WellTemperedClavier

Why Can't a Piano Be Perfectly in Tune? Bach's Prelude in C-sharp Major, BWV 848

Earlier in this series, we looked at simple mathematical relationships in music: an octave has a frequency ratio of 1:2, a perfect fifth 2:3, and a perfect fourth 3:4. These simple ratios help explain why some intervals sound so naturally balanced.However, even a carefully tuned modern piano is not mathematically...