The comma and equal temperament

The difference between a perfectly tuned octave and the octave resulting from a tuned circle of fifths is known as the comma. Over the centuries, numerous approaches have been tried to solve this mystery, resulting in a range of scales (before arriving at equal temperament—the 12-tone scale). Other historical temperaments that have been devised emphasize different aspects of harmonic quality. Each compromises in some way or another. Some maximize pure thirds (Mean Tone) while others emphasize pure fifths at the expense of the thirds (Kirnberger III, for example). Every temperament has its own character, and a given piece of music may sound fine in one key but awful in another. Transposing a piece to a new key can completely change its character. Careful attention must be paid to the selection of temperaments for authentic performances of historic keyboard music. The wrong choice could result in an unsatisfactory and historically inaccurate musical experience.

Equal temperament takes the tuning error (the comma), and spreads it equally between each step of a chromatic scale. The result is actually a scale of equally mistuned intervals, with no interval grossly out of tune, but none in perfect tune. Equal temperament has become the de facto standard for two main reasons:

• Convenience: Retuning an instrument to a temperament that is better suited for a particular piece of music is a hassle. Many instruments are not capable of being alternately tuned—fretted string instruments, for example.

• Portability: All Western musical pieces can be performed (adequately) on an instrument tuned to equal temperament. Obviously, some of the nuances may be missing in pieces that were originally performed in another temperament.