Brains and Membranes
Bassoon Reed Making by Christopher Millard
Chapter 11 – A Useful Equation
I hope you are getting comfortable with visualizing the relationship of the reed to the bassoon. This holistic idea is something we will return to often. But for now, let’s move on to a basic design principle. Size.
Remember our little bassoonist, stuck inside the enormous reed cavity in her dream? All the space around her constitutes an extension of the bassoon bore.
Bassoon bores have a fairly consistent rate of taper; they are conical and therefore should eventually come to a point – an apex. That would be fine for our beer bottle sound production, but we need the energy generator of the reed, and it needs to fit onto the small end of the bassoon. So, we take a nicely tapered cone and truncate it by lopping off the first 25cm of the bocal.
The bocal has a Missing Conical Apex (MCA).
It’s useful to imagine what varying that missing apex might do to the pitch outcomes for the bassoon as a whole. We know that longer bores are flatter and shorter bores are sharper; the essential factor is volume.
A longer reed, a wider reed or a more open reed represent increases in the internal volume of the reed. If we consider a static, non-vibrating reed, it should be really simple to calculate the MCA of the bocal and build a reed with identical internal volume. The problem is, reeds can’t be static. They must be compliant – which is the whole point!
In fact, the reed cavity volume in any bassoon reed is WAY smaller than the theoretical MCA of any bocal. The actual internal volume of a typical reed would make it unplayably sharp if there were no modifying factor.
So, what’s missing in our analysis?
It’s the compliance of the cane.
We can express this most basic concept in different ways:
If you consider the flexibility of the membranes in the context of the internal volume of the reed you will come up with a functional equivalency.
…which is to say…
If you take a given dimension of reed and alter its compliance you will come up with a system that satisfies the missing bore volume at the tip of the bocal
…which is to say…
There are two balancing factors in designing a reed that serves the bassoon at A-440; size and behaviour
…and so forth…
Let’s simplify this and use an equation:
RV x C = MCA
RV means ‘reed volume’ and this is determined by how big the reed is in three dimensions (length, width, height aka L, W, H)
X means ‘is modified by’
C means compliance, which is an acoustician’s way of talking about overall elasticity, flexibility, stiffness, springiness, hardness etc.
= means ‘gives an approximation of
MCA is the idea that a truncated bassoon bore needs a reed valve that will function as the equivalent of the volume of the missing bocal tip.
If you recall the idea of Dialogue in Chapter 8, you could say that one partner in the conversation (the reed) has to be particularly flexible and engaging.
Let’s try out the equation and see whether it makes sense in terms of your own reed making experiences. We’ll plug in some ballpark figures.
Reed volume – you can actually test this volume with a syringe and find reeds ranging from .75 to 1.5 milliliters capacity
Compliance factor – suppose a scale of 1 – 10, where 1 is absolutely stiff and 10 as flexible as possible
MCA – We think of this in terms of functional pitch, not an actual numeral. But assume that a larger MCA will deliver something like A=440 and a smaller MCA will tend to A=447. Just remember, a larger missing conical apex volume will be flatter in pitch than one with a smaller MCA.
So, for the sake of argument we take two reeds of identical design but different compliance:
Reed A: RV [.95] X C [4] = MCA value [3.8]
Reed B: RV [.95] X C [6] = MCA value [5.7]
In this example, both reeds have identical internal volume, but Reed A is less compliant and produces a smaller MCA value. In normal language, we would say same size reed, but stiffer, produces a sharper outcome.
Now let’s consider two reeds of identical compliance but different in design:
Reed C: RV [1.05] X C [5] = MCA value [5.25]
Reed D: RV [1.30] X C [5] = MCA value [6.50]
In this example, Reed D has a larger internal volume and produces a larger MCA value. In normal language, we would say similar compliance reed, but larger volume, produces a flatter outcome.
These simple models probably reflect some of your own experiences. If we take two similar reeds and make one more flexible it will tend to play a little flatter. And if we take two similar pieces of cane and similar profiles, the smaller reed tends to play a little sharper.
RV, reed volume, is defined primarily by length and width. Height [openness] is a third factor but really confuses things for reasons we will dig into in later chapters.
You will have had experiences with reeds that are too flimsy and flat, with certain notes collapsing too easily (1st finger E and wing C#s are the first to go…) When you clip a tip, you are reducing the internal volume of the reed, and reducing the MCA value creating a sharper outcome. And if you make a reed narrower, you will usually find it easier to hold up the pitch. If all your reeds are too sharp, you will probably start increasing your length and the width of your cane.
Of course, anything you do to the dimensions of a reed will have unavoidable effect on its compliance. Clipping a tip not only raises the MCA value due to a reduction of internal volume, but also due to a reduction of compliance.
In the next chapters, I’ll talk about how responses are associated with adjusting the MCA value. I hope what will emerge is a realization that tuning and tone are irrevocably linked.
Eventually, we will come to discuss the often paradoxical observations that emerge in sophisticated reed making. These reflect the intersection and conflicts of some acoustical principles, especially the often competing physics of fixed bars and shell membranes.
But next week, a return to make believe.
Chapter 12 – The Goldilocks Enigma
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
Why, MCA!