Introduction to Acoustics

ise to a more percussive and brighter sound. Higher
partials will also be emphasised by the use of metal
beaters or drumsticks with hard-wooden striking heads
rather than leather or soft felt-covered stick heads. This
is illustrated by the second pulse, which would produce
a softer, mellower sound, without such a strong initial
attack. Clearly, the loudness of the drum note will be
proportional to the mass m of the striking drumstick
head and its impact velocity v, delivering an impulse
of ≈ mv.
Audio illustrates the change in sound of
a timpani note, as the player progressively strikes the
drum with a hard felt stick, starting from the outside
edge and moving towards the centre, in equal intervals
of ≈ one eighth of the radius. Audio illustrates
the sound of a timpani when struck at one quarter of the
radius from the edge, using a succession of drumsticks
of increasing hardness, from a large softly felted beater
to a wooden beater.
In modern performances of baroque and early classical
music, the timpanist will use relatively light sticks,
with leather-coated striking heads, while for music of
the romantic period larger and softer felt-covered drumsticks
will often be used.
Many drums of ethnic origin are played with the
hands, hitting the drum head with fingers, clenched fists
or open palms to create quite different kinds of sounds. In
some cases, the player can also press down on the drum
head to increase the tension and hence change pitch of
the note. For a double-headed drum, the coupling of the
air between the drum heads can even enable the player to
change the pitch and sound of a given note by applying
pressure to the drum head not being struck.
We now consider a number of well-known percussion
instruments based on stretched membranes, which
illustrate the above principles. These will include drums
with a well defined pitch, such as kettle drums (timpani)
and the Indian tabla and mrdanga, and drums with no
defined pitch, such as the side and bass drum.
Kettle Drums (Timpani)
The kettle drum or timpani traditionally used a specially
prepared calfskin stretched over a hollow, approximately
hemispherical, copper kettle generally beaten out of copper
sheet. Nowadays, thin (0.19 mm) mylar sheet is often
used in preference to calfskin for the drum skin, because
of its uniformity and reduced susceptibility to changes
in tension from variations in temperature and humidity.
The drum skin is stretched over a supporting ring attached
to the kettle, with the tension of the skin typically
adjusted using 6–8 tuning screws equally spaced around
Musical Acoustics 15.4 Percussion Instruments 645
the circumference. The player adjusts these screws to
tune the instrument and to optimise the quality of tone
produced. In modern instruments, a mechanical pedal
arrangement can be used to quickly change the tension
and thereby the tuning, by pushing the supporting ring
up against the drumhead. Typically, such an arrangement
can increase the tension by up to a factor of two, raising
the pitch by a perfect fifth. In the modern classical
symphony orchestra, the timpanist will use two or three
timpani of different sizes to cover the range of pitched
notes required.
Figure 15.116 shows the waveform and spectrum of
the immediate and delayed sound of a timpani note (the
first drum note in audio ). The initial sound
includes contributions from all the modes excited. This
includes not only the vibrational modes of the drum
head, but also the air inside the kettle, the kettle itself and
even the supporting legs and vibrations induced in the
floor. Many of these vibrations die away rather quickly,
leaving a number of prominent, slowly decaying, drumskin
modes. Note in particular, the strongly damped (01)
mode at ≈ 140 Hz and the less strongly damped modes
(02) and (03) modes at 210 Hz and 284 Hz, tuned ap-
(dB)
0
–20
–40
–60
–80
–100
0 200 400 600 800 1000
(Hz)
1s
Fig. 15.116 Decaying waveform of a timpani note and FFT
spectra at the start of a note (upper trace) and after 1 s (lower
trace)
Part E 15.4