For some general information on profiles, if you've tuned a full range of reeds, you'll have noticed some basic patterns. Low reeds are generally thick at the tip and thin close to the root of the reed, often even weighted at the tip because the starting sheet thickness didn't add enough weight by itself at the tip. Mid range reeds are more level seeming and high reeds go from thick at the root to thin at the tip. It is quite possible to make a set of reeds that are all flat, but you end up with low reeds that are much longer and high reeds that are even shorter. Reed profiling allows you to make a set of reeds that lets you get at least a reasonable volume match between the large low reeds and the tiny high ones as well as notes that all play at similar pressures, which is crucial to a decent instrument.
When you make a reed, the pitch is determined by the length, the stiffness and the mass of the reed. you can vary all three and still get the same note. The key is understanding how they work together. At the root, mass makes very little difference because the reed moves very little there, but stiffness counts a lot because that is the place of greatest bending stress. Stiffness counts very little at the tip because it does very little bending there, but mass counts a lot because that is the point of greatest motion (and inertia ) somewhere along the length of the reed, stiffness and mass have equal and opposite effects on pitch. You can change the reed thickness here with little effect on pitch ( the balance point moves as material is removed ), but can adjust the overall stiffness of the reed in this area.
Reeds are always in my experience thinner in this neutral area than would be required for pitch because a set of reeds built on straight line profiles are much too stiff. I have a little gizmo that measures reed stiffness, and a high G with a straigh line taper from root to tip will measure around 40 (units) where a properly profiled reed will measure around 8. This is a huge difference for two reeds with the same length and width. The difference is the reduction in the neutral area and the area above and below it to spread the effect out and create a smooth bending reed.
Low reeds with straight line profiles are also too stiff, though not as much. The problem there is that they will not spread the bending evenly across the reed's length and may fail prematurely because of excessive bending at the root. In order to get a even sounding set of reeds, low reeds need to be less stiff than mid range and high reeds less stiff than both of them. Ideally, the reeds will vary evenly from bottom to top in a sort of skewed bell curve.
Low large reeds need to have their stiffness reduced to keep them from overpowering the mid range reeds as well as to feel the same when played. Low reeds that are too soft however will be much more subject to the influence of air pressure on pitch, so there is a limit to how soft they should be compared to the mid range reeds. High reeds being quite small, need to be quite light in order to play at the same pressure as the lower reeds since the reed's stiffness follows a linear slope relative to size while the pressure acting on the reed varies geometrically.. We are aided in getting enough volume out of the higher reeds by the fact that they sit in the area of our hearing that is more sensitive even while their size is so much reduced.
Mid range reeds are more nearly level in profile, and in an ideal set, you might have one reed that was dead flat, but most of them still have a reduced center section to keep the stiffness down. This doesn't mean the center will be the thinnest part, only that it will be below a straight line taper.
Reeds need to bend evenly. Part of the overall profile is directed at this end result. Rather than removing metal from one location, you balance the removal both above and below to keep a smooth bend. Low reeds should taper back to full thickness close to the root to avoid a sharp bend and high stress area. High reeds need to be thinner back from the tip so it isn't just the tip that wiggles up and down.
One thing worth keeping in mind is that whan you remove metal, stiffness is effected more quickly than mass. It takes a lot less removal of metal at the root end of the reed to lower the pitch than it takes removal of thickness at the tip to raise it back again.
A last note, reeds are the result of the preferences of the maker. some favor lighter reed sets which while more responsive, have limited dynamic range and tend to be more on / off. Heavier reeds sets take a bit more effort to play, but have greater dynamic range and maximum volume. While the
Wheatstone folks used a surface grinder to generate uniform profiles of=ver a lot of instruments, Many reeds from other makes were done by hand and show the preferences of the person who filed them. There is no right profile, only a range of profiles that work. If you are replacing a reed, you want to match the character of the profiles used so your reed blends in rather than stands apart from the rest.
A last , last note, Side Tapered reeds are effectively partially profiled in width. They add stiffness near the base sideways rather than in thickness and can bend smoothly with less attention to the thickness profile. They allow slightly larger high reeds than parallel reeds, and side tapered reeds usually vary from nearly parallel low reeds to quite tapered high reeds, allowing a flatter thickness profile overall.
Edited by Dana Johnson, 23 May 2014 - 02:40 AM.