4.3 Bore Profiles of Brass Instruments
145
Fig. 4.37 EFP for two tubes of the same sounding length 2834 mm: a plain cylinder (blue circles)
and a cylinder with a Denis Wick 5AL mouthpiece and mouthpipe (red squares) (Color figure
online)
Fig. 4.38 Increase in equivalent cone length L ec when the first section of the plain cylinder is
replaced by a Denis Wick 5AL mouthpiece and mouthpipe
gently tapering mouthpipe. The introduction of the mouthpiece makes no significant
difference to the frequencies of the first two impedance peaks (whose EFP values
are not shown in Fig. 4.37); as expected, the mouthpiece is behaving in the lowfrequency range like a cylindrical tube of the same length. As the peak number
increases, the EFP difference also grows; at the tenth peak, whose frequency is close
to f R , the introduction of the mouthpiece has reduced the EFP by 45 cents. Since
the pitch D5 is at the top of the normal playing range of the tenor trombone, we
can summarise the effect of the mouthpiece on intonation by stating that it has little
effect on the pitches of the low register but flattens the high register notes by an
amount which increases with the number of the natural note.
In Fig. 4.38 the change in equivalent cone Length L ec due to the mouthpiece is
plotted as a function of frequency. This curve shows that the increase in effective
145
Fig. 4.37 EFP for two tubes of the same sounding length 2834 mm: a plain cylinder (blue circles)
and a cylinder with a Denis Wick 5AL mouthpiece and mouthpipe (red squares) (Color figure
online)
Fig. 4.38 Increase in equivalent cone length L ec when the first section of the plain cylinder is
replaced by a Denis Wick 5AL mouthpiece and mouthpipe
gently tapering mouthpipe. The introduction of the mouthpiece makes no significant
difference to the frequencies of the first two impedance peaks (whose EFP values
are not shown in Fig. 4.37); as expected, the mouthpiece is behaving in the lowfrequency range like a cylindrical tube of the same length. As the peak number
increases, the EFP difference also grows; at the tenth peak, whose frequency is close
to f R , the introduction of the mouthpiece has reduced the EFP by 45 cents. Since
the pitch D5 is at the top of the normal playing range of the tenor trombone, we
can summarise the effect of the mouthpiece on intonation by stating that it has little
effect on the pitches of the low register but flattens the high register notes by an
amount which increases with the number of the natural note.
In Fig. 4.38 the change in equivalent cone Length L ec due to the mouthpiece is
plotted as a function of frequency. This curve shows that the increase in effective