Why can the same piano pitch be called C-sharp or D-flat?

On a piano, the ability to call the same pitch by two different names, such as C-sharp ($C♯$) and D-flat ($D♭$), is known as enharmonic equivalence.

This occurs because modern keyboard instruments use a system called equal temperament, which divides the octave into 12 equal semitones. In this system, a single physical key on the piano is tuned to produce one specific frequency, but that frequency can be notated in two different ways depending on the musical context or key signature being used.

While these tones sound identical on a piano, they are distinct in musical theory and notation. The choice of name depends on the scale or harmonic structure of the piece; for example, a composer might choose $D♭$ over $C♯$ because it is easier to read within a specific key. In contrast, on instruments like violins or in older tuning systems such as just intonation, these pitches may be played with slight differences in frequency to suit the intonation of the music.1