The harmonic series and brass valve combinations
If you play a valved brass instrument, you've probably noticed something strange: the same fingering can play several different notes. With no valves pressed, a trumpet can play a low C, a G, the C in the staff, an E, a G, and more. This guide explains why, using something called the harmonic series, and shows how valves fit into the picture.
What a partial is
When you buzz into a brass instrument, the air inside the tube vibrates. A tube of a certain length can vibrate in several ways: as one whole wave, in two halves, in three thirds, and so on. Each of those ways produces a different note, called a partial. Together, the partials form the harmonic series.
Your embouchure and air choose which partial you play. A looser, slower buzz gives a lower partial, and a firmer, faster buzz gives a higher one. That's why brass players talk about "finding the right partial."
| Partial | Trumpet, open (written) | Interval from the one below |
|---|---|---|
| 2nd | Low C | (starting note) |
| 3rd | G | Perfect 5th |
| 4th | C (3rd space) | Perfect 4th |
| 5th | E | Major 3rd |
| 6th | G | Minor 3rd |
| 7th | B♭ (quite flat, rarely used) | About a minor 3rd |
| 8th | High C | About a major 2nd |
Notice that the partials get closer together as they go up. That's why high notes are harder to hit accurately: the next partial is only a small step away.
How valves lengthen the tubing
A longer tube makes lower notes. Each valve, when pressed, sends the air through an extra loop of tubing, making the instrument longer and lowering every partial.
- Valve 2 lowers the pitch by a half step.
- Valve 1 lowers it by a whole step.
- Valve 3 lowers it by a step and a half (a minor 3rd).
Combining valves adds their effects. Valves 1 and 2 together lower the pitch a step and a half (the same as valve 3 alone). 2 and 3 lower it two whole steps, 1 and 3 lower it two and a half steps, and all three lower it three whole steps. With seven combinations (open plus six valve combinations), you can fill in all the gaps between the partials.
Trombones do the same thing with the slide (see Trombone slide positions). Each position, from 1st to 7th, lowers the pitch by a half step, just like the seven valve combinations.
Why 1-3 and 1-2-3 run sharp
Each valve's extra tubing is measured to lower the pitch of the open horn by the right amount. When you press two or three valves, the horn is already longer, so each valve's tubing makes a smaller difference than it should. The result: the combinations 1-3 and 1-2-3 play noticeably sharp.
How players fix it:
- Trumpet: use the third-valve slide ring to push the slide out on low D (1-3) and low C♯ (1-2-3). Many trumpets also have a first-valve slide trigger.
- Euphonium and tuba: many have a fourth valve, which can be used to replace the sharp combinations. Double horn players switch to the B♭ side instead.
- Alternate fingerings: on some notes, valve 3 can replace 1-2, and it's slightly flatter. Your teacher can tell you when that's better.
Same fingering, different notes
Because every fingering has its own harmonic series, one fingering can play many notes. Open on trumpet plays C, G, C, E, and G. Valve 2 lowers all of those by a half step: B, F♯, B, D♯, F♯.
The opposite is also true: many notes can be played with more than one fingering. The E in the top space of the staff on trumpet can be played open (the 5th partial) or with 1-2 (on a higher partial of that fingering). This is where alternate fingerings come from, and they're useful for tricky passages and tuning.
Brass Trainer shows a written note and asks for its fingering or position, and it accepts common alternates. When you answer, you'll hear the note, so you can connect the fingering, the partial and the sound.
Lip slur practice
A lip slur moves between partials on the same fingering, without using your tongue. It's the best way to train your embouchure to find partials accurately.
- Start small. Slur between two neighboring partials, such as open G and the C above it on trumpet. Go slowly and keep the air steady.
- Go through the valve combinations. Play the same slur open, then with 2, then 1, then 1-2, then 2-3, then 1-3, then 1-2-3. Each step moves down by a half step.
- Add partials. When two-note slurs are easy, add a third partial above.
- Use air, not pressure. Faster air helps you go up. Pressing the mouthpiece harder into your lips does not.