Brains and Membranes

Bassoon Reed Making by Christopher Millard

Chapter 15 – Resonance

In previous chapters, I’ve presented a different interpretation of the term ‘response’.  It’s the idea of 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.  So ‘re-sound’ -which makes sense to modern musicians, who think of the prolongation of sound through reverberation.  A resonant hall, for example. Resonance in speech is additionally 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 subjective – and meaningful – uses of the word ‘resonance’.

But resonance has a more objective meaning which we see in physics:

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.

resonance, conch

Little Bassoonist hears the resonance in a seashell…

LB, tiny again, climbs back inside the cavernous bassoon reed and watches the flapping membrane activity above and below her.  It all seems enormous to a miniature bassoonist, but the actual movement of the cane is very small – displacements of less than a millimeter.  And yet, a 2.5-meter bassoon bore, with complex bore resonances pumping out over 90db of sound energy, is all being driven by these very small membrane oscillations.  This is resonance.

At the small end of the bassoon, periodic variations in pressure control the frequency of the reed oscillations.  When efficient input response to airflow matches the output response of cooperative membrane compliance, the coupled bassoon/reed system achieves ideal sonority.  Minimal energy supply achieves maximum acoustical efficiency.   This is resonance.

Resonance is getting more tonal ‘bang for the buck’.  Resonance happens when the MCA value of the reed creates the most in tune collaboration.  Resonance occurs more easily for a Papa Bear reed at the expense of increased effort; with a Mama Bear reed in the right register and sensitive air supply; and for a Baby Bear reed when embouchure can be relaxed sufficiently.  Resonance, in both its subjective and objective definitions, happens when appropriate tuning meets comfortable embouchure and air behaviour.  Resonance is the result of fruitful acoustical dialogue between standing wave and reed – when that faithful partner complies willingly.

Sometimes the simplest ideas reveal deep wells of meaning. 

In the study of bassoon reed making, the idea that tuning and tone are inextricably linked reveals a path to better outcomes.

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.

Just as spectral analysis of light reflected off a distant object can tell us what elements it contains, so spectrum analysis of sound reveals what component frequencies it contains.

You can see above that the energy peaks show very clear 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 their fundamental H1 origin.  The reed chosen for the test was particularly compliant and rich in sonority because it was highly cooperative in supplying energy to all these higher harmonics.  It happily adapted its oscillations to the complex demands of the harmonic series for C natural.   Human ears create a strong perception of the fundamental H1 because of the reinforcing alignment and strength of the higher harmonics.  This is a great example of resonance!!  Small membrane activity = extraordinary harmonic complexity.

It’s important to note that graphs like this take a snapshot of the average harmonic components in a sustained bassoon tone.  They don’t reveal much about the more ephemeral and transient inharmonics, frequencies that are present in the attack of a note and pop up for brief moments throughout a long tone.  Inharmonics are not members of the harmonic series family, but they still contribute to the character of the sound.  As we will see in a later chapter, inharmonics are particularly relevant at the beginnings of notes.

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.  When a bassoon/reed coupled system is in a particularly resonant condition we tend to see more energy in the first few harmonics.  The bore resonances of the bassoon are asking for cooperation from the reed across a multitude of component harmonics.  When things go well, less blowing energy produces amplified standing wave behaviours.  This is resonance. 

Our little bassoonist is not sure what to make of all this information.  She just wants a good sound and to be reasonably in tune.  Of course, it’s the tuning itself that gives good sound.  We tend to use the word ‘tuning’ to describe sharp or flat, but I prefer a much 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.

Like many young bassoonists, LB often winds up playing quite sharp.  But she should take note that there’s a surprising maximum upper limit to her sharpness.  It’s quite difficult to play at A=446hz 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 native natural bore frequencies of a well-designed bassoon prefer to have their way.  Bassoons are carefully set up to work efficiently [with resonance] at either A=440hz or A=442hz.  Undersized MCA value reeds will sharpen the intonation, but the bore resonances quickly rebel.  Sonority quickly gets very unpleasant and very uneven. The distortions are not equally distributed throughout 3 octaves either.  Those 3rd and 4th harmonic ladder areas in the tenor range and above will sharpen significantly more than their ancestor 1st and 2nd harmonics.  Inertia increases with higher frequency oscillations.  The flow of acoustical dialogue diminishes and sonority is compromised. Resonance is lost.

So, what about flatter reeds? I have to confess one of my life-long goals was to achieve the resonance that a A=438hz setup delivers so easily, but somehow still operate in a 440/441 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’.

Designing and trimming reeds is primarily a process of finding an average pitch centre that serves to maximize resonance while optimizing embouchure and air preferences.

Looking back at 46 years of orchestral work, I know that balancing my own sound aspirations with reasonably balanced embouchure and air support remains a life-long quest.

 

LB asks a really important question: should she play slightly sharper reeds and relax down into the work pitch of her colleagues, play slightly flatter reeds and hold up her pitch with more effort, or play reeds that are perfectly balanced and comfortable, delivering optimal resonance with sensible demands on embouchure and air?

If you like that third answer, congratulations.  And best of luck.  Most of the time you are going to be dealing with one tendency or the other.  You need to be aware of the benefits and drawbacks wherever your fine tuning takes you.

LB is remembering her visit to the Bears’ House.  She couldn’t choose just one reed, so she took all three.  Now she’s experimenting with the relative comfort and effort the three reeds demand.  Like most bassoonists, LB is remarkably clever, and has come up with a way of evaluating her Bear reeds.

This is how LB is thinking about her Bears and their reeds, lines A, B and C.  Line D represents her own particularly crappy reed that she can’t seem to fix.

The graph x axis represents the ascending registers of the bassoon.  The y axis represents ‘Effort’, a theoretical ‘mash’ 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 produce resonant sonority 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?  [Probably larger MCA values, more Papa Bear style?].  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 [as in 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.

On the grid

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.

Next chapter, we’ll look at Crows, Roosters, Ravens and other Multiphonics.

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 Chapter18 – Chickens & Eggs Doodles & Design by Nadina

 

 

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