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Before the start of the First World War, the C. F. Martin company was trying to build ukuleles, but the first production models didn't appear until 1916. In 1920, Koa wood became available for ukes and the model 2-K appeared.
While this example does not carry a serial number, we know that because it's Koa it can't be before 1920; it also has nickel-plated Patent tuners, which appeared in 1923. The C. F. Martin logo is stamped on the back of the headstock, which changed to a decal in 1932, and until 1934 bar frets were used. We are dating it to the late 1920s, but it could have been built as late as early 1932.
This is a very nice instrument in good condition for its age. The body is entirely Koa, with a mahogany neck and Brazilian Rosewood fingerboard. The bridge is Koa with a wooden saddle insert, possibly also Brazilian Rosewood. The bar frets have very little wear, and a period correct trap-door case is included.