Trumpet
The Trumpet is the highest instrument in the Brass Family
It has a written standard range of F#3-D6 and traditionally excels in fanfare-type passages, but modern trumpets (and variants such as flugelhorn and cornet) can also perform delicate, soft melodies as well.
While the trumpet can’t play as fast as most woodwind and string instruments, it still can be written for virtuosically in both a solo and ensemble setting, depending on context.
Idiomatic writing for the trumpet usually is scalic or features leaps of up to an octave; writing larger leaps than this can increase the risk of ‘split’ notes or mispitches.
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It really depends on your player and its probably best to ask them.
As a general rule, the highest note for an professional orchestral trumpet player is a concert D6 though high school level trumpet players will likely struggle with a Bb5.
If writing for a lead trumpet player or jazz group the upper bound is much higher. Most lead players will be able to play up to a F6 and some will be able to go beyond up to Bb6.
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Surprisingly, it’s pretty much the same as a regular Bb/C trumpet.
The upper bound would be a written top line F (either D6 or Eb6 depending on whether its A or Bb Piccolo), though some repertoire pushes up a tone to a written G.
Stamina is a big concern on piccolo, don’t write for the piccolo to stay in this register for long swaths, touch it and get back down, or pick your moments to let the upper octave shine!
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Historically, trumpets were pitched in many keys because they didn’t have valves and so could only play the harmonic series. In the Baroque Era they were in D, classical Era meant the development of crooks (lengths of tubing that allowed one trumpet to be changed to play in multiple keys) and so trumpets were found in A, Bb, C, D Eb, E, F etc so that they could play in the key a composer desired.
The late classical period developed the keyed trumpet allowing the trumpet to play chromatically but with tonal inconsistencies. Shortly after, the valve was invented and trumpets could play chromatically with even tone. This led to the standardisation of the Bb trumpet as the default instrument as it had a balance of sound and range that covered most if not all of the existing repertoire.
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As mentioned in the history section, historically the trumpet was written in whatever key the piece was in.
Nowadays most of the repertoire is played on Bb or C trumpet depending on where you live and what the standard is. Though we have acces to the D, Eb, and Piccolo trumpets as well.
These auxilliary instruments were invented to make increasingly difficult music in terms of agility and register more manageable (or even playable at all!). As these trumpets are higher pitch, they are also shorter in length so