An intonation system for a stringed musical instrument, a stringed instrument including the intonation system, and a method of setting up a stringed instrument. An instrument such as a guitar includes a bridge having bridge string saddles that can be adjusted separately to raise or lower a single string and to adjust the position of the bridge end of the vibrating length of the string. The instrument also includes an adjustable nut assembly by which to adjust the position of the nut end of each string individually. The structures by which the string saddle positions are adjusted are substantially concealed, largely retaining a conventional appearance of the musical instrument.