164
4 After the Lips: Acoustic Resonances and Radiation
Fig. 4.57 Effect of opening the first hole on the input impedance of the model serpent. Solid blue
line: hole closed. Dashed red line: hole open (Color figure online)
f c
c
2π
b
a
1
(sl e ) 1/2 ,
(4.70)
where s is the inter-hole spacing.
Equation 4.70 can also be used to estimate the cutoff frequency of a conical
instrument provided that the ratio b/a is approximately the same for all the open
holes. An example is provided by the ophicleide. The five holes nearest the bell
have an average spacing s 15 cm; assuming equal values of h and b/a for all
five holes give a predicted cutoff frequency, f c = 475 Hz. This is considerably
higher than the value of 305 Hz for a single tonehole calculated using Eq. 4.69. The
tonehole lattice is effective at reflecting the wave arriving from the mouthpiece over
a bigger-frequency range, leading to an increased number of high impedance peaks
and a potential improvement in the centring and stability of the played notes in this
frequency range. Opening all the five lowest holes on the instrument is in fact an
often preferred alternative fingering for the note D2.
Closed toneholes also have a frequency-dependent influence on sound transmission, but in this case, the closed holes behave as a low-pass filter. Above the cutoff
frequency, a lattice of closed toneholes attenuates the sound waves travelling down
the bore. Strong reflections can also occur at frequencies for which the height h of
the closed branch is equal to a quarter wavelength of the sound wave. These effects
can be important in instruments like the bassoon, with long and narrow toneholes
(Chaigne and Kergomard 2016), but for the relatively short and wide toneholes on
labrosones, they are of little significance.
4.5 Mutes
In audio technology the term ‘muting’ refers to the silencing of a signal. In a musical
score, the instruction ‘mute’, or the Italian equivalent ‘con sordino’, has a different
meaning. Mutes used on musical instruments are not normally designed to suppress
4 After the Lips: Acoustic Resonances and Radiation
Fig. 4.57 Effect of opening the first hole on the input impedance of the model serpent. Solid blue
line: hole closed. Dashed red line: hole open (Color figure online)
f c
c
2π
b
a
1
(sl e ) 1/2 ,
(4.70)
where s is the inter-hole spacing.
Equation 4.70 can also be used to estimate the cutoff frequency of a conical
instrument provided that the ratio b/a is approximately the same for all the open
holes. An example is provided by the ophicleide. The five holes nearest the bell
have an average spacing s 15 cm; assuming equal values of h and b/a for all
five holes give a predicted cutoff frequency, f c = 475 Hz. This is considerably
higher than the value of 305 Hz for a single tonehole calculated using Eq. 4.69. The
tonehole lattice is effective at reflecting the wave arriving from the mouthpiece over
a bigger-frequency range, leading to an increased number of high impedance peaks
and a potential improvement in the centring and stability of the played notes in this
frequency range. Opening all the five lowest holes on the instrument is in fact an
often preferred alternative fingering for the note D2.
Closed toneholes also have a frequency-dependent influence on sound transmission, but in this case, the closed holes behave as a low-pass filter. Above the cutoff
frequency, a lattice of closed toneholes attenuates the sound waves travelling down
the bore. Strong reflections can also occur at frequencies for which the height h of
the closed branch is equal to a quarter wavelength of the sound wave. These effects
can be important in instruments like the bassoon, with long and narrow toneholes
(Chaigne and Kergomard 2016), but for the relatively short and wide toneholes on
labrosones, they are of little significance.
4.5 Mutes
In audio technology the term ‘muting’ refers to the silencing of a signal. In a musical
score, the instruction ‘mute’, or the Italian equivalent ‘con sordino’, has a different
meaning. Mutes used on musical instruments are not normally designed to suppress