NOTE: all the percussion sound samples were performed by Matteo Manzini on 04/12/2007. Sound engineer: Valerio Carboni.

Structure of the instrument

Snare drum: top head	Snare drum: bottom head

The snare drum is a drum with a cylindrical shell. The model shown is the short-shell version of the military snare drum, and is used as part of a drum kit. The shell is metal (although in other models it can also be made of wood) and is about 20 cm high. The shell is closed at both ends by synthetic heads about 35 cm in diameter. Note that a set of snares is fitted on the bottom. It consists of a bundle of strands (in this case twisted metal wires), which can be brought into contact with the head, or moved away from it, by means of the adjusting screw and rods visible at the top of the image showing the underside of the instrument. The snares have a very precise acoustic function, illustrated in the next section. Unlike other drums of comparable size, which can be struck with the hands, the snare drum is struck exclusively with wooden sticks.

Acoustic characteristics

Acoustics means first of all geometry.

By looking at the instrument we can get an idea of which parts contribute to producing the sound, and of how they are coupled. They are:

1. The top head
2. the bottom head
3. the snares
4. the shell

The top and bottom heads are coupled to each other both through the air enclosed in the drum and through the vibrations of the shell. The snares are coupled essentially only to the bottom head, because the vibrations of the shell are essentially only radial.

Let us neglect the effect of the shell for the moment, and concentrate on the heads. The vibration modes of a single ideal membrane are described on the page normal modes of a circular membrane, and are also illustrated for the timpani. In that case we noted that the effect of the air enclosed in the large kettle-shaped bowl is decisive for producing a sound of definite pitch.

The case of the snare drum, however, is very different: the shell is cylindrical, and it does not enclose much air. The effect of the air is enough to couple the top and bottom heads, but the resulting sound is always of indefinite pitch. The drum still produces a broadband noise, but a rather "round" one, at least as long as the snares are not engaged.

The top head is excited directly by the stroke, and will therefore move according to a superposition of its normal modes. Given the radius, density and tension of the head, we can calculate its frequencies and compare them with those of the whole instrument.

The air inside the drum is compressible, so it behaves like a spring with respect to the two heads, which can in turn be considered as masses attached to springs (the heads also have elasticity). The simplest physical model is then to study the drum as if it were two coupled oscillators. Let us start with a "model drum", assuming that the two heads have equal mass and tension (even though this is not true for real drums). We know from physics how this system behaves (see the discussion of coupled oscillators).

If each oscillator considered on its own has frequency ${\displaystyle f_0}$, coupling through a spring produces two distinct frequencies ${\displaystyle f_1}$ and ${\displaystyle f_2}$ such that ${\displaystyle f_1<f_0<f_2}$. This is exactly what happens in the snare drum; indeed, it is not difficult to show that the two heads vibrate in the same normal mode. The two frequencies correspond to a different phase between them. In particular: if the heads oscillate in phase, the frequency will be lower than that of the single isolated head, while if they oscillate in antiphase it will be higher.

The reason? Simple, at least for the (0,1) modes: just recall the general formula for "any" mechanical oscillation:

${\displaystyle f\propto \sqrt{\frac{K}{m}}}$,

where K is the elasticity of the system and m its mass.

• In the first case (heads in phase) the frequency drops because the air between them moves together with the heads. What counts is not its elasticity but its inertia, which adds to that of the heads. So m increases, and f decreases.
• In the mode in which the heads are in antiphase, instead, the centre of mass of the air does not move, so the contribution of the air is reduced to its spring effect alone, which adds to that of the heads. Now K increases and, consequently, f increases too.

the first normal modes of the heads of the snare drum
single-head mode	heads in phase	heads in antiphase
{0,1}
{1,1}

Nomen omen

The drum roll (the Italian name of the instrument, rullante, comes from rullo, roll) is obtained by combining the double-stroke technique with the sticks (one stroke from the wrist, one from the fingers) with the effect of the snares, which are set vibrating by the bottom head and add a dry, crisp character to the succession of strokes, as well as a full-band background noise.

The trace shows that the pulses produced follow each other at an average distance of only 4 hundredths of a second, equivalent to a rate of as many as 25 strokes per second. Even when a portion of the sample is played back at half speed, the succession remains very dense.

waveform	sonogram	Audio
PC_Rullo.mp3 Roll, first loud, then soft	PC_Rullo_mezza_vel.mp3 Soft roll, half speed

Bringing out the harmonics

The spectrum emitted by the snare drum extends over the whole audible band and, at least in the short time of the impact, shows no particularly evident peaks. A high-resolution analysis is needed to attribute the peaks to the modes of the heads. However, some peaks remain fairly evident during the (relatively longer) time of free vibration. In our examples they are to be attributed to the vibration modes of the metal shell of the instrument. The sound produced by this set of frequencies is rather inharmonic, but some of the modes associated with these frequencies decay much faster than others, allowing one note or another to emerge from the sea of sound.

The player can adjust the colour of the sound (not the pitch, because the instrument remains of indefinite pitch) by striking the top head at different points. In the following examples the striking point is moved progressively towards the edge, and the corresponding colour becomes gradually brighter.

waveform	sonogram	Audio
		PC_ArmoniciR.mp3 PC_ArmoniciR

waveform	sonogram	Audio
		PC_ArmoniciR2.mp3 PC_ArmoniciR2

The role of the snares

As explained in the first section, the snares can be moved with a screw and drawn away from the bottom head, until they are no longer in contact with it even during the strokes. The sound of the instrument loses its "metallic" colour, and becomes the sound produced only by the resonance of the system formed by the heads, the metal shell and the air enclosed in the instrument.

waveform	sonogram	Audio
		PC_CordieraR.mp3 PC_CordieraR

Uses of the sticks

In this example the sound of the instrument on a single stroke is modified by striking with the stick first only the head, then only the metal rim of the shell, and then both together.

waveform	sonogram	Audio
		PC_MezzoCostaPienoR.mp3 PC_MezzoCostaPienoR

Check your understanding

Further reading and links

• Related questions and answers:
  • In a snare drum, why does the frequency change depending on whether the two heads vibrate in phase or in antiphase?