# Graphing the clarinet

A note on the clarinet

We could use this as a graphical representation of a single note played on the clarinet. Let’s say this is a mid-range note, played with its ordinary fingering, at a moderate loudness. It’s a quarter note in a moderate tempo, lasting about a second.

If you know anything about graphs, you know that they represent the input and output of a function: they visualize something in terms of something else. So it would be useful to ask: what are these somethings in the case of this graph?

The X (horizontal) axis is easy: it represents units of time. The curve on the graph is actually a series of points, and each point represents the value of Y (the vertical axis, or the function’s output) at time X. You can imagine a vertical cursor line traversing our X axis from left to right, showing the value of Y at each successive now-time.

Example 2

Returning to Ex. 1, if this represents a single note played at a moderate loudness, then what does Y represent? This question bears pondering, since it’s more complicated to answer than it seems. Two obvious answers that spring to mind are loudness1 and felt effort. Neither answer is bad, but they’re not quite right either. Let’s consider each in turn.

If Y represents loudness, the note gradually ascends from silence to a moderate loudness, and then returns. But this is an ordinary note that does not feature a crescendo or decrescendo. Our perception of a note played without a deliberate crescendo or decrescendo is that it has a more or less constant loudness. There might be a slight climb at the beginning, and especially a fading away at the end, but it starts more or less instantly and does not fluctuate. This graph shows a gradual climb and a gradual descent, not the clean onset and offset we would normally expect.

As for felt effort, like loudness it is certainly related to the Y axis of the graph. However, a quirk of human anatomy complicates the relationship between the felt effort involved in blowing and the actual output of blowing. I’ll take this issue up in detail below.

An answer that works a little better than loudness or felt effort (both of which are related to our Y axis, but not straightforwardly) is that Y represents air stream. We can define this in terms similar to electrical current or water flow: the amount of air that passes a given point per second.

Example 3

Clarinetists will have noticed a problem with the model to this point: it’s possible to use a non-zero air stream while getting zero clarinet sound. That is, there’s a threshold of resistance beneath which no clarinet sound will be produced, regardless of the air stream. If we are to accurately represent the act of playing this single note, we will need to show this threshold somehow.

The threshold could be represented by a horizontal dotted line drawn across the graph. When the value of Y intersects with this threshold line, a clarinet sound will be produced. Above the threshold, the air stream will correlate more or less with loudness. Below the threshold, no clarinet sound2 is produced regardless of the air stream.

Example 4: A note on the clarinet, with resistance threshold and loudness indicated.

In other words, we can define loudness as “the air stream at time X, minus the value of the threshold.” More air gets you more sound – except below the threshold, where the amount of air is irrelevant. There are some real advantages to this model. One is that we’re able to explain how a sound event with a relatively sharp onset and offset can come from the gradual physical phenomenon of blowing. The audible sound is like the tip of the iceberg – shaped and constrained by something invisible and below the surface.

This gets at a subtle point that is often lost on clarinetists (though never players of larger reed instruments, for whom this issue is much more salient): there is a non-zero lag time between the beginning of your breath action and the beginning of audible clarinet tone. In general, this lag time correlates with the resistance threshold – so a more resistant setup results in a longer lag time.

Example 5: Graph indicating the non-zero lag time between beginning of air stream and onset of clarinet tone.

The model outlined to this point serves us relatively well for one note. However, we rarely play just one note, and the resistance threshold on the clarinet differs from note to note. We need to introduce another complication.

### Resistance curves, loudness, and crescendo

Resistance is affected by three factors. One is the setup of the instrument: reed, mouthpiece, and so on. This is relatively constant, at least for any single playing session – it’s not something you can change on the fly, so it’s not something we need to address here. One is the pitch you’re currently playing.3 For any given setup, each pitch has its own resistance threshold. The third factor is more complicated, so we’ll consider it separately below.

For now, let’s consider the resistance thresholds of different pitches. By mapping the various resistance thresholds of the successive pitches played in a single breath, we can come up with a resistance curve for that passage.

Example 6: Air stream curve (blue) and resistance curve (orange). At any given moment, the vertical distance between the orange and blue lines indicates loudness.

You’ll see that unlike our air stream curve, the resistance curve is not particularly curvy. Because the resistance threshold stays constant across the duration of a given pitch, it moves only when the pitch changes. And it moves all at once, hence its jagged profile. A general observation is that the human action of blowing will produce a curve with gradual slopes – only rarely will straight lines be involved. Changes in pitch (and therefore resistance), however, are mechanical phenomena that can occur all at once.

For any given clarinet setup and sequence of notes, the resistance curve can be determined in advance. This makes it a relatively static structure against which the more dynamic air stream can play off. The resistance curve does not change. The artistry of clarinet playing is in the way you deal with it.

Example 7: An attempt to maintain static loudness across a passage with varying resistance.

Ex. 7 shows that, to maintain a relatively static loudness across a passage, it might be necessary to modulate the airstream quite a bit – depending on the resistance of the notes you’re playing. This is an interesting feature of clarinet playing that’s worth exploring in more depth: sometimes you need to make drastic changes in your blowing across a single passage in order to make it sound smooth and undisturbed.

This becomes more interesting when we consider crescendo and decrescendo. Because loudness correlates straightforwardly with air stream above the threshold, a crescendo will often involve an increase in air stream, and a decrescendo a decrease. However, this is not always the case: because the threshold can move from note to note, producing a crescendo or decrescendo may sometimes involve a static or even opposite blowing action.

Example 8: Crescendo without any change in blowing action.

In Ex. 8, you can see that the blowing action remains constant once it starts. However, the resistance steadily decreases. If the distance between the orange and blue lines represents loudness, then you can see that the loudness steadily increases without any change in the blowing. In other words, this constant blowing will create a crescendo. You can easily imagine the same thing in reverse: a constant blowing action producing a decrescendo as the resistance increases.

### An anatomical digression

We are now poised to complicate the notion of felt effort. I mentioned above that felt effort is related to our Y-axis value, but it does not track with it straightforwardly. In other words, the effort we perceive ourselves expending while we play is not necessarily proportional to the air stream we get. The relationship is somewhat more complex than that. To explain, it will be necessary to discuss the anatomy of the blowing apparatus.

The diaphragm is a large dome of muscle stretched across the bottom of the ribcage. When the diaphragm contracts, it flattens out and creates more space in the chest cavity. This, in turn, causes air to be sucked into the lungs. Inhaling is a muscular contraction. Exhaling is a relaxation: the diaphragm relaxes, shrinking the chest cavity and pushing out the air. Ex. 9 illustrates this process: the diaphragm is a dome when it is at rest, and flat when contracted.

Example 9: Animation of the diaphragm’s role in inhalation and exhalation by John Pierce. Public domain via Wikimedia Commons.

Ordinarily the process of exhalation happens quickly, especially for a large quantity of air. However, it’s possible to slow it down.

Think of doing a bicep curl: halfway through the rep, when the dumbbell is close to your shoulder, how do you lower it in a controlled fashion? There are two actions involved: one is the gradual relaxing of the biceps, and the other is a contraction of the triceps, which opposes the biceps (moves the arm in the opposite direction). These structures of opposing muscles recur throughout the human body, and when they act in concert (one muscle gradually relaxing and the other contracting) it is possible to move much more precisely than with one muscle acting alone.

The diaphragm is no exception. It is opposed by the abdominals and some of the muscles of the back. While the diaphragm applies downward pressure to enlarge the chest cavity, these muscles can use inward pressure to push the diaphragm up and shrink the chest cavity.

Since exhaling is a muscular relaxation, it is analogous to the second phase of a bicep curl, when you lower the dumbbell in a controlled motion. In the same way that you would use the opposed action of biceps and triceps to control the descent of the dumbbell, you can use the opposed action of the diaphragm and the abdominals to control the exhalation. This is what we call breath support.

The significance of breath support is that it gives us a way to change the resistance in the blowing system in real time. While there’s no way to make difficult notes less resistant, you can use breath support to smooth out the bumps in the resistance curve, reducing the amount you need to modulate your air stream. We’ll see an example of this in a moment. First, there’s one more twist to consider.

The diaphragm is an unusual muscle. While it is voluntary (it can be consciously controlled), it does not have any sensory nerves (it can’t be felt directly). Breath support is a two-part action, but you can only fully experience one part of it. You can feel the abdominals and the back muscles, but you can only infer what the diaphragm is doing, in part from the evidence provided by your ears.

This complicates our understanding of the blowing apparatus, but it actually helps tremendously with clarinet playing. Because of the diaphragm’s unusual relationship with the conscious will, it responds in some respects more quickly, gracefully, and accurately than a muscle under conscious control (Antony Pay aptly describes it as “magical”). This quality of the diaphragm is extremely valuable, and we do well to make use of it whenever we can.

### Playing with support

As discussed above, breath support gives us a way of modulating the resistance in the blowing system on the fly. It can’t make a resistant note less resistant, but it can smooth out the resistance curve across an entire passage and make it easier to get a uniform loudness. This is the basis of true legato playing across difficult intervals.

For example, take a look at Ex. 10. The sudden drop in resistance in the middle of the passage is a problem. If the player takes no action, there will be a sudden, awkward increase in loudness. Even if the tone is not actually interrupted, there will probably be a bump in the sound that will destroy any sense of legato. The player can try making an abrupt change of air stream, but this could lead to a different kind of awkwardness. Trying to suddenly blow less is likely to be inaccurate and overshoot the mark.

Example 10: A passage with a sudden drop in resistance in the middle. How do we avoid an awkward increase in loudness?

A possible solution is given in Ex. 11, where the increased resistance from diaphragm support is shown as a dark green dotted line.

Example 11: Increase the resistance in the relevant spot using diaphragm support.

What does it feel like to play this passage? The key thing to remember is that it doesn’t feel like you’re doing anything differently at all. At the beginning of the passage, you set the tension of your abdominal and back muscles to more or less match with the resistance threshold. Then you blow as hard as necessary to get the desired loudness. When you come to the awkward, low-resistance note in the middle, you form a clear expectation that it will continue uninterrupted, just like the notes preceding and following it.

You don’t actually do anything differently. The diaphragm will answer your request without any deliberate action on your part. Just like magic.

This essay is my adaptation of several concepts first discussed by the clarinetist Antony Pay. Sadly, most of his work on the mechanics of clarinet playing is not published in any formal venue – instead, it is scattered across various posts on the Clarinet BBoard over the years. In an email exchange a few years ago, Mr. Pay encouraged me to post or publish some ideas I’d had about the notion of breath support after reading his thoughts on the subject. This article can be considered the long-delayed fulfilment of that request.

The two most important contributions Antony Pay has made to the formally published literature on clarinet playing are:

• “Phrasing in Contention,” Early Music 24, no. 2 (May 1996): 290-321.
• “The Mechanics of Playing the Clarinet,” in The Cambridge Companion to the Clarinet, edited by Colin Lawson (Cambridge University Press, 1995): 107-122.

### Notes

1. I deliberately use the scientific term “loudness” over the musical term “dynamic” to separate the two concepts. A forte dynamic, depending on the player, instrument, and musical context, might be represented effectively by many different loudnesses. For present purposes, it’s more useful to talk about physical-perceptual phenomena than musical ones.
2. I make a distinction here between “clarinet sound” and “sound per se.” Blowing into a clarinet always makes audible noise, but we only consider it to be “clarinet sound” when it produces regular vibration of the reed and thus a stable pitch.
3. And the fingering you’re using. Different fingerings for the same note may have different resistance. For now, we do not need to consider this complication.