The most common clarinets used in orchestras and by soloists are the B flat clarinet and the A clarinet. Though the B flat clarinet is called ‘B flat’, on the modern instrument, in fact, its lowest note is the D below middle C.
The B flat clarinet is a transposing instrument which means that the notes it sounds are a tone below the ones written down, so the lowest D would be written E. The A clarinet transposes by a minor third.
The highest note that can be played depends on the player. For normal purposes it is the C three octaves above middle C, but some virtuoso musicians can go even higher, though this is only really for special effects.
The clarinet is normally said to have four registers: the chalumeau (after the instrurment that is its ancestor), the throat, the clarinet and the extreme.
If you blow hard into the clarinet, like all woodwind instruments the note you get is not the fundamental, but a higher harmonic. Unusually, however, on the clarinet the harmonic obtained is not the octave above the note blown but the 12th, ie the second harmonic.
Apart from the B flat clarinet and the A clarinet there were once quite a number of others. Nowadays, the only common other clarinet (other than the bass clarinet, which is really a different instrument) is a bit smaller than its brothers. It is the E flat clarinet. This sounds a fourth above the B flat clarinet.
Joy Farrall talks about different clarinets, but first she explains and demonstrates the clarinet overblowing at the 12th.