304
6 Shocks and Surprises: Refining the Elementary Model
the instrument results in a continuous decrease in the frequency of each air column
resonance. In a normal performance, the player gradually relaxes the embouchure
muscles to ensure that the lip resonance frequency tracks the descending frequency
of the specific air column resonance which is primarily collaborating in the sound
production.
It is an illuminating exercise for a trombone player to make a glissando gesture
while attempting to maintain a constant embouchure. If, for example, the player
sounds the note B 3, which is the fourth natural note of the tenor trombone, the
lip resonance frequency will be close to 233 Hz. As the slide is extended, there
will be an increasing frequency difference between the lip resonance and the fourth
air column resonance: the playing pitch will drop below B 3, but not as much as
in a normally played glissando. Eventually the slide will have moved so far that
the frequency of the fifth air column resonance will approach 233 Hz; the lips will
abandon the partnership with the fourth resonance and jump up to a pitch a little
above B 3. This new partnership with the fifth resonance will continue until the
slide is almost fully extended, when the pitch will again make an upward jump to
gain the support of the sixth resonance.
An experimental study by Cullen et al. (2000) of threshold values of playing
frequencies and corresponding mouth pressures during a glissando with constant
embouchure has helped to illuminate some aspects of the phase behaviour of the
lips. Since it is difficult for a human player to avoid involuntary embouchure changes
which are the fruit of extensive practice in normal glissando playing, the experiment
was carried out using an artificial mouth.
The first step in the procedure was to choose a set of lip parameters such that
the mouth was capable of sounding the instrument over the complete range of
tube lengths available. The mechanical response for this embouchure was then
measured with no mouth overpressure, the forcing sinusoidal acoustic pressure
being generated by the loudspeaker mounted on the mouth cavity. A second
mechanical response measurement was made with a mouth overpressure just below
the threshold for self-sustained oscillation. Finally the loudspeaker was switched
off, and the mouth overpressure increased until a clear note was sounded; the
overpressure was then reduced until the oscillation died out. This procedure was
repeated several times to establish the experimental threshold pressure, defined
as the lowest overpressure at which a stable self-sustained oscillation could be
obtained. The frequency of this oscillation, taken to be the threshold playing
frequency, was also recorded.
Results of this investigation, displayed in Fig. 6.20a, demonstrate how the
threshold values of mouth pressure and playing frequency vary as the trombone slide
is extended. Comparable results of simulations using inward- and outward-striking
1DOF models are shown in Fig. 6.20b.
The measured range of threshold pressure is similar to the range predicted by the
inward-striking model. The outward-striking model predicts much higher threshold
pressure values, but they are still within a range which a human player could
easily produce. Both measurements and simulation demonstrate distinct regimes
corresponding to the fourth, fifth and sixth modes of the acoustic resonator. The
6 Shocks and Surprises: Refining the Elementary Model
the instrument results in a continuous decrease in the frequency of each air column
resonance. In a normal performance, the player gradually relaxes the embouchure
muscles to ensure that the lip resonance frequency tracks the descending frequency
of the specific air column resonance which is primarily collaborating in the sound
production.
It is an illuminating exercise for a trombone player to make a glissando gesture
while attempting to maintain a constant embouchure. If, for example, the player
sounds the note B 3, which is the fourth natural note of the tenor trombone, the
lip resonance frequency will be close to 233 Hz. As the slide is extended, there
will be an increasing frequency difference between the lip resonance and the fourth
air column resonance: the playing pitch will drop below B 3, but not as much as
in a normally played glissando. Eventually the slide will have moved so far that
the frequency of the fifth air column resonance will approach 233 Hz; the lips will
abandon the partnership with the fourth resonance and jump up to a pitch a little
above B 3. This new partnership with the fifth resonance will continue until the
slide is almost fully extended, when the pitch will again make an upward jump to
gain the support of the sixth resonance.
An experimental study by Cullen et al. (2000) of threshold values of playing
frequencies and corresponding mouth pressures during a glissando with constant
embouchure has helped to illuminate some aspects of the phase behaviour of the
lips. Since it is difficult for a human player to avoid involuntary embouchure changes
which are the fruit of extensive practice in normal glissando playing, the experiment
was carried out using an artificial mouth.
The first step in the procedure was to choose a set of lip parameters such that
the mouth was capable of sounding the instrument over the complete range of
tube lengths available. The mechanical response for this embouchure was then
measured with no mouth overpressure, the forcing sinusoidal acoustic pressure
being generated by the loudspeaker mounted on the mouth cavity. A second
mechanical response measurement was made with a mouth overpressure just below
the threshold for self-sustained oscillation. Finally the loudspeaker was switched
off, and the mouth overpressure increased until a clear note was sounded; the
overpressure was then reduced until the oscillation died out. This procedure was
repeated several times to establish the experimental threshold pressure, defined
as the lowest overpressure at which a stable self-sustained oscillation could be
obtained. The frequency of this oscillation, taken to be the threshold playing
frequency, was also recorded.
Results of this investigation, displayed in Fig. 6.20a, demonstrate how the
threshold values of mouth pressure and playing frequency vary as the trombone slide
is extended. Comparable results of simulations using inward- and outward-striking
1DOF models are shown in Fig. 6.20b.
The measured range of threshold pressure is similar to the range predicted by the
inward-striking model. The outward-striking model predicts much higher threshold
pressure values, but they are still within a range which a human player could
easily produce. Both measurements and simulation demonstrate distinct regimes
corresponding to the fourth, fifth and sixth modes of the acoustic resonator. The