What does the term enharmonic equivalents refer to?

The term enharmonic equivalents refers specifically to notes that sound the same but are notated differently. A classic example is the notes E# and F; while they are played on the same key on a piano and produce the same pitch, they are represented by different names in musical notation. This concept is crucial in music theory as it allows for the flexibility of notation based on the harmonic context or key signature being used in a piece of music. Understanding enharmonic equivalents is key for musicians, as it affects tuning, harmonization, and the structure of musical compositions, creating opportunities for modulation and key changes without altering the fundamental pitches played.