The finish is Pallman Magic Oil, a hardwax oil finish that is available in several colors that can be mixed together. The first coat was Black-Brown. The second coat was a mix of 2 parts Dark Brown, 1 part Black, and 1 part Red-Brown. If you want to use a traditional stain and finish, you could achieve a similar color by using Minwax or Duraseal Jacobean stain, followed by 2-3 coats of oil-modified polyurethane, conversion varnish, or waterborne urethane finish in satin or matte sheen.