How did equal temperament solve the wolf-interval problem of meantone temperament?

In meantone temperament, the "wolf" interval—a harsh, strong dissonance—arose because the system was designed to produce pure major thirds by flattening fifths, which limited the number of usable keys. Because the keyboard provided only 12 fixed notes per octave, it could not accommodate the different pitches required for enharmonic equivalents (such as G♯ and A♭) in distant keys. When a composition required a note outside the system's narrow range, the resulting interval was severely out of tune, creating the "wolf".12

Equal temperament solved this problem by abandoning the goal of perfectly pure intervals (except for the octave) in favor of a "divisional" system. By dividing the octave into 12 equal semitones, each measuring 100 cents, equal temperament distributes the necessary intonational defects evenly across all 12 tones of the chromatic scale. Because every interval is identical in every key, the system eliminates the need for specific, non-interchangeable enharmonic notes, thereby removing the wolf interval and allowing instruments to play in all major and minor keys without sounding sourly out of tune.32