I recommend usually to learn the F fingering and then the Bflat fingerings.
When you start to play in Bb maybe is best to forget about F horn for one two months to get used to the flat fingerings. When you feel you can play in Bflat without wrong fingerings then start to use F horn and combining both.
Choosing F or Bflat for a particular passage depend on:
-the intonation of the notes in F and in Bb
-How fast do you need to tongue
-How high
-The color of the sound
-The fingering is easier on F or Bb
Some topics:
-For faster tonguing passages, clear attacks or high register usually recommend Bb horn
-For warmer sound on slower passages F horn is usually preferable.
Bb
-About the intonation you should see the Full Double Horn harmonic series Intonation Tendencies, and check them against the normally sharp fingerings (slightly sharp 1+2; 1+3 & 1+2+3 very sharp) then you will know with fingering will be flat/sharp (I'cover this topic on a
a small book I've wrote
)
Better than thinking on Bb and F, I prefer to think on a small horn (Bb) getting larger as you use more fingers and increase the tone length
Bb hrn[/td]
[td]
A hrn[/td]
[td]
Ab hrn[/td]
[td]
G hrn[/td]
[td]
F# hrn[/td]
[td]
F hrn[/td]
[td]
E hrn[/td]
[tr]
[td]Bb[/td]
[td]0[/td]
[td]2[/td]
[td]1[/td]
[td]1[/td]
[td]2[/td]
[td]1[/td]
[td]1[/td]
[/tr]
[tr]
[td]side[/td]
[td][/td]
[td][/td]
[td][/td]
[td]2[/td]
[td]3[/td]
[td]3[/td]
[td]2[/td]
[/tr]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td]3[/td]
[tr]
[/tr]
[tr]
[td]
F[/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td]
0[/td]
[td]
2[/td]
[td]
1[/td]
[td]
1[/td]
[td]
2[/td]
[td]
1[/td]
[td]
1[/td]
[/tr]
[tr]
[td]
side[/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td]
2[/td]
[td]
3[/td]
[td]
3[/td]
[td]
2[/td]
[/tr]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td]
3[/td]
[tr][/tr]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td][/td]
[td]
F hrn[/td]
[td]
E hrn[/td]
[td]
Eb hrn[/td]
[td]
D hrn[/td]
[td]
Db hrn[/td]
[td]
C hrn[/td]
[td]
B hrn[/td]
So, choosing for example a larger tube length on the lower note of a jump and a shorter tube length for the higher note might help (but this can be done just in Bb or just in F as well)
Keep in mind when playing on a shorter tube you will need more air quantity to avoid a poor sound, and when playing on a large tube you will require to use greater air speed to avoid a fuzzy atack.
Quite similar to ride a bicycle with multiple gears and use them on different situations.