374
7 The Amazing Diversity of Brass Instruments
will not have matched that of the trumpet of the period. Today, orchestral cornet
parts are often played on trumpets: since the designs of cornets and trumpets have
converged, this matters much less.
7.6 Going Further: Alternative Taxonomies
Brassiness Potential has been extensively used in this book as a parameter which can
be derived from physical measurements of an instrument—measurements such as a
maker might use to specify the design of an instrument model—and which directly
relates to the acoustical properties of an instrument which determine timbre. It is
also possible to use other parameters to construct a taxonomy. One such parameter,
which also relates to brightness of timbre, is defined by
N =
2L peak
πD peak
,
(7.2)
where L peak is the distance from the mouthpiece receiver to the point on the bore
axis at which the horn function peaks, and D peak is the bell diameter at the same
point. The values of length and diameter at the horn function peak are used rather
than the values at the bell exit because the widest parts of a flaring bell make a
minimal contribution to standing waves. The position of the horn function peak can
be derived from measurement of the bore of the instrument (see Sect. 4.3.7), and is
relatively insensitive to measurement error. The parameter N is found empirically to
approximate to the number of impedance peaks of significant size (Pyle and Myers
2006).
Figure 7.54 is a scatter plot of parameter N and minimum bore for typical
instruments in 8-ft C and 9-ft B . There is a similarity with the B / D min scatter
plot for instruments in 8-ft C and 9-ft B , Fig. 7.35.
In Sect. 2.2.5 we introduced the concept of the cutoff frequency of the bell of
a brass instrument. Sound waves of a frequency below cutoff are mostly reflected
when they reach the bell end of an instrument, while waves with a frequency above
cutoff are mostly radiated. A typical plot of input impedance against frequency for
a brass instrument, such as that shown in Fig. 4.12, shows that above a certain
frequency the height of the peaks decreases markedly, and in a region around a
higher frequency the peaks become small and effectively disappear. These are the
effects of the weakening reflection and strengthening radiation at the bell with
increasing frequency. The player experiences the peaks as slotting (see Sect. 1.2.2);
at the high pitches corresponding to frequencies where the peaks are insignificant or
absent, the notes are difficult to sound and to play in tune.
Assigning a single cutoff frequency to take account of these effects is not always
possible. Several methods giving figures for cutoff frequency have been proposed.
For bells with pronounced flares, such as those of trumpets and trombones, a cutoff
frequency can be derived from the peak value of the horn function, which in turn
7 The Amazing Diversity of Brass Instruments
will not have matched that of the trumpet of the period. Today, orchestral cornet
parts are often played on trumpets: since the designs of cornets and trumpets have
converged, this matters much less.
7.6 Going Further: Alternative Taxonomies
Brassiness Potential has been extensively used in this book as a parameter which can
be derived from physical measurements of an instrument—measurements such as a
maker might use to specify the design of an instrument model—and which directly
relates to the acoustical properties of an instrument which determine timbre. It is
also possible to use other parameters to construct a taxonomy. One such parameter,
which also relates to brightness of timbre, is defined by
N =
2L peak
πD peak
,
(7.2)
where L peak is the distance from the mouthpiece receiver to the point on the bore
axis at which the horn function peaks, and D peak is the bell diameter at the same
point. The values of length and diameter at the horn function peak are used rather
than the values at the bell exit because the widest parts of a flaring bell make a
minimal contribution to standing waves. The position of the horn function peak can
be derived from measurement of the bore of the instrument (see Sect. 4.3.7), and is
relatively insensitive to measurement error. The parameter N is found empirically to
approximate to the number of impedance peaks of significant size (Pyle and Myers
2006).
Figure 7.54 is a scatter plot of parameter N and minimum bore for typical
instruments in 8-ft C and 9-ft B . There is a similarity with the B / D min scatter
plot for instruments in 8-ft C and 9-ft B , Fig. 7.35.
In Sect. 2.2.5 we introduced the concept of the cutoff frequency of the bell of
a brass instrument. Sound waves of a frequency below cutoff are mostly reflected
when they reach the bell end of an instrument, while waves with a frequency above
cutoff are mostly radiated. A typical plot of input impedance against frequency for
a brass instrument, such as that shown in Fig. 4.12, shows that above a certain
frequency the height of the peaks decreases markedly, and in a region around a
higher frequency the peaks become small and effectively disappear. These are the
effects of the weakening reflection and strengthening radiation at the bell with
increasing frequency. The player experiences the peaks as slotting (see Sect. 1.2.2);
at the high pitches corresponding to frequencies where the peaks are insignificant or
absent, the notes are difficult to sound and to play in tune.
Assigning a single cutoff frequency to take account of these effects is not always
possible. Several methods giving figures for cutoff frequency have been proposed.
For bells with pronounced flares, such as those of trumpets and trombones, a cutoff
frequency can be derived from the peak value of the horn function, which in turn