Fingerings has always been on the mind of horn players. Most of the fingering charts provided have always ended on the High C above the treble clef stave (in F). One such comprehensive web resource is that from Colin Dorman (http://colindorman.com/french-horn-exercises/fingering_charts/). In the comprehensive resource, he shared the recommended fingerings for all types of horns, include the descant and Single Bb with independent A-stopped and F-extension, highlighting the strengths and weaknesses of each permutation. Mr Wendell Rider (Principal Horn, San Jose Symphony) shared a fair bit of his considering on the matter as well (http://www.wendellworld.com/html/FingeringChart.pdf).
That being said, what about the fingerings for the notes beyond the High C above the staff. A common rule is to apply what was used for the lower octave to the high octave, as shown in http://www.thefrenchhorn.net/docs/fingeringchart.pdf
However, we would like to highlight a different perspective by Dr John Ericson (Horn Professor, Arizona State University).
“Most fingering charts end at written high C. Lots of players will finger above high C with the fingerings from an octvave lower on the B-flat horn — C# as T23 for example — but actually there are better fingerings. High E is a good harmonic fingered open on the Bb horn, so that is the harmonic to use as a basis for these fingerings. Thus:
It ends up being the same fingerings as two octaves lower but on the F horn. High F would also be T0 and really, above high E, you can play every note T0. They are still petty difficult notes to hit, but are a little easier with these fingerings than with the fingerings from an octave lower.”
At Bishan North Horn Club, we have tried these fingerings and find that they work well for most horn makes. Somehow, the more conservative high notes using Bb horn lower octave’s fingerings works very well for Alexander 103s. Let us know what you think.