How (Natural) Brass Instruments Work

Published by Jeremy on 2023-07-03

Introduction

One thing that I've noticed is that it's hard to find concrete information on the physical mechanics of brass instruments- and all the sources that I can find require an understanding of how pipes resonate. I'm guessing that most people do not know how exactly pipes behave, or if they knew, have probably forgotten. So with that in mind, I want to try and attempt a more... accessible explanation. So, here goes nothing:

To try and reduce the amount of concepts that I need to explain, we're going to simplify things. Most brass instruments have valves- but we're going to ignore those pesky valves for now. Right now, we are going to stick to the valveless, or natural, horn.

Pipes?

So, firstly: brass instruments are just long brass tubes wrapped into a specific shape. So to understand how brass instruments work, first we must understand how pipes resonate.
Remember, specific sounds have a frequency. Low notes have a low frequency, and higher notes have a higher frequency. Pipes will only resonate- or amplify- for certain frequencies. The lowest note that a pipe can amplify is called the fundamental frequency, or first harmonic. The frequency of this low note is dependent on the length of the instrument- a fact we will come back to eventually.

Open vs Closed End

Pipes behave differently depending on which sides are open- they resonate differently if both ends are open than if only one end is. We play brass instruments by placing the lips inside a mouthpiece, creating a small aperture (or opening) which air flows through. This aperture is small enough where it might as well be closed- so basically, brass instruments are tubes with only one open end.
With a closed end pipe, it only amplifies odd harmonics- it only amplifies odd multiples of the fundamental. So, say our fundamental frequency is 110 hz- the next pitches we can play are 330 hz, 550 hz, 770 hz, etc. These are the odd multiples- the fundamental multiplied by odd integers like 3, 5, & 7.

Problems with Pipes

Well, you might be thinking that the trumpet isn't just a straight tube that's been coiled into a funky shape- and you're right. This pipe of ours can only play a set range of pitches, and most don't match notes. Let's look at why.

Go to Google and look up a tone generator, and listen to these frequencies: 110, 220, 440, 880, and 1760. They all probably sound similar, just some are higher pitched and some are lower pitched. That's because according to music (and how our brain interprets sounds), these are all the same note- they're all an A. Weird, right! Now, look at those numbers again. See how they each are double the previous frequency? In music, to go up an octave (basically, playing the same notes but higher pitched) requires you double the frequency. So going to a different note (such as C to C#) isn't a fixed frequency change, it's proportionate. Every note in music is related to the other notes by a ratio- not a fixed difference, but a ratio.

The problem is most of the frequencies we can play on a tube are sort of.... worthless. Remember, all we get are odd pitches- which means that not only are there many notes on these even multiples we can't play. we can't even play octaves. That, however, is a problem we can solve.

The Bell and Mouthpiece effect

It's good that we have all these frequencies we can play, but we really want some different notes. That's where the bell and mouthpiece come in. Currently we're only interested in one aspect of their role- they adjust the pitches we play at. The bell tends to raise these pitches, and the mouthpiece helps to limit the amount the higher notes are raised by. This has a pretty cool side effect- instead of being able to play 110, 330, 550, and 770 hz, (with a proper bell and mouthpiece) our instrument will play at 220, 330, 440, 550, 660, and 770 hz! We're losing the fundamental frequency, but now we can actually do fun things like play octaves (like jumps from 110 to 220 hz, 220 to 440 hz)!

Problem solved?

Well, no. Notes aren't perfectly adjusted, and we still don't have many notes in the low range. But recall: the rate at which we get we get new frequencies we can play at is faster than the rate at which we get new notes. Let's go with a slightly different example where our fundamental frequency is 55 hz. Because of how the bell and mouthpiece work, we lose the fundamental but gain even harmonics above it. Here's a table of the frequencies we can play at, and the pitch (I will include the fundamental but remember it's not a playable note).

HarmonicFrequencyNote
155 hzA1
2110 hzA2
3165 hzE3
4220 hzA3
5275 hzC♯4
6330 hzE4
7385 hz~G4
8440 hzA4
9495 hzB4
10550 hzC♯5
11605 hzD𝄲5
12660 hzE5
13715 hzF𝄲5
14770 hz~G𝄳5
15825 hz~G♯5

At the beginning of our range, we can only play As and an E, but as we go up in our range more notes start to appear. So when instruments like the natural trumpet were popular, melody parts had to be played very high up in the range. And thus you couldn't even use modern conveniences like piccolo trumpets for the high parts!

And what's with those weird symbols? Well, if you see 𝄳 or 𝄲, those are special symbols called half sharps and half flats. The regular ♭ and ♯ mean that we're talking about a note which has been raised or lowered by half a tone, or a semitone. Our half sharps and half flats denote a note which has been raised or lowered by a quarter tone- or half a semitone. And the notes with a tilde (~) in front of them are very... inexact, and will also require you to correct the pitch before they're useful.
Most brass instruments- and even many natural horns- featured a variety of pitch adjustment mechanisms, and players also often used techniques no longer taught today. But, we'll get into that at a another time.

Conclusion

So, brass instruments are funky pipes. That's it! I plan on doing another piece on pitch adjustment- toneholes, keys, valves, tuning and hand slides, and even a few techniques that players use. When I write that piece, I'll add a link on this page- if there's no link, it's not written yet!

And as for the resources I used- give these a look. They go more in depth than I did- especially the first link. The general concepts, & note pitch equations