Traditionally, in classical music, a quartet of string players - two violins, with a viola and a cello. When people refer to a quartet in this context, it's usually a string quartet. If there were to be formed an Everything Quartet (for the word "String" is often omitted, as in Kronos Quartet or Arditti Quartet), the members would be asked if Beethoven's Große Fuge were in their repertoire, and they'd have to point out that they were actually a barbershop quartet, or a sax/piano/bass/drums jazz quartet or something.

One variation is the piano quintet, which is not - as it sounds - a quintet of pianists, but the string quartet augmented by one piano.