it depends what key u r in. when people say u play 3rds above the lead line to make a harmony they do not mean all majour thirds. this depends on the key and the note you are harmonising with. it could be a majour or minor third.

for example we play in e majour. and we have a harmony in thirds. if a note is played the third of that note is played, this is the note after the next note in the scale. the key of e majour which has the following notes; E, G flat, A flat, A, B, D flat, E flat, and then repeats. so if an e is played the harmony note would be an A flat. if an A is played the harmony note is a D flat. if an e flat is played a g flat is played. the interval between the notes is either a majour third ( 4 semitones) or a minor third (3 semitones). these intervals hold true in all the basic keys but there are a few weird keys were the harmonie would be an augmented third (five semitones).

you can harmonise in any interval so try them all, i quite like doing it in fourths.

hope this helps