;
Valves 2 and 3 down, 4 half steps, Db;
Valves 1 and 3 down, 5 half steps, C;
Valves 1, 2, and 3 down, 6 half steps, B.
Finally we’re just one half-step above the low Bb in the harmonic series, which we can hit with no valves down. As added value we get more notes below the low Bb, all the way down to E. Some brass instruments have 4 or more valves to extend this low range even lower.