Brains and Membranes
Bassoon Reed Making by Christopher Millard
Chapter 11 – A Useful Equation
Imagine yourself sitting inside your reed. All that space around you is part of the bassoon – It’s just a different shape than most of the bore.
Bassoon bores are conical with a fairly consistent rate of taper. Most cones come to a point, an apex, but as we need to fit a reed at the end of the cone we have to take that nicely tapered conical apex and lop off the first 25cm.
This truncated portion of the bocal is the Missing Conical Apex (MCA)!
It’s useful to imagine what varying the volume of 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 increases volume of the bore. If we consider a static, non-vibrating reed, it should be possible to calculate the missing portion of the bocal and build a reed with the same internal volume.
In fact, the reed cavity volume in any bassoon reed is significantly smaller than the theoretical MCA of any bocal. The actual internal volume of a typical reed would make it unplayably sharp. So, what’s missing in our analysis?
A vibrating reed is not static; its volume changes as it responds to the bassoon. The flexibility of the membranes expands the effective internal volume of the reed.
…which is to say…
If you take a given dimension of reed and adjust its compliance you will achieve the equivalent missing bore volume for that truncated bocal.
There are essentially two factors in designing a reed: size and flexibility.
Let’s think of it this way… RV x C = MCA
I’ll explain.
- 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 a way to think about design and trimming that explains a wide range of approaches to reed making. It’s the idea that a truncated bassoon bore needs a reed that will substitute for the missing volume at the bocal tip.
Recalling the idea of Dialogue in Chapter 8, you can see 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 – This is not an actual number. It expresses a relationship. Just assume that a large MCA will deliver something like A=438 and a small MCA will tend towards A=445. A larger MCA volume will produce a flatter pitch than one with a smaller MCA.
So, for the sake of argument we take two reeds of identical design but different compliance. I’ll make up some arbitrary numbers reed volume and 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 flexible and produces a smaller MCA value. Same size reed = stiffer = 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 so it produces a larger MCA value. Similar compliance reed with larger volume = 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.
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 effect 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.
By the way, reed volume is easily defined by length and width. The third dimension – openness] – is critical, but really confuses things for reasons we will dig into in a chapter.
In the next chapters, I’ll talk about how response can be associated with adjusting the MCA value. I hope what will emerge is a realization that tuning and tone are irrevocably linked.
There are 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.
Just for fun, let’s return to some make believe…
Chapter 12 – The Goldilocks Enigma
Chapter 1 – Starting Down The Path Chapter 2 – It’s A Simple Question? 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 MyLipsChapter 15 – Resonance Chapter 16 – Corvids & Cacks Chapter 17 – Chickens and Eggs Chapter 18 – Chiaroscuro Chapter 19 – Donuts Chapter 20 – Balance
Doodles & Design by Nadina
Why, MCA!