But the oddest of all electric guitars has to be the fretless. They don’t show up often, but when they do, they tend to make a stir, as did the Bartells fretless guitar from the 1960s.

Guitars come in all shapes and sizes and with everything from four strings — as in the tenor guitar — to 17, as in Gibson’s Style-U model. Because fretless guitars are, you know, fretless ...