Most brass instruments, such as the cornet shown below, have valves which are pressed in various combinations to change the note played.
The length of tubing of a cornet (or trumpet) is about 1.4 metres (4.5 feet) with no valves pressed. The lowest note that can be played with this length of tubing is a C (concert Bb).
Each valve opens an extra length of tubing, increasing the effective length of the instrument and lowering the pitch of the note played.
When a valve is up (not pressed) the air goes straight through the valve but, when the valve is pressed down, the air is diverted into an extra length of tubing before returning to the main tube.
When no valves are pressed, the cornet is said to be “open” and the air goes straight through each valve. Notes that can be played include C and G.
The 2nd, or middle, valve opens a short length of additional tubing which lowers the pitch by a semi-tone. A semi-tone is the difference between any 2 notes, black and white, on a piano keyboard. E.g. C to B, or G to F#/Gb (see keyboard below).
The 1st valve, nearest the mouthpiece, opens a longer length of additional tubing which lowers the pitch by a tone. A tone is the same as 2 semi-tones, or moving 2 notes, black and white, on a piano keyboard. E.g. C to A#/Bb, or G to F (see keyboard below).
The 3rd valve, furthest from the mouthpiece, opens an even longer length of additional tubing which lowers the pitch by a tone and a half, or 3 semi-tones. This is the same as moving 3 notes, black and white on a piano keyboard. E.g. C to A, or G to E (see keyboard below).
A little maths will tell you that pressing the 3rd valve is the same as pressing valves 1 and 2 together (note – this is not strictly true – see technical health warning below!).
By pressing combinations of valves it is possible to lengthen the tubing even more and lower the note by a semi-tone each time:
Pressing valves 2 and 3 together opens a total length of additional tubing which lowers the pitch by 4 semi-tones. E.g. C to G#/Ab, or G to D#/Eb (see keyboard below).
Pressing valves 1 and 3 together opens a total length of additional tubing which lowers the pitch by 5 semi-tones. E.g. C to G, or G to D (see keyboard below).
Pressing all 3 valves together opens a total length of additional tubing which lowers the pitch by 6 semi-tones. E.g. C to F#/Gb, or G to C#/Db (see keyboard below).
Semi-tone steps down from the notes, C and from G, on a piano keyboard – each black and white key is a semi-tone lower than the key to its right, and a semi-tone higher than the key to its left.
Note that the black keys are named after the white keys either side of them. E.g. the black key between C and D is called C# (“C sharp”) because it is a semi-tone higher in pitch than C, and it is also called Db (“D flat”) because it is a semi-tone lower in pitch than D.
Some brass instruments use rotary valves rather than piston valves. They look and work differently, but they do exactly the same job to add extra lengths of tubing to the instrument and lower the pitch.
Technical health warning /small print
Note that the above is a simplification, and some instruments have additional valves, and/or other ways to alter the tuning by smaller amounts as the instrument is being played.
In order to lower the pitch by a semi-tone, it is necessary to lengthen the tubing of the instrument by 6% each time. The new length of the instrument will then by 1.06 times what it was. To lower the pitch by another semi-tone we must lengthen the tubing by 6% of the new length.
Imagine we have a simple tube the same length of a cornet/trumpet i.e. about 140 cm. We can play various harmonics including C and G.
In order to lower the pitch by a semi-tone we must lengthen it by 6% (6*140/100) which is 8.4cm. The new length of the tube is then 140 + 8.4 = 148.4 cm.
Now, you might think that in order to lower the pitch by a tone (2 semi-tones) we need to lengthen the tubing by twice as much, i.e. by 2 * 8.4 = 16.8 cm. But you’d be wrong! Because each time we want to lower the pitch by another semi-tone, the additional tubing required gets longer.
So, to lower the pitch of our extended tube by another semi-tone, we need to lengthen it by 6% of 148.4 cm (6 * 148.4/100) which is 8.9 cm. We have now lengthened our original tube by 8.4 + 8.9 cm = 17.3 cm. The new length of our tube, pitched 2 semi-tones lower, is then 140 + 17.3 = 157.3 cm.
Similarly, in order to lower the pitch by 3 semi-tones, we need to add a further 6% of 157.3 cm which is about 9.4 cm, i.e. we need lengthen our original tube by 8.4 + 8.9 + 9.4 = 26.7 cm. the new tube will be 140 + 26.7 = 166.7 cm.
Therefore on a cornet/trumpet the 2nd valve tubing must be 8.4 cm long, in order to lower the pitch by one semi-tone; the 1st valve tubing must be 17.3 cm, to lower the pitch by two semi-tones; and the 3rd valve tubing must be 26.7 cm, to lower the pitch by three semi-tones.
But now there are some problems!
Firstly, we claimed above that pressing valve 3 is the same as pressing valves 1 and 2 together. Is this true? No! Because the valve 3 tube is 26.7 cm, but the sum of the valve 1 and 2 tubes is 8.4 + 17.3 = 25.7 cm and there is a difference of 1 cm (do the maths)!
Also, to lower the pitch by 4 semi-tones we need to press valves 2 and 3, but the total length will be a bit shorter than it needs to be, and the problem gets worse lowering the pitch 5 semi-tones by pressing valves 1 and 3, and worse still lowering it by 6 semi-tones by pressing all 3 valves!
To lower the pitch by 4 semi-tones, we really need an additional length of tube = 8.4 + 8.9 + 9.4 + 10.0 = 36.7 cm, but the sum of the valve 2 and 3 tubes is 8.4 + 26.7 = 35.1 cm, a difference of 1.6 cm!
To lower the pitch by 5 semi-tones, we really need an additional length of tube = 8.4 + 8.9 + 9.4 + 10.0 + 10.6 = 47.3 cm, but the sum of the valve 1 and 3 tubes is 17.3 + 26.7 = 44.0 cm, a difference of 3.3 cm!
To lower the pitch by 6 semi-tones, we really need an additional length of tube = 8.4 + 8.9 + 9.4 + 10.0 + 10.6 + 11.3 = 58.6 cm, but the sum of the valve 1, 2 and 3 tubes is 17.3 + 8.4 + 26.7 = 52.4 cm, a difference of 6.2 cm!
What all this means is that any note played on our brass instrument, with more than one valve pressed at the same time, will be sharp (pitched higher than it should be). Notes played with all 3 valves pressed will be very sharp!
But do not despair! There are things we can do to overcome this problem:
The 3rd valve tube can be made longer so it is better in tune when used with valves 1 and 2. Although playing with all 3 valves pressed will still be sharp (higher in pitch than it should be), and notes played with just valve 3 pressed will be flat (lower in pitch than they should be).
Trumpets and cornets have a finger slide on the 3rd valve tube which allows the player to adjust the length of the 3rd valve tube as they play, making it longer or shorter as required. Then, the player can learn to push the slide out a bit when using the 3rd valve in conjunction with the other valves. This makes it possible to keep all notes in tune.
Some brass instruments have a 4th valve which is normally made long enough to lower the pitch by 5 semi-tones. The 4th valve can then be used instead of valves 1 and 3. Also, valves 2 and 4 can then be used instead of valves 1, 2 and 3 – it will still be slightly sharp but much better than it was!
Another thing we can do, especially when playing higher notes on our instrument, is to use alternative valve combinations. E.g. on a cornet, there are 2 notes we have to play with all 3 valves pressed: low F#/Gb and low C#/Db. Unless we have a 4th valve (see above) there is no alternative for these notes. But for harmonics above them, there are alternatives: e.g. the next higher F#/Gb can be played (in tune) with just valve 2 pressed (because it is harmonic of B); the next higher note that can be played with all 3 valves pressed, A#/Bb, is normally always played with just valve 1 pressed, etc. See Yamaha’s interactive diagram showing alternative valve combinations (“fingering”).
Also, the skilled brass player is often able to keep notes in tune by the way they vibrate their lips. Remember it is the speed of these vibrations that determine the note that is played, and there is a surprising amount that the player can do to make the note a bit sharper (higher in pitch) or flatter (lower in pitch) just by the way they buzz, without pressing or releasing any valves, and without playing a higher or lower harmonic note (a different pitched note played with the same length of tube e.g. C and G). This skill is called “lipping”.