One name not too familiar today in horn circles in that of Harry Berv. He wrote a very interesting horn method, published in 1977, A Creative Approach to the French Horn.
Harry Berv and his horn playing brothers Arthur and Jack joined the NBC Symphony in 1938, having previously performed in the Philadelphia Orchestra. At the time of the publication of A Creative Approach to the French Horn Berv was 66 years old and still an active teacher and freelance hornist in New York. He is much more progressive in his approach to fingerings than one would guess of a Curtis grad from way back in the day. Many teachers present fingerings as being essentially fixed; Berv called that approach “archaic” and “counterproductive” and he also embraced the use of descant and triple horns.
FINGERINGS ARE a controversial area in horn study, as is the combination use of the F and Bb horns. I am personally convinced that for the horn player to adhere strictly to one system of fingerings only makes this challenging instrument more difficult to master.
I recommend and teach that fingering is individual to a degree, and that horn players will and should find certain combinations, using F and Bb horn, with which they feel most comfortable and which provide them with the best overall sound and technique for getting around the horn. It must be pointed out that a fine horn player may very well find it necessary to change his system of fingerings to compensate for the variations found in various makes of horns. It is my feeling that to adhere to an inflexible system of fingering is counterproductive and makes one rely too much on the embouchure to overcome all the technical problems of the instrument. Approach the horn with an open mind regarding fingerings, and you will be able to clear up problems without loss of sound and play passages with greater security and evenness. Trumpet players alternate Bb, C, and D instruments to cope with different compositions. The horn player, who normally uses his F and Bb horn all the time, can certainly use different fingers to help him; he should not feel that he is being unethical or incorrect. Symphony horn players today [1977!] are beginning to use double horns in Bb and high F or even triple horns in F, Bb, and high F to facilitate difficult passages that are really hazardous on the conventional instrument.
To begin with, the horn player must practice and be familiar with all the fingerings on the F and Bb horns throughout the entire range of the instrument, which is what makes possible the use of the double horn as a complete instrument.
Placing a taboo on any specific range in regard to fingering or the use of either the F or Bb horn in any octave is archaic. As you can see from the chart of the overtone series, almost any note can be played on either horn.
He does however note that the “vast majority” of alternate fingerings are only used in special circumstances and notes one occupational hazard of the use of alternate fingerings.
However, you should realize that alternate fingerings must be used with great care. You may believe that in a given circumstance an alternate fingering will make the right note come out, or the note come out right. Realize, however, that there is always a good chance of your missing the note entirely if you are not perfectly accustomed to the alternate fingering. You have, after all, been using the usual fingering in your everyday practice over the years. You know just the correct air pressure and feel of the note on the lip. You cannot expect that you will suddenly forget all this and instantly readjust. The chance is you may not make it! You might play a note that will embarrass you, the conductor, your colleagues and the audience. Therefore, if it is at all possible, it might be better for you to try conscientiously to get over the difficulty by staying with the fingerings you have always used.
On the topic Berv leaves this final thought.
As your playing progresses you will find more and more that correct fingering contributes enormously toward expression and tone and is in fact highly individual. You must experiment with all fingerings until you find the one that is best suited to you, one which most helps you in your technique, tone, and phrasing—the one, in fact, that most helps you express yourself musically.
UPDATE: See also this post and especially comment #2, from a student of Harry Berv.