This page contains appendices to our scientific papers about clarinet articulation. It links to sound files and video and relates these to some figures from the papers. (For background, there are also less technical explanations on Clarinet Articulations our Introduction to Clarinet Acoustics.)
Almeida, A., Li, W., Smith, J. and Wolfe, J. (2017) "The mechanism for initial transients on the clarinet" J. Acoust. Soc. America, 142, 3376-3386. Copyright (2017) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The preceeding article may be found at J. Acoust. Soc. America.
Two figures from the study on human players paper are reproduced here. The pressure measured inside the player's mouth (Pmouth) is plotted in black. The pressure inside the mouthpiece (pmp) is dark grey and the radiated sound near the bell (prad) is light grey. Only Pmouth has a substantial DC component. Below them are two sound files for each graph: one was recorded inside the barrel of the clarinet, near the mouthpiece; Immediately below this is the radiated sound recorded simultaneously near the bell. The barrel recording is the darker timbre, because it is dominated by the fundamental, whereas the high harmonics radiate more efficiently from the bell.
The note is written C5 (sounding Bb4 on this transposing instrument). On these graphs, t = 0 (vertical dashed line) is by definition the instant when the tongue ceased contact with the reed. In the first figure, four different articulations are shown. For the normal articulation, the player played the note given in standard notation with only the expression mark mf (moderately loud). For the accent, '>' was marked over the note. As is usual in music, sforzando was indicated with the letters sfz and staccato with dots above the notes. In the staccato graph, the vertical arrow shows the moment when the tongue touched the reed to stop the note; the tongue was not used to stop the note in any other articulation.
In the following two graphs, the same player was asked to start the same note 'as softly as possible', both using the tongue (left) and without using it.
Effect of initial reed displacement and tongue acceleration
Figures from the clarinet-playing machine paper are reproduced here. Below each are sound files for each graph: the top row is the sound recorded inside the barrel of the clarinet, and below that is the radiated sound measured near the bell. The barrel recording is the darker timbre, because it is dominated by the fundamental, whereas the high harmonics are radiated more efficiently by the bell.
The top row in the figure plots the displacement y of the reed tip and the tongue, measured from the position of mechanical equilibrium for the reed. Two values of initial reed displacement Δy0 and two values of tongue acceleration a and force Ftongue are compared. The second row is a linear plot of the pressure in the barrel of the clarinet (pbarrel). (The magnified insets show the change in pbarrel at tongue release; the two scale bars are 20 Pa and 10 ms, respectively.) On the bottom two rows, each of the graphs plots three pressure signals on a logarithmic scale. The oscillating signal in pale grey is, again, pbarrel. The black line is the amplitude p1 of the first harmonic of pbarrel. The grey line is the amplitude p3 of the third harmonic.
Below the sound files are links to reduced versions of the videos used to produce the top row of graphs. These have been undersampled (from 8000 to 100 fps) to keep the files small and the videos short. (The short versions will typically run at ¼ speed).
After tongue release, the timing of the growth in reed vibration and sound depend on the initial displacement y0 of the reed and the tongue acceleration a. Here t200pa is defined as the time taken for pbarrel to reach 200 Pa (140 dB with respect to 20 μPa) after tongue release. The t200pa for (a) to (c) above is 77, 41 and 32 ms, indicating that vibration and sound reach higher values sooner following either a larger initial tongue displacement or a larger tongue acceleration. However, this variation does not appear to be caused by the reed having a greater initial potential energy (due to larger y0) or larger kinetic energy at release (larger a), because in each case the reed stops in its equilibrium position after tongue release for at least about 10 ms. Instead, the effect of y0 and a on the onset appear to be due to their transient effects on the air flow into the mouthpiece: in (c), the initially closed reed channel opens in about 7 milliseconds. p1, the amplitude of the first harmonic in pbarrel, shows a very rapid increase above noise levels that coincides with the action of tongue release in (b) and (c) above. This shows that either large tongue acceleration a or large initial displacement y0 of the reed can produce the immediate large change in p1. Similar sudden rises above noise in the p1 in the barrel were also observed when human players performed accents (see above). In both cases, however, it should be noted that, outside the bell, p1 does not rise suddenly above the noise (bottom row of Fig. 2) and no 'click' is heard in the sound files provided for these figures.
As the vibration of the reed grows, it quickly becomes asymmetrical as the reed approaches the lay. For the same tongue force Ft and initial displacement y0 of the reed [(a) and (b)], the main difference in reed motion due to the large change in a is that, for large a, the vibration reaches any given value earlier. When there is both a large initial displacement y0 and a large acceleration a (figure c above), there is (for this example) a further difference: the third harmonic rises abruptly above background and remains proportionally stronger during the rise in both reed motion and sound. In the barrel pressure, the third harmonic is below the first by about 14 dB in (a) and (b) and 12 dB in (c). In the quiescent state, however, the third harmonic has the same level (86 dB) in all three cases. (In the radiated sound, the sound level of the third harmonic is closer to that of the first because the bell radiates high frequencies better than low.)
For the three cases shown above, the exponential rate r of increase of the fundamental in pbarrel is 475±20 dB.s−1, indicating that (with constant P and F), the tongue force and acceleration have little effect on r. The amplitude (RMS) of the third harmonic p3 also shows an exponential increase with similar rate. This similarity in r is an important result: while the action of the tongue affects the timing of the rise, it has little direct effect on the transient. Instead, the tongue motion has an important effect on the air flow, because moving the tongue and reed changes the aperture into the mouthpiece.
Effect of lip force and blowing pressure
For the cases in the next figure, the tongue force and tongue acceleration were held constant while the steady force F exerted by the lip and the steady blowing pressure P were varied between experiments. The same variables are plotted as in the figure above. The first three rows show the effect of varying mouth pressure. Comparing the second and fourth rows shows the effect of lip force.
The examples above exhibit initial transients that are initially exponential (and so appear linear on these dB plots). According to the simple model in Li et al (2016b), the rate r of exponential growth in the initial transient is given by
r = (10log10e)*(Rreed+Rbore)/(RreedRboreC),
where the small signal conductance 1/Rreed = ∂U/∂P is the slope of the quasi-static dependence of the flow U past the reed on the mouth pressure P, C is the compliance in a parallel RboreLC resonance that empirically represents the impedance peak of the bore near which the instrument plays, Rbore represents the losses in the bore.
At high values of P, ∂U/∂P is negative because increasing P tends to close the reed aperture. When Rreed is negative and –Rreed < Rloss, r is positive and the initial transient has an exponential rise which continues until the small signal approximation fails and the defnition of Rreed no longer represents the U(P) curve. For any given lip force F, there is a finite range of the
the U(P) curve that satisfies
–Rreed < Rloss, and this determines the playing régime.
Negative rates of exponential growth
At values of P below the playing range mentioned above, the slope of the U(P) curve is insufficiently negative, i.e. –Rreed > Rloss, which gives a negative r, and so exponential decay is predicted. An example is given below: P is 2.34 kPa and F is 2.5 N. An abrupt increase in pressure is due to the disruption of air flow when the tongue releases the reed. This initiates a standing wave in the bore, whose amplitude decays exponentially, with a rate that may be slower than that produced when the reed is immobilised by the tongue (as at the end of a staccato note).
The sound level is low, especially the radiated sound.
This example comes from Inwood et al. (2016).
Here, tonguing by players was studied using a mouthpiece, on which a pressure transducer was mounted to measure the blowing pressure. Microphones in the bore and near the bell measured sound. An endoscope mounted next to the mouthpiece allowed observation of the player's tongue and also (usually) the motion of the reed. An example is shown below.
Over about 20 ms, the reed is pulled away from the mouthpiece (a-b), beyond its equilibrium position, by the saliva on the tongue. After release at (b), the reed relaxes to its equilibrium position (c), losing the potential and kinetic energy imparted by the tongue. Meanwhile, however, the pressure pulse has travelled to the tone-hole array and back. Successive interactions of the pulse with the reed amplify the signal and build up the standing wave in the bore. The horizontal bars in the third and fourth graphs show the distance between microphone and reed divided by the speed of sound. The note is D3, the lowest on the Bb clarinet.