How Trumpets Work

Table of Contents

About Sound

Sound is the human perception of variations in air pressure. Musical notes are regular, repeating variations in air pressure typically created by a vibrating string, reed, or membrane. The speed of these variations determines the pitch of the sound (faster is higher, slower is lower) and is measured in cycles per second, or Hertz (abbreviated Hz). The range of human hearing is roughly between 20 Hz and 20,000 Hz, with 20 Hz being the lowest rate of vibration actually perceived as sound (slower is more like a feeling), and 20,000 Hz (or 20 kHz) being the highest note that most people can hear. So Music is Physics!

For example, the typical tuning pitch of an orchestra is A440… 440 Hz. The nature of human hearing is geometric, with each successive octave being either two times faster (e.g. A above the treble staff at 880Hz) for ascending octaves, or half as fast (e.g. A below middle C at 220Hz) for descending. The so-called “even tempered” scale fills in the chromatic notes, with each successive note being the twelfth-root-of-two times the frequency of the next lower note. So, Music is also Math!

Tone and Timbre

Why is it that every instrument makes a different sound, even when playing the same pitch?

The reason is that most notes (that is, sounds at a certain pitch played by an instrument) are actually complex sounds built of a fundamental pitch and a series of “overtones” or partials that are softer (lower in volume) than the fundamental pitch and that, combined, create a characteristic waveform (see below). This gives  the note its characteristic tone quality or timbre (pronounced TAM-ber). This is why you can recognize the sound of a specific person’s voice, or a specific musical instrument. The characteristics of each instrument, each mouthpiece, and in fact each player, determines the timbre of that player’s sound.

How does a Trumpet Work?

In the case of brass instruments, the lips form a vibrating membrane. The trumpet is fundamentally a cylindrical or conical tube of a specific length (the open Bb trumpet is about 1.48 meters or 4 ft 10 inches long). The trumpet is a “buzz-lipped aerophone”; in other words, a wind instrument where the vibration of the air column is created by buzzing the lips.

Each specific length of tubing has a characteristic, fundamental pitch, which has a “standing” wavelength exactly the same length as the tube. In the case of the Bb trumpet, the fundamental is the Bb on the second line of the bass clef, an octave below the Bb below middle C. Additional notes are enabled in three ways:

  1. By “overblowing” the fundamental to reach successive harmonics a.k.a. overtones (e.g. concert Bb, F, Bb, D, F, etc.), each of which is an integer multiple of the frequency (= integer fraction of the wavelength) of the fundamental. This is the way natural trumpets such as bugles work. These instruments are limited by the spacing between the partials to “bugle calls” until they reach the high register. 
  2. By adding additional lengths of tubing to create a longer instrument, thus creating a lower pitch. Trombones use slides to lengthen their tubing. Trumpets, cornets, horns, euphoniums, and other valved instruments use valves that divert air into one or more crooks of different lengths. This allows the instruments to fill-in the chromatic notes between the harmonics.
  3. A combination of the two, above. 

The Harmonic Series

The resonating frequencies of a brass instrument are determined by the length of the tubing, starting with “the fundamental”, which is the lowest note on the instrument. In theory, there is no limit to how high a brass instrument can play, as long as the player has the strength and skill to continue overblowing the fundamental. In practice, the fundamental is rarely if ever played. A high school player should expect to have a 2-½ octave range… from low F# to high C, but a professional — especially a high-note specialist, will typically be able to play an additional ½ to 1-½ octaves… to “double-high C” and sometimes beyond!  And it is possible to play below the low F# (these notes are called “pedal tones”), once you get the hang of it (see The Warm-Up). 

The harmonic series is based on integer multiples of the fundamental frequency. For example, the open notes of a trumpet (written) are shown below. Each successive note is an integer multiple higher than the one before, i.e. if the fundamental C is x (in fact, x in this case is approximately 130.813 Hz), the octave C is 2x, the next interval (G) is 3x, the next octave C is 4x, etc. Note that each octave is 2x the previous octave, i.e. 2x, 4x, 8x, and 16x. This also applies to the other notes, e.g. the G’s are 3x, 6x, and 12x. Again, Music is Math!

To be perfectly accurate, the above explanation is a simplification of the actual physics of brass instruments. The reality is much more complex. The trumpet acts as a closed-ended resonator, and the interplay of the mouthpiece, tubing, and bell work to enable the entire overtone series. If you are interested in more detail on the physics of the trumpet, here are a few references:

  1. Brass instrument (lip reed) acoustics: a collection of linked pages on the University of New South Wales (Aus) website. This site has a particularly excellent and complete explanation not only of brass acoustics, but of others. 
  2. Musical Acoustics (trumpet): a collection of linked pages on the Georgia State University, physics website
  3. Everything Trumpet: an introduction by the late, great Reynold Schilke, with a number of links, some of which (including the two above) actually still work 🙂

What the Valves Do

Valves (and trombone slides) add additional tubing, or crooks, to the instrument, which lengthen the overall instrument and lower the ENTIRE overtone series. Trombone positions (i.e. “2nd position”, etc.) represent successive half-step lengthenings of the fundamental (1st position) tubing. Other brass instruments do this with valves. These valves are very consistent between instruments in the way that they work:

  • The second valve lowers the pitch of the open instrument by one half-step
  • The first valve lowers the pitch of the open instrument by two half-steps
  • The third valve lowers the pitch of the open instrument by three half-steps
  • The fourth valve (when there is one) typically lowers the pitch of the instrument by five half-steps, in order to enable filling the gap between the fundamental and first harmonic.

The pitch can be lowered further by combining valves. For example, 1-2 combination lowers the pitch by 3 half steps, just as does 3rd valve, which means that 3 is a universal replacement for 1-2. The following table shows how this works:

So the valves can lower the pitch of the trumpet chromatically to F# below low C, and can fill the gap between low C and middle-G in the treble staff. From there, fingerings start to overlap, creating an increasing number of alternative fingerings. Below are common alternate fingerings:

Pitch Tendencies of Fingerings - the Math

Let’s use a Bb trumpet as an example. The open length of a Bb trumpet is about 58 inches. In an even tempered scale (as on a keyboard), each successive rising half step is the 12th-root-of-2 higher in frequency than the note below it. If you think about this, it means by the time you get to the 12th note of the chromatic scale, you are 2x the previous octave, which is the correct ratio for octaves.

So the 2nd valve has to add the 12th-root-of-two (minus 1) to the length of the instrument, or about 3.5 inches (the actual number is  3.448859… but let’s keep it simple) to the length of the open trumpet. The 1st valve has to add the 6th-root-of-2 to the instrument to achieve a two step drop (12th root times 12th root), which is 7.10279… call it 7.103 inches to the trumpet. But wait! 7.1 inches is more than 2 x 3.5 inches! That because the lengths are not additive, but multiplied. Now comes the fun: to lower the pitch by 3 half-steps, you need to add (the 12th root x 12th root x 12th root = 4th root = ) 10.974 or almost 11 inches, which is more than 3.5″ + 7.1″ !! This means that the 1-2 combination will be sharp, which necessitates adding about 0.4″ using the 1st valve slide to bring it down to pitch. Of course, if you’re good, you can lip it down, but that would cause the note to lose its focus. 

Each successive, additive fingering — i.e. 1-3 and 1-2-3 — creates a similar but even greater challenge, which is why it is critical for us to learn to use our 1st and 3rd valve slides when we face these fingering combinations.

The only caveat is that there are times when you WANT to be a bit sharper (or flatter!) than the even tempered note, such as when you are playing the 5th of a chord (or sometimes the root, if the players playing the 3rd can’t move their note).  You can read about this in the section entitled Intonation.

Bottom line: let your ears be the judge!