A system for dividing an octave into 12 pitch steps, each of 100 cents. This has the effect of making all semitones equal in size. This became necessary once keyboard and fretted instruments became popular. It should be understood that the note A which appears in F# minor should have a slightly different frequency from the note A which appears in C major (this fine distinction is one of the reasons that pitch and frequency are not quite synonymous). This would normally be dealt with automatically by a proficient player on an instrument with continuous pitching such as a violin. A keyboard instrument would properly have to be tuned to a particular key, if music was then played in a different key, some or many of the intervals sounded would be flat or sharp. However since it was not convenient to retune these types of instruments correctly whenever a new key was required, various compromises were attempted. Equal temperament was one such compromise whereby the error was distributed equally between all the notes. This made the performance of music in different keys possible on the same instrument without retuning, in celebration of which J. S. Bach wrote not one, but two books, each of 24 preludes and fugues (a prelude and fugue in both the major and minor forms of 12 keys).
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