There are two aspects to the real-time processing of language in which we all indulge on a day-to-day basis. One is hearing what others say to us, or in the case of written language and sign languages, seeing what others are saying to us. This is the problem of speech perception, and a fundamental part of it for spoken languages is the recognition of speech sounds. The other is producing language ourselves, speech production. For spoken varieties of language, this includes the problem of control of the muscles of the vocal tract (lungs, throat, tongue, lips) responsible for making the sounds. For sign languages, it is the problem of control of movements of the hands and face. In psychology, the organisation of movement is referred to as motor control.
Speech perception
Suppose you are singing a note on a certain pitch. If you wish to sing a different note, one option you have is to shift to the new note gradually and continuously (you can also jump straight to it, but this option doesn't concern us here). This indicates that the pitch of the human voice, determined by the rate at which the vocal cords vibrate, admits of any number of gradations. Now contrast this with someone playing two notes on a piano. A piano has a finite number of discrete notes, and as a consequence it isn't possible to play a note between C and C#; it is, however, perfectly feasible to sing such a note.
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