I use the accordion to accompany my singing, which has a certain symetry, as my singing is about as popular as the accordion! However, Peter, you did ask, and the way I do it is as Alex describes, playing strong rythmn on the left hand, and chording with the right hand on the keyboard end, by playing D, F# and A for D major, D, G and B for G major, and just E and A for A major. If I need to bung in a B minor chord, I just play D and F#. In this way I don't have to move my hand position at all, and I don't make any mistakes (err, well, mostly not!). I then do a middle eight bars, playing the tune on the right hand, which varies the piece. I don't play the tune of the song on the right hand whilst I'm singing for two reasons. One, I'm more likely to lash up the playing because I'm trying to remember words, and two, if you take away the left hand, you are left with a one dimensional copy of the tune which is dull and boring.

Another trick I use is running down the arpeggio very rapidly, which gives the accompanimemt a bit of rocking, but I am talking about fast rollicky-bollicky (sorry Alex!) Irish songs or shanties.

It's a great instrument to accompany singing, because the rythmn section is so rich and strong.