I've written about triplets before, in fact my other web site has a very good article. But I will talk about them again because trying to produce triplets is an obsession for all beginners. (I've given up on trying to use the other site, the NSA will have more luck getting in and changing it.)
My first lesson on the Irish tenor banjo was with Gerry O'Connor (his web site seems to be gone) who is, by any reckoning, the triplet king. He was not that eager to teach our group of beginners how to do triplets but we hounded him until he showed them to us. Gerry was reluctant for a reason, he doesn't think that beginners should worry about what is, after all, only an ornament. The fact that he makes his living with triplets aside, he wants people to play the music and you can do so without the triplet, especially in sessions where they are lost in the mix of instruments.
Triplets are there to emphasize rhythm and "lift" which is a unique quality of Irish music. They are not part of the tune and in fact need to be placed in different places if you are going to play the tune more than one time if you don't want to be boring. Some musician's styles use the triplet a lot while others don't. At some point when you are experienced enough to have a style, you will discover which end of the triplet scale you belong.
Another ontological issue has to do with naming triplets. For classical musicians a triplet is a written series of three notes in the period of time that two notes should be played. In Irish music such musical triplets exist, usually in hornpipes, but mostly they are ornamental. Enda Scahill defines a triplet as different notes played in the ornament while the term "treble" is used for three notes that are the same. Since we are going to look at mechanical technique, which for the right hand is the same no matter which notes you play, I will continue to confuse you and call them triplets.
When I first started to play Irish music in our local session, I played my mandolin. It became clear that I was not going to be heard very well with my mandolin so I found a B&D Silver Bell in a local music shop and went to the dark side. I struggled with the music and especially struggled with triplets during this period. Now I realize that the culprit was not my technique (which sucked, a lot) so much as my inability to hear where triplets should go and my anxiety every time I tried to produce one in the session. I could barely produce them at home where I was safely away from my friends scrutiny.
Gerry showed us what he did. He didn't use the McTwist, a technique taught by Roger Landes and others, instead he used a wrist triplet which involves only using his wrist stroke.
Here is my take:
I made this video a number of years ago and I still use the wrist triplet with some of the McTwist features. Often I think I am using one of the techniques and am really using both.
Learning to play triplets is hard work for such a simple action. Anxiety resulting in muscle tension is the reason most of us have a hard time getting triplets to work. When you watch really good players make triplets you can hardly see what they are doing. Look at the video of Enda Scahill playing the "relaxed hand" and you will see him barely move yet the sound comes out.
I don't recommend trying to make triplets at the start of your banjo career, but most of the time that advice is ignored, so when you do try, relax and sing the music in your head. If you miss, you miss, if you get it, great, but the music comes first.
Here is a compilation of experts playing triplets I (I can't get it to come up on this blog.)