2.1 Scientific Measurements of Brass Instrument Behaviour
35
following part, in which the note is sustained at a constant amplitude, is described
as the ‘steady state’.
The nature of the starting transient has an important influence on how the sound is
perceived by a listener (Grey and Moorer 1977). In the example shown in Fig. 2.2c,
the period of rapid growth lasts around 60 ms, which is a fairly typical value for
many orchestral brass instruments (Luce and Clark 1967). An instrument judged by
the player to be highly responsive is likely to be one on which it is easy to play
notes with short starting transients (see Sect. 1.2.10). This type of clean attack is
favoured when the frequencies of the air column resonances supporting the note
are harmonically aligned but can be disrupted by unwanted reflections due to sharp
bends, sudden changes in cross-section or partial blockages in the instrument bore
(Benade 1976).
The peak-to-peak amplitude of the pressure signal shown in Fig. 2.2b starts to
grow again after t = 2 s, when the crescendo begins. A zoom into a 50- ms-long
section of the signal starting at t = 4.25 s, marked by the green box in Fig. 2.2b, is
shown in Fig. 2.2d. At this point the sound had reached the maximum level of the
crescendo, and the peak-to-peak amplitude of the pressure signal has risen to 3.2 Pa.
In the time interval displayed, the pressure has a waveform characterised by a large
positive peak followed by a small negative peak, a small positive peak and a large
negative peak; this pattern repeats almost exactly every 2.86 ms. The repetition time
is called the period T of the signal. The number of times that the waveform repeats
in 1 second is called the frequency f . For the note played in this example
f = 1/T = 1/0.00286 = 350 Hz.
(2.1)
As a first approximation, the repetition frequency of the signal can be associated
with the perception of pitch: a doubling of frequency makes the pitch rise by
an octave. The relationship between the amplitude of the signal and the musical
dynamic level is clear from Fig. 2.2b: the increase of loudness in the crescendo is
correlated with the increase in the vertical width of the signal, which corresponds to
the difference between maximum and minimum values of the pressure. The form of
the pattern of the repeating section of wave in Fig. 2.2d is associated with the timbre
of the sound. In reality, however, the relationship between the perceptual quantities
(pitch, loudness, timbre) and the objective quantities (frequency, amplitude, waveform) is more complex: for example, the pitch of a note of fixed frequency can in
some circumstances change significantly if either the amplitude or the waveform is
modified (Fastl and Zwicker 2007; Roederer 2009; Hartmann 2013).
Before the start of the note in Fig. 2.2c, the value of the pressure is shown as 0. It
is important to realise that what this graph illustrates is the acoustic pressure, which
is the change in the steady pressure of the atmosphere due to the arrival of the sound
wave. In mathematical terms
p tot = p atmos + p ac
(2.2)
35
following part, in which the note is sustained at a constant amplitude, is described
as the ‘steady state’.
The nature of the starting transient has an important influence on how the sound is
perceived by a listener (Grey and Moorer 1977). In the example shown in Fig. 2.2c,
the period of rapid growth lasts around 60 ms, which is a fairly typical value for
many orchestral brass instruments (Luce and Clark 1967). An instrument judged by
the player to be highly responsive is likely to be one on which it is easy to play
notes with short starting transients (see Sect. 1.2.10). This type of clean attack is
favoured when the frequencies of the air column resonances supporting the note
are harmonically aligned but can be disrupted by unwanted reflections due to sharp
bends, sudden changes in cross-section or partial blockages in the instrument bore
(Benade 1976).
The peak-to-peak amplitude of the pressure signal shown in Fig. 2.2b starts to
grow again after t = 2 s, when the crescendo begins. A zoom into a 50- ms-long
section of the signal starting at t = 4.25 s, marked by the green box in Fig. 2.2b, is
shown in Fig. 2.2d. At this point the sound had reached the maximum level of the
crescendo, and the peak-to-peak amplitude of the pressure signal has risen to 3.2 Pa.
In the time interval displayed, the pressure has a waveform characterised by a large
positive peak followed by a small negative peak, a small positive peak and a large
negative peak; this pattern repeats almost exactly every 2.86 ms. The repetition time
is called the period T of the signal. The number of times that the waveform repeats
in 1 second is called the frequency f . For the note played in this example
f = 1/T = 1/0.00286 = 350 Hz.
(2.1)
As a first approximation, the repetition frequency of the signal can be associated
with the perception of pitch: a doubling of frequency makes the pitch rise by
an octave. The relationship between the amplitude of the signal and the musical
dynamic level is clear from Fig. 2.2b: the increase of loudness in the crescendo is
correlated with the increase in the vertical width of the signal, which corresponds to
the difference between maximum and minimum values of the pressure. The form of
the pattern of the repeating section of wave in Fig. 2.2d is associated with the timbre
of the sound. In reality, however, the relationship between the perceptual quantities
(pitch, loudness, timbre) and the objective quantities (frequency, amplitude, waveform) is more complex: for example, the pitch of a note of fixed frequency can in
some circumstances change significantly if either the amplitude or the waveform is
modified (Fastl and Zwicker 2007; Roederer 2009; Hartmann 2013).
Before the start of the note in Fig. 2.2c, the value of the pressure is shown as 0. It
is important to realise that what this graph illustrates is the acoustic pressure, which
is the change in the steady pressure of the atmosphere due to the arrival of the sound
wave. In mathematical terms
p tot = p atmos + p ac
(2.2)