This is stopped Horn tutorial.
Players discovered that by inserting the hand into the bell of the horn they could alter the pitch of the instrument for improved intonation and additional pitches, and that they could also make the tonal color darker and more mellow. This technique was known by hornists in the 1720s at the latest. By gradually closing the hand in the bell one can lower any sounding pitch one half step with moderate stopping, and any pitch may be lowered to a half step above the next open pitch by combining full stopping and "lipping" the note down.

While the hand in the bell does not need to be used to produce diatonic and chromatic notes today, as it was in the Classical period, the hand is still needed in the bell to maintain the proper tonal color of the horn. Correct hand position for the modern valved horn is closely related to the hand position used on the natural horn.

A correct basic right-hand position on the horn is a very important first element to make stopped horn work correctly. The fundamental elements of a proper right hand position for the horn are to cup the hand slightly, as though to hold water in it, and to place it inside the bell so that the backs of the fingers touch the bell throat, allowing an opening of approximately two inches between the heel of the hand and the opposite side of the bell. A basically correct hand position can vary, but there are several issues to consider:

A correct hand position is very closely related to that which would be used on the natural horn. You should be able to open and close the throat of the bell by simply "shutting the door" with the heel of the hand. The hand should not "float" in the bell, and it should not need to be moved "in and out" of the bell to go from an open to a closed position.
One may wish to place the hand so that the thumb and first finger can support the bell when playing standing.
How open or closed the heel of the hand needs to be must ultimately be gauged by the ear. The tone should not sound like one has something stuffed into the bell (too closed), and should not sound like a trombone either (too open).
Pitch level is affected by how open or closed the bell is--an open position sharpens the horn and a closed position flattens the horn. Hand position must be consistent.
Above all, to place the hand in the bell with the palm against the inside of the throat of the bell, as is seen all too frequently in beginners, is totally incorrect. Besides having a poor, sharp tone, the playing qualities of the horn actually suffer because of the improper hand position, especially in the upper range of the instrument.

This leads us more directly back to our topic, the stopped horn. Stopped notes are an effect unique to the horn. A basic rule for fingering stopped notes on the horn is to finger the note a half step below the note you want to play, close the bell tightly with the right hand, and play only on the F horn for intonation.

As you slowly close the hand in the bell the pitch will get lower. However, once the bell is TIGHTLY closed, the pitch will rise by approximately a half step. There is some controversy as to exactly what is really happening acoustically, but a good way to think of it is that you are shortening the horn by "cutting off" the end of the bell with the hand.

The tightness of the closure of the bell is quite important; you want to seal the bell with the right hand. Just as with the natural horn you don't want to "shove the hand in the bell;" the motion is much more like "closing a door," with the hand as the door. A key element to achieving a tight seal for many players is the thumb. There must be no leakage around the thumb; it helps to keep the thumb to the side of the palm and first finger. Don't allow the thumb to leave a hole. Hold the air in just like you would if you were holding water in the horn bell.

A tight seal is especially important to the production of stopped notes below the staff. With a tight seal it is very possible to play stopped horn down to the bottom of the range of the horn, but when the seal is not tight the notes simply won't come out with anything approaching the characteristic "buzzy" stopped horn sound.

If you play stopped horn on the F side of the double horn pitch will generally be close to being in tune, raised ½ step above the open notes. If you play stopped on the B-flat horn though, many notes will be nearly 3/4 of a step higher--in other words, badly out of tune. Some naturally flat fingerings are however quite usable on the B-flat side of the double horn; experimentation is very much in order when in doubt.