How does a harmonium work?

An Indian harmonium is a wooden box about the size of a small suitcase. You pump air with one hand and play the keys with the other.

At the back is the bellows, a hinged flap you swing open and shut. Each push forces air through a one-way valve into an inner reservoir, a second bellows held shut by springs. The springs squeeze the air, so it waits under a small, steady pressure.

Above the reservoir sits the reed board: rows of little chambers called reed cells, each holding a brass reed. There is one row, or bank, of reeds for each voice. Pressing a key lifts a padded valve, the pallet, and the air rushes out through that key's reeds. Stop knobs choose which banks get air. The sound escapes through the grill.

No pipes and no strings: each note is a tiny brass tongue buzzing in a slot. Unlike a flute, where the air in a tube sets the note (see FluteClear), here the reed sets it.

Each reed is a thin brass tongue, riveted at one end over a slot cut in a brass plate. The tongue fits the slot so closely that you can barely see light around it.

Air under pressure pushes the tongue into the slot. Like a diving board, it bends, then springs back, overshoots and swings through again. Each time the tongue leaves the slot, a gap opens and a puff of air escapes. Hundreds of puffs a second are the sound. It is called a free reed because the tongue swings freely through its slot, instead of beating against a frame like a clarinet reed. How fast the air squeezes through the gap follows Bernoulli's rule (see BernoulliClear).

The tongue swings at its own natural frequency, like a ruler twanged on a desk. For a strip clamped at one end, f = 0.56 · (t / L²) · √(E / 12ρ): thicker is higher, and longer is much lower, because length counts twice. Brass gives about 580 × t / L².

Makers tune a reed by scraping it. Scrape near the tip and you remove weight where it swings most, so the pitch goes up. Scrape near the root and you weaken the spring, so the pitch goes down.

Your hand can't push air perfectly evenly. So a harmonium has two bellows. The one you pump, at the back, swings open to suck in room air through a flap valve, then you push it shut and the air is forced through a one-way valve into the reservoir inside.

The reservoir is a second bellows held shut by springs. As it fills, its top board rises and the springs push back harder. Their push, spread over the board, is the wind pressure: about 0.5 to 1.5 kilopascals, the weight of a 5 to 15 cm column of water. That is only about 1% above the air around us, but it is plenty to make a reed speak.

Every open reed lets air out, about a tenth of a litre each second. Hold a chord on three banks and nine reeds drain the reservoir quickly, so you must pump faster. Stop pumping and the springs keep the sound going for a few seconds, then the pressure falls and the reeds stop speaking. Pump harder and the reservoir sits fuller, the pressure rises, and the harmonium plays louder: that is its only volume control.

Under every key sit several reeds, one in each bank. The stop knobs slide shutters that let air into a whole bank, or keep it out.

On a three-reed harmonium the banks are named like voices. The male reeds sound the note you see on the key. The bass reeds sound an octave lower, with long, heavy tongues. The female reeds sound an octave higher. Add them together and one key plays two or three reeds at once, for a fuller, richer sound.

Each reed gives a whole ladder of harmonics: 2, 3, 4 … times its frequency. An octave bank adds reeds whose harmonics land right on top of the male reed's, so the chart gets taller rather than more crowded. Reeds are never tuned exactly the same, so their harmonics beat slowly against each other and the sound shimmers. Some harmoniums add a second male bank tuned a few cents sharp on purpose. This musette gives a wavy, accordion-like beat of a few times a second.

Drone stops open extra reeds that sound all by themselves while the stop is out, usually Sa and the Pa below it, so a singer always hears the home note.

A singer or a sarangi player can slide to any pitch. A harmonium can't: each key has reeds tuned once, in the factory. Most are tuned to equal temperament (12-TET), the same system as a piano, where every semitone is exactly 100 cents (see PianoClear).

Equal temperament is a clever compromise. It lets you play in any key, but only the octave is truly pure. The pure intervals, which singers settle into naturally, are simple ratios: Pa is 3/2 of Sa (702 cents), Ga is 5/4 (386 cents, not 400). Hindustani music goes further, with shrutis, finer pitches that shift from raga to raga, and slides (meend) between notes.

When two notes are a little off a pure ratio, their harmonics clash and beat. An equal-tempered Sa and Ga on a harmonium beat about ten times a second. This is why many musicians, including Rabindranath Tagore and the British critics behind the 1940 ban on All India Radio, called it the wrong instrument for Indian music. Players answer with how they play: short notes, graces, and following the singer.

Many harmoniums have a scale changer: the whole keyboard slides sideways over the reed board, so the key you play as Sa can sound a different reed. You keep your fingering and the singer gets their own pitch.

European reed organs stood on the floor with foot pedals. Missionaries and traders brought them to India in the 1800s, but Indian musicians sit on the floor. In Calcutta, Dwarkanath Ghose of Dwarkin & Son, who opened his firm in 1875, is widely credited with the answer: a small box with a bellows at the back pumped by hand, and drone stops for Indian music.

It was cheap, easy to carry, loud enough for a crowd and always in tune with itself. Within a few decades it was everywhere: bhajan and kirtan, the Sikh kirtan of the gurdwaras, Sufi qawwali (think of Nusrat Fateh Ali Khan's party), Marathi and Parsi theatre, and later film songs.

Not everyone was happy. Its fixed, equal-tempered notes can't glide or match the shrutis, and from 1 March 1940 All India Radio banned it from its music broadcasts. The ban was only partly lifted in 1971. Meanwhile great players showed what it could do: Govindrao Tembe, Appa Jalgaonkar, Manohar Chimote, and Tulsidas Borkar, who received the Padma Shri in 2016.