Apparatus for adjusting the tuning of a musical instrument to cause the instrument to sound in just intonation while the instrument is being played comprises a data base in memory (52) for storing an array of just intonation tone identifiers (54). The tone identifiers in the array are arranged by key, chordal root and tone according to just intonation relationships defined by the ratios of a scale selected by the musician. A selector unit (20) is provided for enabling a musician to select a key (22) and/or a chordal root (24), as a result of which a CPU (48) retrieves from the array a set of tone identifiers in just intonation corresponding to the selected key or chordal root and transmits them to the sounding means of the instrument. The system may be used with electronic tone generators (42), instruments with strings (65), and organ pipes (102).