A few things I’ve picked up over my years of playing horn.
BTW: old photo
Fake High C: On some horns a high C can pop out while pressing the first valve of the F side down halfway. This is not recommended for performance as the tone quality of this note suffers. A way to try it is to play a normal third space c on the f side and slowly press down the first valve. Usefull for effect.
Fake High D:Pull out completely the first tuning slide of the F-horn. Playing this combination (T1) produces a stable, well centered tone, which blends quite well in the context of baroque music (e.g J.S.Bach kantata nr.100 in G). This is of course not the case with symphonic, post-romantic parts, or with contemporary music.
Double horn transitions: transitioning from each side of the horn should be undetectable and the point on transition is not set in stone( i.e. not always Ab). The notes middle Ab up to second line C have identical fingerings and should be in tune, and have identical timbre on both sides. It is advisable to use the Bb side down to Ab and then switch when descending as is common custom, but use the F side up thru 2nd line C when ascending before switching to Bb. This switch point masks the change valve more effectively making the tone sound more uniform in moving lines.
Fundamental pedal CC: if you have a double horn and cannot achieve the pedal C (2 ledgers below bass clef) on the F side of the horn, it may be played T13. The tone quality will sound closer to that of a Baritone horn, but you will have achieved the note.
Reading a trombone/baritone part in bass clef: read the notes as if in tenor clef and adjust the key signature accordingly. Pay attention to play notes Low F and lower, with the Bb side as much as possible. The tone quality will be uncharacteristic of the Horn and closer to that of the baritone, and have more stable entrances.
Wind/dragon breath effect: You can emulate wind or dragons breath as a sound effect on horn. Take out the mouthpiece and place it back wards in your mouth, hold the mouthpiece so that the mouthpiece receiver on the horn floats about halfway into the mouthpiece cup. Blow into the shank, this should give a nice wind or large animal breath effect useful in theatre.
Range: the horn can cover up to 4+ octaves and covering that range with one mouthpiece can give a strained and false sound in it’s lower and higher range. Parts are always written in paired high parts and low parts. Traditionally 1 + 3 are high, and 2 + 4 are low, with a 5th player (bumper) doubling the lead for loud sections in large ensembles. The parts can always be expected to cover 2.5 to 3 octaves each in either direction. Unless you specialise as a 4th horn, bring two mouthpieces. You will want your regular medium-ish mouthpiece, and most common is a separate low horn piece that is deeper with a bigger bore. This of course may be backwards if you play 1st, then you will be of the persuasion to use a single Bb or descant horn to facilitate the upper range and are use a shallower medium to small cup that will support that horn.This use of a separate horn with one mouthpice is common for leads instead of carrying a separate mouthpiece for the double horn, since they are asked to cover a tessitura in the higher range and usually no lower than about low Gb.