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The clarinet is both a family of instruments and a single instrument that belongs to the single reed group of woodwinds, which also includes saxophones. Clarinets are used in both orchestras and bands, and featured in Klezmer music, woodwind quintets, wind ensembles, and woodwind choirs.

The single reeds that are members of the clarinet family are as follows, arranged from lowest to highest.
Contrabass clarinets in Bb are the lowest clarinets, ranging an octave lower than the bass clarinet. They are the only clarinets that may be made entirely of metal, and they resemble contrabassoons in appearance.

Contra-alto clarinets in Eb, although sometimes also referred to as contrabasses, have some differences: the range is higher, the transposition is different, and the instrument is characteristically made of rosewood.

Bass clarinets in Bb range are an octave below the bass clarinet, and the ambit is similar to the bassoon. The lowest note depends on whether the particular bass clarinet has an extension. It is notated either in the treble or the bass clef, sounding either a major second or a major ninth lower than written.

Alto clarinets in Eb are used primarily in bands and wind ensembles. They sound a major sixth lower than written and are not generally considered a solo instrument.

Basset horns in F sound a perfect fifth below the written part. They are no longer a standard instrument for orchestral writing, but are used in older pieces, such as Mozart’s Requiem, for historical accuracy. There is also a rarely used basset clarinet in A with a low C.
Soprano clarinets are the clarinets in Bb or A that most people are referring to when they simply say “clarinet.” Which of these two is chosen for use may depend on the key of the work, with a tendency to choose the Bb instrument for flat keys and the A for works in sharp keys, but this is not a hard and fast rule. In popular music, jazz, and military music, one tends to find the Bb clarinet called for.
Sopranino/piccolo/high clarinets in Db and E, and formerly C, extend the range of the soprano clarinet upwards and are used interchangeably, similarly to the A and Bb clarinets, with Eb being used for flat keys and D for sharp keys.
All the clarinets, regardless of their size or transposition, have the same fingering system. They also all have a “break” – where the transition in fingering can present a problem for the player who is not expert.

The clarinet was invented by Johann Christoph Denner at the very end of the 17th century and based upon the chalumeau, a single reed with eight finger holes and a range of about an octave. In the 18th century, the instruments were made of wood or ivory and had three or four sections and two keys – Denner’s innovation.

Today, there are two keywork systems – the French and the German – and five parts. The first part is the mouthpiece, to which the reed is held by a ligature. Next comes a barrel joint that attaches the mouthpiece to the upper joint of the instrument, where the left hand plays. After that comes the interconnecting lower joint for the right hand, followed by the bell.

There are many well-known clarinet passages, including the opening theme in the first movement of Tchaikovsky’s Symphony No. 5 and Ivan the Cat’s theme in Prokofiev’s Peter and the Wolf. There are many noted clarinetists, whose numbers include Woody Allen, Benny Goodman, Artie Shaw, Richard Stoltzman, and Evan Ziporyn.

From: http://www.wisegeek.com/what-is-a-clarinet.htm