We have explored the idea of ‘response’ as a two-way dialogue between bassoon and reed.  Let’s shift our attention to another word that has a big impact on our reed making. Resonance.

The Latin word resonantia [echo] stems from the word sono, meaning sound.  Literally ‘re-sound’ – which makes sense to modern musicians, who think of the prolongation of sound through reverberation.  A resonant hall is a common example. Resonance in speech is seems enhanced by the action of the resonating chambers in the throat and mouth.  Resonance in human relationships describes mutual understanding or trust between people, a form of ‘rapport’.  These are all  meaningful uses of the word ‘resonance’.

But in nature, in physics, and in musical instruments, resonance has a more precise meaning.

A vibration of large amplitude in a mechanical or electrical system caused by a relatively small periodic stimulus of the same or nearly the same period as the natural vibration period of the system.

In musical instruments, resonance occurs when a vibration of large amplitude is produced by a small vibration occurring at the natural frequency of the resonating system.  This is a pretty clear description of how bassoons react to reeds, isn’t it?  Small amplitude oscillations – like the relatively small vibrations in the reed membranes – sustain a much larger amplitude standing wave in a bassoon bore.

Let’s shrink down and climb back inside the reed once more. Flapping membranes enclose our space yet the actual movement of the cane is very small.  Displacements of less than a millimeter can somehow produce a fortissimo.  A 2.5-meter bassoon bore, with complex bore resonances pumping out over 90db of sound energy, is all being sustained by these very small membrane oscillations.  This is resonance.

At the reed end of the bassoon, periodic variations in internal acoustic pressure control the frequency of the reed’s operation.  When both efficient response to incoming air and cooperative membrane compliance are optimal, the coupled bassoon/reed system achieves ideal sonority.  Think of it this way: minimal energy supply achieves maximum acoustical efficiency.   This is resonance.

I think of good resonance as getting more tonal ‘bang for the buck’.  Optimal resonance happens when the MCA value of the reed creates the most in tune collaboration.  Resonance is the result of a fruitful acoustical dialogue between standing wave and a faithfully compliant reed.

One of the best ways to understand the fascinating complexity of bassoon tone is use spectrum analysis.  There are numerous applications available for computers, tablets and smartphones, most using Fast Fourier Transforms.  These algorithms deconstruct a sampled tone to show the frequencies and the amplitudes of its harmonics.

Here is a spectrum analysis showing the relative energies of the component harmonics in a single note.  It’s a snapshot of C3 [in the bass clef staff] that I measured on one of my bassoons.  On this graph, the vertical axis represents the strength of a harmonic component and the horizontal axis represents its frequency.

You can see above that the energy peaks demonstrate the logical beauty of harmonic relationships, because the frequency of each peak is a simple multiple of a fundamental.  In this case, the first harmonic [H1] measures 130hz, and the successive harmonics [H2 – H15+] are all logical members of the harmonic series for this note.  Incidentally, you might notice that the fundamental frequency of the note we hear – C natural at 130hz – is not actually the strongest measurable component in the spectrum.  But look at all those strong harmonics at 260hz, 390hz, 520hz, 650hz etc.  They all contribute richly to the auditory experience of a C natural!

When a bassoon/reed coupled system is in a particularly resonant condition we see increased energy in the first few harmonics. This leads to an important characteristic behaviour that distinguishes the bassoon from many other instruments.  It has a strong formant. 

A formant is a specific frequency range that is amplified by the bore and tone holes and leads to much of the instrument’s unique timbre.  You can think of it as ‘built in character’.  Bassoons have a strong first formant between 450 and 500 hz, which means that the harmonics for any given note that lie within this range tend to be the strongest in the spectrum. In the above example, the third and fourth harmonics lie in the formant range and are particularly strong.  The most successful reeds are those cooperate most efficiently within the formant frequencies.

The reed used in the test above was compliant and rich in sonority because it was highly cooperative in supplying energy to both the formant frequencies and numerous higher harmonics.  It has happily adapted its behaviour to the complex bore resonances for C natural.  Did you notice that the fundamental is not the strongest partial?  Our human auditory system create a strong perception of the fundamental H1 because of the reinforcing alignment and combined energy of the other harmonics.  This is a great example of resonance, where minimal membrane activity creates maximal harmonic complexity.

Most of the sound energy in this graph is produced by the first 6 harmonics, but you can also see the significant contribution made by higher frequency components.  The bore resonances of the bassoon are asking for cooperation from the reed across a wide range of component harmonics.  When things go well, less blowing energy produces amplified standing wave behaviours.  This is resonance.

What are you to make of all this information?  You just want to make a good sound and to be reasonably in tune.  But while we tend to use the word ‘tuning’ to describe sharp or flat, I prefer a broader definition that incorporates some of the ideas of the MCA concept.  A well-tuned engine runs efficiently; a well-tuned reed maximizes resonance because it is acoustically efficient.  It’s the tuning itself that leads to a good sound.

Many young bassoonists wind up playing quite sharp.  Here you should take note that there’s a surprising maximum upper limit to this sharpness.  It’s quite difficult to play at A 446 hz because a bassoon engaged in an acoustical dialogue with a small, stiff reed will only bend its natural resonances so much before the system is hopelessly compromised.  The natural bore frequencies of a well-designed bassoon prefer to have their way.  Bassoons have evolved to maximize resonance in a range from A 439 hz to A=444 hz.  Undersized MCA value reeds will sharpen the intonation, but the bore resonances suffer.  Sonority and projection are quickly compromised and are not equally distributed throughout 3 octaves.  Those 3rd and 4th harmonic ladder areas in the tenor range and above will sharpen significantly more than their ancestor 1st and 2nd harmonics.  Resistance and inertia increase with higher frequency oscillations.  The flow of acoustical dialogue diminishes and resonance is lost.

And what about flatter reeds? I have to confess one of my life-long goals was to achieve the resonance that a A 438 hz setup delivers so easily, but somehow still operate in a typical A 440/442 orchestral environment.  Flat reeds usually have sufficiently large MCA values to allow the bassoon to find all those cooperative resonances, but there are physical challenges involved in constantly supporting ‘from below’.

Throughout my own 50 year orchestral career I tried to balance my sound aspirations with reasonable embouchure effort and air support.  Sometimes I succeeded…

Designing and trimming reeds is a process of matching good intonation with maximize resonance while optimizing individual embouchure and air preferences.

She remembers her visit to the Bears’ House  She couldn’t choose just one reed, so she took all three. As she experiments with the relative effort the three different reeds demand she comes up with a way to visualize it all…

This graph shows how Goldie is thinking about her three bears reeds, labelled A, B and C.  Line D represents her own particularly crappy reed that she can’t seem to fix.

The graph’s x axis represents the ascending registers of the bassoon.  The y axis represents ‘Effort’, a combined ‘mashup’ of embouchure and air.  The idea is that the plotted lines represent the change in workload.  The steeper the curve, or the higher its placement, the more effort is required to maintain resonance all the way up to the high end.

Take a look and think of your own reeds.  Do some of them remind you of line A?  Papa Bear style, large MCA value?  Does line C make you think of stuffy, sharp reeds that nevertheless give you a better shot at high D’s?  Perhaps most importantly, do you think the measurement of your work level could be plotted in a fairly straight line??  This is really important: the idea of response linearity where increased effort is predictably even. Line D has a big curve going up, which describes a reed that is okay until it reaches the tenor range, at which point the embouchure and air effort becomes relatively more demanding.

Linearity is a concept that’s quite universally appealing in both instrument design and reed making.  For LB, it’s a way of describing a comfortable climb up the ladders in her Stairway to Heaven.

Chapter 16 – Corvids and Cacks

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

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