Brains and Membranes

Bassoon Reed Making by Christopher Millard

Chapter 13 – Stairway to Heaven

In the previous chapter I suggested playing the full range of the bassoon with no help from the embouchure.  The test illuminates the role the embouchure plays in controlling for register and tuning.  An acoustician would say the embouchure ‘dampens’ the reed and allows the ‘standing waves’ within the bore to dominate and control the dialogue. More simply, the embouchure works to bring the instrument under control. But let’s start with ascending scales. We need to understand why embouchure damping is necessary to achieve the full range of the bassoon. 

If you get stuck below, take a break and do an online search for videos and animations of both transverse and longitudinal waves.  Take time to look at the concept of standing waves.  Videos using ropes or Slinkys are helpful for bassoonists wanting to visualize these acoustical behaviours.

At the bottom of this chapter you’ll find an explanation of standing waves.

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

As a diligent practicer of sales, Goldie loves climbing up and down her bassoon ladders, especially when they take her all the way to high E and F.  But all the previous experience of trampolines, caves and missing apexes 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 Goldie 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.’

Consider the first 20 notes of the bassoon scale from low Bb [Bb1] to open F [F3].  This is where the bassoon bore operates in its ‘fundamental’ register.  It is using the lowest possible frequency available for the length of the tube.

Goldie  takes a big breath and begins playing a low G. Whether she plays loud or soft the pitch is predictable.  The length and volume of that low G2 bore has a fundamental frequency at 98hz.  This is the lowest ‘bore resonance’ for that fingering.  Remember, just like beer bottles, enclosed spaces have natural resonances.  What makes wind instrument so colourful is that multiple bore resonances will occur simultaneously.  For that low G bore length there will be a second resonance operating at twice the frequency 196hz [G3].  A third resonance will occur around 294hz [D4], another at 392hz [G4].  There will be many more, with higher and higher frequencies.  It’s like a giant dance floor with numerous conga lines weaving in and out of one another!  Each of the lines of dancers are moving at multiples of the slowest, twice as fast, three times as fast, four times as fast.  All these other resonances are related to the G2 in predictable ways, all harmonics 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 E flat 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.

If you want to learn more about this please read this blog post ‘In the Money’

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 higher than expected. 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.  Softer reeds helps this process.

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 rich 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.

In the next chapter, Goldie finishes her climb up to the Sacre balcony.

Chapter 14 – Reed My Lips

Standing Waves – A 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.  You can think of these interactions as the various conga lines on giant harmonic dance floor collide with each other. 

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, it’s worth noting a very interesting quirk of the bassoon in its fundamental range. Towards the bottom end electronic spectrum analysis measures fairly weak 1st harmonics, despite the fact that we hear the fundamental 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.