The clarinet and the soprano sax are both about the same size. So why does the clarinet play so much lower? This is something I have often vaguely wondered about and then forgotten about pretty quickly. This time, I thought I’d do some research and see if I can actually find out why it’s the case.
The clarinet has a closed-end cylindrical bore, whereas the soprano sax has a closed-end conical bore. For a closed-end cylindrical bore, the fundamental wavelength is four time the length of the tube and for a closed-end conical bore, it’s twice the length of the tube. This gives about an extra octave on range for the cylindrical bore.
Both the clarinet and the soprano sax have one closed end and one open end. By this I mean that the mouthpiece is blocking one end of the tube (by tube I mean the main body of the instrument). The tiny hole between the mouthpiece and the reed is not significant here. The other end – the end where the sound comes out – is open.
The main difference between the clarinet and the soprano sax is the shape of the bore (that’s the actual name for the tube). The clarinet has a cylindrical bore. This means the width is the same all the way down it. This isn’t actually quite true, as it varies a bit at the ends, but the bit where the wave resonates is cylindrical. The sax has a conical bore. This means it’s wider at the top than the bottom and gets wider at a constant angle.
This difference in bore is the reason that the clarinet can play a lot lower than the soprano sax. There’s quite a bit of physics in the answer, but I’ve tried to simplify it as much as possible. There are some terms I’ll need to explain first, and then I’ll go into the actual reasons that the shape of the instrument determines its pitch.
How does sound resonate in a woodwind instrument?
Before I go into this section, I want to list a few terms that I’ll be using in the article. Firstly, when I refer to a sound wave, I’m thinking of a sine wave, something that looks like this:
- Wavelength – the length (usually in nanometres or microns) of a single repetition of the wave, e.g. the length from one of the highest points to the next highest point
- Frequency – how quickly the wave repeats (how squashed it is in time) – this determines the pitch of the note
- Amplitude – this is the distance from the highest point to the lowest point (again probably in nanometers) and determines how much energy the wave is carrying
- Periodic – a wave that repeats the same pattern with time, i.e., it cycles through the same set of positions
- Natural frequency – the frequency at which an object will vibrate without any external help (everything has a set of natural frequencies)
- Resonance – the increase in amplitude of a wave which has hit its natural frequency
- Waveform – a set of frequencies that make up a single sound
- Fundamental frequency (wavelength) – the lowest frequency (longest wavelength) of the waveform, which is the main pitch that you hear in a note
Sound travels through the air in a wave. If no sound were lost over time, the wave would look like this forever. In real life, the amplitude will decrease over time until the sound is lost (damping). The frequency of the wave gives its pitch and is measured in Hz. This is what we mean when we say that the A we tune to is 440Hz.
Any sound that you hear will have a waveform – it will be made up of a set of frequencies. The clarinet and the sax both produce sound when air is blown into the mouthpiece. The reed on the mouthpiece starts to vibrate, creating the waveform. This passes through the instrument, leaving at the first open hole it finds. The length it travels to get to a hole is a determining factor for the pitch. The other main determining factor is the shape of the bore the wave passes through.
A particular bore shape will have a particular set of resonant frequencies. The shape of the clarinet is different to the shape of the soprano sax, so their frequencies will be different. For an instrument with a closed-end cylindrical bore (like the clarinet), the fundamental wavelength is twice the length of the bore. This is the resonant wavelength in the tube, and dictates the sound we hear.
The difference with the cylindrical bore of the clarinet is that the fundamental wavelength is four times the length of the bore. This comes from doing some fairly complicated physics with wavenumbers which I won’t go into here. However, the fact that the fundamental wavelength that resonates in a clarinet bore is twice as long as the one that resonates in a soprano sax bore is the reason why the clarinet is able to play lower.
As we’ve already said, the frequency of the note determines its pitch. The wavelength is directly related to the frequency by the equation wavelength = speed of light/frequency. This means that when you change the wavelength, you also change the frequency, as the speed of light is constant. If you’ve changed the frequency, you’ve then changed the pitch.
We know the fundamental wavelength in a cylindrical bore is twice as long as the fundamental wavelength in a conical bore. The relationship between the wavelength and the frequency tells us that if the wavelength increases, the frequency decreases. A lower frequency means a lower pitch. Therefore, if the wavelength of a cylindrical bore is twice the length as a conical bore, the frequency of the cylindrical bore will be half the frequency of the conical bore. Therefore the cylindrical bore has a lower pitch.
With pitches, when you double the frequency, you go up by an octave. Here, we’ve doubled the frequency of the fundamental sax wavelength compared to the clarinet. This means the clarinet is capable of playing an octave lower than the soprano sax. In reality, this is not quite the case. The lowest note on the clarinet is D3, whereas the lowest note on the soprano sax is Ab3. This is just under a fifth higher than the clarinet. So why is this?
I don’t actually have the full answer to this question. My belief is that it just comes from the actual tone hole positions on the instruments. The lowest tone hole on the clarinet does not give exactly the same bore length as the lowest tone hole on the soprano sax. It is likely to be this difference that means that the difference in pitches isn’t exactly an octave. This part isn’t necessarily correct, but to me it seems the most obvious explanation.