The earliest known clarinet (from clarino, Italian for trumpet) had two keys and was developed by the German Johann Christian Denner and his sons, notably Jacob Denner, in the early eighteenth century. The chalumeau was the ancestor of the clarinet and was probably the same as an instrument called the mock trumpet. Not much is known about the chalumeau as only replicas exist today, but one improvement made in the two-key clarinet was the introduction of a small hole near the top of the instrument, the speaker-key hole, which could be covered by the thumb or uncovered in order to over-blow, raising any note played by a twelfth (an octave and a fifth).
The basset horn, a clarinet pitched in F with extra curved tubing, was in use by the 1780s. Mozart wrote for it in The Magic Flute and the Requiem. The basset clarinet, related to the basset horn, was also in use around this time and was the instrument on which Anton Stadler performed Mozarts Concerto (of which he was the dedicatee) and the Quintet. Neglected for a century and a half, the basset exists today only in reconstructions of the original. It is essentially an extended clarinet (in Bb or A) with extra keys for the right thumb to take the range down to written C.
By 1812 Ivan Müller, a Parisian, had designed a thirteen-key clarinet. Before this time pads had been made of felt, which leaked air, but he introduced a new type of pad which was covered in leather or fish bladder and was airtight. This improvement allowed many more keys to be added. The new placement of keys made the clarinet much more acoustically sound (in tune). Müllers clarinet was further developed by various makers and players such as Adolphe Sax, Carl Bärmann and Oskar Oehler, resulting in the modern German (Oehler) system clarinet which can have between seventeen and twenty-seven keys.
Boehm system clarinets, which normally have seventeen keys, were first exhibited in Paris in 1839 by Hyacinthe Klosé who invented this system of fingering. Theobold Boehm had earlier designed a flute fingering system that inspired Klosé, involving ring-keys that allow a finger to close several holes at once.
One other type of clarinet is still played, mostly in Folk music: the Albert or Simple system clarinet, named after its designer Eugene Albert (a pupil of Saxs) and derived from Müllers clarinet. It has more un-keyed holes than either the Boehm or German clarinets, which makes it easier to slur notes. Also, like the German clarinet, it has a large (around 15.25mm) cylindrical bore.