9.1 Brass Instruments in the Ancient World
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mately conical instrument curved into an almost complete circle with a diametral
supporting strut. The musician in the centre is holding a lituus, whose shape
resembles a shepherd’s crook; a considerable section of the bore is approximately
cylindrical, but the final section is a curved conical bell.
As part of the European Musical Archaeology Project (EMAP 2018), reproductions of the Etruscan cornu and lituus have been constructed. The fact that the two
instruments are shown in close proximity in Fig. 9.1 and in other contemporary
images suggests that they were probably played simultaneously. Part of the remit
of the EMAP team was to organise public concerts in which the reproduced
instruments could be demonstrated. Since there was some flexibility in the choice
of absolute length scale of each instrument, it was requested by the musicians who
were to play the instruments that they should be scaled to play ‘in tune’ (Campbell
et al. 2017). But what does ‘in tune’ mean in this context?
The underlying problem is that the cornu has an almost conical bore throughout
(like an alphorn), whereas a large fraction of the lituus is cylindrical (like a
trombone). Figures 9.2 and 9.3 show the effect of increasing the conicity of an
originally cylindrical tube 3 m long on the equivalent fundamental pitches of its
acoustic modes (Sect. 4.3.4). The input radius is maintained constant at 10 mm; as
the cone half-angle is increased from 0 to 1 ◦ , the EFP of the first tube resonance
increases by 900 cents, while the EFP of the resonances from the sixth upwards are
not significantly changed. It is therefore impossible to find a length-scaling factor
which can bring a mostly conical instrument into tune with a mostly cylindrical
instrument over its whole range of resonances. Shortening the cylinder would raise
the lower resonance frequencies, bringing them closer to those of the cone, but the
higher resonances of the cylinder would then be much higher than the corresponding
resonances of the cone.
The EFP plots in Fig. 9.3 were derived from input impedance curves calculated
numerically using the transfer matrix method (see Sect. 4.7). Applying the same
Fig. 9.2 A set of tubes, each with an input radius of 10 mm, a length of 3000 mm, and output radii
ranging from 10 mm to 50 mm
403
mately conical instrument curved into an almost complete circle with a diametral
supporting strut. The musician in the centre is holding a lituus, whose shape
resembles a shepherd’s crook; a considerable section of the bore is approximately
cylindrical, but the final section is a curved conical bell.
As part of the European Musical Archaeology Project (EMAP 2018), reproductions of the Etruscan cornu and lituus have been constructed. The fact that the two
instruments are shown in close proximity in Fig. 9.1 and in other contemporary
images suggests that they were probably played simultaneously. Part of the remit
of the EMAP team was to organise public concerts in which the reproduced
instruments could be demonstrated. Since there was some flexibility in the choice
of absolute length scale of each instrument, it was requested by the musicians who
were to play the instruments that they should be scaled to play ‘in tune’ (Campbell
et al. 2017). But what does ‘in tune’ mean in this context?
The underlying problem is that the cornu has an almost conical bore throughout
(like an alphorn), whereas a large fraction of the lituus is cylindrical (like a
trombone). Figures 9.2 and 9.3 show the effect of increasing the conicity of an
originally cylindrical tube 3 m long on the equivalent fundamental pitches of its
acoustic modes (Sect. 4.3.4). The input radius is maintained constant at 10 mm; as
the cone half-angle is increased from 0 to 1 ◦ , the EFP of the first tube resonance
increases by 900 cents, while the EFP of the resonances from the sixth upwards are
not significantly changed. It is therefore impossible to find a length-scaling factor
which can bring a mostly conical instrument into tune with a mostly cylindrical
instrument over its whole range of resonances. Shortening the cylinder would raise
the lower resonance frequencies, bringing them closer to those of the cone, but the
higher resonances of the cylinder would then be much higher than the corresponding
resonances of the cone.
The EFP plots in Fig. 9.3 were derived from input impedance curves calculated
numerically using the transfer matrix method (see Sect. 4.7). Applying the same
Fig. 9.2 A set of tubes, each with an input radius of 10 mm, a length of 3000 mm, and output radii
ranging from 10 mm to 50 mm