duelling duet.
Much depends on the mode of the tune.I do use thirds sometimes, and sometimes I play two notes of a chord the first and fifth, without the third, sometimes i play the first note[for example if it is a whole beat crotchet and add a note a third below for half a beat].Sometimes, Sometimes.
I do not agree with GENERALLY for anything, my approach is entirely dependent on the tune, although ON OCCASIONS I leave out the third, dependent on mood, sometimes using the third can establish it as being minor is appropriate because it gives a sadder feel.
leaving out the third means it is unclear if it is major or minor, sometimes that is appropriate sometimes it is not.
Incidentally the third not is the most out of tune note on equal tempered instruments such as theEC, the interval of a fifth is the interval that is least out of tune.my song accompaniment books are available from my website.