A taan is a quick flourish of notes, the brilliant counterpart to the slow unfolding of alap. Taans typically arrive in the faster (drut) stretches of a khayal or instrumental gat, sweeping up and down the raag's permitted notes at speed.
There are many kinds: a sapat taan runs straight up and down; a vakra taan zig-zags; a gamak taan is heavy and shaken; a bol taan uses the words of the bandish. However fast and elaborate, a taan must obey the raag's grammar — only its allowed notes, in its characteristic shapes — and resolve cleanly on the sam.
The ability to spin long, accurate, inventive taans is one of the clearest measures of a vocalist's or instrumentalist's mastery.