Carol, IKS (I know very little) about accordions, but I could find and refer you to information on a very interesting instrument of the same family: the Argentinian BANDONEON, the heart of the tango, raised to the level of symphonic masterworks by the genius of Astor Piazzolla. This instrument lacks a piano keyboard, it is always hold on your knees, has two sets of buttons, a very wide extension and is totally chromatic.The bandoneon does not sound. It CRIES. It would be impossible to play tango in any other instrument. It is sad, melancholic, romantic and pretentious as we Argentinians are.
However it is not a local invention. It came with Italian and Mid-European immigrants by the end of the 19th century and suffered minor modifications. Today, the gratest living bandoneonists could be Dino Saluzzi, with a long and succesful European career, and Osvaldo Piro in Buenos Aires. If someone is interested, please tell me and I'll prepare a Web tour.
Un abrazo - Andrés