Do any of you ever label, or have seen labeled, the various horn fingerings with respect to the natural horn crook that gives the same fundamental pitch? To explain more clearly, let's use the 1-2 fingering on the F horn/side. This is the valve equivalent of the D crook. Can this fingering be referred to as the "D fingering" or the "D valve"? Or maybe even the "D 'crook'"?
For your average beginning or intermediate student, such nomenclature would likely lead to confusion - because they typically don't understand all the physics and math behind valved brass mechanics, *and* because they haven't been educated about the natural horn (or horn history in general). Also, the fact that different brasses are pitched in different keys means you have to keep reassigning names when moving from horn to trumpet, or from Bb tuba to Eb tuba, etc. Oh yeah....there's also the issue of written pitch vs concert pitch, and the physical 'key' of an instrument refers to concert key.
But for professional horn players and horn geeks in general, such a system could be useful, since we tend to think more in terms of crooks and partials and the harmonic series.
Anyway, I like the idea of note-named fingerings, but am concerned over the confusion they could impart.
I've never heard of anybody doing that, but I suppose as long as whoever you're talking to knows what's up, it wouldn't be a problem. I would stick to calling the fingerings by number, though, because that's the norm I've seen and it would be easier to communicate. You could try setting a trend, but I hate to say that it probably won't fly since beginners usually learn what a fingering is before they learn what a key is, and so numbers are the first thing encountered in most circumstances.
I think that understanding harmonic series and brass constuction is important, but this system is unneccisarily complicated for someone learning fingerings. As well, at higher level playing the last thing that you should be concentrating on is valve combinations (these should be muscle memory), so I don't know how this system would benifit a player. Also when changing to Bb side of the horn, you would have to have a complete different set of crook names for fingerings. But like I said, I still think it is important to have an understanding of how your instrument works...but notation is about communication.
You can't have everyone refer to those fingerings as 'crook' equivilants. It is much better to know the key your horn is in (typically Bb or F) and understand the transposition from that key. So 2nd valve is always 1/2 step (From Bb it is A,From F it is E-natural).
The majority of players will be playing a standard double horn in Bb and F. And I have heard professionals pass the word down the line to play a certain passage "as though you're on D horn".
But to assume 12 is D Horn won't work because some people play Horns in different keys. My main horn in the orcehstra is a Bb/F horn. My friend in Ohio has a descant in Eb/Bb. My main horn in pit of a musical is in C/G. So 12 on my C/G horn is A horn or E horn not D horn.
Regardless, yes everyone should know what transposition each valve combination is going to put their horn in. But don't assume each valve combo will be the same for each horn.