The Eb horn can go all the way down to several notes under the bass clef. As written for the horn. So the notes you show are quite easy for an Eb horn (although the 3rd horn would not like to play these notes since they tended to be high horn players, but that is what he was doing with his 9th anyway is switching things around)and many modern day orchestras shift their horn seating for Beethoven's ninth.

The phrase you have below is simple enough for our modern day horn and would not be very difficult for an accomplished hand horn player. I do not specialize in hand horn but I can play that passage easily enough.

Next question.

Good call on the 'old notation' Yes those notes are playable on a valveless horn. How hard is it? The C is quite easy and anyone should be able to play it. The lower G should be easy, but horn players who do not practice the low range might have issues trying to get the low G out. Starting on low C and then going down makes it easier than just trying to start on the low G all by itself. But it is very attainable.

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Oh and did you notice the scoring for the horns?

There is often only three parts being played and it is inidcated that it be played by the 1st and 2nd in Bb and the 4th in Eb. The 3rd horn sits out through much of the piece. Isn't that interesting?

This happens a lot, where the 3rd horn sits around twidleing his (or her) fingers while the 1, 2, and 4 play all over the place.

As effective or as efficient?
Back around this time there were high horn players who rarely ever played below a G on the staff, and low horn players never went up much higher than C, if that. They were truely 2 different styles and methods of playing horn. A horn player was either a high horn player or a low horn player and doing both was unheard of and pretty much just not allowed. So, composers built their chords for the horns giving 1 and 2 priority and then giving the root, or lower note to the second set of horns and since it was often a bass note, the low horn player of the second group would play it. Because it was too low for the 3rd (or 1st Eb).

What is "hand horn"? I'm pretty sure that it's changing the pitch by moving your hand in the bell, but would you mind explaining it in a little more depth?

Hand Horn explained.
Hand horn is playing a horn with no valves.
Before valves were standard composers had to know what notes were possible on each instrument. To play hand horn you adjust your hand in the bell usually by closing it off in varying degrees to hit the notes that are not in the overtone series. So some notes will actually be stopped in order to play. Composers knew this at the time and wrote accordingly knowing the timbre they would get.

Lots of professional horn players in orchestras today want to play off the original parts and not transposed parts because it will give them a feel for what the composer was writing.

Don't get misled into thinking it was as hard as it is today. Today on a modern insturment it can be a real challenge because the bell is so big. Hand horns have much smaller bells and although still challenging, much easier to play on a smaller bell horn. Many are only 9 inches across.

Well, I think all notes below C second space are playable on the natural horn. What I meant to say in my earlier statement is the composer needed to understand the harmonic series to know which horn notes were open, which were partially closed and which were completely stopped. So he knew what colors he woudl be getting.

The open notes on a natural horn in todays key of F would give you these concert pitch notes for the horn in descending order from C second space treble clef.

C, Bb, G, E, C, G, C, C.

So this is why you see horn 1&2 in Bb playing with Horn 3&4 in Eb. So you can have C,B,Bb,A,G,F,E,D,C,B,G,D,C,G,C all sounding open using both sets of horn. And of course you can have the horns switch to another key. They can pick up their horn in G, then put that down and pick up Horn in D,put that down pick up Horn in Bb-alto, etc.

In Donizetti's Comic Opera DON PASQUALE. He has the horns go through every key there is. A fun fun opera to practice your transposition on.