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.

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.

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 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.

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  Doodles & Design by Nadina

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As our Little Bassoonist climbed the ladders into the high register she found herself thinking about the adaptations she makes in the upper register. Her teacher often reminds her to increase air support as she ascend; scaling ladders and scaling registers both demand effort. We usually think supplying faster air or more ample air is an important part of ‘holding up’ the pitch of the upper registers. I’m going to present a slightly different take on all this.

Unless our reeds are too sharp [Baby Bear!] and stuffy, it’s usually not a problem to get a lot of sound in the lower fundamental register. In fact, most reeds with optimal compliance produce more sonority at the lower end and less at the top. The bassoon is a bottom-heavy instrument. Flutists, who struggle with the bottom octave, are frequently jealous of the ease with which we can honk out low Bbs, though flutists have a relative advantage in the upper octaves.

LB’s teacher demands she practice her scales with a bit of crescendo in the ascent and a corresponding diminuendo in the descent. This guidance isn’t because ascending phrases always require expressive growth or descending phrases always require diminishing tone, although that is frequently appropriate. Rather, the habit of adding more support in an ascending passage is a strategy to correct the imbalance inherent to bassoons: loud and edgy at the bottom and squeezed at the top.

Chapter 13 examined the acoustical reasons for this diminishing sound profile.Each step to a higher register is achieved by eliminating a strong lower harmonic; sonority can suffer as we optimize the remaining higher frequency resonances. Increased embouchure damping reduces the richness of sound by reducing the cumulative energy of these remaining harmonics. Even modest damping changes the contours of the membranes and thereby increases inertia. As we move to higher frequencies, the slight closure of the reed not only alters the MCA value but changes how the blades respond to the Bernoulli effect. Tenor register pitches in particular become less responsive to nuance and articulation.

How does our little bassoonist respond to this? By increasing air supply. Mimicking a crescendo during an ascending scale compensates for the reduced amplitude of the reed membranes. If we must lose the 1st and 2nd harmonics and all their energy, we need to rebalance input air supply simply to maintain the impression of even dynamics.

LB is sometimes confused by these discussions. The balance between air support and embouchure can be minefields in the pedagogy of both playing and reed making. She aspires to play in the third octave by moving the air faster, but she sometimes expects too much. Most reeds required a bit of help from the lips.

Chapter 10 saw our little bassoon character inside a huge, imaginary reed.

Climbing back inside, LB observes in slow motion the blades flexing. There are changes in the overall shape of the membranes as the player moves from low register to high register. In addition to an observable reduction in the aperture gap, she sees a reduction in the flapping motions in the wings. This concave collapse of the wings results from increased embouchure pressure, which transfers into these wider, thinner areas of the membranes. When blades are held a bit tighter, larger motions are restricted and help dampen the lower harmonics as well as move the reed into a Mama Bear or even Baby Bear dimension.

Repeating the experiment with lips on the reed but with only enough embouchure to seal the air will have taken you a little bit further – depending on how light your reeds are. But rather instinctively, we tend to dampen the embouchure and increase air support as we ascend.

But….

LB remains slightly confused. Surely, she thinks, accelerated air supply must have an effect on pitch!? And indeed, it does.

This is a very confusing phenomenon, because in other instruments excessive volume tends to lower pitch. We see this flattening effect in the clarinet when it’s overblown. However, the bassoon will usually sharpen with increased air flow. We see this in vibrato production when the intermittent acceleration of air several times a second not only causes repetitive increases in volume but also in pitch. Sufficient air flow into a bassoon reed will also sharpen the upper bore resonances, and at an exaggerated rate! In fact, the intonation effects of embouchure and air increase substantially as we move into higher bore resonances. That’s why vibrato is so hard to temper up high, and pitch bending in the high register can be so extreme. The physics are elusive, but we presume that increased air velocity through the aperture must raise the natural frequencies of the membrane ‘shell’ as well as cause greater inward displacement of the blades and decrease that theoretical missing conical aperture. So, there’s absolutely real physical reasons why air speed might sustain both register and pitch. The evidence is with us constantly.

Next week, in Chapter 15, we are going to explore Resonance. It may not be what you think…

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  Doodles & Design by Nadina

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Brains and Membranes

Bassoon Reed Making by Christopher Millard

Chapter 13 – Stairway to Heaven

In Chapter 12, I left you with an assignment: try playing the full range of the bassoon with no help from the embouchure.  The test reveals the critical role that the embouchure plays in controlling for register and tuning.

From an acoustician’s point of view, the embouchure ‘dampens’ many of the natural harmonics of the reed itself and allows the ‘standing waves’ within the bore to control the dialogue.  I’ll touch below on this subject. For this and the following chapter I’ll focus on the need for embouchure damping in controlling both the MCA value (Missing Conical Apex, Chapter 11) of a reed and helping the complex fingerings of the bassoon select for the correct register.  This chapter puts our little bassoonist to work with ascending scales and helps her understand why embouchure damping is a necessary component in tone production.  But we’ve got to dive into some tricky areas.

If you get stuck, take a break and do an online search for videos and animations of both transverse and longitudinal waves, with special emphasis on standing waves.  Videos using ropes will show you how simple it is to visualize harmonics of transverse waves; videos using Slinkys or animations are especially helpful to us as wind instrument players.

Our little bassoonist loves to play scales.  Even melodic minors…

LB loves climbing up and down her bassoon ladders, especially when they take her all the way to high E and F.  But all this investigation of trampolines, caves and missing cones has got her wondering.  How does the bassoon manage to operate over three and half octaves and what role does the reed play in the process?

Let’s start by reminding LB of the conga line image in Chapter 3.  Compression waves move forward and then reflect backward from the open end of the bassoon.  Longer bores operate slower conga lines.   She understood that pretty easily.  We can also tell her that the term ‘fundamental’ is just a way of saying that a conga line has a lower limit to its frequency. The conga line for a low A can rock back and forth 110 times a second, but no slower.   To be clear about the terminology, we say ‘the fundamental resonating frequency is the 1st harmonic.’

For an explanation of ‘standing waves’ and an introduction to nodes/antinodes skip to the end of this chapter.

Consider the first 20 notes of the bassoon scale from low Bb [Bb1] to open F [F2].  This is where the bassoon bore operates in its ‘fundamental’ register using the lowest possible frequency for a given length of tube.

LB takes a big breath and begins playing a low G. Whether she plays loud or soft the pitch is predictable and constant.  The length and volume of that low G bore has a natural resonating frequency of @98hz, which we call a ‘bore resonance’.  Just like beer bottles, many enclosed spaces have natural resonances.  The amazing thing about wind instruments is that multiple bore resonances will occur simultaneously.  For that low G bore volume [designated G2] there will be a second resonance operating at twice the frequency – 196hz [G3].  It’s like a superimposed conga line on the same dance floor! A third resonance will occur around 294hz [D4], another at 392hz [G4] and there will be many more.  All these other resonances are related to the G2 in predictable ways; they are all harmonics – or overtones – of that 98hz conga line.

Nature blesses us with a really simple rule for calculating the frequency of these harmonics, based on a simple formula.  LB, a very clever bassoon avatar, notices the relationship between the harmonics:

• 98hz X 2 = 196hz [the same as G3!!]
• 98hz X 3 = 294hz [that’s a tenor D!!]
• 98hz X 4 = 392hz [same as high G!!]

Even without her digital calculator, which she left in the bear’s house, she figures out the next harmonic ought to be around 490hz – which happens to be pretty close to a high B.

From her second balcony perch, LB can see that the first ladder is a kind of first generation, the next ladder a very cooperative second generation and now she has to climb a third generation ladder based on removing two lower harmonics.

With Eb4 [311hz] she begins the climb to the third balcony. This ladder is shorter still and looks a bit rickety; the rungs are flimsy are not evenly spaced. This third ladder traverses the tenor register of the bassoon and things get a bit kooky. Although she’s never really taken the time to look at her fingers, she sees that tenor Eb uses almost the same fingering as G2 and G3. She simply adds a couple of big leaks in the air column by lifting two fingers, which immediately silence the resonances of the G2 and G3 harmonics. The 3rd harmonic in a series is a simple calculation: 3 times the frequency of the fundamental. So why does this fingering not deliver 294hz [D4], a nicely predictable 12th like on a string instrument. What’s going on?

 It would seem logical to LB that the 3rd resonance for the low G fingering would create perfect 12th, but the bassoon won’t behave. Opening tone holes will coax that 3rd resonance frequency. However, the truncated cone of the bassoon bore, the contributions of tone hole volumes and variations in conicity conspire to make this next harmonic sit sharper than predicted. LB’s tenor Eb fingering is setting up a standing wave at about 311hz which is a half step higher than the expected 3rd harmonic.

A term often used here is the concept of the ‘ancestor’ note.  Tenor Eb is based on bore resonances derived from its ancestor fingering for low G.

Only slightly confused, LBS takes the next step on the ladder – E4 – tenor E. Looking carefully at her well-practiced fingerings, LB sees that this bore volume E is really similar to G2 as well!!! But she has spread out the air column leaks by lifting her LH second finger [and perhaps one or more of her RH fingers as well]. Like most of her bassoon pals she opens the low Eb key on the long joint to darken the tone and bring the pitch down a bit. Nevertheless, it immediately occurs to her that the ‘ancestor’ for E4 must also be G2!! In other words, the basic air column for low G is serving as the ancestor for both half-step sharp AND a whole-step sharp 3rd harmonic resonances. The precise pitch depends on some minor fingering tweaks.

LB is starting to really freak out, but she takes another step up to the dreaded tenor F.  She hates this note.  Then she looks at her hands and sees that she’s playing A2 and making a big air column disruption by opening her LH middle finger.

 Of course, she’s right. That critical second finger leak disrupts the bore resonances for the 1st harmonic A2 and the 2nd harmonic A3. Because of deviations in the bassoon design the next available bore resonance is once again a half-step than predicted. Well – not quite a half-step. Instead of sitting comfortably around an ideal F4 of 349hz, the typical bassoon F4 wants to sit in the 345hz range. So, LB has to use more embouchure damping, reducing the MCA value and stiffening the reed membranes to get tenor F to sit high enough.

She takes another step and moves to F#4. There are two basic fingering options on the German system bassoon; one uses right thumb Bb and the other uses RH 4th finger. LB starts with the thumb Bb fingering. It’s actually comfortably in tune with a resonance close to an ideal 370hz. A careful examination of her fingers shows that she’s really just playing Bb2 and disrupting the two lower harmonics of Bb2 and Bb3 by lifting the first and third fingers of her left hand. [She often substitutes the RH 4th finger F key for the RH thumb Bb, a fingering more in vogue among modern players. Regrettably, it’s a bit of an acoustical anomaly and it’s difficult to calculate its ancestor fingering in the fundamental register.]

 Adjusting to the altitude, LB now steps up to G4. She always likes this note because the bore resonance sits at @394hz and she doesn’t need to hold up the pitch like she did on that funky F4. Now she’s curious about high G’s ancestor note. She realizes that by closing her half-hole she can get the 1st harmonic for this odd fingering to sound. It’s a resonance similar to B2 but then made a quarter-tone sharp by the addition of the low F key. Yep, another compromised 3rd harmonic, but one with less resistance and sitting high enough to feel comfortable. She’s grateful for these creative cross fingerings.

Looking at the first five rungs of the third ladder, LB comprehends they are all 3rd harmonic bore resonances and all acoustically compromised. Yet a HUGE amount of her life as an aspiring bassoonist will be focused on this tenor range. More than any previous notes on the first two ladders, LB realizes that controlling intonation and sonority for these tenor range 3rd harmonic notes requires constant attention to both embouchure and air.

The acoustical anomalies that creep into the upper half of the bassoon require gradual shifts in the dialogue between bassoon and reed.  Altering the compliance of a reed is a necessary precursor for the selection of the higher bore resonances, let alone playing them in tune.  Without some change in the behaviour of the reed – in size and stiffness – the addition of half-holes, open whisper keys, various extra tone hole openings and complicated fingerings are still not enough to allow for controlled sonority and workable intonation.

While increased air supply is a fundamental requirement for climbing the bassoon ladder, some amount embouchure damping – either a little or a lot depending on your approach to reed making – is a necessary support for all those hard-learned fingerings.

Next week, in  Chapter 14 – Reed My Lips – LB finishes her climb up to the Sacré and Ravel Concerto balcony.  We’ll get back to the Bears, MCA theory and begin to look at the behaviour of cane in reed membranes.

Standing Waves – ye olde quick discourse

Standing waves are a bit difficult to visualize without an animation; they are what happens when a wave moving forward bounces back from an open end as a reflective wave, which then interacts with the energy of the following forward moving wave.  This creates constructive and destructive interactions which lead to the reinforcement of positions where high pressure or low pressure dominate.

This image shows the standing wave positions for the harmonics on a string.  It’s essential to make the leap from these transverse waves to longitudinal waves.  Our recurring conga line image is a simple way to think of this.

The conga line will carry a pressure wave forward [incident wave] and backward [reflective wave] to and from the open tone hole.  When those back and forth waves start messing with each other you get areas in the line where the dancers’ motions are constructively amplified and other areas where their motions are restricted.  The ‘big motion’ areas are ‘antinodes’ and the ‘minimal motion’ areas are ‘nodes’.  Any given bore length will tend to set up a conga line where the nodes and antinodes are in predictable places due to the interaction of the back and forth waves.  Because those nodal [not much motion] and anti-nodal [lots of motion] dancers each tend to congregate in their respective stationary positions, we use the term ‘standing wave’ to describe their choreography.

A bassoon bore conga line with the minimum number [1] of ‘antinodes’ and ‘nodes’ will create the 1st harmonic for that length tube. Remember, in the conga line metaphor the dancers represent zillions of air molecules pushing and pulling at each other.

The standing wave behaviour in the first 20 notes brings a lot of energy to the 1st harmonic, but there are other standing waves – harmonics -that want to occupy the dance floor at the same time. The bassoon bore has ‘resonances’ – frequencies that it really likes – all vying for the participation of the molecular conga line dancers. These resonances are closely related as they represent standing waves with progressively increasing numbers of nodes and antinodes. Any of the 20 fundamental bassoon pitches will contain overlapping and coinciding resonance frequencies. They are organized in fairly logical and discrete ways.

By the way, I will address in future chapters a very interesting quirk of the bassoon in its fundamental range. Towards the bottom end, we often measure a fairly weak 1st harmonic, despite the fact that we hear it very clearly. This a psychoacoustic effect where our auditory processing combines the input of 2nd and 3rd harmonics to create the perception of a strong fundamental resonance. This becomes an important conversation when discussing control of sonority, nuance and pitch perception in several critical musical applications.