root frequency, such as just intonation and well temperament. In those systems, a major third constructed up from C did not produce the same frequency as a minor third constructed up from D?. Many keyboard and fretted instruments were constructed with the ability to play, for example, both of G? and A? without retuning. The notes of these pairs (even those where one lacks an accidental, such as E and F?) were not the 'same' note in any sense.

Using the