Its heyday was the sixteenth and early seventeenth centuries, when it was the most highly regarded wind instrument. It was prized for the resemblance of its sound to that of the human voice (considered to be the most perfect instrument) and for its suitability for performing elaborate ornamentation; always considered a difficult instrument, it spawned a select group of highly regarded (and highly paid!) virtuoso players such as Giovanni Bassano and Girolamo Dalla Casa, both of whom worked at the Basilica di San Marco in Venice.
The name derives from the Italian for "little horn" ("corno" - horn, plus the suffix "etto" - small); it is also nowadays often referred to as "cornett" (with two t's to give a distinction from the modern brass instrument, with which it has no connection).
The repertoire for the instrument covers the Renaissance and early Baroque periods. The most well-known work which calls for cornetti is Monteverdi's Vespers of 1610, and there are also important cornett parts in music by Giovanni Gabrieli, Heinrich Schutz and Michael Praetorius. It was used in both sacred and secular music, and besides pieces such as the Vespers which mention the instrument by name, it would have been a natural choice for most high-lying parts, which typically were marked only "canto". Thus it appeared in Waits' bands playing ceremonial and dance music, as well as in church reinforcing vocal lines and playing instrumental canzonas and sonatas.
Its flexibility in the hands of a good player made it suitable for virtuoso display, and at its height it was expected to do anything a violin or a human voice could do; many works of the early seventeenth century are marked "violino o cornetto" (violin or cornett) implying that either was a suitable choice.
The difficulty of its technique meant that even at the height of its popularity there were relatively few really accomplished players, and the instrument went into decline during the second half of the seventeenth century as violin technique developed and as other wind instruments such as oboes became more sophisticated. It has also been suggested that several of the leading players died during the great Venetian plague of 1630, leaving few people to teach the instrument! The use of the cornetto survived longest in Northern Europe; J S Bach calls for it in some of his cantatas, but by this time it would have been considered rather old-fashioned, and by the end of the eighteenth century it had more or less died out.
The cornetto is played nowadays by players involved in historically informed performances (HIP). The combination of woodwind and brass techniques - normally quite different disciplines - and its general intractability make it a challenging instrument, but the result in the hands of a good player is something quite magical - a sound which, perhaps like no other instrument, conjures up the sound-world of a bygone age.