And it’s back to the Acoustics stuff once again. Don’t worry, there will be some less science-y more melodeon-y posts soon!
This, the third part of this series is on how different reeds differ. The first part was an overview of Box Acoustics and the second part (updated recently on the advice of Olav Bergflodt, so give it another read) was on how the reed generated sound.
One can split the sound of a reed into ‘steady state’ (stable, established oscillation) and ‘transient’ (the process of the reed starting to sound). Both of these have an impact on the sound, but in different ways. I will be referring to both of these things throughout this series. In general, steady state is a lot easier to deal with than the transient, but arguably the transient is more important!
How do different reeds differ? They differ most obviously in their material parameters. The resonant frequency of a reed is dependent on the length (longer it is the lower the pitch), the thickness (thicker it is the higher the pitch), the density (denser it is the lower the pitch) and the stiffness of the material (the stiffer it is the higher the pitch). This explanation assumes a rectangular section, constant profile, perfectly clamped cantilever beam. It shows that different materials will produce different pitches, that longer reeds produce lower notes and so on.
Now, the explanation for the fundamental frequency of a reed doesn’t state that the width of the reed has any effect whatsoever on the sound. There are a few reasons for this. The first is that this explanation is only an approximation – it is a solution to a differential equation which does not completely describe the system. In particular it assumes that the vibration of the reed is planar – in one plane. In actual fact, there is a twisting mode of the reed, which is dependent on the width (although it is probably too high a frequency to make a real difference). In my previous post I mentioned that vortices might be formed on the sides of the reeds. I suspect that these vortices, which would be influenced by the width of the reed, have an appreciable impact on the sound. In addition, I suspect that the width also affects the transient response in some way. These may be subjects for another post.
More practically, altering the width of the reed alters the area of the slot. For the same scale reed, if the slot area is increased (i.e. if the width is increased), then the instrument will be louder, as there is greater airflow. The downside of this is that the air consumption of the instrument will then increase. If the slot area is decreased, by contrast (i.e. if the width is decreased), then the reed will respond quicker, as the pressure difference across it will be greater. Unfortunately, the frequency of a reed varies somewhat with blowing pressure, so a reed with a small slot area is at risk of going out of tune when played hard. So the width is a compromise, like so many other aspects of musical instrument design, balancing loudness, response, air consumption and pitch deviation. A way of getting round this is to make the reed tapered, meaning that the width at the tip is less than the width at the root. The effect of this is to improve the response for a given slot area, as the mass per unit length is less at the tip.
If we assume that we have a reed which is made from one particular material with a constant density (such as steel), then we can change the fundamental frequency through the length and the thickness. There are obviously infinite combinations of length and thickness which will result in the same fundamental. I am going to refer to the relationship between length and thickness as the ‘Scale’ of a reed (to borrow terminology from organ building). A ‘Long Scale’ reed is one where the length is long and the thickness thick, a ‘Short Scale’ reed is one where the length is short and the thickness thin. To a first approximation at least, the resonant frequencies of these reeds are identical, however their other characteristics are very different.
In organ building, according to Wikipedia, the larger the diameter of a given pipe at a given pitch, the fuller the sound becomes. With reeds, the longer the length of a reed at a given pitch, the quicker it responds. This is because a long scale reed requires less force than a short scale reed to deflect. It is true that a short scale reed has a greater pressure difference across it than a long scale reed, however this increased force is less than the difference in deflection force, meaning that long scale reeds respond quicker than short scale reeds. In addition, a ‘long scale’ reed is capable of much greater variation in volume, due to the increased size of the slot (greater airflow). On the downside, it uses up more air, meaning that the bellows need to be proportionally bigger. Bigger bellows mean less playing force for the same pressure, meaning that the playing style changes quite drastically. Finally, as with the width, short scale reeds are more vulnerable to pitch deviation. So the scale of the reed is an immensely important quantity, which affects all aspects of a box.
I suspect that the scale of the reed changes the sound of the box more radically than the quickness of response. A thought is that although at steady state the frequency content of the two reeds should be identical, at the transient stage the relative strengths of the different frequencies may be different, due to the two reeds being excited in subtly different ways. It requires more study to see whether this is so.
Up until this point, the profile of the reed (i.e. the thickness along the reed) has been assumed to be constant. This is not necessarily so. Indeed tuning the reed by removing metal alters the reed profile – it is therefore obvious that altering the reed profile has an effect on the sound! In the third year of my degree I proved that this was the case, that taking metal off the tip of a reed raised the pitch and taking metal off the root lowered it.
The profile of the reed has a greater impact than just the fundamental frequency however. Some reeds are fitted with a mass fixed to the tip and are known as “weighted reeds”. On many melodeons, the bass reeds are not long scale, but are short scale weighted reeds. This makes a lower tone for a shorter length (desirable for space reasons) with lower air consumption. They are also cheaper, as a box may have exactly the same length reed fitted for each bass note, but with a different tip mass.
Unfortunately there are drawbacks to using weighted reeds. At very low flow rates (i.e. at low bellows pressures) weighted reeds may have a similar response to unweighted reeds. However, at high flow rates they lag significantly behind unweighted reeds, something with which most box players will be intimately acquainted. I presume that this is because of the high mass per unit length at the tip causing the response of the reed to suffer. For this reason, high end boxes are increasingly being fitted with long scale bass reeds.
As an aside, it was recently pointed out to me that the scale of reeds going up a row on a box changes. I was at a loss to explain this until Ian Dedic reminded me that the ear has a varying response to frequency – hearing high pitches louder than low pitches. In order to make the volume of a row even therefore, the slot area will have to decrease as the pitch increases. One way of doing this would be to keep the scale constant and vary the width. However, the response of reeds also needs to be kept constant up a row, so the increased pressure of the width decrease would have to be balanced by a shorter scale, increasing the deflection force on the reed. And of course if a reed dimension is taken below a certain point it may no longer sound properly, due to manufacturing defects, viscosity effects and so on. Therefore the scale of reeds will have to change across the box in order to achieve a homogeneity of sound. Interestingly this is also true of organ pipes, although for different reasons.
Hopefully that illustrates the effects of changing the length, width and thickness of a reed. There is a lot of content in this post and some of it I am more sure of than others. So if you see something which you do not consider to be right then please let me know and I’ll amend it. The next post in this series will be on the plate, the slot and how the reed sits in them. Until then take care and enjoy this video, which has nothing whatsoever related to the above, but is an amazing spectacle (Thanks to Gary from l’Accordéonaire for bringing this to my attention).