The Aruch Hashulchan (O. Ch. 583 :3) writes ," On the first night of Rosh Hashana
we avoid eating sour and bitter foods.
Pepper is an exception, because ,you can't eat fish without pepper."
Many years ago I heard, that in Yeshivas Telz they served chrain on R.H.
The reason, I heard was, you can't eat Gefilte fish without chrain.