Duet concertina
Duet concertina - name given to several types of Concertina
"In the same way as the Maccann is related to the English system, the Jeffries is related to the Anglo system. The Crane is a rethink, and mine is a discovery rather than an invention. That's the way I see it". - Brian Hayden
In fact there are several systems of duet concertina, each as separate from each other as an anglo is from an English, but all set out to cure the same perceived problem: how to give an accompaniment to a melody without going schizoid. The answer is the same in all cases: put the low notes on the left hand side, and the high notes on the right hand side and have some overlap between the two sides. The player can then play the melody on the right hand, with an accompaniment on the left, thus the name of "Duet".
The main duet systems are:
MacCann
the key layout looks fairly illogical, but it was apparently designed for speed rather than logic and there are certainly some very fine players around! Fairly easy to get one. 57 or more buttons, but sometimes can be huge instruments with up to 80 buttons and the range of a piano!
The most famous MacCann player to have been recorded is probably Alexander Prince. Other old-time players include Tommy Williams and Reuben Shaw.
Crane
also known as Triumph by the Salvation Army who used it a lot. A pretty straightforward, logical system. Supposedly doesn't lend itself to fast playing, but I've only ever heard MacCann players say that, and the Crane players I've asked do not agree. Again some very good players around. 35, 48 and 55 button models exist. Fairly easy to find one.
Jeffries
designed for anglo players to convert to. Has a "home key" such as G and is apparently difficult to play chromatically, thus players tend not to stray far from the home key. Much rarer than the first two, mostly due to the very regrettable practice of converting them into anglos.
Hayden
a modern system. Another logical and straightforward duet system, with some ingenious characteristics that make key transposition easy, but quite hard to get because it's modern. I once asked Brian Hayden how many Hayden duets there were in the world, and after some thought he said "Oh, about 60". However this situation is changing markedly for the better, as Stagi have started making accordion-reeded Haydens, a Russian bayan maker has made prototypes and intends to go into production with a potentially excellent instrument (the fabled Haydenovskaya), and now that The Button Box have started making anglos and Englishes they intend to return to their long-held plan to make Haydens. Otherwise the only option is to get one built to order by C & R Dipper or Steve Dickinson. Late news: significant delays on the Haydenovskaya, but Marcus Music have started serious development.