Why do some instruments transpose? Why not simply write them all at concert pitch?
There are several reasons, most with long histories. The most important for our purposes are: first, transposition helps the player by having a common fingering system across the various members of the same instrumental family; second, it makes the notation sit more comfortably within the staff lines and helps avoid too many ledger lines. What the conductor needs to be aware of are the standardised conventions in use in modern scores.
To illustrate the issue of fingering systems, let’s look briefly at the clarinet family.
If a clarinettist sees the note shown in example 1, s/he will produce the note by closing the holes corresponding to the thumb, index finger, middle finger and ring finger of the left hand.
However, depending on which clarinet the player is using, it will sound at one of several other pitches as shown in Example 2.
If transposition wasn’t in use, each of those other instruments would have a completely different set of fingerings and the player would have to remember which one to use for the instrument being played. Since the mind and fingers react instinctively to the notes on the page during fast passages, it would be incredibly difficult for the performer to differentiate consistently. A better option is to change the notes on the page through transposition. The performer can therefore be a “doubler” very easily by learning only one fingering system for all sizes of instruments in the family. The notes designated on the score by the composer are adjusted to ensure that the correct pitches for each instrument will sound.
Although many instruments have a compass that far exceeds the notes on a single staff, transposition helps ensure that the most commonly used range of notes stays on or at least reasonably close to a single staff without changing clef. It also avoids having to deal with multiple C, G and F clefs as might be found in early examples of orchestral scores, such as the one you saw in section 3.1 above.
Finally, over the years certain instruments have become standardised because of their sound, intonation, and common usage. In the case of horns, for instance, before the invention of valves, which did not come into common orchestral use until the third quarter of the nineteenth century, horns used to play in different keys by inserting various lengths of tubing called “crooks.” Since the crook put the instrument into the key of the piece, and the composers were mindful of the fact that the available notes were limited, there was no need to designate key signatures. The advent of valves eventually led to a standardisation of the double horn pitched in F and B-flat. That being said, many pieces of older music still exhibit parts for horns in E-flat, E, C basso, and almost every other conceivable pitch. The conductor needs to be especially alert to the type of horn noted in each score to be performed.
In older scores, timpani parts might also be perplexing. Earlier composers utilised timpani to play almost exclusively on the tonic and dominant. A composition in the key of D would require the timpani to tune to the pitches D and A, but the notes on the staff would be written as C and G. The pitches C and G were used as a kind of universal representation of tonic and dominant. The actual tuning of the drums did not matter in relation to the notation. The performer would hit the tonic drum when C was written and the dominant drum when G was written. See Example 3.