Music for modern trumpets is written in treble clef (for the bass trumpet too!).
The trumpet in C is a non-transposing instrument, i.e. the sound is as written.
The other two standard trumpets sound lower than written: the trumpet in Bb sounds a major second lower, the trumpet in A a minor third lower.
All the other modern trumpets, that means the higher-pitched piccolo trumpets in D, Eb, E, F, G, Ab and high Bb sound higher than written – the trumpet in D sounds a major second higher, the trumpet in high Bb a minor seventh.
This notation was also customary for the natural and long valve trumpets of the Classical and Romantic periods.
No key signature at the beginning of the score
Unlike other transposing instruments such as the clarinet, the trumpet part – like that of the horns and timpani – has always been written without key signature at the beginning of the staff. This tradition dates back to the very beginnings of orchestral music and is still maintained today.
Performing older trumpet parts
In 19th century scores the modern trumpeter often finds himself confronted with parts written for the long valve trumpets usual at the time (in A, Bb, C, D, Eb, E, F, G and Ab). Nowadays, these parts are played by the modern trumpet, since modern instruments have much the same compass as the old ones did.
Although the tubing of the old trumpets was twice as long as that of today’s instruments, the playable range was more or less the same because the two deepest naturals did not speak and the wider bore enabled overblowing to the 16th natural. However, the sound of the old valve and natural trumpets was extremely powerful and full.
If the instrument playing the part (which is usually a trumpet in Bb or C) is in a different key from the notation the modern trumpeter must transpose accordingly. In 19th century scores the F trumpet is very often called for on account of its particularly pleasing timbre. If a part written for a trumpet in F is to be played on a trumpet in C the musician must transpose to C.