The topic of vibrato has long been a controversial one in the horn world. Gunther Schuller in Horn Technique does address the topic generally, and in terms of production he particularly notes that
Vibratos are produced on the horn in a variety of ways, and I think they are all justifiable if used with taste and discretion. It doesn’t really matter if the vibrato is produced in the throat, by the hand in the bell, or by gently shaking one’ head or the horn. These (and possibly other methods not known to this writer) can be used to add a feeling of warmth and ‘flow’ to a phrase.
Fred Fox in Essentials of Brass Playing suggests that the best vibrato would be a breath vibrato.
The breath vibrato is the subtlest…. By using the air stream the vibrato seems to be more inside the sustained tone rather than the whole tone being waved around….
He suggests the feeling of performing this vibrato is similar to that of gently laughing “ha-ha-ha-ha.” Fox notes that
With a little practice this regulated air impulse can be controlled from the barely-heard to the very-obvious, as one chooses. At its subtlest, it can make the tone more alive without seeming to have any vibrato!
Harry Berv in A Creative Approach to the French Horn recommends the use of a type of hand vibrato that involved finger movement in the bell.
The player distorts the flow of air through the bell by moving the fingers (primarily from the knuckles to the fingertips) in a rapid, fluttering motion. This results in a rippling, tremulous effect in the tone, one which would be difficult to control if the player attempted to effect it with throat or chin action. For this reason I recommend using the fingers, and only the fingers, to produce vibrato.
Douglas Hill recommends in Collected Thoughts on Teaching and Learning, Creativity, and Horn Performance “the study of three distinct types of vibrato.”
1. First, there is an intensity vibrato used to intensify a musical line by pulsating the airstream. Sometimes called a diaphragmatic vibrato, this technique is more successfully controlled at the throat opening. The steady stream of air flows through a rapid partial opening and closing of the throat.
2. Second and least effective, is the timbral vibrato that colors the sound to a subtle degree by changing the vowel formation inside the mouth as the tone is sustained.
3. Third and equally as effective as the first, is the pitch vibrato, which adds a fluctuation slightly above and slightly below the blown pitch through and adjustment of the aperture, often due to the movement of the lower jaw.
Hill does not recommend movements of the right hand in the bell or to shake the horn above all because they sound too mechanical but also they can “quickly tire the lip.” He includes in his book exercises to learn intensity, timbral, and pitch vibrato.
Personally, my own vibrato production approach is most similar to that presented by Fred Fox (and Hill, his number 1). But back to the controversial side of vibrato, there are strong opinions in some quarters that the horn should not have any vibrato in the sound. It is something to scope out very carefully in relation to actually winning a job playing the horn in some areas of the world. I have a personal story in that regard but it is one for another day. Suffice to say, there are strong opinions out there; this article is a good place to start for more on that.