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…

‘Scale’ comes from the Italian word scala, meaning a ladder or staircase.

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.

With her reed placed on the truncated end of her bocal, LB continues playing her low G, but begins to really listen!

She realizes that all this warm, complex, mysterious, colourful, engaging, resonant bassoon sound that she loves is uses a broad spectrum of overtones cooperating with that low G2 bore volume.  Harmonics are what gives the bassoon – and all acoustic instruments – their character

LB closes all her keys and plays a low Bb, then B & C, slowly climbing the 20 step ladder that takes her to open F.  Listening more deeply than she ever has before, LB starts to hear some of those higher components.  They are participants in the harmonic series, sounding octaves, twelfths, and compound tenths and many more.  Each note on her bassoon seems to have a slightly different balance of harmonics which just adds to her infatuation with the instrument.

These 20 notes are rich in the 1st order of harmonics for each length of bore.  So, LB asks, if the first 20 notes are in the fundamental range, what happens with the 21st note and higher????  She reaches the open F and steps onto the first balcony of the bassoon house.  There is a new ladder leading up from here, a bit shorter and a bit less sturdy.  The first rung is marked “F#3” [half-hole F#].   Cleverly perceiving the pedagogical scale metaphor, LB sees she can no longer rely on the big 1st harmonic ladder anymore because her first finger half-hole “collapses” the standing wave for the 1st harmonic.  From here on up those lower 20 notes are silenced.  Stepping on the first rung she sounds the F#3 frequency of 185hz.  She senses there is a 1st harmonic wanting to burst through that open first finger, but she understands she’s left most of it on the 9th rung of the first ladder.  She climbs step by step.  G3 and G#3 are all based on the same length of tube as G2 and G#2, but the half hole leak muffles their 1st harmonics as well.  A2 briefly tries to reassert itself when she attacks A3 [220hz], but LB quickly opens the whisper key vent and uses a flick key to discourage the brief 1st harmonic croak.  She uses similar tricks on Bb, B and C.  C#4 and D4 complete the climb through the 2nd harmonics and she steps out onto the second balcony.  Someone is practicing the Berceuse above her.

bassoon

“Crap.  I should have stuck to the flute.  All those 12ths were in tune.  Don’t tell me this tenor F4 is another sharpened 3rd harmonic resonance!!”

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.

 

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 Doodles etc by Nadina

conga line, standing wave

Stand-n-Wave!

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