Brains and Membranes
Bassoon Reed Making by Christopher Millard
Chapter 20 – DONUTS – Part 1
Visualizing form and function is a critical skill in achieving better reeds. If you can imagine a clay coffee mug emerging from a donut, you might also see how the reed aperture morphs from the reed tube. In this chapter, I’ll explore the transformation of reed geometry from the butt end to the tip aperture and discuss how that evolving radial structure influences the behaviour of the reed.
Imagine a coffee mug made of modelling clay. You probably saw a demonstration of this idea in high school, where donuts and coffee mugs were used as an introduction to topology, a field which considers how an object’s shape can be substantially deformed without losing its core properties. In this case, just one hole!
Okay..this model is not quite right, is it? In actual reed making tube cane must first be cut and folded, which alters its identity as a ‘one hole’ object. Though we start with a single stick, the reed emerges from two flexible planes, which we shape, contort, and bind together. Only after building your blank can we go back to visualizing the reed as a long, extruded, and deformed donut!
Let’s do a quick overview of an actual bassoon reed. We start with a tube of cane – diameter @ 25mm – split it into quarters, gouge out the soft pulp on the inside, then using a shaper we remove enough from each of the pieces to create our typical arrowhead flare. This modified ‘stick’ is just a slightly rounded quadrangle, with a curve matching the original growth radius of the cane. It’s a memory of life in the field! As we gradually deform the material to follow this imposed shape, we must both reduce and expand that initial growth radius.
Consider the transformation of that piece of cane. Molding the butt end to a conical mandrel and binding it with wires and string produces a tube with about a 5mm interior diameter. Now, follow what happens with the ever-widening shape. There’s a gradual expansion of the curvature all the way to the tip aperture, where a cross-section suggests the radius of a much larger tube. You’ve significantly reduced the original growth radius in the tube and greatly expanded it in the aperture. Somewhere towards the mid-point of your finished reed, you’re likely to find a curvature matching the original growth radius of the cane. That’s a happy place for the cane, a kind of neutral position where the material is experiencing the least altered radius and the least internal stress.
Our forming techniques are necessarily aggressive, securing both a fitting for the reed on the bocal and a comfortably open radius for the embouchure at the other. All the shrinkage and expansion of the radius from bocal to tip places demands on the innate elasticity and resilience of arundo donax. The reduced diameter sections will try to spring open, requiring brass wire to harness the outward radial force. At the other end, the much-expanded radius at the reed tip will be inclined to close, requiring longitudinal strength to counteract the inward collapse.
Despite the forces we impose on the curvature of the cane, there will always be some residual memory of its original growth radius! It’s important to understand that our profiling and construction techniques encourage additional ‘imposed’ memories. We need to manage and balance these conflicting opening and closing tendencies. .
To understand the concept of an ‘imposed’ memory in wood, let’s imagine a curved laminate chair. Curved wood furniture is made by subjecting wood laminates to heat and moisture, producing permanent changes in the form and the resilience of the material. A piece of plywood can be transformed into an elegant piece of furniture which behaves as if it the wood had naturally grown this way.
Let’s explore what happens when we shrink or expand the natural curvature of cane. Earlier in this blog series I mentioned the term ‘elastic modulus’ – which is a material’s elastic resistance to deformation under stress. Cane demonstrates elastic modulus in both radial and axial [longitudinal] dimensions. That’s just a complicated way of saying that cane is flexible in three dimensions. Shrinking the radius of the tube is like tightening a violin string, creating more internal tension and more resistance to vibration, and a tendency to vibrate at a higher pitch. You might expect that expanding the radius thru the blades to the tip would be akin to loosening a string, producing less tension and slower vibrations. But this is not actually the outcome, because a deformation to a larger radius is still flexing and stressing the cane, and it still wants to return to its original radius. Think of it this way: if you constrict a 25mm diameter tube into a 10mm diameter tube it will want to open and if you force that same tube into a 100mm diameter it will want to close. Now, both actions stiffen the cane, but the radial enlargement out towards the tip occurs in softer material due to the profiling. More on this in a moment.
Arundo donax wants to retain the resilience of its original growth radius, but subjecting cane to the heat and conformational stress of blank building ‘overwrites’ much of that radial memory. The response of cane to mandrels, pliers, heat, and moisture becomes a permanent part of the reed’s identity after it dries.
We need a way to make Arundo donax pliable enough to establish and maintain this new curvature memory. Our principal tool is the profile. Without the removal of the bark, and the parenchymal material beneath it, we wouldn’t achieve all the necessary contours; nor could we take acoustical advantage of the more flexible material in the softer parts of the cane. This allows reed membranes [blades!] to respond to the complex pressure oscillations within the bore. Profiling reed blades gradually attenuates the innate radial memory of the cane, gradually weakening the elastic modulus along the longitudinal axis of those blades.
In Chapter 18 of Brains and Membranes, I described balancing ‘shell’ and ‘fixed bar’ behaviour. I’ll jar your memory: shell physics are strongly correlated to radial elasticity, fixed bar physics with axial [longitudinal] structure. These are the Yin and Yang of reed mechanics – not distinct or separate behaviors, but rather aspects of an integrated view. Membranes, trampolines, diving boards, etc… It’s where elasticity meets structure and delivers acoustically efficient response.
This rather esoteric discussion of the topological structure of reeds boils down to visualizing how the changes in radius might impact the stiffness of cane at any axial point in the blade membranes. We often get unexpected and unwanted irregularities in the radial transitions from collar to tip. I think intonation, response, and sound quality depend on successfully managing the transformations from small to larger radius.
- Radial compliance is bound to the shell behaviour of the membranes
- Axial strength reflects the functioning of the fixed bar and the longitudinal strength of the reed
Axial structure is just a fancy way of describing longitudinal stiffness… Diving boards, twanging metal rulers, etc… Some profile elements exaggerate longitudinal strength – spines and rails are the obvious examples. But axial integrity relies on more than profile design; our dimensions and our methods of tube construction are critical. Mandrels, shapers, wires, bevels, wrapping and glues all influence the longitudinal resilience of your reed and modify the contribution of fixed bar longitudinal behavior.
In Part 2, our Little Bassoonist will try to make practical sense of this…
Text by Christopher Millard
Read more about Christopher Millard. Chapter 1 – The Craftsman Chapter 2 – Can you explain how a bassoon reed works? Chapter 3 – Surf’s up! Chapter 4 – The Physicist’s Viewpoint Chapter 5 – The Big :Picture Chapter 6 – We’ll huff and we’ll puff… Chapter 7 – Look Both Ways Chapter 8 – Dialogue Chapter 9 – The Big Bounce Chapter 10 – The Incredible Shrinking Bassoonist Chapter 11 – A Useful Equation Chapter 12 – Goldilocks’ Dilemma Chapter 13 – Stairway to Heaven Chapter 14 – Reed MyLips Chapter 15 – Resonance Chapter 16 – Corvids & Cacks Chapter 17 – Lift Chapter 18 – Chickens and Eggs Chapter 19 – Chiaroscuro Illustrations by Nadina