The position of the right hand in the bell is a crucial element for intonation, tone color, range and many other aspects of playing. It should be thought of as an extension of the horn.

The hand should be inserted into the bell in a vertical position, as far as it will go without forcing. The hand should be slightly cupped, and the fingers held together so that no air can pass between them (think of a princess waving her hand). The thumb should be in a relaxed position reaching towards the second joint of the index finger.

The horn should rest on your thumb and index finger, which should be supple. The bell sits on a triangle shaped by the upper part of the index finger, the body of the hand with the thumb as the hypotenuse. The hand supports the bell while directing the air column away from the body. Avoid playing into the body as a stuffy tone will result. Think of the air column extending beyond the end of the bell with the hand and body forming two parallel walls through which the tone must pass.

If the hand is placed palm up (horizontally) the air column travels into the body and compromises projection. It's also impossible to use this hand position while standing or when quickly to stopped horn. It's also much harder to adjust the hand for intonation or tonal changes.