Clarinet

It is not common knowledge how old music - instrumental music - really is. What we learnt at school is probably outdated at best, but mostly really wrong. We use to think that instruments came up not long before Sumeria. But flutes from bones have already been well known and used in the Stone Age.

The oldest flute that we have today is from Baden-Wurttemberg, Germany, and is approximately 35,000 years old. It was produced from a swan's bone, at a time when drills were completely unknown. It has a nearly perfect pentatonic scale (like chinese music today).

This is probably no coincidence. Other very old instruments have the same scale which tells us that folks already had a clear sound system idea 35,000 years ago. But: You only need a correct scale system like this if musicians want to play together. Shepherds for example won't need this - playing solo - and therefore typical shepherd's instruments will have a completely different system (like Arabic scales) with which you can't play together - but then again, you will find those systems are well defined, too.

This old artefact with the perfect scale is no proof yet but you better get used to the idea that musical instruments and woodwind ensembles played in the Stone Age already - making music in ensembles seems to be less a hobby of a few but a basic part of being human.

How does a clarinet works?

The clarinet player provides a flow of air at a pressure above that of the atmosphere (technically, about 3 kPa or 3% of an atmosphere: applied to a water manometer, this pressure would support about a 30 cm height difference). This is the source of power input to the instrument, but it is a source of continuous rather than vibratory power. In a useful analogy with electricity, it is like DC electrical power. Sound is produced by an oscillating motion or air flow (like AC electricity). In the clarinet, the reed acts like an oscillating valve (technically, a control oscillator). The reed, in cooperation with the resonances in the air in the instrument, produces an oscillating component of both flow and pressure. Once the air in the clarinet is vibrating, some of the energy is radiated as sound out of the bell and any open holes. A much greater amount of energy is lost as a sort of friction (viscous loss) with the wall. In a sustained note, this energy is replaced by energy put in by the player. The column of air in the clarinet vibrates much more easily at some frequencies than at others (i.e. it resonates at certain frequencies). These resonances largely determine the playing frequency and thus the pitch, and the player in effect chooses the desired resonances by suitable combinations of keys. Let us now look at these components in turn and in detail.

The reed controls the air flow

The reed is springy and can bend. In fact it can oscillate like a spring on its own---for a clarinettist this is bad news: it's called a squeak. Normally, the reed's vibration is controlled by resonances of the air in the clarinet, as we shall see. But it's also true that the reed vibration controls the air flow into the clarinet: the two are interconnected.

Let's imagine steady flow with no vibration, and how it depends on the difference in pressure between the player's mouth and the mouthpiece. If you increase this pressure difference, more air should flow through the narrow gap left between the tip of the reed and the tip of the mouthpiece. So a graph of flow vs pressure difference rises quickly: it has positive slope. However, as the pressure gets large enough to bend the reed, it acts on the thin end of the reed and tends to push it upwards so as to close the aperture through which the air is entering (the arrow in the sketch at left). Indeed, if you blow hard enough, it closes completely, and the flow goes to zero. So the flow-pressure diagram looks like that in the graph sketched below.

The reed (as any clarinettist will tell you) is the key to making a sound. The player does work to provide a flow of air at pressure above atmospheric: this is the source of energy, but it is (more or less) steady. What converts steady power (DC) into acoustic power (AC) is the reed. The first part of the graph is something like a resistance: flow increases with increasing pressure difference. Just like an electrical resistance, an acoustic resistor loses power. So in this regime, the clarinet will not play, though there is some breathy noise as air flows turbulently through gap between reed and mouthpiece. The operating regime is the downward sloping part of the curve. This is why there is both a minimum and maximum pressure (for any given reed) that will play a note. Blow too softly and you get air noise (left side of the graph), blow too hard and it closes up (where the graph meets the axis on the right). (In the diagram above, the upper curve could represent a stiffer reed or a more open mouthpiece, or less lip force: in call cases, more pressure is required to close the reed.)

Readers with a background in electricity, seeing the region of the curve in which flow decreases with increasing pressure, will recognise this as a negative (AC) resistance. Whereas a positive resistance takes energy out of a circuit, a negative resistance puts energy into the circuit (as happens in eg. a tunnel diode oscillator). In the clarinet, it is indeed this negative AC resistance that provides the energy lost in the rest of the instrument. Most of the energy is lost inside the bore, in viscous and thermal losses to the walls, and a relatively small fraction is emitted as radiated sound.