SCIENCE OF ARTICULATION SCIENCE OF ARTICULATION

radiates higher better than the Because a travelling variation in pressure and a three-metre long ‘’ (a plastic fundamental, whereas the sound inside is a sound wave.) When this sudden tube) while we worked on understanding is dominated to a great extent by the change in pressure reaches the bell, it and quantifying transients. fundamental. is reflected and returns, and when it Over a tenth of a second or so, these Initially, the reed is pushed towards the reaches the reed it is reflected again (more reflecting waves grow in size, due to SCIENCE OF mouthpiece by the tongue amplification by the reed (frame (a) from the high- and the player’s breath. speed video) and the graphs The clarinet has been studied Let’s see why. Imagine a begin as the reed begins to sudden increase in pressure move. For about 0.02s, the scientifically in more detail than in the bore arriving at the reed stays in contact with reed. It pushes the reed ARTICULATION the wet tongue, which pulls any other , but away from the mouthpiece, the reed beyond its point of which increases slightly Some recent scientific studies of clarinet mechanical equilibrium. (If most studies have concentrated the aperture between you exaggerate your tonguing reed and mouthpiece. This – a bit like slap tonguing – on steady notes increased aperture allows you can probably feel the slightly more air to enter the By Weicong Li, André Almeida, Lauren Inwood, John Smith and Joe Wolfe tongue pulling the reed.) mouthpiece, which increases At (b), the reed’s springiness has pulled about reflections and resonances on our the mouthpiece pressure: an arriving (School of Physics, University of New South Wales, Australia) it away from the tongue and it begins website). In practice, this is complicated increase in pressure produces an even to return to its mechanical equilibrium because, especially for high notes, the larger increase in pressure. Conversely, a position (c): its rest position for this reflected wave returns while the tongue decrease in pressure arriving at the reed The clarinet has been studied scientifically provides us with a tireless, reproducible, Figure 1 shows results for the low E blowing pressure and lip force. Tongue and is still moving with the reed. So one of our pulls it towards the mouthpiece, reducing in more detail than any other wind experimental subject, which has exactly on a B flat clarinet (D3 concert, 147 Hz) reed have no further contact during the experiments used a normal mouthpiece both the aperture and the flow of air ➡ instrument, and much is well understood. and independently controlled blowing tongued normally. The mouth pressure and note except in the case of staccato, when Our lab has a website explaining pressure, lip force and position, tongue barrel pressure are shown in kilopascals the tongue touches and immobilises the acoustics, including our own contributions force and acceleration. It also has a (kPa); one kPa is 1% of atmospheric reed to begin the final transient. on and , especially transparent mouth, in which we can drill pressure (or about 0.15 psi for Americans). The reed is stiff and light. So, if there HOW DOES THE REED CONVERT THE on the frequency response of instruments, holes without asking the university ethics The change in pressure in the air near the were no lip, it would return to equilibrium, on how pitch, loudness and timbre are committee. You can hear it play on our bell is much smaller and shown in pascals. overshoot and proceed to oscillate at ENERGY OF STEADY AIR FLOW INTO related to blowing pressure, lip force and website. The site also has the scientific At the right of the curves, we notice also its own resonance frequency of a few SOUND ENERGY? vocal tract properties, and on the use of reports of our research, so we omit the that the sound wave at the bell has a thousand vibrations per second. But the vocal tract on altissimo notes, pitch technical details and most of the results in more interesting shape than that inside the lip slows the reed’s motion and also bending, bugling and . Most this brief account. the instrument. This is because the bell has mechanical losses. These effects In the absence of a resonating bore, let’s see how the flow U into the mouthpiece studies, however, have concentrated discourage the reed from vibrating at depends on blowing pressure P. At first, U increases rapidly with increasing on steady notes. The start and end of high frequencies — occasional squeaks P. But if you blow hard enough, P will close the reed against the mouthpiece, reed displacement (mm) notes (collectively called transients) are 0.3 excepted. So, because of tongue and lip, stopping the flow. This occurs at lower P for large lip force (red curve on the important to the quality of the sound and b 0.2 c the motion (a–c) is much slower than graph) than for small (blue). Consider playing with P and U values given by the elegance of the performance. Several 0.1 a the natural vibration of the reed. At (c), the red dot. The ratio of pressure to flow for steady or DC flow (the reciprocal students and staff in our lab have worked 0 the reed has lost the mechanical energy slope of the dashed line, P/U) is the DC resistance for this point and, like an on transients over the last few years, 4 initially provided by the tongue: from here electrical resistance, it takes energy out of the system. But now consider the mouth pressure (kPa) which explains the number of authors on it will be driven only by the sound wave ratio of small change in pressure to the corresponding change in flow (∂P/∂U for listed for this brief report, which aims 2 in the bore. mathematicians). Near the red dot, increased pressure decreases the flow, and to explain some of our recent results in As in most examples we recorded, the vice versa, so the resistance for a varying or AC flow is negative (reciprocal slope simple language. 1 barrel pressure (kPa) blowing pressure in Figure 1 gradually of the solid black line). So the positive DC resistance of the reed takes energy Two studies involved experts and 0 increases throughout the attack. Here, it out of the steady flow and the negative AC resistance puts some of that energy students playing modified clarinets. -1 is about 1kPa above atmospheric when into the oscillating air flow. These had sensors to measure blowing the reed starts to move. When the note Airflow vs blowing pressure pressure and sound in the player’s mouth 5 radiated sound pressure (Pa) starts, the blowing pressure is about and microphones in the barrel and bell. In 0 2kPa. Consequently, as the reed moves one study, a sensor on the reed measured -5 away from the mouthpiece (a–b) and back tongue contact. In the other, an endoscope towards it (b–c), the aperture into the 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 inside the mouth recorded high-speed mouthpiece correspondingly increases and time (seconds) video of tongue and reed motion. decreases, producing a sudden increase Two additional studies used an Figure 1: Three frames from the high-speed endoscope video as a clarinettist tongues low E (below). then decrease in airflow. These changes automated clarinet playing system. We The images correspond to the times labelled a, b and c on the top graph, which shows the reed’s in flow produce a small increase then hasten to say that this machine is not displacement from its initial position. The graphs above show the pressure in the player’s mouth, decrease in pressure in the mouthpiece. intended to replace musicians. Rather, it the sound pressure in the barrel, then the sound outside the bell (from Inwood et al., 2016). One of our technical papers explains these changes and gives experimental measurements of them: the physics of the process is somewhat similar to the ‘water hammer’ that one hears sometimes in old plumbing. For now, just note that the early changes in the pressure are tiny and, on this scale, only just visible on the graph before 0.03 s. The change in pressure travels down the bore at the speed of sound: 340 metres per second. (Why this speed?

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into the mouthpiece, which lowers amplification system, once the pressure On a different timescale, Figure 2 shows reverse: a resonance of the bore is driving notes have slowly falling blowing pressure. rise much above this value, the note starts the pressure further. So the combination peak in the mouthpiece is equal to the whole notes. It graphs three different the reed. The player’s vocal tract also has Near the end of the note, the pressure falls slowly. When we asked players to play of the mouth pressure and the elastic reed pressure in the mouth, then further pressure measurements (bell, mouthpiece resonances, but usually the frequencies slowly below the break-even value: the minimal attack, they raised the pressure provide amplification for pressure waves opening of the reed does not increase and mouth) for four different articulations: of the vocal tract resonances occur value where reed amplification just makes slowly until the note started, then either reflecting at the reed. See the box for the maximum mouthpiece pressure – we normal tonguing, with accent, sforzando, well away from the playing frequency. up for losses. So for this player’s accented held it steady or reduced it slightly before another way of understanding the reed call this saturation. Further, if the reed and staccato. The note is C5: written C in (Interesting exceptions occur in pitch and sforzando notes, the decay rates are slowly increasing it again. For a given lip gain. (This simple argument neglects the vibration is so big that the reed actually the middle of the stave. On this time scale, bending, altissimo, bugling and the first slower than for the normal note, which is force, however, tonguing can start notes at time for the reed to accelerate and so it closes the mouthpiece aperture, the we don’t see the individual vibrations, just bar of Rhapsody in Blue; see our web site in turn slower than the staccato, where the lower blowing pressure than the starting fails for high notes. the envelope of the sound wave. for details.) amplification is ‘turned off’ suddenly by pressure in a slow pressure increase. This is related to Two studies involved experts The sound pressure in the mouthpiece is Notice how the blowing pressure is the tongue. For human players, the coordination of one of the limits to much larger than that at the bell, but their varied during the note, and how the From thinking about the explanation tongue release and increase in blowing the high range of envelopes are roughly the same shape. moment when the tongue releases the in the box, you can probably see that the pressure was different at different pitches: the instrument.) and students playing modified Unlike the others, the average pressure reed is coordinated with the blowing reed gain depends on blowing pressure, for all articulations at the higher pitches, Over most in the player’s mouth is not zero, because pressure. For the normal note, the mouth lip force and position, lip damping, reed the tongue almost always released the of the example clarinets. These had sensors to the player is blowing high pressure air pressure builds at the slowest rate and ‘hardness’, the shape of the mouthpiece reed before the break-even point; this shown in Fig 1, to power the instrument. Notice that the reaches its maximum value shortly and the amplitude of the note. Further, rarely happened for low notes, particularly the amplification measure blowing pressure and black line for the mouth pressure becomes before the note reaches its maximum the losses depend on the note played and with expert players. There is a likely gain of the wider when the note starts: that wider amplitude. It then stays constant at that acoustic properties of the clarinet with explanation for this. First, low notes have system is about sound in the player’s mouth shading is the sound measured in the value throughout most of the note. In a given fingering, so the rate of increase longer vibration cycles (a note an octave three decibels mouth. The vibrating reed produces an the accented and sforzando notes, the in sound after tonguing is a complicated lower has a vibration that takes twice as per cycle: each oscillation in pressure is vibration doesn’t get any bigger – though oscillating flow into the clarinet and an pressure reaches a long), so the same amplification per cycle roughly 40% bigger than its predecessor, the aperture can stay closed for longer. oscillating flow of equal magnitude into higher value than gives a lower rate of exponential increase and has twice the energy. A sequence As the note approaches saturation, the the mouth. However, the sound pressure for the normal note, Two additional studies used (in decibels per second) for lower notes. whose amplitude increases by the same proportional rate of increase falls below in the mouth is smaller than that in the but is then reduced, Further, lower notes saturate at higher factor over equal times is an exponential exponential and, in just several cycles, the mouthpiece. This is because the clarinet so that the note an automated clarinet playing pressure amplitudes. For notes initiated increase. Exponential increases cannot note reaches its steady amplitude (Figs 1 resonates at the frequency of the note amplitude is, as with the same pressure perturbation, continue indefinitely. In the case of our and 2). played — and more importantly, the required, largest system, which provides us these effects give longer transients for near the start and low notes. By starting the transient for low reduces through it. with a tireless, reproducible, notes above the break-even point, players pressure in mouth pressure in mouthpiece pressure at bell Observe that, in the achieve transient times more comparable normal note, the with those of high notes. 5 5 experimental subject normal accent tongue is released at As Figure 2 suggests, when playing at the lowest blowing mf, our players used the highest blowing pressure. From our brief discussion of function of all these factors. Experiments pressures and thus achieved the highest the amplification at the reed, we expect under controlled conditions using the exponential rates of increase for accents that lower blowing pressure causes less playing system showed that increased and sforzando. In fact, their attacks for air flow into the mouthpiece and lower tongue force or initial reed acceleration these articulations were much like their 0 0 initial amplification, and therefore a make the note start earlier after tongue attacks for normal notes at ff. We also slower rate of increase in the sound release, but do not affect the exponential noted that expert players could achieve

pressure (kPa) amplitude. Probably without thinking, the rate of increase. Large tongue forces or faster rates than students. Finally, not pressure (kPa) player has done this because he wants sudden tongue release can however cause all clarinettists use the same tonguing the normal note to start more slowly than the higher harmonics to grow more quickly, technique. For some, unlike Figure 1, the the accented, sforzando and staccato which affects the timbre of the transient. tongue motion had a large component of tongue releases reed tongue releases reed notes. (Most players in our study could not Clarinettists sometimes like to start a motion parallel to the reed. For others, -5 -5 describe confidently their coordination of note slowly. If the tongue releases the the sides of the tongue curled upwards 010.5 1.5 2 010.5 1.5 2 tongue and pressure.) reed when the blowing pressure is below on either side of the reed. For further time (sec) time (sec) To understand the end of the notes, let’s the break-even value, then the note does discussion and detail, and for much more consider first the staccato final transient. not start until the break-even value is about clarinet and saxophone acoustics, Here, the tongue immobilises the reed, reached. If the blowing pressure doesn’t we refer you to our website. n 5 5 tongue touches reed to stop vibration so the sound wave in the bore receives no amplification. The sound cannot stop sforzando For further discussion and detail, and for staccato immediately, however. (If it did, we’d hear a ‘click’ or ‘pop’ at the end of the note.) The energy stored in the standing sound much more about clarinet and saxophone wave in the bore is gradually lost, as heat 0 0 to the walls and as sound energy radiated acoustics, we refer you to our website from the bell and tone holes. The fraction of energy lost in each cycle is nearly pressure (kPa) pressure (kPa) constant, so this produces an exponential Acknowledgments. We thank the Australian Research Council for support, Yamaha for decay in the amplitude. instruments, Légère for reeds and our volunteer subjects. tongue releases reed For the other notes, the decay is slower. In each of these, the note is stopped by The introductions ‘Clarinet Acoustics’ and ‘Saxophone acoustics’ are at -5 tongue releases reed -5 gradually lowering the blowing pressure. http://newt.phys.unsw.edu.au/music/ or search ‘music acoustics’ 010.5 1.5 2 010.5 1.5 2 As it is lowered, the amplification factor time (sec) time (sec) gradually falls; when the pressure reaches The scientific papers supporting the present article, as well as sound files and video, a level at which the amplification factor in are at http://newt.phys.unsw.edu.au/jw/articulations.html Figure 2. The pressures measured at the bell (pale), in the mouthpiece (darker) and mouth (black) for four different articulations. The dashed line a cycle becomes less than the fraction lost shows the moment when the tongue ceases to touch the reed, an arrow (in staccato only) where it touches the reed again. (From Li et al., 2016). each cycle, then the note begins to decay. A multimedia introduction to waves and sound is at For this player, the accented and sforzando http://www.animations.physics.unsw.edu.au or search ‘physclips’

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