Brains and Membranes
Bassoon Reed Making
by Christopher Millard
Chapter 9 – The Big Bounce
Before we go any further, I want to introduce a new term to your reed making vocabulary – membranes.
It’s a nice, 100% organic word.
A membrane is a pliable sheet or layer – especially of animal or plant origin.
It comes from the Latin membranus,meaning skin. Skin separates and contains what’s within the body – while remaining pliable, compliant and responsive to our external environment. Reed ‘membranes’ separate and contain what’s within the bore – remaining pliable and responsive to that internal complexity as well as the external pressure from our lips.
The walls of the bassoon and bocal are mostly stiff and only slightly responsive to internal vibration. The top and bottom blades of our reeds are an extension of those walls, but they are highly compliant. Wood, rubber linings and metal walls give way to the ‘living’ membranes of the pressure-controlled reed valve.
Timpani heads are stretched membranes; indeed, they were originally made from calf skin. Their vibrational frequencies are determined by variable tension and to a much lesser extent the natural frequencies of the drum they’re attached to. A timpanist can control the pitch of his drum by altering the internal tensions of the membrane. This process is at play when we are designing profiles.
Reed membranes share similarity to drum heads [higher tension = higher frequencies] but governed by longitudinal, radial and diagonal elasticity. Compared to the quite broad pitch flexibility available to the timpanist, bassoonists deal with a much smaller range of frequency adjustments. The basic pitch is primarily governed by the length of bore. And while the difference between a very relaxed membrane [a soft, flat reed] and a very stiff membrane [a hard, sharp reed] may only be a quartertone in pitch difference, that small variation presents a universe of heartache.
Using the world membrane helps me to think of the behaviour of reeds in more holistic terms. I think we waste a lot of time thinking about how individual parts of the reed operate independently. [You might recall my reference to Mr. Schoenbach’s assertion that different notes came from different parts of the reed?] Now I’m able to think of each of the two membranes [top blade and bottom blade] as singular entities – stretching, contorting and vibrating in a totally interconnected way.
Have you ever jumped on a trampoline? Every part of it is interconnected. There’s no better way of imagining holistic, elastic behaviour.
Practice Milde while bouncing.
The reed pressure valve has a primary function – to modulate airflow by closing and opening. The two membranes [top and bottom blades] respond to the motion of air from our lungs. This ‘input response’ governs our need to design membrane profiles that are thinner at the tip and the sides, in order maximize and leverage the conversion of airflow into periodic vibration.
The idea of first blowing the reed closed is critical to understanding why we profile as we do. For the membranes to bend inwards they require the selective flexibility achieved by our approaches to profiling: the Bernoulli effect increases with air velocity, so it’s most pronounced where the gap between the membranes is minimal. Therefore, we profile the membranes to be more flexible in those regions, which explains the universal tendency to make tips and sides thinner than backs and centers.
We can’t make an attack if the tip is too thick. There is an immediate functional connection between thin tips and input response: the membranes must come together willingly to begin the dialogue between airflow and vibrating bore.
The mechanics of input response are governed by relative tensions of the membranes – from side to center, front to back and diagonally. All are connected at a cellular level. The combination of profile and internal structure determines how efficiently the reed responds to the Bernoulli force, both initiating and maintaining the sound.
Jumping on trampolines is actually a pretty useless way to learn Milde. But, it’s a great model for visualizing some of what reed membranes actually do.
If bassoons produced simple sine wave sounds with no harmonics, the reed/membrane/trampoline/timpani analogy would be really easy to visualize.
But acoustic musical instruments all include sound profiles with rich harmonics.
Reed membranes that are happily compliant with a specific harmonic tend to be compromised in unexpected ways by other harmonic components. I’ll explain…
If you are still jumping on that trampoline, consider this: there is usually a very large area that gives you good lift. Trampolines become less efficient as you move to the edges, but they remain accommodating to all kinds of bouncing. But the minute a second person joins you the behavior of the trampoline becomes more complex. Imagine you have a dozen people bouncing: everyone’s bounce impacts the sweet spots for everybody else. If you all coordinate your jumps at a single frequency you can effectively manage the trampoline’s elasticity. But if you all have independent jumping frequencies, the sweet spots are not evenly distributed, creating chaotic uncertainty about each individual’s bouncing success.
Our trampoline bouncers include very slow jumpers with large mass and slower bouncing preferences, average size jumpers with average size preferences and little, itty-bitty, fussy tiny ones with very high frequencies. The trampoline membrane has to make sense of all this – slower fundamental harmonics all mixed up with faster overtone harmonics. All this jumping starts to assume a repetitive character.
The fattest bouncers are happy to jump at 55hz, their close friends choose to bounce twice as fast [110hz] and their relatives bounce three times as fast [165hz] and their children like to go four times faster [220hz].
So imagine each jumper represents a specific bouncing frequency in the complex sound waves within the bore. The compression-rarefaction waves that the bassoon naturally likes to utilize are all pushing and pulling on the internal membrane surface, vying for energy and reinforcement. Different frequencies ask for different modes of flexing within each membrane; slower and wider flexing for the fundamental and quicker, more narrow flexing for higher harmonics. This describes output response, i.e. the membrane complying with the acoustic needs of the bassoon itself.
I can go back several paragraphs and repeat almost word for word: The mechanics of output response are governed by the relative tensions of the membranes. The combination of profile, cane resiliency and internal structure determines how efficiently the membranes comply with the internal acoustical forces, both responding to and reinforcing the vibrational frequencies within the bassoon.
There you go, a trampoline membrane operating as a musical instrument with a fundamental and a family of harmonics.
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 Chapter 20 – Donuts Part One / Donuts Part Two Doodles & Design by Nadina
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