Brains and Membranes

Bassoon Reed Making by Christopher Millard

Chapter 18 – CHICKENS AND EGGS

Matching profiles, shapes and dimensions are critical steps in reed making.  As I argued in Chapter 11 – A Useful Equation – there is a logical balance between volume, mass and compliance.  To satisfy the bassoon’s need for a workable missing conical apex, larger reeds need decreased compliance and smaller reeds need increased compliance.  It’s a simple relationship: more flexibility is required to make a small reed happy, less flexibility is necessary for the larger reed, so we make thicker profiles for Papa Bear reeds and thinner profiles for Baby Bear reeds.  The principles of dialogue, response, resonance and tuning underly this basic relationship between size and flexibility.

Reed design takes on a whole new level of complexity when we discover that different kinds of profiles seem better suited to different sized reeds.  Spines, rails, tips, channels and hearts are all part of our vocabulary and how we visualize our ideal designs.  It seems clear that different profiles seem specifically suited to different shapes and dimensions.  As we experiment and evolve, we juggle back and forth between changing shapes and changing profiles.  Experimentation and an open mind will always lead to new investigations.  Try this, that…soon we are overwhelmed with variables.  But what comes first…the profile or the shape?? To answer this, we need to do a brief dive into an area of reed physics that I’ve not yet addressed.

When I was a young student at the Curtis Institute in the early 70’s, I made weekly pilgrimages to the Academy of Music to hear the Philadelphia Orchestra.  Bernard Garfield’s extraordinary artistry illuminated every passage he played.  The tone was always resonant and warm and proved the perfect vehicle for his sophisticated musicianship.  Though he was not my teacher, I studied his preferred approach to reed dimensions and profiles.  Garfield’s profile included a delineated tip area, a spine, a pronounced heart and thinning of the sides to bring this smaller dimension reed into perfect tuning.

Most of you will have pursued some form of this very standard, heart-focused profile.  It’s a really good model and one that made a lasting impression on me.  As the years passed and my own preferences for response, embouchure, and tonal character evolved, I began moving to larger reeds with longer tip tapers, eventually eliminating that little area of thickness that we call the heart.  Despite the fact that I was getting better outcomes, I struggled with letting the heart-focused profile go. That early imprint nagged at me, like a commandment that I disobeyed with reluctance!!

For years I have assumed that my long tipped, heartless reeds sounded fine because that profile simply works better for the larger dimension reed.  It’s an observation made by many of us who lean to larger reeds.  But I’ve also come to appreciate that the heartless profile works better because of my embouchure and my preferred ‘effort level’ [Chapter 12 – The Goldilocks Dilemma]. Long tip tapers demand a different relationship between embouchure damping and air delivery.  Let me explain.

Most of my descriptions of the blades of a reed have emphasized the three-dimensional view of membranes as shells containing and responding to standing waves within.  The missing conical apex model is reasonably good at predicting the interaction of volume/size and compliance in designing acoustically responsive reeds.  But let’s branch out here and consider the behaviour of the blades in a simpler two-dimensional context: the idea of the ‘clamped bar’.

Diving boards are a great example.

You can get a really good idea of how length and stiffness effect both amplitude and frequency in a clamped bar.  Take a metal ruler and hold one end on to a table, letting most of the length sit free.  Give it a good “TWANG!” …

Shortening the free length of the ruler increases the frequency of oscillation because pitch rises and falls according to the free vibrating length of the ruler.  This is a classic example of the elastic properties of a linear object like a reed blade.  There’s a beautiful equation covering these relationships of stress and strength, expressed in Young’s Modulus. Thomas Young [1773-1829] is right up there with Bernoulli in my book.  He’s responsible for the wave theory of light, too.  Smart guy, but never played the bassoon.

When we observe a clamped bar, we are seeing something oscillate at a natural resonating frequency, with no external influences.  As the past 17 chapters have argued, bassoon reed oscillations are primarily controlled by the standing wave within the bore.  Compliance slightly modifies frequency – the flexibility of the cane determines the efficiency with which the pressure-controlled valve operates.  It’s reasonably easy to visualize how the membranes function as servants to the internal bore frequencies – remember trampolines and tympani heads?   But when we shift our attention to the diving board viewpoint – the blades as two-dimensional clamped bars – we see that profile variables influence pitch according to which notes on the harmonic ladder we’re playing [Chapter 13 – Stairway to Heaven]. A deeper look at the metal ruler behaviour will help us in seeing the effect of profiles on the two-dimensional behaviour of a reed blade.

Your twanging ruler is a somewhat limited representation of the behaviour of the reed blade because this metal bar has uniform thickness, width and stiffness.  Reed blades are considerably more complex as they have variable width and decreasing thickness from throat to tip, and variable compliance due to internal cane structure.  And never forget – your ruler’s vibrating frequency is not being controlled by a standing wave; its behaviour is entirely determined by its own dimensions!

Twanging metal rulers will be sharper if the steel is thicker, flatter if they are wider, sharper if they are shorter.  But what happens with your ruler when you change its thickness in one specific area?  This is actually quite easy to test.  If you glue/tape a bit of cardboard to the tip of the ruler you will discover the twanging pitch will drop!  Adding mass [front-loading] to the tip of the clamped bar lowers its natural frequency.  Now try adding some material towards the fixed end.  Back-loading mass here will raise the frequency.

Do you see any parallels in your reed trimming experience?  Leaving tips thick will typically tend to lower pitch just as leaving backs thick will typically raise pitch.  Now, while distribution of mass on the clamped bar explains this relationship, remember that much of the complex physics of a reed is governed by the three-dimensional interacting factors of the membrane shell and the internal standing wave.  Nevertheless, this alteration of mass at the tip and its effect on pitch is frequently observed, even though it seems at odds with the behaviour of membranes and shells.

Here is the paradox: while increased membrane thickness as a whole decreases reed compliance and raises pitch, increasing thickness at critical points of the profile can lower pitch.   Furthermore, the pitch effects of front-loading or back-loading mass are exaggerated as we move to higher notes.  A perfectly content reed with an ideal MCA for response in the bass clef is often flat in the tenor range if the tip region is too thick.

These confusing inconsistencies between the sharpening effect of thicker blades and the odd flattening effect of thicker mass at the tip of the reed can drive you crazy.  Implementing the principles of the MCA theory [volume, dimensions and compliance] will get you most of the way to a functioning reed, because the bassoon’s standing wave frequencies tend to dominate the three-dimensional physics of membranes.  But the critical final trimming that delivers a musically flexible reed must be increasingly respectful of the two-dimensional physics of the blades as clamped bars.

Shell physics and bar physics engage in dialogue with the bore in differing ways; the push and pull of their interactions lead us to develop profiles that are comfortable for our individual embouchure and air preferences.