How Do Drums Work? A Stretched Membrane With Untidy Physics

When a stretched membrane is struck it vibrates in patterns called modes, each with lines and circles that stay still while the areas between them move up and down. For a string the frequencies of these modes are exact multiples of the lowest, so the ear fuses them into one pitch. For a circular membrane the mathematics produces frequency ratios determined by the zeros of Bessel functions, which are irregular numbers with no simple relationship, so the modes clash rather than reinforcing. The ear hears a thud with a vague sense of highness or lowness rather than a note. Striking position matters enormously, because a mode with a stationary line at the point of contact will not be excited, so hitting the centre emphasises the fundamental circular mode and hitting near the rim brings out the modes with diameters across the head, which is why the same drum produces a deep boom or a bright ring depending on where the stick lands.

One family of drums produces a definite pitch, and the way it does so demonstrates the principle. The Indian tabla and its larger companion have a black circular patch on the head, made of a paste of iron filings, rice or other materials built up in layers, positioned off-centre on the larger drum and centrally on the smaller. The added mass changes the relative frequencies of the modes and shifts several of them into an approximately harmonic relationship with the lowest, which is why the tabla sings a recognisable note while a Western drum does not. The effect was analysed mathematically by C. V. Raman in the 1930s, the same physicist who won a Nobel Prize for the scattering effect that carries his name, and it remains one of the more elegant demonstrations that pitch in percussion is an engineering achievement rather than a given.

Each component of a drum kit drum affects the sound in identifiable ways:

• •The batter head, struck by the stick, whose tension sets the frequencies and whose thickness and coating shape the attack and damping
• •The resonant head underneath, which is coupled to the batter head through the air in the shell and adds sustain, and whose tension relative to the top produces either a pitch bend or a steady tone
• •The shell, of wood or metal, which contributes less than most drummers believe according to acoustic measurement, with head choice and tuning dominating
• •The bearing edge, where the shell meets the head, whose profile determines how much of the head is free to vibrate and is one of the more consequential details
• •The vent hole, which lets air move so the heads are not sealed against a fixed volume
• •On a snare drum, a set of wires stretched against the lower head which rattle in sympathy, adding a broadband noise that is the instrument's defining sound and which also responds to other drums playing nearby

Drums are close to universal and the construction varies with materials and purpose. Frame drums, a skin on a shallow hoop, are among the oldest and appear from Ireland to Central Asia to the Arctic. The djembe of West Africa is a single-headed goblet drum played bare-handed, capable of a wide tonal range from the centre to the edge, and traditionally carved from a single piece of wood. The tabla pair supports the rhythmic cycles of North Indian classical music, played with an extremely developed finger technique and a spoken syllable system that names every stroke, so a rhythm can be recited before it is played. Taiko drums in Japan are played as an ensemble with full-body movement that is part of the performance. Steel pans in Trinidad are a twentieth-century invention, tuned by hammering distinct note areas into an oil drum head, and are the rare percussion instrument with full melodic capability. Talking drums in West Africa have tension cords squeezed under the arm to change pitch in flight, allowing them to imitate the tonal patterns of speech closely enough to carry messages.

The drum kit is an American invention of the early twentieth century and its cause was economic. Theatres and dance halls employed several percussionists, and around 1900 the bass drum pedal made it possible for one player to operate bass drum and snare simultaneously, after which cymbals, tom-toms and other instruments were added within reach of one seated player. The hi-hat evolved through several forms into the pedal-operated pair of cymbals that anchors most modern playing. The consequence was that a rhythm section could be smaller and cheaper, which mattered for jazz and then for every popular form since, and that one person became responsible for coordinating four limbs independently, which is the technical demand the instrument is known for. Electronic drums and programmed rhythm followed from the 1980s, and the enduring difference is that a struck membrane produces a different sound with every strike and a sample does not, which is why velocity layering and round-robin sampling exist and why the argument about whether a machine can replace a drummer keeps being had.

A drumhead's modes of vibration sit at frequency ratios that are not whole-number multiples, so the sound has no definite pitch, and where the head is struck determines which modes are excited and therefore the tone. The Indian tabla achieves a clear pitch by adding a patch of loaded paste that shifts several modes into a harmonic relationship. Head tension and type dominate the sound far more than the shell, and the drum kit was assembled around 1900 because a bass drum pedal let one player replace several.