There are some very clear reasons why organists should learn to transpose. Among them - playing with vocalists and performing in a lower or a higher key to accommodate keyboard compass are most easily understood.
After all, if your vocalist is not feeling like singing in a higher key today, instead of choosing another piece, an organist could offer to transpose. Also if the range of the piece is rather broad and you maybe required to play a note which is not there on the keyboard, one option would be to transpose to a lower key.
But here's another rather surprising reason to develop a skill to transpose music at sight: sometimes it's very handy when you play with instruments in an ensemble, too. Let me explain.
Suppose you have a historical organ which is tuned in Chorton pitch (about half-step higher than normal - ca. 466 Hz.) and you have to play with early Baroque instrument ensemble (consort). Since you knew in advance that your organ is tuned to 466 Hz, your instrumentalists brought with them their instruments which were tuned to that pitch level, too.
But when you get together for a rehearsal at the organ, you find out that because of the higher temperatures in the room (or maybe because of passing of the centuries), the organ pitch level rose to about 474 Hz. It's of almost no consequence to you, of course, but the instrumentalists, especially the wind instrument players, would be in a very bad situation.
Since their instruments are tuned to 466 Hz, there is no way they could adjust to 474 Hz pitch that the organ has now - simply their mouthpieces wouldn't go in anymore to make the tuning higher.
They would be very upset, of course. What to do? How could you save the concert?
You could transpose your accompaniment (continuo) pieces one half-step lower which would make the organ sound too low (in comparison with the wind instruments). But now they could take out their mouthpieces a little and adjust to the sound of the organ.
Usually there's more room to lower than to raise the pitch level of the wind instruments so that would be OK for them. I guess it's not the ideal scenario because playing on high pitch is different than playing on the lower pitch for them. Nevertheless, it's much better than nothing.
So there you have it: learn a skill to transpose music at sight not only for yourself but also for the sake of other musicians who might perform together with you.
By the way, this is one very practical reason that organs tuned in Chorton were more suited to accompany vocal and choir music back in the day while organs tuned in Kammerton (ca. 415 Hz - about half-step lower than normal) were meant to be used with chamber music ensembles.
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