The most common Trumpet around the world is the Bb Trumpet. It is so named because its lower open notes correspond pretty closely to a Bb triad. There are other trumpets, I’ll get to those in a bit.
LOW NOTES
Most trumpets have 3 valves which can lower its range to a tritone below its named key (which is a low C on the sheet music for that Trumpet). The player of a Bb Trumpet would call that lowest note an F#, which is a Concert E. By the time they’ve played for a year or two any Trumpet player should be able to play those notes – it’s just that they don’t.
If you’re wondering about a C Trumpet, which is commonly used in Symphony Orchestras, they too are able to reach a tritone below their named key, so concert F#. If you’re trying to decide whether your Trumpet part should be in Bb or C use the one that best suits the key(s) you’re using.
The only other trumpet that you might want to write for would be a piccolo trumpet. Most Piccolo Trumpets are built in Bb and A these days. The Bb setup is exactly one octave above the regular Bb trumpet, the A only a semitone below. Most Piccolo Trumpets now have a fourth valve which extends their range but it isn’t really there so that you can write melodies in that register. For every thousand times that valve gets used, 999 of them are reading Baroque era D Trumpet parts in the Piccolo A setup so that the printed low C (transposed to a low F for the A instrument) is playable. If you didn’t understand that, don’t write those notes.
It was trendy for a while to have four valve Flugelhorns but you can’t count on a player to have one. They’re built in Bb so treat them like a Bb Trumpet.
HIGH NOTES
There is no known limit on the upper range of a Trumpet. At some point it sounds more like a dog whistle than a Trumpet but that range is well beyond that of most players, 99.9% of players.
The highest note you should consider writing for Trumpet really depends on who you are writing it for. If your writing anywhere above the staff you will have to think about who you’d like to play it.
Somewhere in the first few years of playing many Trumpet players will have a solid grasp on a G at the top of the staff (Concert F). Others will not. Late in high school the better players will have a high C (Concert Bb) that sounds pretty good. College and Symphonic players maybe a tone or two higher. As most Trumpet players approach their upper limit the sound they make will suffer, so use those notes cautiously
There are Trumpet players whose range is well above that high C. Most of them play jazz or commercial music but there is the odd Baroque specialist as well. 1st Trumpet parts in popular styles routinely venture into the stratosphere but there just aren’t that many players around who can make them sound good. Unless you know who you’re writing for and that they can play those notes, don’t write them. You want your parts played well.
One More Thing …
Thanks to Adolphe Sax and his contemporaries the modern Trumpet is fully chromatic within its range.

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