Sadly, the cornets are a sound that we have almost entirely lost from the band. At one time, the Cornet was the most important brass instrument in the band. Today, the trumpet has completely taken over this role. Most people nowadays see no difference between the two instruments. I see a huge difference.
To define the family of cornets we would say that they are brass instruments whose bore is roughly one-half cylindrical and one-half conical.
The cornet family is the most technically flexible family in the entire brass section. Just take a look at the virtuosic writing for the instrument pre-1950. In this regard, it they are the most woodwind-like group in the brass section.
I will be treating the cornet family in a rather different manner than most orchestrators. In most texts, the Cornet is grouped with the trumpets while the lower members of the family are grouped with either the Horn or the tubas. Here, I group four instruments together into a single, cohesive family. Namely, these are the E-flat Soprano Cornet, the B-flat Cornet, the Alto Horn, and the Baritone Horn.
One term I am going to avoid in the book is that of saxhorn. Saxhorns were the creation of Adolph Sax, and were really two separate families put together. One group was akin to the cornets, while the other was akin to the tubas. As to what instruments are true saxhorns and what are not, I will leave that to historians. I, however, will only talk about the instruments that exist today.
When thinking of these instruments, I find it helpful to remember that the name “cornet” means “little horn.” In this regard, it should be treated more closely to the Horn instead of the trumpets. However, the smaller cornets (E-flat and B-flat) will always be played by trumpeters. Brass players specialize in ranges and not families like woodwind players do. So for a woodwind player to be able to play any size of clarinet is not a huge hurdle to cross, but for a brass player to play every size of instrument in their family (like cornets) is almost unheard of.