How to Play the Horn
The biggest mystery of the horn-putting the right hand in the bell

In contrast to the modern horn, the natural horn originally had no bell, and the only way to change the pitch was by changing the speed with which air was blown into the instrument. As a result, the notes that were emitted were limited to natural harmonics. C, G, C, E, G, B♭-horn players jumped around this arrangement of notes, and they could not play a phrase that included D or F. What changed all that was the hand-stopping technique.

Hand-stopping is no longer necessary to produce semitones because the horn has valves now. However, hand-stopping is still used today to support the instrument and to make minor adjustments to the pitch or timbre.
For example, playing the F horn slightly stopped with the right hand produces a tone called half-mute: a muddled, warm timbre that is a semitone lower than the note on the music.

Using the right hand to completely seal off the bell increases the pressure of the air blown into the instrument, and a keen metallic tone about a semitone higher is produced. This is called hand-stopping, and it is used to create a certain mood in a song. Hand-stopping is indicated by a "+".

In terms of physics, the hand-stopping technique raises the pitch to a little above the next lower harmonic, but in terms of music, it is probably easier to think of it as raising the pitch.
When blowing normally, hand-stopping will raise the pitch of the F tube by a semi-tone, and the B♭tube by a two-thirds tone.
Some horns have a gesttopft key, which lowers the pitch by the same amount that it rises. Horns with this key can play the note indicated on the score, but those that do not have this key must play a semitone lower when hand-stopping.