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1st Edition

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We instruct our employees with access to your Personal Information that it is to be used only in adherence with the principles set forth in this policy and applicable laws. This approximation is crude, and in practice the wave extends somewhat beyond the first open tone hole: For the technically minded, we could continue the electrical analogy by saying that the air in the open tone hole has inertia and is therefore actually more like a low value inductance.

The impedance of an inductor in electricity, or an inertance in acoustics, is proportional to frequency. So the tone hole behaves more like a short circuit at low frequencies than at high. This leads to the possibility of cross fingering , which we have studied in more detail in classical and baroque flutes. The frequency dependence of this end effect means that the low note played with a particular fingering has a smaller end effect than does the corresponding note in the next register.

If the clarinet really were a perfect cylinder with tone holes, then the registers would be out of tune: This effect is removed by variations or perturbations of the cylindrical shape, including the shape of the mouthpiece, an enlarging of the upper region of the bore, and a gradual flare in the bottom half of the instrument, leading to the bell. Register holes Holes can also serve as register holes. For instance, if you play Bb3 call this frequency f o and then open the register key or speaker key , you are opening a hole one third of the way down the closed part of the instrument.

See the middle diagram below. This hole disrupts the fundamental, but has little effect on the higher harmonics, so the clarinet 'jumps up' to F5 3f o. Where to put it? The acoustically obvious place to put a register hole is at a pressure node of the upper note which is also a region of large pressure variation for the lower note.

Clarinet acoustics: an introduction

Opening the bore to atmospheric pressure at a pressure node makes no difference to that note. The trouble is that each note in the upper register has its pressure node at a different position. One can imagine a clarinet that had a separate register hole for each note, but that would be a lot of keys. In fact, only one register hole is used for the second register from B4 to C6. Looking at the diagram below, we see that it its position is a compromise: This is not a big problem in practice.

The register hole is small, so it is not really a 'short circuit', except at low frequencies. We explain how the mass of the air seals the hole at high frequencies below. So it does not too much affect the third and higher harmonics. It does however disrupt the fundamental, and that is its purpose: We mention in passing that the saxophone has two dedicated register holes for the second register and an automated mechanism that allows only one key to operate the hole appropriate to each end of the range.

Multiple register keys have been tried on the clarinet, but have never become popular. The speaker key is the register key used for the second register. In higher registers, other register holes are used: This hole is designed primarily as a tone hole, so it is bigger than it need or should be for an ideal register hole.

This defect is not so important because it is used only for high frequencies, where its inertance is large. However some players partly cover this hole half-holing when using it as a register hole. Let us open an aside to answer a question that has been asked a few times: What happened to the fifth harmonic? When we play E3, the reed vibrates at the frequency of E3 about Hz for a Bb clarinet. In a steady vibration, only harmonics odd or even of this frequency are possible, and they are exactly harmonic. See How harmonic are harmonics? The odd harmonics are supported by the resonances of the bore, and so the resultant sound spectrum is rich in odd harmonics but has weaker even harmonics, at least at low frequencies.

See How the reed and pipe work together. When we play B4 , the reed vibrates at the frequency for this note about Hz for a Bb clarinet , which is three times the frequency of E3. Again, in steady vibration only harmonics odd or even of this frequency are possible. The fifth resonance of E3 approximately G 5 is still present, as the impedance spectrum for B4 shows, but there is nothing to put energy into a vibration at that frequency. Observe also that we are now in the clarino register about which see the general comments on the page for B4.

The resonances that one might have expected to support the 3rd and 5th harmonics of B4 — i. However, the acoustic response of the clarinet is strong enough to help all of the harmonics of the reed to some extent, and the resultant sound spectrum has no strong differences between even and odd harmonics.

We return to discuss register holes in more detail below , after we have discused the frequency response. Cross fingering On the modern clarinet, successive semitones are usually played by opening a tone hole dedicated to that purpose. Being a closed, cylindrical pipe the clarinet overblows a twelfth, and so one would need eighteen tone holes to cover the chalumeau and throat registers before repeating fingerings using the speaker key as a register hole. Because players don't have this many fingers, the clarinet requires keys and clutch mechanisms, so that one finger can close or open two or more holes.

When cross fingering is used, it is usually used to control other holes. For instance, one of the fingerings for the note B3 is a simple fingering: The other is a cross fingering: An open tone hole connects the bore to the air outside, whose acoustic pressure is approximately zero. But the connection is not a 'short circuit': So the pressure inside the bore under a tone hole is not at zero acoustic pressure, and so the standing wave in the instrument extends a little way past the first open tone hole. There's more about this effect under Cut-off frequencies.

Closing a downstream hole extends the standing wave even further and so increases the effective length of the instrument for that fingering, which makes the resonant frequencies lower and the pitch flatter. The effect of cross fingerings is frequency dependent. The extent of the standing wave beyond an open hole increases with the frequency, especially for small holes, because it takes more force to move the air in the tone hole at high frequencies.

This has the effect of making the effective length of the bore increase with increasing frequency. As a result, the resonances at higher frequencies tend to become flatter than strict harmonic ratios. Because of this, often one cannot use the same cross fingerings in two different registers. Because the clarinet's tone holes are relatively large, cross fingering makes only modest changes to pitches in the chalumeau and clarino registers, but they can sometimes be useful in adjusting the pitch. A further effect of the disturbed harmonic ratios of the maxima in impedance is that the harmonics that sound when a low note is played will not 'receive much help' from resonances in the instrument.

Technically, the bore does not provide feedback for the reed at that frequency, and nor does it provide impedance matching, so less of the high harmonics are present in the reed motion and they are also less efficiently radiated as sound. See Frequency response and acoustic impedance. To be technical, there is also less of the mode locking that occurs due to the non-linear vibration of the reed.

As a result, cross fingerings in general are less loud and have darker or more mellow timbre than do the notes on either side. You will also see that the impedance spectrum is more complicated for cross fingerings than for simple fingerings, especially in the region around 1. We have studied cross fingerings more extensively on flutes than on clarinets, by comparing baroque, classical and modern instruments. We have not yet studied a chalumeau or classical clarinet to compare with the modern instrument.

See cross fingering on flutes or download a scientific paper about crossfingering. Other effects of the reed As well as controlling the flow of air, the reed has a passive role in clarinet acoustics. When the pressure inside the mouthpiece rises, the reed is pushed outwards. Conversely, suction draws the reed in towards the bore.

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Thus the reed increases and decreases the mouthpiece volume with high or low pressure. Techncially, we say it is a mechanical compliance in parallel with the bore. Indeed, it behaves a bit like an extra volume of air a millilitre or two, depending on hardness , which could also be compressed and expanded by changing pressure in the mouthpiece.

It has the effect of lowering the frequency of each resonance a little. However, soft reeds move more than hard reeds, so soft reeds lower the frequency more than do hard reeds. Further, this effect is greater on high notes than on low, so soft reeds make intervals narrower and hard reeds make them wider. This is useful to know if you have intonation problems.

An Introduction

Cut-off frequencies When we first discussed tone holes , we said that, because a tone hole opens the bore up to the outside air, it shortened the effective length of the tube. For low frequencies, this is true: For high frequencies, however, it is more complicated. The air in and near the tone hole has mass.

For a sound wave to pass through the tone hole it has to accelerate this mass, and the required acceleration all else equal increases as the square of the frequency: So high frequency waves are impeded by the air in the tone hole: Low frequency waves are reflected at the first open tone hole, higher frequency waves travel further which can allow cross fingering and sufficiently high frequency waves travel down the tube past the open holes. Thus an array of open tone holes acts as a high pass filter: This is one of the things that limits the ability to play high notes on the clarinet.

The stiffness of the reed is another: The player can alter the cut-off frequency, and this is one of the effects used to achieve the spectacular glissando in the opening bars of Gershwin's Rhapsody in Blue. The player begins by gradually sliding the fingers off the tone holes, with the principal effect of changing smoothly the end effect at the open tone hole, and so the pitch. This provides most of the glissando up to the thorat register. From this register up, the player changes the position and force of the lower lip on the reed, thereby changing its natural frequency and also uses the resonances in the vocal tract.

Normally, the resonances of the instrument are so strong have such high acoustic impedance--see below compared with those of the vocal tract that the latter make only modest changes to the pitch. However, the player can reduce the strength of the instrument resonances by lowering the cut-off frequency below that of the note being played. To do this, the fingers are kept very near to the tone holes, partially covering them, so that the tone holes are effectively very small.

In this state, the resonances of the vocal tract can be stronger than those of the instrument, so the note played tends to follow that of the tract resonances, which the player increases smoothly — with some considerable help from the change in the natural frequency of the reed as the player's bite changes simultaneously. There is a detailed discussion of these effects in this paper. There is a more detailed explanation of cut-off frequencies and their effects on this page.

Frequency response and acoustic impedance of the clarinet The way in which the reed opens and closes to control the air flow into the instrument depends upon the acoustic impedance at the position of the reed, which is why we measure this quantity. The acoustic impedance is simply the ratio of the sound pressure at the measurement point divided by the acoustic volume flow which is just the area multiplied by the particle velocity.

If the impedance is high, the pressure variation is large and so it can control the reed. In fact, the resonances, which are the frequencies for which the acoustic impedance is high, are so important that they 'control' the vibration of the reed, and the instrument will play only at a frequency close to a resonance. There is simple explanation on What is acoustic impedance and why is it important? The section below shows how the major features of the clarinet's shape give rise to its acoustic impedance spectrum, and thus to how it operates.

This figure shows in black the calculated impedance spectrum for a simple cylinder the impedance is given in decibels: A suitable reed attached to the input of this tube would play near the frequencies of the peaks, which are in the ratios of the odd harmonics 1: The curve in red is for the same cylinder, with a simple bell at the end.

Note that the bell makes the pipe longer, so each peak and trough has been moved to lower frequencies, as expected. Note however the change in the overal shape: This is because the bell helps the sound waves in the bore to radiate out into the air. Incidentally, the presence of a large, effective bell is what makes brass instruments loud: More sound radiated means less sound reflected, so the standing waves are weaker.

See a Problem?

This effect is less noticeable at low frequencies: Incidentally, this frequency dependent effect of the bell is what makes brass instruments brassy: The effect of the bell is that of a high pass filter: In this, it acts much like the cut-off frequency effect of the tone holes. In fact, one important purpose of the clarinet's bell is to provide a high pass filter for the lowest few notes, so that they have a cut-off frequency and so behave more similarly to the notes produced with several tone holes open.

We could state this another way: For the few notes mentioned, however, few or no tone holes are open, so the reflection condition is different, and so a purely cylindrical clarinet would have a noticeably different timbre for these few notes. So the bell performs a similar function for these notes.

Clarinet acoustics: an introduction

At frequencies well above the cut-off, the bell has other functions, including directional radiation of high frequencies. So that is one reason why the clarinet departs from its approximately cylindrical shape for the last few tone holes. It is also non-cylindrical for a few centimetres at the other end. Which brings us to the effect of the mouthpiece. Here, the red curve is the same as the one we saw above: Now the black curve is for a cylinder plus a bell plus a conical constriction at the opposite end, which has approximately the same effect as a mouthpiece: This has several effects.

First, it raises the impedance overall. This is because it functions like a horn or an impedance matching transformer, connecting a small area where the same flow would require more pressure and therefore high impedance to a large area. Second, it does this more effectively at high frequency for maxima all of which are shifted by dB than for minima where the high frequency minima are much less deep than are the low frequency minima. This however is not important to the clarinet, because it operates at maxima, but is an important consideration in the design of flutes. Third, it makes the peaks and troughs asymmetric.

At high frequencies, the minima move to lower frequencies while the maxima occur at higher frequencies. Of course the bore is not exactly cylindrical: The effects of these are to make subtle differences to the relative tuning of the registers. Vocal tract effects In the simplest model, the mouth is considered as a source of high pressure air, and the reed is loaded acoustically only by the acoustic impedance of the bore of the clarinet, which is downstream.

The acoustical effects of the vocal tract upstream are often small.

Brass instrument (lip reed) acoustics: an introduction

They can, however, be important and even dominant if the player produces a resonance in the vocal tract whose acoustic impedance is comparable with that of the bore. This is easier to do in the higher registers, where the instrument's resonances are weaker. Vocal tract resonances are important in various effects including pitch bending and the famous glissando from Rhapsody in Blue.

Here is a scientific paper on vocal tract effects in the clarinet — more are listed below. The effect of reed hardness In the preceding section we have ignored the compliance of the reed , discussed above.

This acts in parallel with the bore, and its impedance decreases at high frequency, so its effect is to reduce the rise in impedance with frequency: Further, the very high resonances are weaker and occur at lower frequency when you use a soft reed. On this figure, the single dots are the experimentally measured impedance spectrum for E3 , with a value of the compliance corresponding to a hard reed. The continuous line actually the experimental points joined together shows the spectrum for a soft reed.

At low frequencies, there is not much difference, but you can already see a slight difference in frequency: As you go to higher frequencies, you see that the soft reed gives lower peaks. Lower peaks are harder to play, so the hard reed makes it easier to play high notes. Unfortunately, a hard reed also makes it easier to play squeaks. To understand more about the detailed shape of these impedance curves, see the discussion of the experimental results for E3.

More about register holes Now that we know about impedance spectra, we can better understand the effect of register holes, which we met above. In the graph below, the single dots are the experimentally measured impedance spectrum for E5 , which plays at the second maximum of the curve. The continuous line is that for C 6 , which plays at the third maximum.

The only difference in fingering is that the hole for the left index finger is opened, and here acts a register hole. Notice that its effect is small at high frequencies. As we saw above , the inertia of air in the hole effectively 'seals' the hole, so that high frequency waves pass by as though it were closed. At low frequencies, however, the effect is greater, and this register hole substantially reduces the height of the second maximum.

It also raises its frequency, and takes it out of the harmonic series with other peaks. These effects, especially the former, make the second peak harder to play, and so provided you use the appropriate embouchure , the instrument will play the third maximum, which is C 6. We have not mentioned the first maximum. It has already been weakened and shifted by the speaker key, which is open here. However, its maximum is not all that weak and a careless embouchure and low blowing pressure could find you dropping down to a muffled low note near that frequency.

Further, the fourth peak is pretty high, too. With a hard reed and blowing hard, there's a danger of jumping up to this note, too. Which is why the altissimo register is hard to play. There is more discussion of the altissimo register on the experimental page for C 6.

More detailed information and your questions Now it's time to look at the set of measured impedance spectra and relate them to the sounds and sound spectra produced. Go to clarinet acoustics and click on the names of the notes. Or, if the answer's not there, you can ask.

More papers on music acoustics are listed here.